GB2091439A - Gas Laser Cavity Mirror - Google Patents

Abstract

The mirror is for a gas laser eg CO2 having a molecular band spectrum containing a plurality of lines at whose wavelengths laser action can be stimulated and is designed to select a single one of these lines. The mirror is formed by a stack of not more than twenty alternate high and low refractive index layers, the layers not all having the same optical thickness, but each having a zero dispersion corrected optical thickness substantially equal to an odd integral number of quarter wavelengths of the selected line. Each of these numbers is either equal to a fundamental number or nearly or exactly equal to a multiple of that fundamental number. A number qualifies as a fundamental number of a stack based on that number of quarter wavelengths possesses a reflection peak at the selected line, at least one other peak between adjacent bands in the spectrum but no other peak within the band containing the selected line. An exemplified mirror has layers of zinc selenide spaced by layers of gas e.g. air or vacuum. A piezo-electric bimorph may be arranged to change the thickness of one layer to enable switching between selected lines.

Description

SPECIFICATION Selective Mirrors for Molecular Band Structure Gas Lasers This invention relates to laser mirrors and laser mirror systems, and in particular to mirrors for lasers capable of lasing at a wavelength corresponding to a particular line in a molecular band structure. Typical of such lasers are CO2 lasers and CO lasers. The present invention is concerned with the design of mirrors whose reflectivity is such a function of wavelength that the laser emission is caused to be stimulated at one particular emission line by virtue of the relatively reduced reflectivity of the mirror or mirror system at all other lines within a particular band or group of bands.

A conventional design of dielectric mirror comprising a stack of alternate high and low refractive index layers of equal optical thickness, hereinafter referred to as a 'simple stack', is not generally suitable for this purpose because a relatively large difference in refractive index is required to give the required peak reflectivity with a small enough number of layers to be practical, and this means that, if the stack is selective enough to provide adequate discrimination between adjacent emission lines, the peaks of reflectivity in its spectral characteristic are so closely spaced that an emission line will coincide with a reflection peak at more than one place in the emission spectrum.

Previously this problem of selecting a single emission line has been resolved by using a diffraction grating as one of the laser mirrors, in which case it is the dispersion effects of the grating that is used to limit the laser emission to a single line. A disadvantage of this approach is that the grating is relatively susceptible to damage, and also its reflectivity is low compared with that achievable with a dielectric mirror.

This invention discloses how dielectric stacks can be designed with layers of unequal optical thickness, hereinafter referred to as 'complex stacks', to provide adequate selectivity to discriminate between adjacent emission lines, while yet retaining an adequate separation between high reflection peaks to prevent coincidence with emission lines at more than one point in the relevant part of the emission spectrum. In accordance with the teachings of the present invention a molecular band structure laser can be constructed for operation at a single line using one spectrally selective mirror according to the present invention and one other mirror. The other mirror may be a total reflector or a partial reflector, and it also may be spectrally selective.Alternatively, the laser can be constructed using two spectrally selective dielectric mirrors each of which is composed of layers of equal optical thickness, but in which the optical thickness of the layers of one mirror is not equal to that of the layers of the other.

A single dielectric layer exhibits a reflection peak at every wavelength for which its optical thickness is equal to an odd integral number of quarter wavelengths. If it is assumed that layer thicknesses for a complex stack can range between one and several hundred quarter wavelengths in optical thickness, and that the number of layers forming the stack may typically be in the range from four to ten, or perhaps more; it is clear that there are going to be many millions of possible designs satisfying the minimum criterion that the optical thickness of the layers are not all equal. The performance of any particular design can be calculated by evaluating a matrix product for a range of wavelengths to cover the spectral range of interest.This is clearly time consuming, and it is also evident that the overwhelming majority of these designs will not be satisfactory, either because their principal reflection peaks are not high enough or are too close, or because they exhibit subsidiary reflection peaks that are too high and occur in inconvenient parts of the spectrum coinciding with unwanted emission lines.

The present invention reduces this number of potential designs to manageable proportions by restricting attention to designs based on special fundamental numbers of quarter wavelengths and upon multiples and near-multiples thereof. It is found that such designs are much more likely to be satisfactory than the others. The number of potential designs to be considered may then be further reduced by establishing a limit to maximum thickness of any layer in the stack derived from bandwidth considerations. A reduction is also possible by excluding from consideration designs which possess a common multiple which is a multiple of a fundamental number, but not itself a fundamental number.

For instance, if 25 was a fundamental number, and the layer thicknesses were all multiples of 75 quarter wavelengths, such a design could safely be excluded from consideration if 75 was not a fundamental number.

The fundamental numbers are derived by considering the periodicity of the reflection peaks of simple stacks. A number qualifies as a fundamental number if a simple stack based on that number of quarter wavelengths possesses, in addition to the reflection peak at the selected line, at least one other peak between adjacent bands in the molecular spectrum, but no other peak within any branch of interest within that spectrum.

According to the present invention there is provided a laser mirror for a gas laser whose active medium is a gas having a molecular band spectrum containing a plurality of lines at whose wavelengths laser action can be stimulated, which lines are arranged in bands, wherein the mirror is provided by a complex dielectric stack of not more than twenty layers not all of the same optical thickness defining a set of interfaces at which there is a refractive index difference, each of which layers has a zero dispersion corrected optical thickness substantially equal to an integral odd number of quarter wavelengths of a selected one of said emission lines, which integral odd number is either a fundamental number or a number not more than five different from a multiple of that fundamental number; which fundamental number is a number such that a simple dielectric stack of layers of the same materials as those of the complex stack, each having a zero dispersion corrected optical thickness equal to the fundamental number of quarter wavelengths of the selected line, would possess, in addition to the reflection peak at the wavelength of that line, no other reflection peak within the two branches of the band containing the selected line, but at least one other reflection peak between the two branches of the band containing that selected line and those of an adjacent band; and wherein the combination of the zero dispersion corrected optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance at the wavelength of both emission lines adjacent the selected line and within that branch of its band is not more than 50%, and such that the reflectance is not more than 85% at the wavelength of any emission line within the two branches of the band containing the selected line other than selected line itself.

There follows further description of the background to this invention and a description of illustrative embodiments of the invention. The description refers to the accompanying drawings in which: Figure 1 is a diagram showing the arrangement of emission lines of the CO2 band structure at which laser action can be stimulated. The diagram also shows the periodicity of reflection peaks for simple stacks of selected order number.

Figure 2 is a diagrammatic representation of a seven layer total reflector complex stack.

Figure 3 is a diagramatic representation of a four layer partial reflector complex stack.

Figure 4 is a generalised diagram of a stack of layers of different refractive index and thickness.

Figures 5 to 8 are graphs showing the spectral characteristics of examples of partial reflector complex stack intended to be selective against all lines of both CO2 laser emission bands other than the P20 (001-100) line.

Figures 9 to 12 are graphs showing the spectral characteristics of examples of partial reflector complex stack intended to be selective against all lines in the CO2 001-100 band other than the P20 (001-i 00) line.

Figure 1 3 is a graph showing the spectral characteristic of a total reflector complex stack selective against all lines in the CO2 001-100 band other than the P2O (001-100) line.

Figures 1 4A and 1 4B are graphs showing the spectral characteristics of a dual line selector design of complex stack that is switchable from one emission line in one band to another line in another band, and Figures 1 so, 1 SB and 1 SC are graphs showing the spectral characteristics respectively of two individual stacks, and then that of their combination when arranged to form a laser cavity.

The band structure of a CO2 laser is depicted schematically in Figure 1. It has four main spectral regions where laser emission can occur. These are at 10.6, 10.3, 9.6, and 9.3 microns, and are respectively the P and R branches of the 001-100 and 001-020 CO2 bands. Throughout the bulk of this specification attention is focussed in the main on the particular CO2 transition P20 (001-100) lying at 10.59 microns. This is purely exemplary; the same principles of design can be applied to emission lines at other wavelengths in this or other molecular band structure emission lasers including for instance the CO laser.

Returning attention to Figure 1, this Figure also shows the positions of reflection peaks for a simple stack composed of-dispersionless alternately higher and lower refractive index layers each having an optical thickness of 47 quarter wavelengths (47A/4, jl=1 0.59 microns). This has a reflection peak at the selected emission line P20 (001-100), two peaks between the 001-1 00 band and the 001-020 band, but no other peak within any of the four branches of these two bands.

For non-dispersive media, the periodicity of reflection peaks is given by the formula: 1 2 P= =~ 2nd mA where nd=mJL/4 and where n is the refractive index of the layer d is the physical thickness of the layer and m is an odd integral number.

It can be seen that 47 quarter wavelengths is not the only number of quarter wavelengths for which all other reflection peaks fall outside the four branches of the two emission bands. The same is true for 49 and 45 quarter wavelengths. By way of contrast 65 quarter wavelengths has a reflection peak in the other branch of the same emission band, while 97 quarter wavelengths has no other peaks in the 001-100 band, but has a peak in each branch ofthe other emission band.

It has previously been stated that the problem of using a simple stack is that, if its reflection peaks are sufficiently separated for only one to coincide with any of the branches, then, either its bandwidth is too great to provide adequate discrimination between adjacent lines, or it requires to have so many layers to obtain the required peak reflectivity that it would be impractical to manufacture. This arises because bandwidth and magnitude of peak reflectance are both functions of the difference in refractive index between high and low refractive index layers.

The theoretical peak reflectance R is determined both by the number of layers and their refractive indices.

1-Y 2 Rp=- (1) 1+Y where Y=nH (nH/n,)r~ for a self supporting stack.

and V=n, (nH/n,)' for a stack on a high index substrate, and where nH is the refractive index of the high index material of the stack, n, is the refractive index of the low index material of the stack, and r is the number of layers in the stack.

A typical stack for a CO2 laser may be made using zinc selenide for the high index layers (nH=2.4028) and air (vacuum or other gas having a refractive index not substantially different from unity) for the low index layers (nL = 1.0).

With these materials a seven layer stack has a theoretical peak reflectance in excess of 99.6% which is adequate for a total reflector for a CO2 laser, while a four layer stack has a theoretical peak reflectivity slightly in excess of 95%, which is suitable for a short cavity length laser partial reflector.

Figure 2 is a diagrammatic representation of a seven layer zinc selenide/air stack total reflector. In this stack layers 20 of zinc selenide of the required thicknesses are spaced apart by the required distances by means of annular spacers 21 made for instance of silica.

Figure 3 is an equivalent representation of a four layer partial reflector stack. In this case a substrate 32 is required upon which to build the assembly of zinc selenide layers 30 and spacers 31 because their number is even. The opposite face of the substrate is provided with an antireflection coating 34 in order to suppress any effect it might otherwise have upon the spectral characteristic.

If it is assumed that the ideal bandwidth B1 is half the separation between the wavenumbers k~ and k, adjacent the wavenumber k0 of the wanted line, then the relative bandwidth is given by

From the standard thin film matrix theory, as for instance set out in the book entitled "Thin Film Optical Filters", by H. A. Macleod, published by Adam Hilger Ltd 1 969, a high order quarter wavelength simple stack has a characteristic matrix [M]=

where nH is the refractive index of the higher index layer nL is the refractive index od the how layer ans # is the phase thickness of the layers, thus 2# nd #= # i.e.

#0 #B=2#.mB.

4 where mB is the order number # k =.mB.

2 k0 (number of selected line quarter wavelengths of optical thickness of the simple stack having the "ideal" bandwidth B,

Therefore

Now it can be shown that at the boundaries of the high reflectance regions the components of the leading diagonal of the matrix [M] satisfy the relation (ma1+m22) 2 i.e.

Therefore

From (2)

Therefore giving

In the case of a simple stack consisting of alternate layers of zinc selenide and air designed for the P20 line the relevant values are k0=944.19476 (P20) cm-1 k1= 945.98096 (P18) cm-1 k-1=942.38407 (P22) cm-1 nH=2.4028(ZnSe) nL=1.0 (Air) yielding mB#285 Therefore to achieve the "ideal" bandwidth for discriminating between adjacent lines requires, for a zinc selenide/air stack, an order number mB about six times the fundamental number 47.A much smaller value of the simple stack 'ideal' order number mB would be provided by reducing the refractive index difference between the low index and high index materials of the stack, for instance by using zinc selenide with zinc sulphide (nun2.2), but this would drastically increase the required number of layers to restore the magnitude of 'Y' in equation 1 to its original value. Thus a total reflector might typically require to have a hundred layers or more to achieve a peak reflectance of 99%.

The evaluation of the simple stack "ideal" order number mB is useful in giving a guide as to the magnitude of the multiples of the fundamental number likely to be required to produce an acceptable complex stack design. In general it is found necessary for one or more of the layers to have an order number at least as large as m6, while it is also found preferable to avoid using layer thicknesses with an order number in excess of 2mB. The avoidance of excessively thick layers is generally desirable because such layers will tend to make the bandwidth unnecessarily narrow with the result that manufacturing tolerances need to be held to more stringent limits and also temperature effects become more pronounced.

it has previously been stated that the number of possible designs of complex stack is, according to the teachings of the present invention, reduced to manageable proportions by restricting attention to designs based on special fundamental order numbers and their multiples and near multiples. Such designs possess a spectral characteristic exhibiting a pattern that is repeated with a periodicity equal to that of a simple stack having an order number equal to that of the fundamental number. However within the fundamental period there will be a subsidiary reflection peaks in addition to the main peak.

(In a complex stack using inexact multiples the pattern will be slightly distorted from one period to the next). It has been explained that the choice of fundamental number is determined by consideration of this fundamental periodicity in relation to the spacing and extent of the branches of the emission bands of the laser. Then it has been explained what factors affect the selection of the highest possible multiple for any given complex stack.

Now attention is directed to the selection of the multiples. First, it will be evident that, since each layer thickness is to be substantially equal to an odd number of quarter wavelengths, exact even multiples are not suitable. Therefore near-multiples differing by one from an exact multiple are acceptable. If attention is restricted to designs for which near-multiples differed from exact multiples by not more than one, then the range of possible designs becomes very restricted, and may not embrace any designs that will fulfill all the other necessary criteria. Attention is therefore broadened to include at least those near-multiples differing by not more than three from exact multiples, and in specially severe cases this may be expanded to consideration of near-multiples differing by not more than five from exact multiples.

By way of example the choice of suitable layer thicknesses for a zinc selenide/air complex stacks for selecting the P20 emission line from the 001-100 band of a CO2 laser will now be considered. It is seen from Figure 1 that designs of complex stack based on the fundamental numbers 47, 49, or 45 should exist that are capable of satisfying the design criteria necessary to select the P20 emission line from the 001-100 band and discriminate between it and all the other emission lines of that band, and also between it and all the emission lines of the 001---020 band. Such a stack can be used with a spectrally non-selective second reflector to form a single emission line selective laser cavity.If however the non-selective reflector is replaced with a spectrally selective reflector that has a reflection peak covering the wanted P20 emission line, and has a region of reduced reflectivity covering both branches of the 001-020 band, then the criteria for selecting fundamental numbers for the complex stack can be relaxed because the shape of the spectral characteristic of the complex stack in the region of the 001-020 band is no longer of any importance. Referring again to Figure 1 it is seen that fundamental numbers of 95, 97, and 99 are additionally acceptable for complex stacks not required to discriminate against emission lines in the 001-020 band.The spectrally selective second reflector may be provided for instance by a simple stack having a bandwidth that is large compared with the separation between individual emission lines.

The use of a spectrally selective second reflector is particularly advantageous when the complex stack is being used as the total reflector for the laser. This is because the particularly high peak reflectance required for the wanted line, and provided by the use of a stack with a larger number of layers, typically seven, is liable to be more susceptible to the incidence of inconveniently high reflectivity subsidiary peaks. It is generally somewhat easier to find acceptable designs for a partial reflector complex stack, consisting typically of four layers, that will cover both bands, and this enables the use of a metallic total reflector, such as one of diamond turned copper. However more designs of partial reflector are possible if use is made of a spectrally selective total reflector.

Table 1 lists the layer thicknesses examined for a 001-100 band P20 line selective reflector, firstly for a complex stack which would be selective against competing lines in both emission bands, and secondly for those that would be selective only against completing lines in the 001-100 band.

These layer thicknesses are expressed in terms of order number, i.e. numbers of selected line quarter wavelengths of optical thickness. For this purpose only order numbers below 401 were considered.

To find a partial reflector design of complex stack consisting of four layers, one of the fundamental numbers was first chosen together with its associated "primary" multiples (i.e. those multiples and near-muitiples closest to the exact multiples). Each possible design that can be generated by allowing each of the layers to have any of these thicknesses was then examined. If none of these designs had been found acceptable from mathematical analysis the search would have been broadened to include the slightly more remote near-multiples differing by up to three from the exact multiples, and if this failed the search would have been broadened still further to include near-multiples differing by up to five from the exact multiples.

For each design a calculation was made of the reflectance at the relevant CO2 emission line wavelengths. This calculation was conveniently made with the aid of a computer using the matrix method referred to previously in which each layer, as depicted in Figure 4, of thickness d5 and refractive index nS (s ranging from 1 to r) is characterised by the matrix

where

The characteristic matrix for the entire stack is then given by the matrix [B] formed by the product:

The reflectance R of this stack at any wavelength is then given by

The computer program which was used to evaluate these reflectances was then also used to apply three tests to the resulting sets of reflectivities. First designs which exhibited excessive reflection bandwidths were rejected.Bandwidth was deemed excessive if the reflectance at either P 1 8 or P22 was in excess of 50%. Second, designs were rejected if the reflectance at any relevant line other than P20 exceeded 85%; and third, they were rejected if the reflectance was greater than 80% at more than five of the relevant lines other than P20.

The actual values set to form these three iimiting conditions are somewhat arbitrary, being designed with the primary aim of rejecting less satisfactory designs if more satisfactory ones exist. The computer program is designed to test each computed reflectance before proceeding to the next so that if a test specification is not met no further calculations are made in respect of that design, and thus no further time is wasted before proceeding to the examination of the next design. If for some other lirie no satisfactory designs are obtained with the stringent limits set out above, then these limits can be progressively relaxed, perhaps first by eliminating the third limit altogether, and then by raising the threshold of the first limit to 60% and that of the second to 90%.

Table 2 lists some designs which met all the design criteria for a partial reflector for the P20line of the CO2 001-100 band, and, for the purposes of comparison, some designs which did not. Their respective performance in the three tests is set out. The spectral characteristics of some of these designs, and of others, are shown in Figures 5 to 12, the characteristics of Figures 5 to 8 are those of designs selective against all lines of both bands other than the P20 001-100 band line, while those of Figures 9 to 1 2 are of designs that are selective against the other lines of the 001-1 00 band but not those of the 001-020 band.

The same basic analysis used for the 4 layer partial reflector designs was then repeated to derive the 7 layer total reflector design whose spectral characteristic is depicted in Figure 13. This design is selective against all the other lines of the 001-100 band but not against those of the 001-020 band, and it must be further noted that the third limitation, namely that there be no more than five subsidiary reflection peaks having a peak reflectance in excess of 80%, has been waived.

It may be noted that in the foregoing specific examples of designs of complex stack for the P20 (001-1 00) CO2 lines the lowest fundamental numbers considered have been ones for which a simple stack of the same order number possesses two reflection peaks between the 001-100 and 001020 bands. From an inspection of Figure 1 it is apparent that a satisfactory fundamental number in the region of 33 exists for which the equivalent order number simple stack possesses only one reflection peak between the bands. Some designs based on the fundamental number of 33 have been examined.

Clearly this use of a smaller fundamental number gives rise to a larger number of alternative multiples with an order number of less than 401. In the designs that were tested it was found that the satisfactory designs were based not only on the fundamental number of 33 but also upon that of 45, and it was for this reason that attention was concentrated upon the higher fundamental numbers.

Attention is now turned to a special type of reflector incorporating a dilation element that can be used to change the optical thickness of one element of the complex stack by one quarter wavelength.

This enables the design of a dual wavelength selector which can be switched between providing high reflectance at the wavelength of one potential laser emission line to provide high reflectance at the wavelength of another. (When it is providing high reflectance at either one of these lines the reflectance at the other line is low). A convenient way of achieving the requisite dilation is to use an annular piezo-electric bimorph for the spacer defining one of the low index layers.

The design selection procedure is initially the same as for the single line partial reflector that is selective against all other lines in both bands, but with the exception that two further criteria are imposed: the design must include a layer of the fundanlental thickness and also all the other layers should be even multiples (to within five and preferably within three quarters of the design wavelength) of the fundamental thickness.

At the design wavelength all of the layers are an odd number of quarter-wavelengths thick, and so a reflection peak occurs. At the wavelength corrresponding to the period bisector, an identical reflection peak is frustrated only by the fact that the fundamental thickness layer has an optical thickness which is an even number of quarter-wavelengths thick. Changing the thickness of the fundamental layers by A/4, where A is the design wavelength, now reverses the situation. At the design wavelength a reflection peak is frustrated by the optical thickness of the fundamental thickness now being an even number of quarter-wavelengths thick. At the wavelength corresponding to the period bisector, a reflection peak occurs since all of the layers present optical thicknesses that are an odd number of quarter-wavelengths thick.

The particular design of zinc selenide/air complex stack whose configuration and spectral characteristics are shown in Figures 14A and 14B is based on the design: 179H 45L 217H 89L Hsubstrate.

where the design wavelength corresponds to the P20, (001-100) line- of a CO2 laser, and where rH substrate means that the 89L air layer is bounded by a high index (zinc selenide) substrate whose other major surface is provided with an anti-reflection coating, as illustrated in Figure 3.

Changing the 45L to 46L produces a reflection peak in the P branch of the CO2 001-020 band which is not centred on any line. However, by making the design wavelength P22(001100) instead of P20 (001-100), the change from 45L to 46L produces a reflection peak close to the P20 line in the P branch of the 001-020 band. The mismatch can be rectified by making extremely small changes in the relative layer thickness. Thus a match is secured with the following design:

45.006L 179.07 # 270.98H 89.06L substrate 45.955L The two characteristics for this design are depicted in Figures 1 4A and 1 4B.

The description has so far considered in detail laser cavities formed by a complex stack acting as one laser mirror, and some other form of reflector for the other mirror It would of course be possible to use a second complex stack for the second mirror, but this is not normally necessary or desirable.

However attention is finally directed to a special form of complex stack formed in two separate parts which co-operate to form a laser cavity.

Each part is itself a simple stack, but optical thickness of one part is different from that of the other. Moreover considering the two parts together as a single entity there is produced a complex stack satisfying the previously set out design criteria concerning multiplicity in relation to fundamental order numbers, bandwidth in relation to adjacent emission lines and selectivity in relation to the suppression of all other emission lines.

An example of such a two-part complex zinc selenide/air stack for the P20 (001-100) CO2 line is given by: 291H 291L- 291H 291L 291H 291L 291H for the total reflector, whose spectral characteristic is given in Figure 15A, and:- 195H 195L 195H 195L HSubstrate for the partial reflector, whose spectral characteristic is given in Figure 15B. The spectral characteristic of the combination is given in Figure 15C.

The foregoing analysis has neglected the effects of dispersion. In the case of materials whose dispersion is effectively linear over the range of interest, dispersion produces a small perturbation which affects the fine tuning of a spectral characteristic, but not to any significant extent its general shape. The transmission, T, of a layer of refractive index, n, and physical thickness, d, bounded by vacuum is given by 16n T= (n+1)4+(n-1)4-2(n-1)cos2# where 2nd cos2#=cos2#.

For a material that is effectively linearly dispersive over the particular wavelength range of interest.

n=n(#)=n0-g# where nO is the extrapolated zero wavelength index.

In this case 2n0d cos28=cos[2#.

jl where $b=47rdg Therefore the periodicity 1 n(#) 2 P= = .

2n0d n0 m# where m is the order number (number of quarter wavelengths of optical thickness) of the layer.

The effect of the phase # is to translate the transmission characteristic with respect to a wavenumber abscissa. This effect together with the fact that the period is now a function of the extrapolated zero wavelength refractive index, n0, and the physical thickness, d, results in a zero dispersion corrected, or effective optical thickness order number, meff, satisfying the relationship me"=m+K (K even) (K odd) where K=1+int(#/#) where int(#/#) is the integer below the #/# for non-integral values of #/#, and is the value of #/# for integral values of #;/7r For materials such as zinc selenide and zinc sulphide which are effectively linear dispersive over the wavelength range of the emission lines of a CO2 laser, the basic design work, that is the generation of the fundamental and multiple thicknesses, may be satisfactorily carried out using the zero dispersion corrected numbers of quarter wavelengths m6ff. Computer generation and selection of satisfactory designs may also continue to use these zero dispersion corrected values.Since the difference between the characteristic obtained using n(A) and m and that obtained using nO and meff are slight, it is only worthwhile using n(A) and m to check designs that have been found satisfactory using nO and meff, All the foregoing examples have been concerned exclusively with stacks in which all the alternate layers of a stack have a refractive index equal to a first specific value while all the intervening layers have a refractive index equal to a second specific value. It should be clearly understood however that the invention is not limited exciusiveiy to such structures, but is applicable also to stacks where there are three or more different values of refractive index.

Normally replacing for instance one zinc selenide layer of a stack with an equivalent thickness layer of zinc sulphide makes little difference to the overal shape of the transmission characteristic.

Changes of this sort may however be useful in particular instances, for instance on mechanical grounds where a particularly thin high refractive index layer is wanted and one of zinc selenide is considered rather too fragile.

It is also to be understood that where reference has been made to the optical thickness of a layer of a stack, this includes a composite layer, the componentes of which are so close in refractive index that effctively they function as a single layer. Thus for instance Table 3 lists this calculated transmissivities, T(ZnSe), at specific CO2 emission lines for the 7-layer zinc selenide fair stack.

195H 97L 291H 195L 195H 97L 389H whose characteristic is depicted in Figure 13, and contrasts these with the transmissivities, (T ZnSe: S), for a similar stack in which the 389H layer of zinc selenide is replaced with 195H of zinc selenide plus 194H zinc sulphide. The comparison reveais that the caracteristic has not been very greatly changed by the substitution.

Table 1 List of Possible Thicknesses, Expressed as Numbers of Design Quarter Wavelengths

87 133 177 223 267 313 89 179 269 :135 : :225 : :315 91 181 271 137 227 317 91 139 185 233 279 327 For P20 (001-100) 47: 93 : 141 : 187 : 235 : 281 : 329 selected from 95 143 189 237 : 283 331 001-100 and 001-020.

145 243 341 97 195 293 49: : 147 : : 245 : :343 99 197 295 149 247 345 101 199 297 187 377 283 189 379 95: :285 : 191 287 381 193 191 385 For P20 (001-100) 289 193 387 selected from 97: :291 : # 195 389 001-100.

293 197 391 195 295 339 99: 197 :279 .

199 299 201 Table 2 Design Acceptance Criteria Bandwidth Reflectance atP18:P22 (whichever greater) Maximum Reflectance at an Unwanted Line Number of Unwanted Lines at which Reflectance in Excess of 80% Overall Design Status "A": Accepted "R":: Rejected

Designs Designs Selective against Selective against 001-100 and 001-100 001-020 bands band only 197H 195H 197H 245H 343H 197H 389H 291H 291H 195H 99L 147L 49L 147L 147L 147L 97L 291L 195L 97L 343H 197H 295H 197H 245H 295H 195H 97H 97H 291H 49L 147L 99L 147L 49L 245L 291L 97L 97L 97L HSub HSub HSub HSub HSub HSub HSub HSub HSub HSub 53% 27% 73% 67% 49% 20% 21% 45% 71% 67% rail Pass Fail Fail Pass Pass Pass Pass Fail Fail 81% 79% 81% 87% 82% 82% < 80% < 80% < 80% < 80% Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass 2 0 2 10 1 3 0 0 0 0 Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass "R" "A" "R" "R" "A" "A" "A" "A" "R" "R" Table 3 Line P44 P42 P40 P38 P36 P34 P32 A(P20)/R 0.9753 0.9775 0.9796 0.9818 0.9839 0.9860 0.9881 T(ZnSe) 0.4914 0.8463 0.0038 0.6149 0.3530 0.3485 0.3716 T(ZnSe:ZnS) 0.5403 0.7718 0.0038 0.5141 0.3789 0.3806 0.3598 P30 P28 P26 P24 P22 P20 P18 0.9902 0.9922 0.9942 0.9961 0.9981 1.0000 1.0019 0.2428 0.1872 0.4492 0.8514 0.8814 0.0036 0.9016 0.2269 0.1592 0.4414 0.8345 0.8297 0.0035 0.8538 P16 P14 P12 PlO P8 P6 R6 1.0038 1.0056 1.0074 1.0092 1.0110 1.0127 1.0471 0.9146 0.2604 0.3224 0.3336 0.1932 0.1931 0.6500 0.8818 0.2773 0.2570 0.3236 0.1930 0.1553 0.5576 R8 R10 R12 R14 R16 R18 R20 1.0460 1.0449 1.0437 1.0426 1.0414 1.0401 1.0389 0.2735 0.8739 0.4502 0.1199 0.0038 0.0185 0.6455 0.3068 0.8579 0.4444 0.0868 0.0036 0.0188 0.5567 R22 R24 R26 R28 R30 R32 R34 1.0376 1.0363 1.0350 1.0336 1.0322 1.0308 1.0294 0.7304 0.2440 0.9615 0.3214 0.5506 0.4968 0.4345 0.7334 0.2702 0.8123 0.2345 0.5193 0.4215 0.4246 R36 R38 R40 R42 R44 1.0279 1.0264 1.0249 1.0234 1.0218 0.3209 0.4893 0.4079 0.3412 0.0433 0.2587 0.4546 0.4541 0.3688 0.0354

Claims (23)

Claims

1. A laser mirror for a gas laser whose active medium is a gas having a molecular band spectrum containing a plurality of lines at whose wavelengths laser action can be stimulated, which lines are arranged in bands, wherein the mirror is provided by a complex dielectric stack of not more than twenty layers, not all of the same optical thickness, defining a set of interfaces at which there is a refractive index difference, each of which layers has a zero dispersion corrected optical thickness substantially equal to an integral odd number of quarter wavelengths of a selected one of said emission lines, which integral odd number is either a fundamental number or a number not more than five different from a multiple of that fundamental number; which fundamental number is a number such that a simple dielectric stack of layers of the same materials as those of the complex stack, each having a zero dispersion corrected optical thickness equal to the fundamental number of quarter wavelengths of the selected line, would possess, in addition to the reflection peak at the wavelength of that line, no other reflection peak within the two branches of the band containing the selected line, but at least one other reflection peak between the two branches of the band containing that selected line and those of an adjacent band; and wherein the combination of the zero dispersion corrected optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance at the wavelength of both emission lines adjacent the selected line and within that branch of its band is not more than 60%, and such that the reflectance is not more than 90% at the wavelength of any emission line within the two branches of the band containing the selected line other than selected line itself.

2. A laser mirror as claimed in Claim 1 wherein the layer of the complex stack having the greatest optical thickness has a zero dispersion corrected optical thickness of less than twice mB where

where k is the wavenumber of the selected line, k, and k~, are the wavenumbers of the lines adjacent the selected line, and n11 and n,, are respectively the refractive indices of the high index and low index materials from which the complex stack is constructed.

3. A laser mirror as claimed in Claim 1 or 2 wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance is not more than 90% at the wavelength of any emission line at which laser emission can occur other than the selected line itself.

4. A laser mirror as claimed in any preceding claim wherein the fundamental number is a number such that said simple dielectric stack possesses at least two other reflection peaks between the two branches of the band containing that selected line and those of an adjacent band.

5. A laser mirror as claimed in any preceding claim wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that the reflectivity at the wavelength of both emission lines adjacent the selected line and within that branch of its band is not more than 50%.

6. A laser mirror as claimed in any preceding claim wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance is not more than 85% at the wavelength of any emission line within the two branches of the band containing the selected line other than the selected line itself.

7. A laser mirror as claimed in Claim 6 wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance is not more than 85% at the wavelength of any emission line at which laser emission can occur other than the selected line itself.

8. A laser mirror as claimed in any preceding claim wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance is greater than 80% at the wavelengths of not more than six of the emission lines within the two branches of the band containing the selected line.

9. A laser mirror as claimed in Claim 8 wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that the reflectance is greater than 80% at the wavelengths of not more than six of the lines at which laser emission can occur.

10. A laser mirror as claimed in any preceding claim wherein the selected emission line is a carbon dioxide laser emission line.

11. A laser mirror as claimed in Claim 10 wherein the selected emission line is the P20 (001 - 100) CO2 line.

12. A laser mirror as claimed in any claim of Claims 1 to 10 wherein the zero dispersion corrected optical thickness of one of the layers of the complex stack is substantially equal to the fundamental number of quarter wavelengths of said selected emission line wherein the optical thickness said layer is switchable by an amount substantially equal to one quarter wavelength of said selected emission line, and wherein each one of the remainder of said layers of the complex stack has a zero dispersion corrected optical thickness substantially equal to an odd number of quarter wavelengths of said selected line not more than five different from an even multiple of the fundamental number.

1 3. A laser mirror as claimed in Claim 1 2 wherein each one of the remainder of said layers of the complex stack has a zero dispersion corrected optical thickness substantially equal to an odd number of quarter wavelengths of said selected line not more than three different from an even multiple of the fundamental number.

14. A laser mirror as claimed in Claim 12 or 13 wherein the combination of the optical thicknesses of the layers of the complex stack and their ordering is such that, when the adjustable optical thickness layer is adjusted to a first particular optical thickness substantially equal to an odd integral number of quarter wavelengths of said selected line the reflectance of the complex stack has a peak matched with the wavelength of said selected line, and when the adjustable optical thickness layer is adjusted to a second particular optical thickness substantially equal to an even integral number of quarter wavelengths of said selected line the reflectance of the complex stack has a peak matched with the wavelength of a different one of said lines in said band spectrum at which laser action can be stimulated.

1 5. A laser mirror as claimed in Claim 1 3 or 14 wherein the medium of the adjustable optical thickness layer is vacuum, air, or other gas having a refractive index not substantially different from unity.

16. A laser mirror as claimed in Claim 13, 14 or 15 wherein adjustment of the optical thickness of the adjustable optical thickness layer is effected by means of a piezo-electric element defining the physical thickness of that layer.

1 7. A laser mirror as claimed in any preceding claim wherein all the alternate layers of the stack have a refractive index equal to a first specific value while all the intervening layers have a refractive index equal to a second specific value.

18. A laser as claimed in Claim 17 wherein the second specific value is substantially equal to 1.

19. A laser mirror as claimed in Claim 1 and substantially as hereinbefore described with reference to any one of the specific examples.

20. A pair of mirrors for a gas laser whose active medium is a gas having a molecular band spectrum containing a plurality of lines at whose wavelengths laser action can be stimulated, which lines are arranged in bands, where in each one of the pair of mirrors is provided by a simple stack of alternate high and low refractive index layers of equal zero dispersion corrected optical thickness wherein the zero dispersion corrected optical thickness of the layers of one stack is not equal to the zero dispersion corrected optical thickness of the layers of the other stack and wherein the two mirrors when positioned to form a laser cavity co-operate to form a complex stack as claimed in Claim 3 or any of Claims 4, 5, 7, 9, 10, or 11, when appended to Claim 3.

21. A pair of mirrors substantially as hereinbefore described with reference to Figures 1 5A, 1 5B and 15C.

22. A laser provided with a pair of mirrors defining its optical cavity one of which mirrors is as claimed in any claim of Claims 1 to 19.

23. A laser provided with a pair of mirrors defining its optical cavity, which pair of mirrors is as claimed in Claim 20 or 21. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~