CA1255947A - Optical transmission filter - Google Patents

Abstract

OPTICAL TRANSMISSION FILTER

Abstract of The Disclosure The present invention deals with an optical transmission filter for effecting differential phase delay upon light in a beam polarized in a P dimension, as a function of position within the filter aperture.
The filter employs two lenses of birefringent material, the crystal optic axes of the respective lens materials being oriented in mutually orthogonal positions and at a 45° angle to the P dimension. The lenses have their adjacent surfaces respectively concave and convex with the same radius of curvature and their non-adjacent surfaces flat.
The phase response of the filter is a function of the radial distance of a beam element from the filter axis with spherical lenses and a function of a linear coordinate distance from the filter axis with cylindrical lenses. A two-part construction for one lens, which permits adjustment of the difference in center thicknesses between the two lenses, allows adjustment of the differ-ential phase delay with respect to a spacial reference.

Description

~S5~

OPTICAL TRANSMI SION FILTER

Background of the Invention 1. Field of Invention This invention relates to optical transmission filters for systems employing polarized coherent beams, and more pa.rticularly to filters exhibiting a dierential phase delay to the components of a polarized beam element as a function of element position within the filter aperture. The invention further relates to adjustable optical transmission filters.

2. Description of the Prior Art The invention is applicable to optical systems, such as lasers employing polarized coherent radiation. In lasers, the optical SS9'~

resonator acting to provide optical feedback for the gain medium aids in esta~lishing an internal beam and the two influence the characteristics of the beam produced. Since t~ae external beam derived from the laser s derivea from the internal beam, the resonator and the gain medium also affect the nature of the external beam.
An ideal characteristic of a laser apparatus is that it have a large natural aperture and produce a large, high energy high quality beam. ~he "larger" ~he beam, the-higher the energy, and the smaller the far field beam divergence (ideally a minimum), ! 15 the aperture being the critical parameter in defining this beam property. seam quality is a relative term used to characterize a beam in reference to a standard beam. Beams resulting from __ _ ~25S~f~7

- 3 - - ~ ~

operation of an optical resonator in a pure TEMoo mode for instance, may be represented as providing a standard beam referred to as "Gaussian". In a "Gaussian" beam, the intensity peaks in the center of the beam and grad~
ually decreases to the margin of the beam. Meanwhile, the phase of the ~Gaussian" beam remains relatively constant at the center of the beam and then changes rapidly at the perimeter of the beam to a large value leading to a phase reversal. Conversely, in an intensity profile of the beam, the phase is changing most rapidly where the beam intensity is approaching a minimum. In a beam showing evidence of multi-moding, the intensity then may reappear as a second fringe whose phase may be dis-placed lBOD from the phase of the central fringe.
In practical apparatus, the beams are often of substantially poorer quality than standard "Gaussian"
beams, unless correction is provided. Typical issues in the design of an optical resonator, which influence beam quality, are whether the optical resonator is stable, unstable, or a combination of the two termed "stable/un-stable". ~ypical issues in the design of the gain medium are whether the medium is circular or square or rectangular ~IL2SS~'7 in cross-section, whether it has slanted end faces~
(cut at the Brewster angle),-~nd the presence of thermal focusing effects as the medium is operated. In all such designs, the quality of the beam is likely to suffer as the aperture of the system is increased or as the power is increased. In laser systems, polarized operation is frequently desirable in that it permits electro-optically "Q-switched" operation and aids in achieving improved laser operation, the improvement being in improved b~am quality and increased power.
Accordingly, within the optical resonator where the beam is formed, in the near field where a beam is coupled from an optical resonator to a utilization device and in ; the far field, means for adjusting the phase of a waveIront 1, may be of advantage in improving operation of a laser or a laser system.
A further problem posed in practical laser systems, is the requirement of fractional wave accuracy in the phase correction means itself, making it desirable that the correction filter be adjustable to simplify its own fabri-cation. Adjustability has the additional advantage, in the event that the system parameters are not accurately known, of making the filter more adaptable to the actual system requirements.

~L255~'7 Summar of The Invention y Accordingly, it is a-n object of the i~vention to provide a novel optical transmission filter applicable to polarized coherent radiation having a phase response which is a function of the position of a radiation element relative to the filter axis.
; A further object of the invention is to provide a novel optical transmission filter applicable to polar-ized coherent radiation, in which a differential phase delay is provided, which is a continuous function of ~he radial distance of each radiation element from the filter axis.
It is still another object of the invention to provide a novel optical transmission filter applicable to polarized coherent radiation in which differential phase delay is provided which is a contin~ous function of ; a coordinate in a plane orthogonal to the filter axis.
It is an additional object of the present in-vention to provide a novel optical transmission filter applicable to polarized coherent radiation having adjustable phase response.
These and other objects of the invention are achieved in a nov~l optical ~ransmission filter for ~Z5~ 7 effecting continuous phase compensation Qf a beam of light, polarized in a P dime~sion, the filter having an optical axis which is concentric with the beam axis.
The filter comprises a first lens of birefringent material of a first center thickness having a surface, which has a predetermined radius of curvature, and a second lens of birefringent material of a second center thickness, having a surface, which has a radius of curvature equal to the radius of curvature of the first lens but of opposi~e sign. The lenses are oriented orthogonal to and concentric with the axis of the beam with the curved surfaces adjacent.
In addition, the crystal optical axes of the materials of the lenses are oriented in mutually orthog-15 onal positions along the axis and at an angle of 45D toa P dimension. The surfaces of the filter lenses, de-pending upon the filter characteristic sought, may ~e spherical or cylindrical.
The phase response of the filter, will have a zero differential phase delay at a zero coordinate value (or zero radius with reference to the filter axis) when the center thicknesses of the lenses are equal. The phase ~2~5~'17 - 7 ~

response may have a non-zero differential phase delay on the axis (and a zero differe-ntial phase delay at some other coordinate value), when the center thicknesses of the lenses are unequal. Accordi~gly, if one desires to translate the differential phase delay characteristic by adding or subtracting a fixed reference delay, the transmission filter may be made to have one lens of adjustable center thickness. This may be accomplished by the compound design of one lens in which the lens consists of a wedged shaped (plane faced) member taper-ing at an angle equal to the tapering angle of the other lens me~ber which provides the curvature. Tile joint tapering restores the filter surfaces to orthogonality to the fil,er axis. ~hen the tapering angle is made sufficiently small, a very fine adjustment of the spacial reference of the filter characteristic, may be ~btained.

, Brief Desc iption o~ the Drawin~s The novel and distinctive featur.es of the invent-ion are set forth in the appended claims. ~he invention itself, however, together with further objects and ad 5 vantages thereof may best be understood by reference ~o ~he following description and accompanying drawings, i~
which:
Figures lA, lB, lC and lD are optical ~ransmission filters for application to laser systems producing 10 pola~i~ed coherent light Pigure lA i9 a two lens optical transmis~ion ilter using orthogonally arranged birefringent materials, the lenses having mating spherical surfaces with fixed, on-axis thicknesses;
lS Figure lB is a three element variation of the optical transmission filter illustrated in F.igure lA, wherein a slideable wedge cooperating with a wedge shaped lens provides a compound lens, whose on~axi~ thickness iB
adjustable in relation to the other lens;

Figure lC is a two lens optical transmisslon filter similar to that illustrated in Figure lA but having mating cylindrical surfaces, the lenses having fixed on-aXiB thicknesses; and ~;~55~47 Figure lD is a three element variation of the optical transmission filter illustrated in Eigure lC, wherein a slideable wedge, cooperating with a wedge shaped lens provides a compound lens, whose on-axis thickness is adjustable in relation to the other lens;
Figure 2A is a perspective view o~ a portion of a coherent optical system comhining an optical transmission filter, which is spherical, and a polarizer, the combina-tion producing a positionally dependent attenuation function in reference to the system axis;
Figures 2B through 2E are auxiliary illustratlons of the na-ture o the bcam as it pxoceeds through the op-tical components illustrated in ~igure 2A, the filter hav:Lnc~
spherical surfaces. The illustrations show .respectively the polarization rotation and the intensity of individual rays forming the beam as a function of their position, Figure 2A after a first polarizer, 2C after the Eilter, 2D after passage through the second polarizer, and 2E
upon reflection at the second polarizer;
2~ Figures 3A and 3B are respectively side elevation and perspective Views of a stable, Q-switched laser resonator utilizing polarized light and incorporating a spherical optical transmission filter-polarizer combination for supporting resonator operation in a TEMoo mode 1255~

and for suppression of other modes, and Figure 3C is a graph illustrating the operation of the optical resonator components in mode suppression;
Figures 4A through 4F illustrate the Q-switching sequence of the Figure 3A-3s embodiment, Figure 4A showing the pump light output, 4A the optical gain, 4C the trigger pulse, 4D the Pockel's cell voltag~, 4E the loss and 4F the laser output pulse;
Figure S is a schematic diagram illustrating a control circuit or the Pockel's cell of the Figures 3A-3B
embodimen-t designed to favour TEMoo mode operation;
Fi~u.re 6 is a graphical illustration oE the transmission profil~s or the laser cavity of the Figures 3A-3B embodiment as a function of the voltage applied to the Pockel's cell during the Q-switchin~ sequence, the process "seeding" the optical resonator Eor TEMoo mode operation;
Figures 7A and 7B are respectively side elevation and perspeckive views of a stable/unstable resonator incorporating a face pumped laser and incorporating a cylindrical optical trans~ission filter-polarizer combination for improved resonator performance;
Figure 8A illustrates a laser system incorporating a spherical optical transmission filter-polarizer combi-nation, in which the lenses of the optical transmission ; filter have an adjustable on-axis thickness. The filter-.~

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polari~er co~bination is used to ancrease the extraction efficiency of the ampllfier by~~increasing the "fill factor~ of the ac~ive material of the amplifier.
Figure 8B illu~trat~ the variation of the tran~-miRsion profile of the filter-pola~izer co~bi~tion of Figure 8A as a function of cha~ge in the center thickness difference between the two lenses of the optical filter;
and Figure 8C illustrates the intensity of the input beam, the filter transmissiQn ~nd the intensity of the transmitted beam in the laser system of Figure BA at a preferred adjustment of the filter; and Fi~ure 9A illustrates a laser sy6tem in which a spheric31 optical transmis6io~ filter i~ employed to : 15 enhance the quality of a beam produced by a pol~rized coherent source;
Figure 9B illustrates the correction of far field ~ivergence of a beam produced by an unstable laser resonator having a Fresnel number of 7.5 (magnification 1.5) by a spherical optical transmission filter;
~ igure 9C illustrates the correction of far field divergence of a beam produced by a ~table laser resonator having a Fresnel number of 8.5 by a spherical optical :

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~S59~7 transmission filter; and Figure 9D i}lustrates ~he e~fect of phase devi-ation across the beam or far field beam divergence.

Description of the Preferred Embodiment The optical transmission filters disclosed in Figures lA, 13, lC and lD are two or three piece optical components designed for use with beams of polarized coherent llght centered on the axis of the filters. The filterq each i,nclude a pair of mating len~es of dou~ly refracti~g material whos~ cxystal optic axes are mutua~ly orthogonal and whose mating surfaces are e~ther spherical ~convex - concave respectively) or cylindrical (convex -concave respectively).
The optical transmission filter 10 of Figure lA, using two spherically surfaced lenses, has a differential phase response to light of a preferred polarization which is a function of the radial coordinate ~f a ray within the filter field. The function i9 symmetrical about t},e axis of the filter. In particular, when the rays are located o~ the filter ~xis, a near zero change in differ-ential phase delay is exhibited between the two selected - orthogonal compQnents of the preferred polarization. As ~ will be seen, the selected components are oriented 45 ~LZ5S~'7 - 13 ~

angle to the preferred (P) polarization and ~re in alignment with the crystal optlc axes of the doubly refracting materials. In one exa~ple, the differential phaqe delay between these selected components, in-crehses as the radial coordinate of the ray measuredfr~m the filter axis increases, the differential delays ~eing e~ual at the same radial c~ordinate irrespective of the angular position about the filter axis. The wave transmission filter may be employed to bring about a rotation o~ th~ polariz~tion vector by 90 in one passage throu~h the filter of a ray at the perimeter of the filter field (analogo~s to a "half wave plate") or to bring about a comparable differential delay upon two passages through the filter of a ray at the perimeter of the filter field ~analogous t~ a "quarter w~e plate").
The wave transmission filter 30, using cylindri-cally surfaced lenses (e.g. Figure lC), has a phase respanqe to light of a preferred polaxi2ation which i5 a function of a transverse coordinate (the S coordinate) of a ray within the filter field. The function is symmetrical about the filter axis. In one example, a near zero di~ferential phase occurs between two selected ~SS~7 - 14 - ~ ~

orthogonal components of the preferred polarization when ~he rays are located on the filter axis, d~fferential phase delay increasing as the S coordinate of thP ray measured from the filter axi~ increases.
sDth the spherical ~10) and cylindrical ~30~
filters are available in an adjustable configuration.
In the adjustable configurations ~20, 40), one lens has an adjustable thickness permitting one to adjust the on-axis differential delay to a value in which the differ-ential phaqe shift between the desired orthogonal components is zero, positive, or negative.
The filters 10, 20, 30 and 40, may he used in combination with suitable polarizers to con~ert the phase response to an amplitude response having the same co-ordinate dependance. The filtera her~in de~cribed may be applied as an optical component within an optical resonator of a laser, in the path between an optical resonator and an optical amplifier, or for far field correction.
The optical transmission filter 10, illustrated in Figure lA, is a two piece spherical unit in which the le~ses 12, 14 are of equal thickness at their centers.

1;Z5S9'~7 The centers are aligned upon the axi~ Z of the as~ciatedoptical system. The lens 12 placed to the }eft in the filter 10 ha~ a first surface 11 to the left (and hidden in the Figure), which i~ flat and a second surface 16 to the right which is spherically concave with a pre-determined radius of curvature (R). The surfaces of the lens 12 are oriented orthogonal to the optical axis (Z).
The lens 1~ has its crystal optic axis oriented at a 45 ~ngle to the P and S axes. The P and S axes are established in the associated optical system by the orientation of the laser medium, which in the case of a face pumped square slab laser, with ends cut at the Brewster angle, lie in planes parallel to the lateral surfaces of the slab. The P coordinate is oriented in a vertical plane, using the orientation~ of Figures lA
and 3A, between the upper and lower (lateral) surfaces of the laser slab and the S coordinate i~ oriented in a horizontal plane between the front and bac~ ~lateral) surfaces of the laser slab. These coordinates define the P and S polariza~ion vectors which are of interes~ in the following description. The crystal optic axis of ~2~4~7 - 16 - ~

the doubly refracting material of the lens 12 is illus-trated by the arrows 13. Thi~ axi~ 19 oriented at 45 to the P-S coordinate~.
The second lens 14, placed to the right in the filter 10, has a first surface 15 to the left (and hidden in the Figure), which is spherically conYe~..
with a radius of curvature R equal to the first lens but of oppo~ite sign. When the two lenses 12 And 14 are assembled togethe~, the surfaces 15, 16 are designed to fit closely together. The second surface 17 of the second ler)s lq to the right, i5 flat. The surfaces (lS, 17) of the lens 14 are oriented orthogonal to the Z axis.
The lens 14 has its crystal optic axis oriented at a 45 angle to the P and S axes. This axis, as indicated by the arrows 18, is oriented orthogonal t the crystal optic axis of the lens 12.
The optical transmission filter 10, which is constructed of the two lenses 12 and 14, exhibits a positionally dependent differential phase shift to the selected components of rays of polarized light passing through the system. The differential phase shift prod~ced ~5~4~7 - 17 - ~ :

is a function of the distance of a ray .from the filter axis. Assuming in a first example, equal radii of curvature for the concave and convex spherical surfaces of the lenses 12 and 14, and an exact match between the thickness of the two lenses at their centers, then the differential phase shift provided to the selected orthogona} components will ~e zero at the filter center, coincident with the z axis. H~wever, if a ray iB
located at the periph~ral portion of the filter fi~ld the ray will pass through a greater thic~ness in the first lens than in the second lens and experience the greatest differential phase ~hift contemplated by the design. When a ray of P polarization is resolved into two selected orthogonal components parallel to the crystal optic axes of the two doubly refr~cting materials and then recombined, the resultant will produce a polari-zation rotation of 90. This will occur when one of the selected orthogonal components experiences a dif ferential phase shift of 180 in relation to the other, which produces a polarization rotation of 90 upon recombin-ation, resulting in an S polarization.
A phase rotation of 30 may occur either upon a ~2555~

~ 18 - ~

sinqle paQsage of a ray at the perimet:er of the filter as de~cribed ln the above example, or upon a second pas~age (also at the perimeter) through a filter of modlfied design. In the Qecond ex~mple, a mirror may be provided to effect a second passage of the ray through the filter, and the filter may have a shallower design in which the differential phase shift at the limits of the field i5 only 90 upon a single passaye of the beam.
After a single passage, the polarization of a ray emerging at the perimeter of the field will be circular.
Upon re~lection from the mirror~ reentry into the filter and a second passage through the filter at the perimeter of the field, the circular polarl2ation of the beam is converted to a linear polarization, rotated 90~ from the original P polarization, to an S polarization.
The spherical optical transmission filter ~ay ta~e either the form illustrated in ~igure lA using two lenses of fixed and equal center thicknesses, or it may take the form illustrated at 20 in Figure lB in which a three element construction is used to provide adjustment of the center thickness of one lens in relation to the other~ The adjustment may be used to bring the center ~5~

-- 1 9 -- ~ ~

thic~nesses of the two len~es into exact equality or into a desired inequality. ~he e~-fect of an unequal adjust-me~t is to produce a net differential phaqe ~hift on the filter axiR and to displace the locus o~ minimum differ-S ential phase shift to a ring around ~he filter axis.
C~nsistently, when the center thic~nesses become unequal, the differential phase shift may become slightly smaller at the peripheral portion of the filter field.
The adjustable spherical optical transmission filter 20, a~ illustrated in Figure 1~, consist~ of A
compound left l~ns 21, 22 and a single element rig~t lens 24. The compound lens is formed of a slideable wedge 21 having flat front and back surfaces and a wedge shaped lens 22 having its flat surface set at an angle orthogonal to the filter axis. When the two elements 21 and 22 are assem~led in correctly aligned slidea~le engagement, with their upper and lower lateral surfaces coplanar, the crystal optic axis of the wedge 21, as illustrated by the arrows 23, has the same rotational orientation as the crystal optic axis of the ler,s eleme~t, as illustrated by the arrows 2S. In acldition, the angle of tapering of the wedge 21 and the angle of tapering of the lens 22 are made equal so that when assembled and ~z~s~

correctly aligned in slideable engagement, the external surfaces of the compound lQn~ 20 ars oriented orthogonal to the Z axis. Thus, the positionally dependent di~fer-ential phase response of the compound three element lans (21, 22, Z4) at specific p~sitions of the wedge will be ub~tantially the same as tha of a comparable two el~m~nt lens of that specific thickness.

In order to permit a fine adjustment of the diferential phase shift so that one may adjust the differential phase shift to a small part o ~ wave length, the angle of tapering of the two lens components (21, 22) is made small enough to effect this precisi~n in ad~ust-ment with a conventional micrometer screw. In a particular case, the angle of the wedge is 21 minutes of arc.
The ~ptical transmi~sion filter 30, illustrated in Figure lC is a two piece unit in which two cylindrical lenses are employed and in which the indi~idual lense~
(32, 34) are of equal thickness at their centers. ~s in the Figure lA embodiment, the centers of the lens elements - ~3Z, 34) are aligned upon the Z axis. The lens 32 placed to the left in the filter 30 has a first surface 31 to r ~

the left wh~ch is flat and a second surface 36 to the right wh?ch is cylindrically concave with a predetermined radius of curvature (R). The curvature is maxi~um in the S-Z plane and is negligible in the P-Z plane. The surfaces of the lens are oriented orthogonal to the Z axis~
The second lens 34 is placed ~o the right in the filter. It has a surface 35 to the left (and hidden) which is cylindrically con~ex. with a radius of curvature ~R) equal to the first lens but of Dppoqite sign. As with the lens 32, the curvature is maximum in the S-Z
plane and negligible in the P-Z plane. When the two lenses 32 and 3~ are assembled together, the surfaces are designed to fit closely together. The second surface 37 to the right of the jecDnd lens is flat.
The surfaces of the lens 32, 34 are oriented orthogonal to the Z axis. ~he individual lenses 32 and 34 of the - filter 30 have their crystal optical axes oriented at a 45~ angle to the P an~ S axes. As before, the crystal optic axis of the lens 32, as illustrated by the arrows 33, is ~rthugonal to the crystal optic axis of the lens 34, as illustrated by the arrows 38.

~S~ '7 The optical tra~smission filter 30 which ie con-structed of the two lenses 32 and 34, exhibits a positi~nally dependent di~ferenti~l ph~e shift to the polarized rays of light. The differential phase S shift varies as a function of the distance of a ~ay from the center of the filter measured along the S
axis. The amount of differential phase shift will be equal for rays at S coordinates of equal magnitude.
Assuming equal curvatures for the concave and convex surfaces of the lenses 32 and 34 and an exact m~tch o the thic~nesses o~ the two lenses at their centers, then the differential phase shift provided to selected components of a polarized ray sn the axis of the system will be zero. However, if a polarized ray is located at the outer limits of the filter field, at the near and far edges of the cylindrical lenses, light will pass through a greater thickness in the first lens (32) than in the second lens ~34) and experience the greatest differential phase shift.
The cylindrical optical transmission filter may also take the adjustable form illustrated in Figure lD
i~ which a three element (41, 42, 44) construction is ~2SS5~ 7 .

: used to provide adjustment of the center thickness of one compound (41, 42) lens in~-relation to the other lens (4~).
The adjustable cylindrical optical transmission ~ilter 40 a~ illustrated ln Figure lD consist3 of ~
compound left lens (41, 42) cooperating with a right, single element lens 44. The compound lens is formed of a slideable wedqe (41) and a wedge shaped lens 42, the two beinq assen~lable to maintain orthogonal external ~urfaces ~nd pa~allel crystal optic axe~.
As in the prior adjustable configuration, the adjustment may be used to bring the center thic~ness of the two lenses (41, 42 and 44) into exact equality or into a desired inequality. In the example of an equal center thickness, the differential pha3e for the selected components of the polarized ray i8 zero on-axis, and varies equally at equal plus or minus S
coordinates.
The effect of an unequal adjustment of the center thic~nesses of the lenses 41, 42 and 44 is to produce a net differential phase shift on the Z axis and to dis-place the locus of minimum differential phase shift to 1~5S~'1'7 - 24 - ~ ~-two stra~ght lines parallel to the P cDordinate axi5 spaced at equal S coordinate distance6 from the ~ axis.
With the une~ual adjustment, the differential phase shift will ~e smaller at the outer margins of the filter S than when the center thicknesses are equal.
In Figures 2A through 2E, an optical transmission filter 10 ~i~h spherical surfaces, as illustrated in Figure lA, is shown in combination with polarizers (51-52), the combination producing a radial attenuation ~unctlon for P polarized light.
As illustrated in ~igure 2A, the combination i~
adjusted to provide a minimu~ attenuation of P polarized light near the Z axis in the filter field and a maximum attenuation near the perimeter of the filter field.
Assuming an applied beam, whose cross-section is analo-gized to a "doughnut" filling the filter field, the filter selects the "hole" of the 'Idoughnut" and rejects the "doughnut". Alternatively the combination may be adjusted to provide maximum attenuation at the central portion of the filter field and minimum attenuation at the peripheral portion of the filter field. Finally, one may make transitional selections intermediate to ~1 2~S~3~7 the fir~t and second adj~stment~ as by using the adjust-able filter 20, in ~hich the c~nter of the field is attenuated to a desired degree ~nd the margin of the beam is less deeply attenuated, the efEect of which i3 to increase the spot size of real beam~ between desired attenuation limits.
In Figure 2A, it is assumed that unpolarized light at the left margin illustrated by the intersecting vertical (53) and horizontal ~54) lines proyresses to the right and impinges on ~he left ~ace o~ the polarizer 51. Only liqht which is of P polarization i9 trans-mitted through the polarizer 51 while light of an S
polarization is ejected off axis and discarded. The nature of the polarization of the light after passage throuqh the polariæer is illustrated in Figure 2B, which shows a magnified cross-section of the field. In particular, the center of the field, as represented by a single full length vertical line, is vertically polar-ized. Also the successive zones surrounding the center, 23 and completing the field, are represented by four rows of four radially positioned, full length vertical lines, are vertically polarized. A plot of the light intensity - 2 6 ~

as a f unction o f the ~adial position of a ray in the filter field i~ illustrated i~-the lower,portion of ~igure 2s. The field may be regarded as uniformly filled with rays of unit intensity.
The P polarized rays 53 then continue until they impinge on the optical transmission filter 10, which, as indicated ~y the arrows (13, 18) has its mutually orthogonal crystal optic axes oriented at 45D to the P polarization. The selected orthogonal components of the ~ays of P polarization, a~ a functlon of increasing radial di~tances from the Z aXi5, receive greatex differ-ential phase ~hi~ts upon passage thro~gh the fllter, and produce correspondingly different polarization rotations.
The rays exiting the filter 10, are symbolized in ~igure 2A by the dots 57, ~paced at wave length intervals, which continue until impingement at the polarizer 52.
The effect of the filter 10 over the different zones of the filter field are best illustrated in ; Figure 2C, which is a magnified cross-section of the field. The upper portion of Figure 2C represents the polarization rotation a~ a function of ray position in successively larger diameter zones lying within the ~ L~t7 - 27 - ~ ~

filter field. The lower portion of the figure illus-trates the S~tensity aa a functton of the radial position of a ray within the field.
The upper portion of ~ig~re 2C i~lustrates the progressi~n of the polarization of the output rays from the filter 10, as the input ray position progresses from the center to the perimeter of the filter field.
The full length vertical lines repre~ent P polarization;
the full length horizontal lines represent S polarization;
10 and the circles indicate circular polarlzation. Ray~ at the center o the filter represented by single ~ull length vertical lines have emerged from the filter 10 without a change in polari~ation and remain of P
polarization. Emerging rays at the next zone repre~ented 15 by four circles have been ~ubjected to a 45 polarization rotatlon and are now circul~rly pol~ri~ed. ~ay~ emerging from the next outer zone represented by four full length horizontal lines have been ~ubjected t~ a 9~ polariza~ion rotation and are now horizontally polarized. At the next 20 outer zone, the emerging rays are circularly polarized as represented by four circles. At the final zone pictured, 3L~Z55~7 emerging rays are again of P polarization as represented by four full length vertical l*nes.
The plot of the intensity of the filtered beam as a function of the radial position of a ray is illustrated 1n the lower portion of Figuxe 2C. The Figure 2C plot resembles the plot provided in Figure 2s, indicating that the filter 10 has provided no significant attenu-ation.
The rays havi~g di~fering polarizations a~ a function o~ po3ition within the fllter field a~ ~
result of passage thrcugh the filter 10, next impin~e on the left face of the polarizer 52.
Ray components of vertical polarization are trans-mitted through the polarizer 52 and continue to the right along the Z axis as indicated by the vertical lines sa.
Ray components of horizontal polarization are reflected by the polarizer 52, and are ejected from the axiR a indicated by the horizontal lines 59.
The effect of the polarizer 52 upon transmitted and reflected rays at different portions of the filter field are illustrated in Figures 2D and 2E, which are magnified views of the field.

~53~L7 The effect of the polarizer 52 upon trsn~mitted rays at successive zones of the filter field are illus-trated in Fiqure 2D. The upper portion of Figure 2D
represents the intensity of the transmitted vertically polarized output rays 58 as a function of ray position in successively larger diameter zones lying within the field. The lower portion of Figure 2D illustrates the intensity as a function of the radial position of a ray within the field.
The upper portion of Figure 2D illu~trate.q the progre~sion of inten~iey of the output xays ~s the ray position progresses from the center to the perimeter of the filter field. The int~i~es are represented by "full" length lines repre~enting full intensity, shortened lines representing less than normal intensity, and dots representing zero intensity. Rays at the center of the field represented by a single full length ~ertical line have emerged from the polarizer without a change in inte~si~ indicating that the filter-polarizer 20 combination has transmitted that ray without phase shift or attenuation. Emerging rays at the next ZGne repre-6ented by four shortened lines represent the vertical ~,~55~ '7 - 30 - - ~

component of rays, which had been circularly polarized, and are now transmitted to the~output at less than normal inte~sity, Rays at the next outer zone, represented by four d~ts had been subjected to 90 of polariza~ion rotati~n, and are now rejected by the polarizer, pro-ducing a zero o~tput, At the next outer zone, the emerging r~ys from the polarizer are of reduced length, indicating that they had been derived from previously circularly polarized rays. At the fi~al zone pictured, emerging rays are represented by four full length vertical lines indicating that the rays have been trans-mitted through the filter-polarizer combination without attenuation.
The lower po~tion of Figure 2D illustrates the selection of rays at a broad central zone of the fiel~, the rejection of rays in a narrower second zone s~rround-ing the central zone, the selection of rays in a still narrower third zone, surrounding the second zone by passaqe of rays of initially P polarization through the filter-polarizer combination.
The effect of the polarizer 52 upon reflected ray~ is illustrated in Figure 2E. The upper portion of l~S~ 7 - 31 ~

~igure 2E represents ~ntenaity of the reflected horLzon-tally p~larized output rays as_a function of ray po~ition in successively larger dlameter zones lying within the field. The lower portion of Figure 2E represent~ the inte~sity ~s a ~unction of the radial poqition of a ray within the field.
The upper portion of Figure 2E illustrates the progression of ~he intensity of the rays 59 reflected cff axi~ as the ray po~ition progresses from the center to ~he perimete~ of the ilt~r ~ield. ~he intensltie~
are represented as in Figure 2D. Ray at the center of the filter field represented by a ~ingle dot have been subjected to no polarization rotation and are not reflected off axis. Reflected rays at the next zone, represented by four reduced lines represent the vertical component of rays, which had been circularly polarized and are reflected off-axis at less tha~ normal i~ten~ity. Reflected rays at the next outer zone repre-~ented by ~our full length h~rizontal line~, have been subjected to 9D~ of polarization rotation, and now appear unattenuated, in the off-axis output. At the next outer zone the reflected rays 59 are of reduced length indicat-ing that they have been derived from previously circularly ;

- 32 ~

pol~rized rays. At the final zone pic~ured, reflected r~ys are represented by dots indicating th~t the rays had been transmitted through the filte:r but not reflected off-axis., S ~he lower portion of Figure 2E illustratefi the rejection of rays at a broad central zone of the field.
The selection of rays of a narrower second zone surround-ing the central zone, the rejection of rays in a still narrower third zone surroundinq the second zone by pa~sage o~ rays of initiall~ P polarizatlon thrDugh the filter-polarizer co~ination.
For purpo~es of introduction to the embo~iment illustrated in Figures 3A and 3B in which the aperture 67 is a critical element, the cross-section of the aperture 67 has been imposed in the Figure 2D embodi-ment illustrating that the aperture 67, lf placed in the transmitted output of the polari2er, should be 6et to allow passage of the broad central zone of the field and be aligned approximately at the lowest point of the second zone surrounding the second zone (a zone of rejection) ~hus, the filtex, the polarizer and the aperture combine to permit unat~enuated passage of a . .

Ll î~

-- 33 -- :

single band of rayB ~lowly yoing from a minimum t~ a maximum and returning to a mi~imum acrosfi the physical aperture 67.
The ~pherical optical transmission filter-polar-izer combination may be employed in the cavity of astable Q-switched laser oscillator for improved operation.
The laser oscillator and its operation are explained with reference to Figure 3A-3C; with Figures 4A-4F, 5 and ~
dealing primarily with the Q-switching operaticn. The fllter-polari~er comblnatlon ls designed to ~acilitate laser operation in a single TE~oo mode ;and to suppress operation in the TE~ol and TEMlo modes. The consequence of single mode operation is an improvement in the uni-formity of the output beam and in divergence in the far lS field region.
The combination offsets the tendency of the laser to produce multiple modes as a result of a thermo optical distortion of the laser gain medium or from an increase in the aperture of the resonator. The optical distortion will tend to cause break up of a single mode beam and to cause the development of higher order modes. Decreasing the intracavity bea~ aperture can be used to control the - 3~ - `

laser beam mode, but results in a l~w lntensity output and inefficient use of energy stored in a gain medium, since the energy not passed by the aperture i~ 108t~
A typical beam aperture for a single mode rod S laser is designed to maintain the Fresnel number N~ at less than 1 i~ order to obtain the desired mode selec-tivity; where Nf = a2/~L, in which a s the laser ~eam radius, ~ is the laser beam wavelength, and L is the optical resonator length. The small beam aperture requir-ed for TEMoo mode operation i5 ~olely dependent on de-fraction loss. The Fresnel numbered mode amplitude and phase relationships in a face pumped laser are described in an article entitled "Resonant Mode Analysis of Single Mode Face Pumped Lasers" in Applied Optics, Vol. 16, page ; 15 1067 and following, on April 1~77, authored by ~.K. Chun et al. The be~m intensity distribution of the TEMoo mode is concentrated at the beam center ~aussian intensity profile~, while in the higher order modes the majsr port.ion of intensity di~tribution is away from the beam center. For a number of la~er appli-cations, operating in the TEMDo mode with the laser energy concentrated at the beam center i8 e~sential to efficient la~er operation, bu~ limiting the beam aperture to control mode also Ii~its beam ~nergy.o~tput. ~he present embodiment e~fect3 increa~e~ in energy and in ~uality of the output beam.
~he laser appa~atus designed f~r ~ingle mode operation comprises a slab 60 of the gain medium of a square cross-section, optical pumping means 61 arranged adjacent to the upper and lower lateral surfaces of the slab, an optical.cavity which includes a first flat partially tranqparent mlrror 62, deini~g o~e end of the optical cavity and a second concave spherical mirror 63 defin1ng the other end of the optical cavity, and the wave transmission filter 10, a Pockel's cell 64, a polarizer 52, and an aperture 67 all installed within the cavity. Light rays generated within the slab and passing through the slab, pass through the two end surfaces of the slab, and are coupled to the optical resonator caYity 62, 63. The slab may be either of a Nd:YAG, or Nd:glass or any suitable laser material designed for laser operation. The Pockells cell 64 and the polarizer 52 cooperate, in operating the optical resonator in a ~-switched mode, the polarizer S2 being '7 - 36 - ~

the means by which energy is diverted f:rom the cavity to prevent oscillation. The partially transmittinq mirror 62 is the point from which the optical output is taken from the cavity.
The optical elements of the l~ser app~ratus of Figures 3A and 3B are arranged alony the ~ axis in pre-scribed orientations in relation to the P and S axes.
As earlier noted, the P and S axes in Figure~ 3A and 3B are e~t~blish~d by the rotational orientation of the slab 6~ about the Z axl~. In particular, the end face~
65 and 66 oE the slabs are cut ~t the Brewster angle ln relation to the upper and lower surfaces. The Brewster angle defines an anglç at which a ray polarized perpen-dicular to the upper and lower surfaces of the slab (P
polarizatio,n) will enter the slab with zero reflection.
At the same time, the srewster cut has the effect of gradually dispersing horizontal polarization, since a horizontally (5) polari7ed component of a ray will l~se a ~ubstantial percentage (typically 20%) in reflection upon each passaqe through the slab.
The laser apparatus illustrated in Figures 3A, 3B and 3C produce~ a short duration high intensity ~ Z~ L?~ 7 - 37 ~

polarized beam o~ coherent electro-maqnetic radiation.
The energy for the output be~m~is ~upE~lied to the gain medium 60 by the flash lamps 61 acting as pumps to pro-duce a population increase (or inversion) of high energy electronic ~tates in the gain medium. The energy stored in the gain medium, which accompanies each flash of the flash lamp, is extracted by the optical resonator under the control of the Pockel's cell 64, to effect "Q-switched" short pulse high intensity operation.
In ~-~witched operation, the Pockel ~Y cell which is installed within the laser cavity, forms an electri-cally controlled optical shutter, operating the resonator cavity between a gain prohibiting (low Q) and a gain permitting (high Q) state. The Pockel's cell effects thi~ change by producing a phase rotation to incident light of suitable polarizati~n, when a control voltage is applied to its crystal constituent. The slab 60, as a result of the use of end faces cut at the Brewster angle, tends to form a beam of P polarization. The ene~gized Pockel's cell, which produces a net 90 polar-ization rotation in the apparatus, combined with the polarizer 52, combines to eject the originally P

1~35'~'7 polarized radiation from the res~nating cavity. ~hiC
reduces the feedback of the c~vity re~onator below that re~uired for lasing. When the control. voltage applied to the Pockel's cell, is removed, the phase rotation disappears, and the feedback of the resonator cavity for rays of P polarization is restored allowing las.ing to occur.
Energized operation of the Pockel' 8 cell pre-cludes resonance within the cavity in the following manner, When the Pockel'g cell i3 in an energi2ed state, it produces a ne~ 90 rotation o the polarization to the components of polarized rays experiencing a double passage through the Pockel's cell. The double passage occurs in the leftward path from the sla~ 60 ~ia the lS polarizer 52 to the end mirror 63 and in the return path to the riyht from the mirror 63 via the polarizer 52 to the slab 60. Essentially all of the light imping-ing on the polarizer 52 from the slab 60 is of a P
polarization, and is transmitted to the Pockel's cell.
When the Pockel's cell is in an energized state, the double passage which' produces a 90 polarization rotation, convertQ the light from a P polarization to S polarizat~, i ~ ~S~7 ; - 39 -in which state it i8 rejected fr~m the res~nator by the polarizer 52 as shown at 68.~-The ejection of this light reduce~ the optical "Q~ of the reso~ator ca~ity below the level required to sustain resonance.
Q-switched short pul~e oper~tion occurs in the following sequence. Before a pumping n flash" ha~ oc-curred a control voltage is applied to the Po~el'~
cell to preclude resonance and allow the population inversion operation. When the peaX ~i.e. a maximum population inversion) has been attained, the voltage applied to the Pockel's cell is removed to allow the rapid depletion of stored energy necessary to produce the desired short duration high intensity output pulse.
Shortly after the output pul6e has occurred, the voltage is reapplied to the Pockel' 8 cell to preven~ resonance ~ntil adequate energy ha~ been stored to generate A
second pulse.
The above sequence of events for Q-switched oper-ation is illustrated in Figures 4A through 4F and utilizes 20 the control circuit of Figure 5. The gain medium is re-currently pumped by flashlamps which has a time dependent optical gain in a laser medium as shown in Figure 4B, s~

- 40 - ~ ~

the period of each se~uence starting at t . The voltage necessary to effecting a 90~ polarizat:ion rotation iB

-applied to the Q-switch prior to to and sustained into the flashlamp pumping period as will be described bPlow, As a result of a pumping flash, optical gain in the lase~
gain medium is created, having a time dependent charac-teristic as shown in Figure 4B. As a next step in Q-switched operation, ~rigger pulses are applied to the control circuit for the Pockel's cell at predetermined time~ ~tl, t2) to cause the Poc~el's cell voltage to decay at prescribed rates from the initial value to zero. This induces a controlled depletlon of the electronic inversion in the gain medium, allowing resonance in the optical resonator with the controlled lS onset of amplification in the gai~ medium. The effect ; is the production of an output laser pulse of improved beam quality.
The control circuit shown in Figure 5, is used to operate the PocXel'a cell, in the Flgures 4A through 4F sequence. In the control network of Figure S, the electronically controlled switches Sl and S2 are connected via two switching networks to the Pockel's ,.

.

1~5~

cell (64). The~e switching networks each entail a capacitor and two resistors. Each capacitor (.003 micro-farad~ is connected in series with a ~0 megohm resi~tor, the combination connected in shunt with each switch. The inter-connection ~f a first cap~citor-resi~tor pair is connected to the high voltage terminal of the Poc~el's cell via the moderately sized reqistor 78 ~56K). The inter-connection of the second capacitor-resistor pair is connected to the high voltage terminal of the Pockel's cell Via a small slzed re~istor 80 (5~ ohms). One terminal o~ each switch Sl, S2 and the Pockel's cell is returned to ground. A voltage source (not shown) having a value adjusted to produce a 90 polarization rotation for a double beam passage (i.e., a quarter wave differ-ential phase shift) is connected to the control networkto operate the Pockel's cell. In the exemplary circuit the control terminal of the source is connected via three (unnumbered) isolating resistors respectively to the ungrounded terminal of switch Sl, of switch S2, and of the Pockel's cell 64. In the example, ~he voltage re-quired for a KD~P Pockel's cell is 3.2 kilovolts. The negative terminal of the source is connected to ground ~s~

to complete the energization circuit.
In the operational eequence, ~he high voltage ie applied to the control network just prior to the time to (at which time the flashlamp is turnecl on) with the electronically controlled switche~ Sl, S2 open. ~hus, from just prior to the time to and from the ti~e to to tl, the Pockel's cell has a constant quarter wave voltaqe applied, which blocks resonant operation of the optical cavity. This blockage i5 a function of radial distance from the axis of the optical system, a~ illustrated by the trans~ission profile 82 of Figure 6 and specifically prevents resonance at the fundamental TEMoo mode and --re.4onance in general. In Figure 6, the radial distance is normalized to the size of the laser beam. At time tl, lS a voltage qpike occurs as shown in Figure lC, closing the electronically controlled switch Sl, and initiatiny a discharye of the Pockel's cell at a first alow decay rate. Since the Pockel 1 5 cell may be represented as a fully charged capacitor of ab~ut 30 picofarads, the voltage on the Pockel's cell will decay with a time constant established by the 56 kilo-ohm resistor 78, and the capacity of the Pockel' 6 cell. The R-C time constant of this discharge path is on the order of ~
few (e.g. 1-3) micro-seconds ~nd produce~ the rate of decay shown in ~igure 4D during the perio~ between tl a~d t2. ~uring the tl-t2 period, the voltage applied to the Pockel 1 5 cell will drop gradually to a voltage ~lightly above the threshold required for single mode Dperation within the cavity, corresponding to the seoond transmission profile illustrated at 86 in Figure 6. The new profile ~86) represents a change from the previous prof~le (82) c~nd permits generation of a slowly growing single mode seed beam. At the time t2, a~s shown in Figure 4C, the electronically controlled s~itch S2 is closed in response to a further control pulse. This closes a second discharge path for the voltage on the Pockel's cell 64 through 50 ohm resistor 80. The R-C
time constant of this discharge path is on the order of a few (e.g. 2.0 - 4.0) nanoseconds, or about one thDu-sandth the time constant for the discharqe path through resistor 78. After time t2, a rapid decay of the Pockel's cell voltage occurs, as shown in Figure 4D. The drop in Pockel's cell voltage allows growth of internal feedback within the resonator cavity, passing through three s~

illustrated intermediate stages until the "final" ~rans-mission profile shown at 84 in Figure 6 i~ reached.
Maximum ~timulation of emis~ion occurs in this tate and the laser output pulse illu~trated at 4F i~ pr~d~ed 5 as the popul ation inYersiOn ln the gain med~um 1R
rapldly dissipated.
The natural decay indicated as a dotted line in Figure 4B as a result of the stimulation is hastened by four orders of magnitud~, producing an actual decay more accurately represented by a vertical ~olid lino. While slopes have been indicated after t2, in the 4B, 4F illus-trations, the microsecond and nanosecond period~ require mixed time scales for'exact illustration. One may explain that approximately 30 nanoseconds after t2, the short duration output pulse of 10 to 30 nanoseconds (represented in Figure 4F) takes place simultaneously with the actual population depletion ~represented in ~igure 4B).
The final transmission proPile 84 of Figure 6 for the Figures 3A-3s embodiment corresponds to the trans-mission profile produced by the filter-polarizer combin-ation which was illustrated in Figure 2D. When these two .

, ~5~ '7 - 45 ~

elements axe present in the resonator cavity, they impose a transmission profile upon t~e total la~er apparatus favoring operation in a TEMoo mode and favoring pro-duction of an output beam 69 of high purity.
S A simple expl~nation for selectlon of the TEMo~
mode in the ~igures 3A, 3~ embodiment is that the trans-mission profile approximates the Gaussin intensity profile of the TEMoo mode. Thus operation in the TEMoo mode is facilitated and operation on the higher order modes, which require facilitation by a spacially inconsistent inte~sity profile, are suppressed. In particular, the be~m intensity of the TEMoo mode is concentrated near the beam center, while the beam intensity for the higher order modes is distributed over distances remote from the beam center. The filter-polarizer combination of the present invention, provides a nearly lossless optical transmission characteristic is pro~ided to the two next higher order modes. This results in conditioning the optical cavity to maximize operation on the TEMoo mode.
The operation of the laser apparatus in effecting selection of the TEMoo mode may be further explained by ; reference to Figure 3C, which illustrates the radial transmiSsion profile of the filter-polarizer combination '7 in the context of the normal distribution of energy in the three releve~t modes. The drawing further illus- ' trates the effect of the aperture 67, which may be regarded as a spaclal filter, and tha intensity profile of the laser beam. The laser b~am profile wi~hin the resonator cavity, ~ut after spacial filtering by aperture 67, approximates the profile of the output beam after passage via the mirror 62 and thus the two may be regarded as quite similar.
The upper graph in Figure 3C illustrates the differential phase shift o the filter 10 as a function of the,radial position of an impinging ray. The phase shift is a second power of the coordinate of the ray.
The transmission profile of the filter-polarizer combin-lS ation is the second graph of Figure 3C. The profile includes a broad central area of high transmission, a narrower ~surrounding~ second zone of low transmission and a third still narrower, surrounding zone of high transmisSion~ The Gaussian TEMo~ mode has a somewhat narrower intensity profile than the transmission profile and is passed substantially unattenuated to the outputO
This is shown at the lowest graph of Figure 3C which is - 47 - ~ -the intensity profile of the output beam of the laser.
Rejection of the two higher order m~des may also be explained using Figure 3C, which shows these intensity profiles. The next higher order mode, the T~Mol mode, has an intensity profile which is low at the beam center and whic~ has two maxima, which occur near the minima of the transmis&iDn profile of the filter-polarizer combination. These zones are usually o~ unlike breadth, and so rejection may not be complete. When, how~ver, an aperture acting a~ a spacial filter is imposed at approximately the point of minimum transmission in the secon~ zone of the filter-polarizer combination, add-itional suppression of the TEMol mode will usually occur. The potential contribution of the TEMol mode 1~ is thus usually quite small, and in a suitable design, the actual contribution may be negligable.
The second higher order mode, the TEMlo mode, is also potentially present but suppressed in the design.
This mode has an intensity profile in which the energy is distributed into three peaks of comparable intensity~
The central intensity peak of the TEMlo mode is at the center of the filter-polarizer transmission profile, ~S~'~'7 - g8 which is also a transmission peak, In addition, the two outer peak~ of the TEMlo mode ~pacially overlap the two outer transmis~ion peaks of the filter-polarizer combln-ation. Thus the TEMlo mode mignt be expected to be present. The spacial f~lter 67 re~ects the two outer peaks, and thus removes a co~siderable portio~ of the TEMlo energy, normally enough to suppress that mode.
In practice, the mechanism for mode selection in the resonator cavity i9 interactive, and the rejection of unwanted modes need not be complete to achieve nearly pure TEMoo mode operation.
The filter-polarizer combination in the Figure 3A-3C embodiment produces several major advantages in laser operation. These advantages flow primarily from th~ suppression of the undesired higher modes and selection of the desired TEMoo mode. One conse~uence of single mode operation is that a higher quality beam both within and without the cavity is produced. In particular, the phase and the amplitude (intensity) across the beam is more accurate and the far field divergence is reduced. A second effect, an indirect consequence of single mode operation, is that when an -- D~9 _ , aperture is employed, of which the edge is placed at the minimum point of the TEMoo mode, the aperture ~ecomes a "soft aperture". This implies, that the beam intensity is small at the margin of the aperture and that Yreanel fringes, which would otherwise worsen the quality of the beam at its boundaries are not present.
In the actual design, the cavity is operated in a stable mode in both dimensions, using a filter of spherical design with Fresnel numbers of about four. The beam diame-ter is approximately ~ millimeters in a slab oE 8 by 16 m:illimet~rs cross-s~c~ion. q'h~ energy per pul~3e :is approximately 150 millijoules.
The cylindrical optical transmission filter-polarizer combination may be employed in a cavity of a stable/unstable Q-switched laser oscillator for improved operation. The laser oscillator and its operation are explained with refere ce to ~igures 7~-7b.

~ .

,55~ 7 The laser Psc~ ~lator of Figures 7~, 7~ comprl~es a ~la~ 81 of the gain mediu~ of rect:angular croq~-6ec~on, optical pumping means 82 arranged adjacent to the larger lateral ~urfaces of the ~lab, an optic~l cavity which includes a first convex cylindrical mirror 83 defining one end of the optical cavity, and a second concave spherical mirror 84 defining the other end of the optical cavity; and a Pockel's cell 85, a polarizer 86, a rectangular aperture 87, a polarizer 89, and an adjust-able cylindrical filter 90 installed within the cavity.
~ he optical elemen~s o~ the laser oscillator arearranged along the optical axis (Z axis) of the apparatus as illustrated in both Figures 7A and 7s. In a left to right sequence, the concave spherical mirror 84 is first, the Pockel's cell 85 is second, and the polarizer 86, the slab 81, the aperture 87, the polarizer 89, the adjust-able cylindrical optical transmission filter 90, and the convex cyli~drical mirror a3 follow in succession.
The optical output of the laser oscillator is derived as a reflection from the le~t face of the polar-izer ~6 as shown at 98. An unused outpu~ 97 also appears as a reflection fro~n the right face of the polarizer 89.

1~5~

The unused output 97 acts as a discard of unwanted energy from the main path of the optical resonator as a result of operation o~ the polarizer filter combination (89, 90), which provides a "soft aperture" active along the S unstable axis of the re~onator. The polari2er-filter combination facilitates operation of the laser-oscillator at high power using a rectangular glab laser at l~rge apertures (e.g. P~nel n~xrs of 40, measured along the unstable axis) while still providing an output ~eam o~
9 ood qua 1 i ty .
The length (L) of the cavity, the radius (Rl) of the convex cylindrical mirror 83 and the radius (R2) of the concave cylindrical mirror 84 define an optical resonator in which stable operation is achieved in a vertical dimension of the beam, the beam being prevented from expanding in the vertical of P dimension beyond the aperture of the oscillator. ~nstable operation is achieved in a horizontal dimension, the beam being per-mitted to expand in the S dimension beyond the apertures ~0 o f th e appara~us.
As noted in the above cited patent application, the slab 81 whose end faces are cut at the Brew~ter .~L;ZS5~9L~L7 - 52 ~

angle has a polarization selective act:ion by which the 8lab i8 optically coupled to rays ~95) of P polarization transversing the optical resonator defined by the end mirrors 83, 84. In the cited arranqement the Pockel 1 8 cell 85 acts as a variable opt~cal power divider within the cavity, capable ~f facilitating or precludil~g lasing by adjustment of the light diverted to the output. The Pockel's cell is ordinarily operated at an intermediate setting by which the amounts of light retained within the cavity and the amounts diverted from the cavity to th~
outpu~ are adjusted to optimize the ou~put. At the right of the slab, in the Figures 7A, 7B embodiment, the polarizer-filter combi~ation 89, 90 ~not present in the cited arrangement), cooperate to provide the soft lS filtering action noted earlier.
The laser oscillator o~ Figure~ 7A, 7B osclllates with light pursuing the following path through the resonator rays 95 of P polarization, which have exited t~e right face of the rectangular laser slab 81, proceed to the risht along the Z axis via the polarizer 89 to the filter 90. The vertical lines ~95) which continue from the slab 81 via the polarizer 89 to the filter 90 i~dicate .

4~

- 53 ~

the p~ssage of P polarized light to the filter 90.
Upon passage through the filter 90, the polari7ation components of individual ray~ of the beam, dependiny upon thB S coordinates of each ray, experience differe~t individual phase 6hifts which pr~duce differi~g polar-ization rotations. The polarization characteristic of the cylindrical filter is comparable to that illustrated in the upper portion of Figure 2C, which illustrates the polarization rotation over the beam cross-section pro-duced by a spherical filter. The polarization charact-eri.~tic Por the cylindric~l unit 90 may be described as lackinq the vertical and retaining the horizontal development of the Figure 2C illustration. More particularly, it may be descrihed as a horizontal section of the Figure 2C illus~ration taken through the center of the beam. The rays modified by the filter 90 are thus approximately represented at 96 in Figure 7A by alter~atinq circles and vertical lines and in Figure 7 by circles implying some degree of mixed polarization.
20 The filtered rays continue rightward until they impinge upon the convex cylindrical mirror 83. The mirror 83 has a l~o~ reflective coating, which causes the rays to S~

- 54 ~

be reflected leftwards. The cylindrical mirror 83 is oriented in relation to the ~xes of the apparatus such that a trace of the mirror in the P-Z plane will be a traight :line while a trace of the mirror in the S-Z
plane will be a circle having a radiu~ Rl.
The rays re~lected leftward from tAe mirror 83 retain the mixed polarization 96 already noted and re-enter the filter 90 at its left face. The rays exit the left face of the filter and proceed leftward until they impinqe on the right face of the polarizer 89.
Any ray components (95) of a P polarization proceed via the polarizer 89 substantially without reflection to the right end of the slab 81. Any ray components (97) of an S polarization exiting the left face of the filter 90, as shown at 97, pIoceed to the right face of the polarizer 89 and are reflected off-axis and discarded as shown.
Continuing now to the left of the slab Bl, ray components 9S of P polarization exiting the left face of the slab 81 continue via the polarizer 86 to the Poc~el's cell 85, passing throu~h the polarizer sub-stantially without reflection. Assuming that the . ,~

:~2~ '7 - 55 - ~

Pockel 1 8 cell i~ in a ~uitably energized condition to effect a 45 polarization, rays components entering the Pockel' 5 cell 85 from the right of a P polarization are subjected to a polarization rotation of 4S producing circular polarization ~g ~hown at 99 in Figure~ 7A and 7B. Upon reflection from the concave spherical mirror 84, and a second pass~ge through the Pockel's cell as, the ray components 95 previously of circular P polar-ization, are rotated an additional 45 converting them to S polari~ation ~98). Vpon impinging upon the left face of the polarizer 86, the components 98 of S polar-ization are directed off-axis forming in the main output path of the laser oscillator.
The ill~strative Pockel' 8 cell setting is one which reduces the feedback within the optical re~onator to zero, and is used to extinguish oscillation. }n practice, the voltage on the Pockel's cell is an intermediate selection in which a division occurs between light derived from the cavity, and that allowed to remain in the cavity.

~ ~5~ 7 - 56 - ~ ~

In ~peration of the ~tablefuns~able resonator~ the be~m which ha~ pursued the pa~h~ described, i9 periodi-cally re~ocused in the P dimen ion by the c~rvatur~ of -the spherical mirror 84 ~nd the mirror 83, effectively flat in the P dimension. The optical design of the resonator is thus chosen to provide a reasonable beam sizé within the laser material. The vertical dimension of the beam is typically approximately half the cross-section of the laser slab, e.g. ~ millimeters, with Fresnel ~umbers of ~bout 4. The other deslgn d~men~io~s are as follow~: slab 139.37 mm long, l5 mm wide, 8 mm thick, Rl is 6 meters, L (cavity length) is 1 meter~
Along the unstable axis, i.e. the S dimension modes are not formally defined, and individual rays, lS when traced through the cavity, "walk off" the lateral apertures of the apparatus. In a practical embodiment, the radius of curvature of the cylindrical mirror ~R2) is 4 meters, producing a "G" stability factor o 1.25.
While higher Fresnel numbers are permitted (e.g. 4D), the quality of the beam is disturbed by Fresnel defraction effects at the lateral edges of the aperture if the filter-polarizer combination i~ not present~ A tapering .

- 57 - -:~

of the intensity profile of the beam in the S dimension provides a s gnificant improvement in beam quality, or conversely, permits higher power operat.ion or larger apertures at the same beam qu~lity.
The filter-pola,rizer combination 90, 89 illu9-trated at the right of the Figure 7A, 7B embodiment produces a "soft" lateral aperture reducing the edge diffraction effects. Typically the design of the filter 90 is adjusted in relation to the lateral edges o~ the apert~re so as to produce a null at the aperture edges to waves transmitted through the polarizer B9 corresponding to the intensity plot illustrated at the lower portion of Figure 2D, The reflected waves are ejected from the cavity as illustrated at the lower plot of ~igure 2E.
The benefit of the filter-polari~er com~ination in the Pigure 7A, 7~ configuration, is primarily the consequence of a "soft" lateral aperture in which a graduated attenuati~n generally following the curves in the Figure 2B-2E series is produced along the S

- 58 - ~-coordinate of the aperture. The primary effect is the avoidance of Fresnel edge defraction effects by reducing the beam amplitude at the lateral margins of the aperture.
~he intensity at these margins would remain unacceptably ; 5 high without such a reductlon. ~he :L~teral amplitude adjustment, recognizing that the modes are undefined - along the unstable axis, permits a somewhat m~re efficient extraction of stored energy from the slab by using more of the width dimension of the slab.
In a practical application, the filter 90 may take either the nonadjustable form illustrated in Figure lC or the adjustable form in Figure lD. In principle, the central thicknesses of the two components of the filter should be equal, and achievement of equality is most easily achieved by the adjustable arrangement.
The filter-polarizer combination may also be used to advantage in more fully utilizing the interaction volume of a laser amplifier used to amplify the output of a laser oscillator as shown in Figure 8A.

~2~

A Gaussian inten~ity proflle 114 from a la~r o~c~ tor 101 operating in a eingle tran0ver~e mode (TEMoo~ may be converted to a more nearly U~lat top" beam inten~ity proflle 115 by operation of the filter-polarizer ~o~bin-ation 103, 104, 105, before application to the inputaperture 107 of a laser ampli~ier 1~8. The ~flat top"
beam intensity profile 115 is preferrable i~ order to obtain a more efficient extraction of stored energy from an amplifier.

The apparatus illu~t~ated in Figure 8A functions in the foregoing manner. The outpu~ o~ the la~er oscillator 101 aq indicated by thë vertical and horizontal marks 109 and 110, may be assumed to contain some components of both P and S polarization, but P
polarization is the primary polarization. The output of the oscillator may otherwise be a~sumed to exhibit an ideal Gaussian amplitude profile as more accurately illustrated at 114 in Figure ~C. The la~er oscillator output proceeds to the right impinging next on the S~'7 - 60 ~

polarizer 103 which transmita light of P polarization to the filter 104 and ejects l-i-ght of S polarization from the transmission path. The polarizer 103 is not essential to the operation of the 6ystem to the degree that the output of the l~Ber o~cillator i8 reBtriCted to P polarization. The filter 104 is preferably an adjustable ~pherical two lens filter as illustrated in Figure lB. The first lens of the filter is a compound lens which includes a slideable wedge for adjusting the center thickne~s of the first lens in relation to the center thickness of the second lens.
The cry~tal optical axes of the two lenRes of the filter 104 are mutually perpendicular and are oriented at a 45 angle to the P coordinate. The curvatures of the lenses are selected to provide the desired polar-ization rotation in a single passage of the beam through the filter. The radius of the lens curvature is in turn determined by the design cross-section of the beam. In particular, for the single passage design, a spot ~0 diameter o~ .90 centimeters requires a radius of curv-ature of approximately 33 centimeters. (For double ... . .. .

pa6sage the radius of curvature i3 approximately double.) The filter~d light nex~ impinges on the polarizer 105 which is oriented parallel to the polarizer 103, for transmi6sion of ray component~ of P polarization and S reflection of componen~s of S polarization. Due to the polariz~tion rotation produced by the filter 104, components of S polarization appear ~nd are ejected by reflection from the transmission path by the polar-izer lOS. The tr~n~smltted remainder i~ ~upplied to the aperture 104 o~ the laser amplifier 108. ~he justif.ication of a spherical design for the filter lenses haQ been on the assumption that the interaction cross-section of the laser material is sguare, and that the entrance aperture 114 is circular. The spherical design will produce an improvement in the fill factor along both the P and S coordinates of the beam.
The transmission profile of the filter polarizer combination is illustrated in Figure 8s for five differ-ent adjustments of the center thickness of the first lens. The independent variable in Figure 8B is the beam ~2S~

r~dius and dependent variable is the re:~ative optical transmission. The entrance ~pe~-ture 107 o~ the laser amplifier should be adju~ted to lie ju~t: within the desired i~teraction 2ro6s-section of the active laser material of the a~plifier. The entrance aperture 107 is set at the minimu~ of the transmission characteristic to minimize Fresnel fringing. When the lenses have equal center thicknesses, the transmission profile 111 i9 followed. ~his profile remains near unity until nearly .2 of the beam radi~3; fall~ to approximately 85~ at .4 o~ the be~m radlus and then falls to ~ero ~t approximately .8 of the beam radius, where the aperture should be set.
As the center thickness difference increases, however, the transmission at the center of the profile falls, and the beam width increases. In the right most member (112) of the family of curves, the beam width provides .85 transm.ission at the center of the beam.
The width of the beam at the .85 transmission point i8 ~0 increased from approximately 0.4 to 0.55 of the beam ~2~

radius. ~he width of the beam measured at the low point shifts from approximately 0. a to .Q9, and defines a new position for setting the entrance aperture of the laser amplifier.
S ~he beam "fill factor" may be increased in typicAl case~ from a ~alue of 40~ to 70~ using suitable design par&meters. The "fill factor" is defined as the fraction of the volume of the lasing material occupied by the beam in relation to an idealized case in which the volume of the l~sing material is completely filled with full intensity illumin~tion. At constant ~nplitude, the sharp edge of the aperture acting upon the idealized beam would cause severe Fresnel diffraction effects.
Accordingly, a "fill factor" substantially less than lS 100% is a practical and desirable compromise.
An illustration of a more nearly optimum trans-mitted beam profile achieved by application of the present inYention is shown in ~i~ure 8C. In ~igure 8C, the in-tensity of a Gaussian input beam i~ qhown at 114, the transmission of the filter-polarizer oombination is ~ss~

shown at 113, ~nd the intensity of the transmitted beam with an improved profile is ~hown at 115. In the cal-culated graph of Figure 8C, The intensity of the trans-; mitted beam remains substa~tially constant to approxi-mately .35 of the beam radius and falls to zero at slightly under .90 of the beam radius. The entrance aperture 107 should be set to this value. The trans-mission curve 113 employed in Figure 8C is an inter-mediate one, second from the right of those illustrated in Pigure 8B. The filter-polarizer combination can provide widely varying transmission characteristics.
The radial position dependent phase shift can be con-trolled with a birefringent lens having one flat face and a positive or negative curvature on its opposite face, defined by ~r) = (2~n~1) It + r2/2R~
in which t = the center thickness of the lens R = the radius of curvature of the lens r = the radius of the lens ~n = the birefringence ~ = the wave length of the light beam.

The ideal homogenous linear phase retardation matrix i~
A iB- _ ~r ~s A~
where A - ~CQ~ (~/2) ] +j ~s~n (~/2) co~ 2a~ ~ A* equal~ the complex conjugate of A, B eguals sin (~/2) sin 2~, C
equals the phase retardation angle (i.e. the differential phaYe delay) and B equals the azimuth angle of the crystal op'tic axes in relation to reference ~P) polar-0 ization. ~he transmitted intensity when ~ is 45P iQT(r) _ co~2 [ ~r)/2].
Th2 matching set of egual but opposite curvature phase retardation plates can avoid a lensing effect avoiding an`unwanted beam expansion. ~y choosing a proper co~bin-

5 ation o~ a radius of curvature R, thicknesq t, and azimuth - angle ~, a wide varie~y of tran6mission characteristics for a particular wavelength for a particular gain medium with a filter unit combined with a polarizer ca~ be selected.
2~ The m~trix relation in the case of two lenses placed between two parallel polarizer9 as shown in Figure 2 can be written as [1 ~l rA1 jB~ rA2 j~21 1~l 1 J L 11 ~ ljB2 A2 l ~
~AlA2-BlB

where 1 C g (~i/23 + i ~in (~i/2)(cos 2 ~
Bi = ~sin (~i/2) (sin 2 ~
and i = the phase retardation angle in A~Bi.
Th~refore, the transmitted inten6ity T where T MxM
T = (AlA2 BlB2) ~AlA2 al~2)~
and T - cos (nl/2 - ~2/2~, for 41 = 45~ and ~2 - 45 (the orthogonal arrange-ment of the crystal axes) for the matching concave and convex phaQe-plates, T(r) ~ c08 [--~~ (tl t2 ( )]

where r ~ the rad~ U8, - the radius of curvature, ~n = the ~ixefringence, 20 tl-t2 = the center thickness difference, ~ ~ the wavelength.
As n~ted earlier, with unequal center thicknesses, the - maximum transmission is displaced from the center. When the center thickness of both lense~ i8 equal, khe maximu~

'7 - 67 - -~

transmission 1~ displaced from the centeI. When the center thlckness of both lenses i9 e~ual, the maximum transmission i8 obtained at the center, i.e. r = 0.
For the case of equal lens thicknesses, tl-t2 = 0, and the two-pass transmission ran be expressed as T(r) = cos2 [2~ ~nr2/R~]
The radius of the curvature of the phase plates, R~ is selected upon the basis of ~he desired beam spot size.
The equation indicates that the transmission of light at the center of the phase plate~ will be nearly 100 per-cent by selectiny the design parameters for the plates of the zero order spherical retardation unit, the inter-cavity beam radius may be expanded to maximize utiliz-ation of the laser gain medium and simultaneously maintain the beam transmission characteristics at their opti~um Yalues over the radius of the beam.
Fiqures 9A, 9B and 9C deal with usage of the filter of ~igure lB in particular, for phase correction o~ the output beam of a laser source. When the filter i5 properly desiqned and adjusted, a simple, efficient and practical means is provided to improve beam quality in larqe spertDre face pumped la6er resonatorr ~.d ~,plifiers.

.. . . .

~2~

- 68 - ~ -The correction der~es from ~ m~themati.cal analysts of resonator mode formation ~nd ~he fAr field diffraction of beams formed under these circ~anc:es. The radial pha e deviation of the be~m within the re~onator in-creases as the Fre~nel number of the resonator increasesand the far field beam, which i~ formed in such a resonator, has a divergence which increases as the radial phase deviation of the beam within the resonator in-creases. When a properly deaigned and adju6ted phase correction filter i8 applicd to the output o~ ~uch a reson~tor, or ampli~ier, op~imized to p~oduce a reduction in far field beam divergence, then the output beam quallty is impxoved without deleteriou~ side effects.
The improvement has application to resonators where large Fresnel numbers are involved, involYing both stable or un~table re~o~at~rs.

While the correction haa application to the radial phase deviation of a re~onator, it ahould be noted that . the correction may be applied with good effect to the output of an optical ~mp1ifier. The phase correction scheme may be applied to certain optical amplifiers which - :j f .': ~

h~ve an internal radial pha~e d~viat-on or to those who~e input has been supplied from a resonator having the indicated radial phase deviation.
With a face p~mped laser (FPL) having a rec-tangular-slab ~eometry, such as is illustrated n Figure3 7~, ~B, it has been possible to generate a large Gau3sian intensity pro~ile of the beam. Despite the fact that beam intensity profile is similar to that of a Gaussian inte~sity beam in the TEMoo mode, the measured far field be~m divergence of this large Gaussian be~m has been several times larger than the diffraction limited case. .Thus the presence of an apparent Gaussian intensity profile will be a necessary but not a sufficient condition for diffraction limited beam divergence~
Analysis, indicates that with such a beam, that the radial phase de~iation between the beam center and edge will increase as the ~re~nel number of the res~nator increases ~his is also true ~or both the stable and the unstable case. Yurthermore, the radial phase deviation will increase f or a fixe~ resonator-cavity length 3S tha beam aperture size increases.

~;ii5~7 - 73 - ~ ~

Applying the Hugen~-~re~nel principle, each point in a resonator mode i~ b~sed on the contri~utions from all the point~ on an OppOQite resonator reflector. Thus, aa the Fre~nel number of the re~ona~or increase~, the radial pha~e ~ariation of the mode increases due to the increased path lenqth differences from all the points of an opposite resonator reflector.
~he resonator modes may be analyzed based on the Kirchhoff-Fresnel diffraction theory. In the one-dimensional case ~'~1 ' ' ., YU(X2) = 'J K~X1~ X2~U~Xl)dXl where u(x21 : the resonator mode (eigenvect~r) at the reflector 2 y : the mode reduction factor (eigenvalue) Klxl,x23 : the geometry of resonator (kernel) Xl'X2 : the coordinate at reflector 1, and 2 al : the half dimension of aperture at reflector 1.
~rom the abD~e, one can define the resultant mode u(x) as u~x) = A(x)exp~ (x)~
where A(x) : the mode amplitude ~ (x) : the coordinate dependent ph~se of mode.

i50~ '7 - 71 - : ~ ~

The far field beam divergence can be estimated by the far field integration of the reson~tor mode, which can be performe~ based on the Fraunhofer dif-fraction theory, which provide~ the b~iq of diffraction-angle-dependent far field beam (V(p)):
~a V~p) = J u(x)exp[-ikpx~dx -a where ~=2~/ ~ : the wavevector 10 ~ : the wavelength u~x) : the resona~o~ rnode p : the diffractlon angle coordinate x : the phyqical coordinate a : the half dimension of ~perture.
Thus, the diffraction angle dependent far field beam intensity will be l~p) = V~p) 2exp[-if(p)3 where f(p) : the angle dependent phase of far field intensity P : the diffraction angle.
The diffraction-angle-dependent far field intensity patterns of resonator modes are of the general form shown in Figures gB and 9C becoming successively more di~ergent 5~947 as the e~ui~alent Fresne! numbers increase. In the range of 2.5 to 7.5, the beam width changes fr~m 5 mm to 8.75 mm, and the maximum phase deviation of the mode increa~es from about 1.2 to 5.1 times the diffraction limited beam divergence.
The effect o~ phase deviati~n in the far field is illustrated in Figure 9D. The horizontal coordinate is the relative far field beam divergence and the vertical coordinate is the normalized far field intensity. The individual curves are plotted for differing pha~e devi- -ations, the "phase deviation" being the observed phase difference between the center and the beam edge for a constant amplitude beam (far field). The individual curves are plotted at 0.2~ intervals from zero to 2~.
The maximum phase deviation plotted (2~) exhibits the greatest far field beam divergence and the lowest phase deviation (uniphase) produces the diffraction li~i~ed far field beam diverge~ce.
Pigure 9D illustrates that the greater the max-imum phase deviation of the mode, the greater the farfield beam divergence. When the phase deviation increases, the peak intensity moves out from the center ~25~47 of the beam and the b~am divergence increa~es. In short, the beam width, phAse devi~tion of the modes, affec~ the f~r field divergence of the output beam.
Analysis indicates that in unstable resonators the phase deviation acr~ss the beam increases rath~r ~mo~thly as the beam aperture size increa~e~. Analysis a3so indicates that the same rate applies in stable resonators with large Gaussian modes. Therefore, it i8 posqible to model thi~ phase deviation as being created by a simple quar~z radial phase plate, and to us~ the model to make a correqponding correction.
0(r) = (2~n/~)[~ + (r /2R)~
where ~n : the birefringence A : the wavelength r : the radial dis~ance : the center thickness R : the rad!us of curvature A computed equivalent radius of a quart~ lens may be obtained from the above radi~l phase relation ~vr different ~mpling points of beam aperture ~iqureR 9B
and 9C demonstrate, for the unstable resonator and ~table resonator, respectively, th~ far field intensity improve-ment that is obtained through this phase correction scheme ~.ZS,S,9'~7 - 74 ~

The phase correction provided i.n the Figure 9B ~nd 9C examplea may be seen tD produce a far field diver~enoe o~ le~ than twice that of a ~diffract.ion iimitëd be~D.
The Figure 9A emb~diment, which m~y be adjusted to proYide the correctton of either the F~gure 9B or 9C examp~e, consi~ts of ~ la~er source 110, the adjust-able spherical filter 111, simil~r to that provided in Figure lB, ~nd for con~enience,the focu~ing len~ 112 of coherent accuracy or focu~ing the ~eam upon the ~creen 113. An lnten~ity plot of the beam croQ~-~ection 1~ provided at 114 as it impinges on the screen 113.
The lens element 112 1~ provided to permit the repro-duction of far field conditions within the confines of a room. For purposes of accuracy, the focal length of the lens should be a~ large as possible consistent with available space and i~ surfaces must be of fractional wave ~ccuracy so as~not t~ lntroduce error. In the absence of the lens 112, the far ~ield pattern may be examined at the neare~t measurement di~tance ~ppropriate for far field conditions.

I -s,,r3~7 :
-- 7 5 -- ~
' The Figure 9B filter utllizeg quart~ in an ad-~u~table design ~8~ ng cyllndrlcal_lens surfacei. The componen~ lenses have a center thic~ness clifference of ~,0716 c~nt~meter~, and a radlu~ of curvat~lre of 7.11 cmO
5 Using ~S" coordinate measurements, the beam width is 8.75 mm, the "equivalent~' Fresnel num~er is 7.5 and the magnification of the resonator optics is l.5.
The Figure 9C filter is also of quartz in an adjustable design using spherical surfaces. The radii lO of curvature of the lenses are 29.56 cm and the center .
thickness difference of the lenses is 0.0534 cm. The beam width i3 6 r~, the Fresnel number i8 ~.S And the r C parameter ls 0.83, The phase correction as described with reference 15 to Figures 9A, 9B, 9C and 9D has a primary applicaticn :
to laser systems in which a polarized output beam is provided and in which Presnel numbers exceed 2 or 3.
The improvement is also applicable to laser ~ystems of larger apertures (i.e. Fresnel numbers as large as 40) 20 where the bea~ approximates a smooth Gaussian or a "flat top" profile. In practical ex~mples, corrections have been achieved for be~ms both under and over a ~ phase ,.
deviation. Phase deviations beyond 2~ appear to repre~ent 1;~5~4~

- 76 - ;~

a practical upper limit for substantial phase correction.
~ he phase compengation, herein provided ~ay be applied using a fil~r with matched spherical lenses in the caQe that the phase deviation of the beam has circu-lar symmetry as in a stable re~onator or ~n unstableresonator. In the event that the reQonator i~ a stable/
unstable resonator, then the phase compensation may entail separate cylindrical elements for separately cQmpensating the phase deviation along the stable and 10 unstable axes. While the compensation ha~ been applied for improvernent o the far field beam, in the typical case, near field beam conditions are also improved.
The adjustable form of the filter herein disclosed is useful in that it removes one critical variable in 15 the prescription of the filter and addi flexibility in a given laser system application.
In far ~ield correction, there are three circum-stances ln which the beam formed by an optical re~onator may require phase correction. In the beam formed in an 20 unstable resonator, adjustable ~pherical optics are appropriate. In the beam formed in a stable/unstable resona~or, adjustable cylindrical opticq are appropriate.

j3~ Z~;,5~3 L~7 In both ca~e~, where formal mode ~truc:ture i8 ab~ent, ~he phase de~iation increase~-signific:antly as the margin of the ~eam i~ approached. ~h~ third clrcumstance re-qulring correction i8 where the beam is created in ~n optic~l re~onator ~n'which th0 fund~m~nt~l mode, while paramount, i~ accemp~nl~d by ~me contrlbution~ from other higher order modes. In far field correcti.on, the phase deviation correction ordinarily need not be zero on-axis, is generally small and increases as the radial dl~tance o the beam element incrqases.
In the ne~r field application, where the beam profile is being modified and the filter is used in combination with polarizers, the adjustability ~eature all~ws one to select the distance from the axis at which the pha~e correction goes through zero changinq from p~aitive to a negative sense and the tran~mission i0 maximum. In profile modlfication, adjustability i8 a~so lmportant for optimized performance.
The filter 10 amployed ln the stable re~ona~or of the Figure 3A-3B embodiment use~ ~pherical lenses of equal center thicknes3 in which the radii of curvature ~LZ~ 3~

- 73 ~

of the ~pherical surfaces are 29.72 cm, the assumed beam di~meter being 6 ~m. The filter 90 employed ln the stable/un3table resonator of the Pigure 7A-7B
embodiment h~ radii of cur~ature equal to 82.54 cm, measured in a horizontal plane alon~ the un~table ~S) ~xis. The filter 90 i~ of an adjustable construction and accordingly, the adjustment is set for optimum performance at equal center thicknesses. The larger ~ran9Ver9e dimengion of the beam in the stable/un~table resonator i9 one cmt I I ' .

Claims (13)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. An optical transmission filter for effecting continuous phase compensation of a beam of light polar-ized in a P dimension, the elements of said beam having a phase which deviates from an ideal reference phase as a continuous function of element position, said filter having an optical axis which is concentric with the beam axis and comprising:
A. a first lens of birefringent material of a first center thickness having a first surface which is flat and a second surface which has a predetermined radius of curvature, B. a second lens of birefringent material of a second center thickness having a first surface which is flat and a second surface which has a radius of curvature equal to the radius of curvature of said first lens but of opposite sign, the surfaces of said lenses being oriented orthogonal to and concentric with said optical axis, the crystal optical axes of the materials of said lenses being oriented in mutually orthogonal positions along said optical axis and at an angle of 45° to said P
dimension, with said second surfaces adjacent.

2. An optical transmission filter as set forth in Claim 1 wherein:
the second surface of each of said filter lenses is spherical to effect a differential phase delay which is a continuous function of the radial distance of each beam element from the axis of the filter.

3. An optical transmission filter as set forth in Claim 2 wherein:
the second surface of each of said filter lenses is cylindrical to effect a differential phase delay which is a continuous function of a coordinate of each beam element referenced to the beam axis in a plane orthogonal to said beam axis and in the plane of said curvature.

4. An adjustable optical transmission filter for effecting a differential phase delay upon light in a beam polarized in a P dimension as a continuous function of position, said filter having an optical axis which is concentric with the axis of said beam, and comprising:
A. a first lens of birefringent material of a first center thickness having a first surface which is flat and a second surface which has a predetermined radius of curvature, the surfaces of said lens being oriented orthogonal to and concentric with said optical axis;
B. a second, compound lens of birefringent material of an adjustable center thickness, having a first surface which is flat and a second surface which has a radius of curvature equal to the radius of curv-ature of said first lens but of opposite sign, said second lens consisting of, a wedge shaped first lens element with flat surfaces, having a cross-section tapered at a first angle, and a second lens element having a cross-section tapered at said first angle, assembled in sliding engagement with said wedge shaped lens element, the external surfaces of said compound lens being oriented orthogonal to and centered on said optical axis, said angle of taper being small enough to permit adjustment of the differential delay accorded to transmitted light to a fraction of a wave length as said lens elements are mutually displaced, the crystal optical axes of the materials of said lenses being oriented-in mutually orthogonal positions along said optical axis and at an angle of 45° to said P dimension with said second surfaces adjacent.

5. An adjustable optical transmission filter as set forth in Claim 4 wherein:
the second surface of each of said filter lenses is spherical to effect a phase compensation which is a continuous function of the radial distance of each beam element from the axis of the filter.

6. An adjustable optical transmission filter as set forth in Claim 5 wherein:
the adjustment range of the difference in center thicknesses includes an adjustment in which a small differential phase delay occurs on-axis and a large differential phase delay occurs at the perimeter of the beam.

7. An adjustable optical transmission filter as set forth in Claim 5 wherein:

the adjustment range of the difference in center thicknesses includes an adjustment in which a substantially zero differential phase delay occurs on-axis and a maximum differential phase delay occurs at the perimeter of the beam.

8. An adjustable optical transmission filter as set forth in Claim 5 wherein:
the adjustment range of differences in center thicknesses includes an adjustment in which a substantial differential phase delay occurs on-axis, a zero differ-ential phase delay occurs at an intermediate radial distance, changing in sense at this distance, and a substantial differential delay again occurs at the perimeter of the beam.

9. An adjustable optical transmission filter as set forth in Claim 4 wherein:
the second surface of each of said filter lenses is cylindrical to effect a phase compensation which is a continuous function of a coordinate of each beam element referenced to the beam axis in a plane orthogonal to said beam axis and in the plane of said curvature.

10. An adjustable optical transmission filter as set forth in Claim 9 wherein:
the adjustment range of the difference in center thicknesses includes an adjustment in which a small differential phase delay occurs at the zero co-ordinate value and a large differential phase delay occurs at a maximum coordinate value at the perimeter of the beam.

11. An adjustable optical transmission filter as set forth in Claim 9 wherein:
the adjustment range of the difference in center thicknesses includes an adjustment in which a substantially zero differential phase delay occurs at the zero coordinate value and a maximum differential phase delay occurs at said maximum coordinate at the perimeter of the beam.

12. An adjustable optical transmission filter as set forth in Claim 9 wherein:
the adjustment range of differences in center thicknesses includes an adjustment in which a substantial differential phase delay occurs at the zero coordinate value, a zero differential phase delay occurs at an inter-mediate coordinate value, changing in sense at this value, and a substantial phase delay again occurs at said maximum coordinate value at the perimeter of the beam.

13. A laser apparatus comprising:
first and second reflector means disposed in optical alignment for defining a resonant cavity there-between;
an active laser medium for producing a beam of coherent electromagnetic radiation disposed between and in optical alignment with said first and second reflector means; and optical mode control means disposed within said resonant cavity in optical alignment with said laser medium for shaping the optical transmission character-istics of said resonant cavity to maximize transmission

Claim 13 continued:
of a desired transverse electromagnetic mode of electromagnetic radiation.