Classifications

• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
  • H01S3/05—Construction or shape of optical resonators; Accommodation of active medium therein; Shape of active medium
  • H01S3/08—Construction or shape of optical resonators or components thereof
  • H01S3/08059—Constructional details of the reflector, e.g. shape
  • H01S3/08068—Holes; Stepped surface; Special cross-section
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
  • G02B27/0025—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for optical correction, e.g. distorsion, aberration
  • G02B27/0037—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for optical correction, e.g. distorsion, aberration with diffracting elements
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
  • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
  • G02B27/4272—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having plural diffractive elements positioned sequentially along the optical path
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
  • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
  • G02B27/4272—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having plural diffractive elements positioned sequentially along the optical path
  • G02B27/4277—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having plural diffractive elements positioned sequentially along the optical path being separated by an air space
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/18—Diffraction gratings
  • G02B5/1861—Reflection gratings characterised by their structure, e.g. step profile, contours of substrate or grooves, pitch variations, materials
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/18—Diffraction gratings
  • G02B5/1866—Transmission gratings characterised by their structure, e.g. step profile, contours of substrate or grooves, pitch variations, materials
  • G02B5/1871—Transmissive phase gratings
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
  • H01S3/10—Controlling the intensity, frequency, phase, polarisation or direction of the emitted radiation, e.g. switching, gating, modulating or demodulating
  • H01S3/10076—Controlling the intensity, frequency, phase, polarisation or direction of the emitted radiation, e.g. switching, gating, modulating or demodulating using optical phase conjugation, e.g. phase conjugate reflection
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S2301/00—Functional characteristics
  • H01S2301/20—Lasers with a special output beam profile or cross-section, e.g. non-Gaussian
  • H01S2301/206—Top hat profile
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
  • H01S3/05—Construction or shape of optical resonators; Accommodation of active medium therein; Shape of active medium
  • H01S3/08—Construction or shape of optical resonators or components thereof
  • H01S3/08018—Mode suppression
  • H01S3/0804—Transverse or lateral modes
  • H01S3/0805—Transverse or lateral modes by apertures, e.g. pin-holes or knife-edges
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
  • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
  • H01S3/05—Construction or shape of optical resonators; Accommodation of active medium therein; Shape of active medium
  • H01S3/08—Construction or shape of optical resonators or components thereof
  • H01S3/08072—Thermal lensing or thermally induced birefringence; Compensation thereof

Definitions

• the present invention relates to lasers and more specifically to laser components and to methods for designing and making laser components which compensate for heat distortion and other distortions or aberrations in the laser system.
• a resonator cavity shown in Figure 1, comprising two reflecting elements 110 and 112, surrounding a gain medium 111.
• the gain medium can be a plasma, a gas, a liquid, or a solid (e.g., a crystal or a semiconductor).
• the gain medium is excited by a power source.
• laser as used in this discussion is meant to be inclusive of stimulated emission oscillators of electromagnetic radiation of any frequency from radio-frequency (RF) to beyond x-ray frequencies. (RF lasers are sometimes called “masers” by others.)
• the laser beam will have one or more "modes".
• a mode in this discussion refers to a "spatial mode", also called a “spatial eigenmode”.
• the mode a characteristic of the laser beam, is created within a laser cavity and has both a power-distribution profile and a phase- distribution profile. These mode profiles are generally expressed in dimensions transverse to the direction of propagation of the laser beam.
• a spatial mode is to be distinguished from a "temporal mode", which describes the frequency characteristics of the laser beam.
• a "fundamental mode” is the spatial mode which has the least loss.
• Amplitude profile 114 of Figure 1 illustrates a Gaussian fundamental mode versus transverse beam radius p.
• Amplitude profile 115 of Figure 1 also illustrates a Gaussian fundamental mode along with a second-order mode shown by curves 116 and 117.
• complex as used in this discussion is mean numbers or functions having real and/or imaginary components.
• modal discrimination describes a function of a laser resonator which can simultaneously provide a small fundamental-mode loss while providing large losses for higher-order modes.
• the modal discrimination is influenced by the chosen fundamental-mode shape, the length of the cavity, and the placement of aperture stops.
• phase-conjugation mirror CPCM
• Cartesian X and Y transverse dimensions CPCM
• the invention teaches how to design and fabricate a custom distortion- compensating phase-adjustment optical element which will correct for distortions in other optical elements, and in particular, correct for heat distortions in a crystal gain medium for a laser.
• the invention also teaches how to design and fabricate a custom phase-conjugation mirror (CPCM) which will accommodate a fundamental-mode beam profile of arbitrary profile in Cartesian X and Y transverse dimensions and correct for distortions such as heat.
• CPCM phase-conjugation mirror
• the invention also teaches how to design and fabricate a diffractive mirror for use as a custom phase-conjugation mirror, which is a mirror that will reflect a wavefront having arbitrary (i.e., a complex mode profile that is not necessarily only real but may have imaginary components) field at the mirror surface and correct for distortions such as heat.
• the invention also teaches using an additional phase element in a laser resonator system having a custom phase-conjugation mirror in order to enhance the phase differential between the fundamental mode and higher-order mode wavefronts over and above the result possible with a single CPCM alone and correct for distortions such as heat.
• the invention also teaches using a dynamic phase element in a laser resonator system having a custom phase-conjugation mirror in order to (a) compensate for dynamic phase changes in elements in a laser resonator system or (b) introduce temporal variations in the output beam profile or power.
• FIG. 1 is a schematic diagram illustrating a prior art laser resonator.
• FIG. 2 is a schematic diagram illustrating an embodiment of a custom phase-conjugated diffractive mirror laser resonator.
• FIG. 3 is a schematic diagram illustrating an embodiment of a custom phase-conjugated diffractive mirror laser resonator with a phase- adjustment element.
• FIG. 4 is a schematic diagram illustrating an embodiment of a custom phase-conjugated diffractive mirror laser resonator with a random phase-adjustment element.
• FIG. 5 is a schematic diagram illustrating an embodiment of a custom phase-conjugated diffractive mirror laser resonator with two custom phase-conjugated diffractive mirrors.
• FIG. 6 is a graph of calculated modal threshold gain versus the grating frequency for a sinusoidal Cartesian pattern for a phase-adjustment element.
• FIG. 7A is a graph of calculated modal threshold gain versus the grating frequency bandwidth for a random Cartesian pattern for a phase- adjustment element.
• FIG. 7B is a graph of calculated modal threshold gain versus the niinimum DMSM line- width a random Cartesian pattern for a phase- adjustment element.
• FIG. 8 is a graph of a cross section of a phase profile showing phase shift amounts on a custom phase-conjugating diffraction mirror.
• FIG. 9 is a schematic of a plan of the phase shift amounts on one mask for an E-beam pattern for fabricating a custom phase-conjugating diffraction mirror.
• FIG. 10A is a schematic of a plan of the phase shift amounts on the first of four masks for fabricating a custom phase- conjugating diffraction mirror.
• FIG. 10B is a schematic of a plan of the phase shift amounts on the second of four masks for fabricating a custom phase-conjugating diffraction mirror.
• FIG. IOC is a schematic of a plan of the phase shift amounts on the third of four masks for fabricating a custom phase- conjugating diffraction mirror.
• FIG. 10D is a schematic of a plan of the phase shift amounts on the fourth of four masks for fabricating a custom phase- conjugating diffraction mirror.
• FIG. 11 A is a schematic of a section showing the second e-beam mask and a sensitized 2-level substrate in the process for fabricating a custom phase-conjugating difi&action mirror.
• FIG. 1 IB is a schematic of a section showing the substrate after developing the resist in the process for fabricating a custom phase-conjugating diffraction mirror.
• FIG. 11C is a schematic of a section showing the substrate after etching in the process for fabricating a custom phase- conjugating diffraction mirror.
• FIG. 1 ID is a schematic of a section showing the 4-level result substrate in the process for fabricating a custom phase- conjugating diffraction mirror.
• FIG. 12A is a schematic of a Mchelson-type interferometer which can be used to measure aberrations, which can then be corrected for.
• FIG. 12B is a schematic of a Mchelson-type interferometer which can be used to measure aberrations, which can then be corrected for.
• FIG. 12C is a schematic of a Mchelson-type interferometer which can be used to measure aberrations, which can then be corrected for.
• FIG. 13 is a schematic of a Mach-Zehnder-type interferometer which can be used to measure aberrations, which can then be corrected for.
• FIG. 14 is a schematic of a corrected laser system 340 having a compensating diffractive element 947 close to gain medium 943.
• FIG. 15 is a schematic of a corrected laser system 440 having a compensating diffractive element 948 at point Z Q farther from gain medium 943.
• FIG. 16 is a schematic of a corrected laser system 540 having a compensating diffractive element 949 merged into one of the cavity mirrors.
• FIG. 17 is a schematic of an interferometer which can be used to measure aberrations for a laser system in which it is impractical to introduce light beam 921 through one of the mirrors of laser system 940, the aberrations which can then be corrected for.
• FIG. 2 is a schematic diagram illustrating an embodiment of a custom phase-conjugated diffractive mirror laser resonator.
• Laser beam 100 oscillates in the cavity formed by output mirror 121, laser gain medium 123, and custom phase-conjugated diffractive mirror 124.
• Aperture plate 122 and aperture plate 128 help to block higher-order modes.
• aperture plate 122 and aperture plate 128 are opaque and have a non-reflective surface.
• Output laser beam 126 is the laser resonator output.
• a designer specifies the phase profile and intensity profile for the fundamental mode 125 of laser beam 100 at a point z along the propagation path of laser beam 100.
• point z is chosen to be at the reflecting surface of output mirror 121, and thus the phase profile for the fundamental mode 125 is specified to be a wave with phase profile having values of only 0 and ⁇ radians, corresponding to a flat surface-reflecting mirror for output mirror 121.
• the intensity profile for the fundamental mode 125 may be specified by the designer to be any arbitrary real positive function (a real function has no imaginary components); e.g., the intensity profile could have an approximately Cartesian square cross section approximated by graph 120 of Figure 2 and described by the super-Gaussian equation:
• a laser beam with a intensity profile having an approximately Cartesian square cross section has many uses in industry and research. Uses include integrated circuit photo-lithography, applications desiring reduced laser hole burning, laser doppler velocimetry, laser radar, optical memories, optical information processing and computing, laser bar-code scanning, projection TV, applications desiring patterns of squares, and laser xerographic printing and facsimile. While this example uses a constant phase profile at point z, the equation for a(x,y) can incorporate any complex-function electric-field profile (one having both real and imaginary components) as well. The discussion of Figure 5 below discusses one such embodiment.
• the designer then dete ⁇ nines the design for the appropriate custom phase-conjugated diffractive mirror by calculating a wavefront of laser beam 100 at the end of each propagation segment of the propagation path starting from point z and ending at the reflecting surface of custom phase-conjugated diffractive mirror 124.
• y is the square root of -1
• u and v are spatial frequencies
• x is a Cartesian distance in a direction transverse to the direction of propagation
• y is a Cartesian distance in a direction transverse to the direction of propagation and orthogonal to x
• a fay) is the angular wave spectrum of _ ⁇ (x,y) at point z* .
• exp( ) is the exponential function
• ⁇ n is the free space wavelength of laser beam 100 and n • is the index of refraction of propagation segment i )
• j is the square root of -1
• L j is length of propagation segment i along the path of propagation
• u and v are spatial frequencies
• du and dv are integration variables for u and v respectively
• sqrt( ) is the square root function
• x is a Cartesian distance in a direction transverse to the direction of propagation
• y is a Cartesian distance in a direction transverse to the direction of propagation and orthogonal to x
• a j (u,v) is the angular wave spectrum of a t (x,y) at point z* .
• a mode profile b(x',y') at the reflecting surface of custom phase-conjugated diffractive mirror 124 is defined as the final mode profile a i+1 (x',y)' for the last propagation segment (ending at the reflecting surface of custom phase-conjugated diffractive mirror 124).
• a mirror reflectance t(x',y') is then calculated which reflects the complex phase conjugate b*(x',y') of said mode profile b(x',y') at said mirror reflecting surface, using the equation:
• Figure 2 shows three propagation segments.
• the first propagation segment starts at point z, is represented by length L-, has an index of refraction n* (not shown), and ends at point z, along the propagation path.
• the second propagation segment (through laser gain medium 123) starts at point z, is represented by length I_ 2 , has an index of refraction n 2 (not shown) equal to the index of refraction of the gain medium, and ends at point z-, along the propagation path.
• the third propagation segment starts at point Z 2 , is represented by length L 3 , has an index of refraction n 3 (not shown), and ends at point 2 ⁇ at the reflecting surface of custom phase-conjugated diffractive mirror 124.
• the above-described method is used to calculate the mode profile aj(x',y)' at point z,; then, using that mode profile as the starting point, the above-described method is used to calculate the mode profile a 2 (x',y)' at point Z 2 ; then, using that mode profile as the starting point, the above-described method is used to calculate the mode profile a 3 (x',y)' at point Zg which is at the reflecting surface of custom phase-conjugated diffractive mirror 124.
• Mode profile b(x',y') is defined as the final mode profile a 3 (x',y) for the last propagation segment (ending at the reflecting surface of custom phase-conjugated diffractive mirror 124).
• a mirror reflectance t(x',y') is then calculated which reflects the complex phase conjugate b*(x',y') of said mode profile b(x',y') at said mirror reflecting surface, using the equation:
• custom phase-conjugated diffractive mirror 124 is then fabricated by known methods (see, e.g., J.R. Leger, ML. Scott, P. Bundman, and MP. Griswold, "Astigmatic wavefront correction of a gain-guided laser diode array using anamo hic diffractive microlenses," Proc. SPIE ⁇ vol. 884 ⁇ , 82 (1988).) to provide mirror reflectance t(x',y').
• One embodiment coats the surface of custom phase-conjugated diffractive mirror 124 with a reflective coating made from a suitable dielectric material using materials and methods known to the art.
• custom phase-conjugated diffractive mirror 124 coats the surface of custom phase-conjugated diffractive mirror 124 with a reflective coating made from a suitable metallic material using materials and methods known to the art.
• custom phase-conjugated diffractive mirror 124 is fabricated using a series of photolithographic masks, much in the same way as modem integrated circuits are.
• custom phase- conjugated diffractive mirror 124 are made from any suitable material (e.g., plastic, resin, or photoresist) such as is used to mass produce compact disks, and arrays of custom phase-conjugated diffraction mirrors can be simultaneously pressed from a single, multiple-image master negative of the desired mirror surface, much in the same way as modem audio compact-disks (CDs) or con_pact-disk-read-only-memories (CDROMs) are. These custom phase-conjugated diffraction mirrors can thus be mass-produced accurately and inexpensively.
• suitable material e.g., plastic, resin, or photoresist
• length L- is made as small as possible and is assumed negligible
• length L*. is made 7.6 cm
• length L 3 is made 102.4 cm.
• L 3 is made long enough that the cavity length achieves sufficient modal discrimination; this modal discrimination seems to increase until L reaches a length of one Rayleigh range 2 ⁇ . Optimization studies on super-Gaussian mode shapes have shown that the modal dis ⁇ -imination is maximized when the cavity length is approximately one Rayleigh range of the super-Gaussian.
• the reflected laser beam 100 starting at the reflecting surface of custom phase-conjugated diffractive mirror 124 with mode profile b*(x',y'), then propagates in the reverse direction along the propagation path to point z.
• laser beam 100 will then have a mode profile a*(x,y), which is the phase conjugate of the mode profile a(x,y) and traveling in the opposite direction.
• a(x,y) is specified as a wave having phase of 0 or ⁇ radians at flat mirror 121, and thus flat mirror 121 will reflect the phase conjugate of a*(x,y), which is a(x,y).
• FIG. 3 is a schematic diagram illustrating an embodiment of a custom phase-conjugated mirror laser resonator similar in many respects to Figure 2, but with a custom phase-adjustment element 127.
• custom phase-adjustment element 127 is to enhance the modal discrimination of the laser resonator system.
• custom phase-adjustment element 127 Another purpose of custom phase-adjustment element 127 is to introduce varying amounts of phase shift into various portions of the transverse cross section of laser beam 100.
• custom phase-conjugated mirror 124 may, but need not, be a diffractive mirror.
• the designer chooses a phase pattern for custom phase-adjustment element 127 to suit the designer's needs.
• custom phase-adjustment element 127 is transparent and is designed to enhance the modal discrimination of the laser resonator system by introducing a phase shift which varies sinusoiddly in both Cartesian directions, x and y.
• the phase-adjustment element has a transmittance t(x,y) that approximates e -' cos ⁇ 2tt ⁇ c ⁇ Jdyy > ) and a laser beam wave length of 1.06 ⁇ m, the diffractive loss for the second-order mode is increased to 72.9%.
• calculations of the modal discrimination which would be obtained by a number of different sinusoidal phase patterns for custom phase-adjustment element 127 are performed. The sinusoidal phase pattern generating the largest calculated modal discrimination is then used to fabricate custom phase-adjustment element 127.
• the method described above for Figure 2 is recursively applied to each propagation segment starting at point z specified by the designer and ending at custom phase-adjustment element 127.
• the mode profile a i+! (x',y)' at custom phase-adjustment element 127 is then adjusted for the phase shift introduced by custom phase-adjustment element 127.
• the method described above for Figure 2 is then recursively applied to each propagation segment starting at custom phase-adjustment element 127 and ending at the surface of custom phase-conjugated mirror 124.
• any custom phase-conjugated mirror can be used for custom phase- conjugated mirror 124, as long as it reflects the complex phase conjugate b*(x',y') of the mode profile b(x',y') defined at the reflecting surface of the mirror.
• a diffractive mirror is used for custom phase-conjugated diffractive mirror 124.
• a mode profile b(x',y') at the reflecting surface of custom phase-conjugated diffractive mirror 124 is defined as the final mode profile a i+] (x',y)' for the last propagation segment (ending at the reflecting surface of custom phase-conjugated diffractive mirror 124); however, in this case, this b ⁇ x' ') also accounts for the phase shift introduced by custom phase-adjustment element 127.
• a mirror reflectance t(x',y') is then calculated which reflects the complex phase conjugate b*(x',y') of said mode profile b(x',y') at said mirror reflecting surface, using the equation:
• b*(x',y') is the complex (having real and imaginary components) phase conjugate of incident mode profile b(x',y').
• the surface elevation of custom phase- adjustment element 127 is fabricated by known methods (see, e.g., J.R Leger, ML. Scott, P. Bundman, and MP. Griswold, "Astigmatic wavefront correction of a gain-guided laser diode array using anamo ⁇ hic diffractive microlenses," Proc. SPIE ⁇ vol. 884 ⁇ , 82 (1988).) to provide the desired phase adjustments at that element.
• the surface elevation of custom phase- conjugated diffractive mirror 124 is also fabricated by similar known methods to provide mirror reflectance t(x',y').
• custom phase-conjugated diffractive mirror 124 coats the surface of custom phase-conjugated diffractive mirror 124 with a reflective coating made from a suitable dielectric material using materials and methods known to the art.
• Another embodiment coats the surface of custom phase-conjugated diffractive mirror 124 with a reflective coating made from a suitable metallic material using materials and methods known to the art.
• custom phase-adjustment element 127 is fabricated using a series of photolithographic masks, much in the same way as modern integrated circuits are.
• custom phase- adjustment element 127 are made from any suitable material (e.g., plactic, resin, or photoresist) such as is used to mass produce compact disks, and arrays of custom phase-adjustment elements can be simultaneously pressed from a single, multiple-image master negative of the desired mirror surface, much in the same way as modem audio compact-disks (CDs) or compact- disk-read-only-memories (CDROMs) are. These custom phase-adjustment elements can thus be mass-produced accurately and inexpensively.
• suitable material e.g., plactic, resin, or photoresist
• custom phase- adjustment element 129 is transparent and is designed to enhance the modal dis ⁇ * imination of the laser resonator system by introducing a phase shift which varies in a pseudo-random but known manner in both Cartesian directions, x and y.
• custom phase-conjugated diffractive mirror 124 compensates for the known and pseudo-random phase shifts introduced to the various portions of the cross section of the mode profile by custom phase- adjustment element 129.
• calculations of the modal discrimination which would be obtained by a number of different random phase patterns for custom phase-adjustment element 129 are performed.
• the phase patterns are generated using different "seeds" in a random number generator. The random pattern generating the largest calculated modal discrimination is then used to fabricate custom phase-adjustment element 129.
• Figure 5 is a schematic diagram illustrating an embodiment of a custom phase-conjugated diffractive mirror laser resonator with two custom phase-conjugated diffractive mirrors 124 and 124'.
• This configuration is conceptually similar to an embodiment shown in Figure 3, with the modification that flat output mirror 121 is combined with custom phase-adjustment element 127 to form custom phase-conjugated diffractive mirror 124'.
• a mode profile b( ⁇ , . y') a*-* th e reflecting surface of custom phase-conjugated diffractive mirror 124 is defined as the final mode profile a i+1 (x',y)' for the last propagation segment (ending at the reflecting surface of custom phase-conjugated diffractive mirror 124).
• a mirror reflectance t(x',y') is then calculated which reflects the complex phase conjugate b*(x',y') of said mode profile b(x',y') - 31 sa id mirror reflecting surface, using the equation:
• a mode profile c(x',y') at the reflecting surface of custom phase-conjugated diffractive mirror 124' is defined as the final mode profile a i+1 (x',y)' for the last propagation segment (ending at the reflecting surface of custom phase- conjugated diffractive mirror 124').
• a mirror reflectance t'(x',y') is then calculated which reflects the complex phase conjugate c*(x',y') of said mode profile cfa, ⁇ ) at said mirror reflecting surface, using the equation:
• t'(x',y.) c * ⁇ y.) / . )
• c*(x',y') is the complex (having real and imaginary components) phase conjugate of incident mode profile c(x',y').
• custom phase-conjugated diffractive mirror 124 is fabricated by known methods to provide mirror reflectance t(x',y'). One embodiment then coats the surface of custom phase-conjugated diffractive mirror 124 with a reflective coating made from a suitable dielectric material using materials and methods known to the art. Another embodiment coats the surface of custom phase-conjugated diffractive mirror 124 with a reflective coating made from a suitable metallic material using materials and methods known to the art.
• custom phase-conjugated diffractive mirror 124' is fabricated by known methods to provide mirror reflectance t'(x',y'). One embodiment then coats the surface of custom phase-conjugated diffractive mirror 124' with a partially-reflective coating made from a suitable dielectric material using materials and methods known to the art. Another embodiment coats the surface of custom phase-conjugated diffractive mirror 124' with a partially-reflective coating made from a suitable metallic material using materials and methods known to the art. Custom phase-conjugated diffractive mirror 124' thus becomes the output coupler for the laser resonator.
• the reflected laser beam 100 starting at the reflecting surface of custom phase-conjugated diffractive mirror 124 with mode profile b*(x',y'), then propagates in the reverse direction along the propagation path to point z.
• laser beam 100 will then have a mode profile a*(x,y), which is the phase conjugate of the mode profile sfay) and traveling in the opposite direction.
• a*(x,y) continues to propagate until it reaches custom phase-conjugated diffractive mirror 124', where it will have mode profile c(x',y').
• calculations of the modal discrimination which would be obtained by a number of various specified phase profiles at various points z for specified mode profile sfay) are performed.
• the specified phase profile generating the largest calculated modal discrimination is then used to fabricate custom phase-conjugated diffractive mirrors 124 and 124'.
• a ring-laser resonator cavity comprising a custom phase-conjugated diffractive mirror 124 is built.
• - point z is specified at a location that is one-half the propagation distance around the ring from custom phase-conjugated diffractive mirror 124.
• the mode profiles around the ring are then calculated in a manner as described for Figure 2, taking into account the phase change introduced at each bending node around the ring.
• the complex mode profile (a mode profile having both real and imaginary components) of the laser beam 100 when it completes the path around the ring will match the starting mode profile sfay).
• the laser mode profile can be chosen to have any real positive function of power distribution and arbitraiy phase distribution by proper design of the mode-selecting mirrors.
• the cavity can be optimized to simultaneously provide a small fundamental mode loss while providing large losses for higher-order modes (a function called "modal discrimination").
• the modal discrimination is influenced by the chosen fundamental-mode shape, the length of the cavity, and the placement of aperture stops.
• the cavity design of the invention preserves high modal discrimination while allowing use of a shorter cavity length.
• One embodiment, shown in Figure 3, comprises a flat output mirror 121, a diffractive mode-selecting mirror 124, and a sinusoidal phase grating 127.
• the designer selects a desired profile for the transverse section of the fundamental mode at the output port, and calculates the Rayleigh-Soimnerfeld diffraction pattern of this selected profile at the mode-selecting mirror after passing through the gain medium 123, any other internal optics, and the phase grating.
• the diffractive profile of the diffractive mode-selecting mirror (“DMSM') 124 is chosen to reflect the phase conjugate of this distribution.
• the reflected light wave will then retrace its path through the phase grating 127 and form the original selected profile at the output mirror 121 (at point z), thus reinforcing the selected profile and defining it as a mode of the cavity.
• Higher-order modes are partially blocked by the aperture 128 placed at the phase grating 127 and the aperture 122 placed at the output mirror 121, producing a high loss for those higher-order modes.
• a Fox-and-Li analysis see AG. Fox and T. Li, Bell Syst. Tech J.
• ⁇ 40 ⁇ 453-488 (1961).) of the above cavity with, and without, a phase grating 127 was performed and the optimum characteristics of a phase grating with a modulation depth of ⁇ 1 radian was studied. Without the grating, a mode-selecting-mirror cavity (with a cavity length of 1 meter) designed for a 20th-order super-Gaussian beam of transverse half-width (0-- 0.6 mm was shown to present a maximum loss to the second-order mode of 48.6 % (which is due to the design of the DMSM in conjunction with the apertures).
• phase-plate spatial frequency corresponding to approximately 4.5 periods across the laser beam transverse cross section, gives the optimal modal discrimiriation.
• the maximum modal discrimination occurs -when the grating has a phase shift corresponding to a sine function.
• the 20th-order 18 super-Gaussian fundamental mode (with square Cartesian beam transverse cross section) is preserved and suffers negligible loss in the cavity.
• Figure 6 is a graph of calculated modal threshold gain versus the grating frequency for a sinusoidal Cartesian pattern for a phase-adjustment element.
• Figure 7a is a graph of calculated modal threshold gain versus the grating frequency bandwidth for a random Cartesian pattern for a phase- adjustment element.
• Figure 7b is a graph of calculated modal threshold gain versus the minimum DMSM line- width a random Cartesian pattern for a phase- adjustment element.
• Figure 8 is a graph of a cross section of the phase shift amounts on a custom phase-conjugating diffraction mirror.
• Figure 9 is a schematic of a plan of the phase shift amounts on one mask for fabricating a custom phase-conjugating diffraction mirror.
• Figure 10A is a schematic of a plan of the phase shift amounts on the first of four masks for fabricating a custom phase-conjugating diffraction mirror.
• Figure 1 OB is a schematic of a plan of the phase shift amounts on the second of four masks for fabricating a custom phase-conjugating diffraction mirror.
• Figure IOC is a schematic of a plan of the phase shift amounts on the third of four masks for fabricating a custom phase-conjugating diffraction mirror.
• Figure 10D is a schematic of a plan of the phase shift amounts on the fourth of four masks for fabricating a custom phase-conjugating diffraction mirror.
• Figures 11A-1 ID form a schematic of a section showing the process for fabricating a custom phase-conjugating diffraction mirror.
• Figure 11 A is a schematic of a section showing the second e-beam mask and a sensitized 2- level substrate in the process for fabricating a custom phase-conjugating diffraction mirror.
• Figure 1 IB is a schematic of a section showing the substrate after developing the resist in the process for fabricating a custom phase-conjugating diffraction mirror.
• Figure 11C is a schematic of a section showing the substrate after etching in the process for fabricating a custom phase-conjugating diffraction mirror.
• Figure 1 ID is a schematic of a section showing the 4-level result substrate in the process for fabricating a custom phase-conjugating diffraction mirror.
• Some applications such as short-pulse Q-switching, require a large mode cross-section and short cavity length.
• the same cavity design was studied with a total length of 10 cm (corresponding to 1/10 Rayleigh range).
• the cavity loss for the second-order mode is 58.3%.
• This large modal dis ⁇ * irnination is significantly greater than a simple DMSM cavity without a phase plate with a length of one full Rayleigh range (in this case, approximately 1 meter).
• phase plate in a mode-selecting-mirror laser cavity permits both a reduction in the required cavity length and an increase in modal discrimination.
• the vast majority of commercial lasers utilize a stable Fabry-Perot resonator to establish the laser mode.
• the Fabry-Perot resonator design produces a low-loss fundamental mode, it has several inherent disadvantages.
• the losses to the higher-order spatial modes are also fairly low, making it difficult to insure operation in a single spatial mode.
• the transverse dimensions of the fundamental mode laser beam are usually small, reducing the amount of power that can be extracted from the gain medium. Increasing the transverse dimensions of the fundamental-mode laser beam reduces the modal discrimination between the fundamental mode and the higher-order modes to an unacceptable level.
• using a Gaussian profile for the fundamental mode may not be ideal for applications that require uniform illumination.
• Unstable resonators can support transverse dimensions of the fundamental-mode laser beam while simultaneously preserving adequate higher-order mode discrimination.
• these resonators have inherently "lossy" fundamental modes, and are not suitable for low-gain laser systems.
• they often have an obstructed output aperture that produces an undesirable near-field pattern (the power-distribution profile as measured near the output port of the laser cavity).
• the cavity shown in Figure 3 contains a diffractive mode-selecting mirror 124 on one end and a flat mirror 121 on the other end.
• a transparent phase plate 127 is placed between these two mirrors to (a) increase the modal dis ⁇ * _rr_ination, (b) increase the output power, (c) decrease the cavity length, and (d) increase the allowed diameter of the laser beam mode.
• the maximum feature size on the DMSM must be made smaller to compensate for the higher spatial frequencies on the phase front at the mirror due to the phase plate.
• the design of the cavity proceeds in much the same way as the simple diffractive mode-selecting mirror.
• the designer first chooses the desired amplitude and/or phase profile of the fundamental mode at any convenient longitudinal location, (e.g., one such location is at the flat output mirror 121, where the complex light field is everywhere real).
• the resulting field of the selected profile propagated through the gain medium 123 (and any other internal optics) to the phase plate is calculated by the Rayleigh-Sommerfeld diffraction formula,
• the reflectance of the diffractive mode-selecting mirror is then chosen to return the phase conjugate of this calculated distribution.
• the diffractive mode-selecting mirror 124 with the chosen reflectance is fabricated using known methods; see, e.g., J.R Leger, ML. Scott, P. Bundman, and MP. Griswold, "Astigmatic wavefront correction of a gain-guided laser diode array using anamo ⁇ hic diffractive microlenses," Proc. SPIE ⁇ vol. 884 ⁇ , 82 (1988).
• phase-conjugate wave will propagate back through the phase plate 127 and gain medium 123 (and any other internal optics) to the output mirror 121, regenerating the designer-selected original distribution and establishing it as a mode of the cavity. If the size of the mode-selecting mirror 124 is made sufficiently large and the two aperture sizes d* and d 2 for apertures 122 and 128 are chosen properly, the loss to this mode can be made very small and it becomes the fundamental cavity mode. The higher-order cavity modes are then calculated by solving the integral equation
• the phase-plate aperture 128 has d 2 chosen to be 4 mm to pass the diffracted super-Gaussian beam with negligible clipping.
• the diffractive mode-selecting mirror 124 was assumed to be arbitrarily large.
• Figure 6 shows the laser threshold gain g ft required for the second-order mode to overcome the cavity diffractive loss.
• the diffractive mode-selecting mirror then simply consists of copies of the simple mode-selecting mirror at each of the diffraction orders.
• Figure 7b shows the effect of finite diffractive mode-selecting mirror linewidth on the threshold gain of the fundamental and second-order modes for two different bandwidths ⁇ f.
• the error bars show the statistical variation in the simulation.
• Very high modal discrimination can be obtained by presenting the diffractive mode-selecting mirror with a sufficiently intricate light field. The price paid for this increased modal discrimination is an increase in intricacy of the mode-selecting mirror.
• Figure 7b shows the effect of mode-selecting mirror linewidth quantization on the modal gains of the fundamental and second-order mode.
• a mode-selecting mirror was designed with a minimum feature size of 2 ⁇ m and 16 phase quantization levels.
• the resulting fundamental cavity mode profile is shown in Figure 4 at graph 120, for a 1.2-mm beam size.
• Graph 120 shows the theoretical two-dimensional fundamental-mode intensity profile of a 10-cm laser cavity containing a random phase plate.
• the finite linewidth and phase quantization of the mode-selecting mirror produce small non-uniformities in the beam profile and result in a fundamental-mode loss of approximately 1.3%.
• the gain required to overcome the losses to the second-order mode was 5.1 (corresponding to a loss of greater than 80%).
• a stable Fabry-Perot cavity with the same cavity length, beam size, and fundamental mode loss has a second-order modal gain of only 1.08, corresponding to a loss of just 7.2%.
• beam diameters of up to 4.5 mm can be used in this 10-cm-long cavity. It is therefore possible to extract a large amount of power from the gain medium, while still maintaining a very small cavity length.
• a new type of laser resonator was implemented that employs an intra-cavity phase plate and a diffractive mode-selecting mirror to produce large-diameter fundamental modes in a short cavity.
• the intensity profile of the fundamental mode can be chosen to suit the application, and the loss to higher-order modes designed to effectively insure single-spatial-mode operation.
• a diffractive laser cavity mirror is described in the discussion for Figure 2 and Figure 5 that can tailor the laser mode profile in amplitude and phase.
• An embodiment of this diffractive element is shown in Figure 2 for a square, flat-top fundamental mode.
• the mirror had a theoretical fundamental mode loss of only 0.001 and a second-order mode loss of 0.57, resulting in high modal discrimination.
• the fabricated mirror was tested in a Nd:YAG laser system.
• the resulting square flat-top mode had an RMS flatness of 1.5% of maximum and a large dis ⁇ * imination against higher-order modes.
• More intricate mirror shapes have been used to tailor the modal profile of diode laser arrays and C0 2 lasers.
• the invention extends this latter technique using diffractive optical elements to tailor the fundamental mode of a Nd: YAG laser.
• careful choice of cavity length and modal filters can provide large modal discrimination.
• the laser cavity shown in Figure 5 consists of two diffractive mode-selecting mirrors spaced by a distance Lj-, the sum of all L- for each propagation segment in the propagation path.
• the design of the diffractive mirrors is chosen to establish the desired mode as the fundamental mode of the resonator system. Let the desired amplitude and phase of the mode just to the left of z be described by 26 ⁇ (x,y), where afay) is a complex function. This can be expressed equivalently in terms of its angular plane wave spectrum _-_,(u,v) as
• j is the square root of -1
• u and v are spatial frequencies
• x is a Cartesian distance in a direction transverse to the direction of propagation
• y is a Cartesian distance in a direction transverse to the direction of propagation and orthogonal to x
• Afav) is the angular wave spectrum of afay) at point Zj .
• a i+1 (x',y)' f > f > A /nvj ⁇ C j 2 ⁇ (xu+vy) ) x exp( j (2 ⁇ L ⁇ / ⁇ ,) (sqrt(7- ⁇ / u) 2 -( ⁇ / v) 2 )) ) du dv
• exp( ) is the exponential function
• j is the square root of -1
• L* is length of propagation segment / along the path of propagation
• u and v are spatial frequencies
• du and dv are integration variables for u and v respectively
• sqrt( ) is the square root function
• x is a Cartesian distance in a direction transverse to the direction of propagation
• y is a Cartesian distance in a direction transverse to the direction of propagation and orthogonal to x
• Aj(u,v) is the angular wave spectrum of ctj(x,y) at point z* .
• the distribution at the reflecting surface of mirror 124 is given by recursive application of the above equations for the propagation path.
• the original distribution sfay has reproduced itself after one round-trip in the laser cavity, thereby establishing itself as a mode of the system.
• the reflectances of the two mode-selecting mirrors are phase-only, they can be easily fabricated as diffractive optical elements. By making these elements sufficiently large, diffractive losses can be kept to a minimum and the loss to the fundamental mode can be very small.
• This phase-conjugate cavity is reminiscent of resonators based on Brillouin scattering or four-wave mixing, see J. Auyeung, D. Fekete, A. Yariv, and D.M Pepper, IEEE J. Quantum Electron. ⁇ QE-15 ⁇ , 1180 (1979).
• the diffractive mirror can be designed to be "lossy" to higher-order modes, making it an effective filter for fundamental-mode operation.
• a diffractive optical element is then produced by performing a "modulo-2 ⁇ " operation on the phase function and quantizing the result into sixteen levels.
• the phase profile of the diffractive element is shown in Figure 8.
• a diagram of a Nd:YAG laser cavity is shown in Figure 2.
• the laser cavity consists of a partially-reflecting flat output mirror 121, a 100%-reflecting mode-selecting mirror 124, and a flashlamp-pumped Nd:YAG laser medium 123. Both mirrors have adjustable apertures 122 and 128 to control their size.
• a Fox-and-Li analysis of the laser modes was performed to study the effect of the mirror phase quantization, laser cavity length, and mirror aperture sizes on the mode shape and mode loss.
• Initial designs of the mode-selecting mirror using four and eight phase-quantization levels resulted in fundamental modes with excessive ripple in the flat-top region.
• the theoretical mode produced by a sixteen-level element was very close to the ideal 20th-order super-Gaussian, with sha ⁇ sidewalls and an
• the cavity length and mode-selecting mirror size were then optimized by calculating the modal loss for the two lowest-order modes as a function of mirror separation and diffractive mirror size. (See, e.g., J.R Leger, D. Chen, and Z. Wang, Opt. Lett. ⁇ 9 ⁇ , 108-110 (1994).)
• a new mode-selecting mirror was calculated to produce the same desired fundamental mode.
• the loss to the lowest-order mode is negligible (O.0001).
• the loss to the next lowest-order mode is seen to peak at a distance z ⁇ , where as above, Rayleigh range
• the finite output mirror has very little effect on the shape or loss of the fundamental mode for mirror sizes greater than 1.2 mm, as expected.
• the loss to the second-order mode is significant and increases with a reduced output mirror size.
• the fundamental mode loss is 0.001 and the second-order mode loss is 0.57. This substantial loss difference makes it possible to pump the laser hard while still niaintaining single-spatial-mode operation.
• the mode-selecting mirror was fabricated by a four-step mask-and-etch process, see J.R Leger, ML. Scott, P. Bundman, and MP. Griswold, "Astigmatic wavefront correction of a gain-guided laser diode array using anamo ⁇ hic diffractive microlenses," Proc. SPIE ⁇ vol. 884 ⁇ , 82 (1988). This procedure resulted in a 16-level phase element with a profile that approximated the phase.
• Figure 9 shows one of the four e-beam masks fabricated to produce the element. Since the smallest features on any of the masks were only 50 ⁇ m in size, wet chemical etching was used.
• the performance of the diffractive mode-selecting mirror was studied first outside the laser cavity.
• a highly expanded continuous-wave (“cw") Nd:YAG laser was used to illuminate a 1.2 mm by 1.2 mm square aperture with a uniform plane wave.
• the mode-selecting mirror was placed 1.10 meters behind this aperture, and the reflected wave studied after propagation back to the square aperture.
• the mirror produced a very well-defined square shape.
• the modal reflectivity was measured by comparing the power in this square image (integrated over a slightly larger square area of 1.3 mm by 1.3 mm) to the incident power. After compensating for the imperfect reflectivity of the gold coating, the modal reflectivity was measured to be 98% to 99%.
• the performance of the mode-selecting mirror inside a laser cavity was studied and tested next.
• the laser cavity was set up as in Figure 2 with a pulsed single-tube flash lamp pumping the YAG rod.
• the pulse rate was kept below 2 Hz to reduce thermal effects on the laser rod; interferometric measurements of the rod by a HeNe probe beam showed these thermal aberrations to be negligible.
• the shape of the mode intensity was measured by a linear CCD camera and frame grabber. It was discovered experimentally that slightly better mode shapes were produced using output apertures 122 having aperture sizes between 1.7 mm and 2.0 mm.
• An embodiment used an output aperture 122 of 2.0 mm, and a corresponding mode-selecting mirror aperture 128 of 16 mm.
• the RMS flatness across the top of the measured beam is 1.5% of the peak value.
• the square shape of the mode schematically represented in graph 120 of Figure 2 was virtually unaffected by the shape of the apertures, even when circular- and diamond-shaped apertures were used. Some degradation of the sidewall steepness was noticed when the output aperture was reduced to below 1.5 mm, but the size of the mode remained relatively unchanged. Larger output apertures were observed to permit multi-spatial mode operation at higher powers, as expected.
• a diffractive mode-selecting mirror was designed to produce a square flat-top mode with very high modal discrimination. Alternate shapes (circular, multiple apertures, etc.) and profiles (tapered, phase-coded, etc.) can be produced as well.
• the design was demonstrated using a flash-lamp-pumped Nd:YAG laser.
• the experimentally measured mode shape is very close to the theoretically predicted shape.
• the fundamental mode loss from this element was predicted to be 0.001 and experimentally measured to be 0.01 to 0.02. This very low loss makes the technique suitable for both low- and high-gain laser systems.
• An aspect of the invention provides the introduction of a low-spatial-frequency phase grating inside a laser resonator employing a diffractive mode-selecting mirror substantially increases spatial mode disc ⁇ * imination while presenting negligible loss to the fundamental mode.
• This configuration has been used to design a very short, highly selective solid-state laser cavity.
• An arbitrary number of custom phase-adjustment elements similar in design to custom phase-adjustment element 129 of Figure 4 may be added to an embodiment of a laser resonator cavity, with the appropriate adjustment to the affected custom phase-conjugated diffractive mirrors.
• a custom phase-adjustment element is designed to dynamically adjust phase.
• a liquid crystal pixel array (without polarizing elements) is used to implement a custom phase-adjustment element 129 as shown in Figure 4.
• the electric field applied to each pixel adjusts the phase of that pixel.
• One use for such an element is to adjust for heat-induced phase changes in the gain medium.
• Figure 12A is a schematic of a Mchelson-type interferometer 900 which can be used to measure aberrations in laser system 940, which can then be corrected for.
• Laser system 940 can be any laser, either of conventional design, or made with diffractive mirrors such as custom phase-conjugated diffractive mirror 124 of Figure 4, or a combination system having some conventional and some diffractive elements.
• laser system 940 In normal operation, laser system 940 would be used alone without any of the other elements shown in Figure 12A In such normal operation, pump light 939 would energize gain medium 943, creating an inverted population needed to cause amplification and lasing in the laser cavity between mirrors 942 and 944 of laser system 940, and also creating a "waste" heat buildup in gain medium 943, and thus distortion in the optical path through gain medium 943 in particular, but also introducing distortion in other optical path segments.
• mirrors 942 and 944 are both partially transmissive to the wavelength of light beam 921. There is generally heat buildup to a lesser degree in each of the other elements of laser system 940, with the resultant distortion of the optical path segments.
• gain medium 943 is a crystal rod or slab of NdYAG.
• the heat buildup in gain medium 943 is often non-uniform across a cross-section and along the length of gain medium 943, due to non-uniform extraction of energy by the laser beam and/or non-uniform coupling of pump light 939 to gain medium 943, as well as non-uniform heat conduction, convection, and radiation out of gain medium 943.
• One primary goal of the design of optical elements for one embodiment of the present invention is to preserve the desired phase profile, even in the presence of distortions such as those due to heat.
• n___ximize the efficiency of laser system 940 by designing mirrors (e.g., 942 and 944) and phase-adjustment elements to transfer maximum energy from the entire length and entire cross- section of gain medium 943 into the laser beam.
• mirrors e.g., 942 and 944
• phase-adjustment elements to transfer maximum energy from the entire length and entire cross- section of gain medium 943 into the laser beam.
• One factor which should be taken into account in the design of the optical elements in the path of the laser beam is the fact that laser system 940 will heat up as a result of waste heat, and will therefore distort each optical path to a greater or lesser extent.
• This heat-up distortion will typically stabilize to a steady-state distortion value at the operating point of laser system 940, wherein the temperature will be fixed at each respective point in each element, depending on such factors as the external temperature, the energy input into each point of each element, and the energy transferred out of each point of each element.
• a distortion- compensating phase element is then designed to provide the complex phase conjugate of this steady-state distortion value, and thus restore the desired mode profile for laser system 940.
• probe laser 902 emits a light beam into beam expander 905, which includes lenses 904 and 906, and then through iris 908.
• the resultant light beam 920 is of a different wavelength than the operational laser wavelength of laser system 940, in order to pass more easily through mirror 944 and/or to be more easily be detected at detector 918.
• the wavelength of the probe light beam 920 is 0.8 micrometers, as compared to the operating laser wavelength of 1.06 micrometers.
• the resultant light beam 920 is directed through beam splitter 910 to generate light beams 921 and 922.
• Light beam 921 is directed into laser system 940, which is kept at an operating temperature distribution (called "hot"), for example, by pump light 939.
• the hot laser system 940 is not necessarily at a uniform temperature throughout, and is typically hotter in some areas than in others.
• Laser system 940 includes mirrors 944 and 942, gain medium 943, and pump light 939.
• one or both mirrors 942 and 944 are partially transmissive at the wavelength of laser system 940's normal operating mode, in order to allow laser amplification, but are more transmissive to the wavelength of the probe light beam 920.
• Light beams 920 through 926 are all the same wavelength
• Light beam 921 after passing through hot laser system 940 is reflected by mirror 941, passes again through laser system 940, and emerges as light beam 923.
• Light beam 922 is directed into laser system 950, which corresponds to hot laser system 940, but is kept at a room temperature distribution (called "cold"), and is not heated by, for example, a pump light source similar to 939.
• the cold laser system 950 is not necessarily at a uniform temperature throughout, but is typically at a uniform room temperature.
• Laser system 950 includes mirrors 954 and 952, and gain medium 953 each corresponding to components in laser system 940.
• Light beam 922 after passing through cold laser system 950 is reflected by mirror 951, passes again through laser system 950, and emerges as light beam 924.
• the present invention can be used in laser systems having conventional spherical mirrors for mirrors 942 and 944, or one can be spherical and the other can be flat, or either mirror 942 or 944 can be a diffractive mirror such as custom phase-conjugated diffractive mirror 124 as shown in Figure 4 and the other a flat mirror such as mirror 121 of Figure 4, or both mirrors can be diffractive such as custom phase-conjugated diffractive mirrors 124 and 124' as shown in Figure 5, or either mirror 942 or 944 can be a diffractive mirror such as custom phase-conjugated diffractive mirror 124 as shown in Figure 4 and the other a conventional curved mirror such as shown for mirror 944 of Figure 12A U.S.
• Patent Number 5,255,283 by Belanger teaches a circular mode-selecting phase-conjugating mirror used to establish a radially-tailored circularly-symmetric profile, and the present invention can be used to correct for distortions in a laser having such a Belanger-type graded- phase mirror.
• mirror 942 is a fully- reflecting mirror, for example a custom phase-conjugated diffractive mirror 124 designed as described for Figure 2, 3, 4, or 5 elsewhere in this specification; and mirror 952 is a substantially similar mirror, and mirrors 941 and 951 can be omitted.
• a mode-discriminating custom phase-adjustment element such as element 127 of Figure 3 or element 129 or Figure 4 is placed between gain medium 943 and either or both mirrors 942 and 944 (at least one of which is a mode-shaping diffractive mirror such as mirror 124 of Figure 4), and a substantially similar corresponding phase-adjustment element 127 or 129 is placed between gain medium 953 and the corresponding mirror 952 and/or 954; thus each element in cold laser system 950 matches the corresponding element in laser system 940.
• the optical elements of cold laser system 950 act to compensate for the refractive effects of light beams 921 and 923 passing through mirrors 942 and 944 of hot laser system 940.
• all of the optical elements of cold laser system 950 are replaced by a series of lenses and phase plates which produce the same optical effect as laser system 950 (which is the equivalent to a cold version of laser system 940).
• the motivation is to provide an "ideal" version of the optical path through the optical lenses and phase plates of this simulated laser system 950 which is to be compared with laser system 940 by interferometer 900, and a corrective compensating phase- adjustment element can be calculated and made.
• Light beam 923 is directed through beam splitter 910 and the portion passing though emerges as ligjht beam 925.
• Light beam 924 is directed at beam splitter 910 and the portion reflecting emerges as light beam 926.
• Light beams 925 and 926 then combine to form a resultant interference pattern, which is then focussed by imaging system 915 onto detector 918.
• Imaging system 915 includes lenses 914 and 916 in this embodiment.
• imaging system 915 is adjusted to produce an image at detector 918 of the wavefronts at a point z in laser system 940.
• detector 918 is comprised of a CCD camera connected to a computer for analyzing fringes.
• point z is at one end of the crystal used for gain medium 943, such as is shown in Figure 14.
• point z is at z ⁇ which is at a distance from the end of the crystal used for gain medium 943, such as is shown in Figure 15.
• point z is at the surface of mirror 942 which is at a distance from the end of the crystal used for gain medium 943, such as is shown in Figure 16.
• point z is at the surface of one end of the crystal used for gain medium 943, and then calculating the effect of propagating that calculated phase profile to the plane of mirror 942 (using the method described for Figure 4 above) to calculate and fabricate mirror 949 to replace mirror 942 such as is shown in Figure 16.
• the fringes of the resultant interference pattern represent the difference in the optical path between the hot laser system 940 and the cold laser system 950, and thus the distortion due to heat.
• the fringes of the resultant interference pattern are converted by standard techniques of interferometry into an optical phase function for the wavelength of laser system 940.
• the particular interference pattern for the wavelength ⁇ - of probe beam 920 must be scaled for the operating wavelength of laser system 940.
• the distortion-compensating correction plate (e.g., element 948) is then formed having a complex phase conjugate function of an optical phase function representative of the first interference pattern.
• "representative of includes being calculated from the fringe pattern of the probe wavelength, or being directly fabricated from the fringe pattern.
• a distortion-compensating phase-adjustment element which presents the complex phase conjugate (i.e., e ( "j ⁇ - y) - ) at the point z along the optical path where the optical phase function was calculated.
• the optical phase function is calculated at a point z close to gain medium 943, and the compensating diffractive optical element 947 is placed close to gain medium 943 in order to correct for the distortion, as shown in Figure 14.
• the resultant corrected laser system 340 includes mirror 944, which is partially transmissive to the wavelength of laser system 940, gain medium 943, compensating diffractive optical element 947 placed close to gain medium 943, and a fully reflective mirror for mirror 942.
• the corrective factor e ( "j ⁇ * y) - 1 for the detected distortion is multiplied (or, equivalently, the -j ⁇ (x , y) distortion-compensating exponent factor is added to the exponent factor of the mode-selecting phase adjustment calculated as described for Figure 2, 3, 4, or 5) into the phase function for a mode- discriminating phase element (for example, as illustrated in Figure 4, a custom phase-adjustment element 129) which is already located at the location plane for compensating diffractive optical element 947.
• the optical phase function is calculated at a point Zo farther from gain medium 943, and the compensating diffractive optical element 948 is placed at point z ⁇ from gain medium 943 in order to correct for the distortion, as shown in Figure 15.
• optical system 915 is adjusted to focus an interference pattern representative of the phase distortion as it would appear at point _? ⁇ -, thus allowing a corrective element having the complex phase conjugate of that phase distortion to be fabricated and placed at point _%.
• the optical phase function is calculated at a point close to gain medium 943, and a corresponding optical phase function is calculated by calculating the effect of propagating this optical phase function to point z ⁇ and the compensating diffractive optical element 948 is placed at point z ⁇ from gain medium 943 in order to correct for the distortion, also as shown in the exemplary embodiment of Figure 15.
• the resultant corrected laser system 440 includes mirror 944 which is partially transmissive to the wavelength of laser system 940, gain medium 943, distortion-compensating diffractive optical element 948 placed at point from gain medium 943, and a fully reflective mirror for mirror 942.
• the corrective distortion-compensating factor e ( "j ⁇ • y) -* for the detected distortion is multiplied into the phase function for a mode-discriminating phase element (such as element 129 of Figure 4) which is already located at the _? ⁇ - plane for compensating diffractive optical element 948.
• Figure 16 is a schematic of an exemplary embodiment of corrected laser system 540 having a distortion-compensating diffractive element 949 merged into one of the cavity mirrors.
• the distortion-compensating surface is added to (or, equivalently, placed onto, or etched into) an otherwise flat mirror which replaces a flat mirror 942 used during the measurement steps, and mirror 944 is either a spherical mirror or a diffraction mirror such as custom phase-conjugated diffractive mirror 124 of Figure 4.
• a conventional spherical mirror such as mirror 944 of Figure 12A is used for mirror 944, and the distortion- compensating calculation is combined onto a diffractive mirror such as custom phase-conjugated diffractive mirror 124 of Figure 4 which is used for mirror 942, and the resultant diffractive mirror is used for mirror 949.
• a flat mirror such as mirror 121 of Figure 4 is used for mirror 944, and the distortion-compensating calculation is combined onto a diffractive mirror such as custom phase-conjugated diffractive mirror 124 of Figure 4 which is used for mirror 942, and the resultant diffractive mirror is used for mirror 949.
• laser system 940 is tested and corrected in its production-type case and with all elements, power supplies, enclosures, fixtures, and positioning devices in place, in order to correct for all distortion sources within laser system 940. This allows compensation for all heat flows as they will occur in laser system 940 in normal operation.
• a custom phase-adjustment element 947 is designed to dynamically adjust phase.
• a liquid crystal pixel array (without pol__rizing elements) is used to implement a custom phase-adjustment element 129 as shown in Figure 4.
• the electric field applied to each pixel adjusts the phase of that pixel.
• One use for such an element is to dynamically adjust for heat-induced phase changes in gain medium 943, for instance due to external factors such as ambient temperature, or internal factors such as varying laser power outputs.
• a series of phase-adjustment elements 947 are calculated and fabricated for various distortion sources such as external factors, e.g., ambient temperature, and/or internal factors such as varying laser power outputs.
• This series of phase-adjustment elements 947 are then placed on a conventional fixture, such as a rotatable wheel, which allows the proper particular phase-adjustment element 947 to be positioned into the laser cavity of laser system 940 for any particular operating condition, such as various power outputs or various ambient temperatures.
• laser system 940 is tested and corrected using a lower-quality element for gain medium 943, in order to reduce the costs for laser system 940, since compensating diffractive optical element 947 or 948 or 949 generated by the distortion-correction method just described can compensate for some crystal distortions and imperfections.
• a high-quality crystal, or an optical element which has substantially identical optical properties is used for gain medium 953, in order to generate a fringe pattern which represents the difference between the high-quality crystal (or other substituted optical element which has substantially identical optical properties to a high-quality crystal at the relevant wavelengths) used for gain medium 953 and the lower-quality crystal used for gain medium 943.
• a high-quality crystal, or an optical element which has substantially identical optical properties is used for gain medium 953, in order to generate a fringe pattern which represents the difference between the high-quality crystal (or other substituted optical element which has substantially identical optical properties to a high-quality crystal at the relevant wavelengths) used for gain medium 953 and the lower- quality crystal used for gain medium 943.
• corrected laser system 340 is then replaced into Mchelson-type interferometer 900 in place of laser system 940, and the above-described correction procedure is iteratively repeated. Since the above- described correction procedure will tend to change the pattern of energy transfer from the inverted population in gain medium 943, the heat-induced distortion will also change as a result of the correction being performed, giving a different distortion and thus requiring further correction iterations until a steady-state heat distribution with the best correction desired (as determined by the number of iterations the designer is willing to perform) is achieved. In addition, distortions which may be masked by larger-scale effects such as gain-medium heating initially may become evident as the sources of those distortions are corrected for.
• Figure 13 is a schematic of a Mach-Zehnder-type interferometer which can also be used to measure aberrations, distortions, and imperfections in laser system 940, which can then be corrected for.
• This setup is used in a manner similar to that described for Figure 12A, above, except that light beams 921 and 922, rather than being reflected by mirrors 941 and 951 respectively and passing though laser systems 940 and 950 respectively twice each, pass through (thus traversing gain mediums 943 and 953 only once) to become light beams 923 and 924 respectively.
• Calculation of the distortion phase function and fabrication of the needed phase compensation plates is performed in a manner corresponding to that described for Figure 12A, above.
• Figure 17 is a schematic of an interferometer which can be used to measure aberrations for a laser system in which it is impractical to introduce light beam 921 through one of the mirrors of laser system 940, the aberrations which can then be corrected for.
• light beam 920 from the probe laser 902 has a wavelength of 0.8 micrometers
• laser beam 999 of laser system 940 has a wavelength of 1.06 micrometers( ⁇ m).
• beam splitter 909 is primarily reflective at 0.8 ⁇ m and primarily transmissive at 1.06 ⁇ m.
• Other aspects of the use of the apparatus shown in Figure 17 are substantially the apparatus in Figure 12C.
• One measurement method for using Figure 17 uses a probe light beam 920 having a wavelength ⁇ , which is a different wavelength from the laser wavelength ⁇ g of laser beam 999 from laser system 940.
• beam splitter 909 is a dichroic beam splitter that is chosen to be anti-reflective (AR) coated for ⁇ *. and at least partially reflecting for ⁇ ,.
• AR anti-reflective
• a second measurement method for using Figure 17 uses a probe light beam 920 having a wavelength ⁇ - which is at a different polarization as the laser wavelength ⁇ *. of laser beam 999 from laser system 940.
• Wavelength ⁇ can be, but need not be the same wavelength as ⁇ *,.
• ⁇ * and ⁇ *. are the same wavelength.
• beam splitter 909 is an element which transmits one polarization well and at least partially reflects another polarization.
• a slab of conventional uncoated glass is used for beam splitter 909, and positioned at Brewster's angle with respect to laser beam 999, and light beam 921 is incident to this beam splitter 909 at the corresponding reflective angle (which is typically not a right angle as shown in Figure 17, but rather an oblique angle).
• laser system 940 lases in a TM polarization, and is not reflected by beam splitter 909.
• Probe light beam 921 is chosen to be incident on beam splitter 909 with a TE polarization, causing at least some of light beam 921 to be reflected into gain medium 943.
• "cold" laser system 950 is not a complete laser system, in that mirror 954 is not used, since mirror 944 is not in the path of light beam 921 or 923.

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