ELECTRONICALLY TUNABLE ACOUSTO-OPTIC FILTER HAVING SELECTED CRYSTAL ORIENTATION

Electronically tunable acousto-optical filters have been constructed wherein light of a first polarization traveling collinearly with an acoustical wave through an optically anisotropic medium, such as a birefringenl crystal, is diffracted from the first polarization into a second polarization and wherein the light of the second polarization may be separated from that of the first polarization at the output. The frequencies of the acoustic wave and the optical wave are related such that the bandpass characteristics of the acousto-optic filter ma> be changed or tuned over a range of optical frequencies by varying the frequencies of the acoustic wave.

As explained in a patent application entitled "Electronically Tunable Acousto-optic Filter Having Improved Light and Acoustic Wave Interaction," Ser. No 101,622, filed on Dec. 28, 1970, by John A. Kusters and issued as U.S. Pat. No. 3,687,521 on Aug. 29, 1972 the interaction between the acoustic and the optica waves is optimized when the two waves maintain collin earity over an appreciable distance of travel through the filter. In many anisotropic media the phase velocitj vector of the acoustic wave and the group velocity vector of the acoustic wave are at an appreciable angle tc one another, and thus these two wave vectors cannoi be simultaneously collinear with the optical wave. A! described in U.S. Pat. No. 3,687,521, the filter is sc constructed that the group velocity vector of the acoustic wave is collinear with the optical wave travelinj along the principal axis of the filter, and the phase velocity vector of the acoustic wave extends off at ar angle relative to the principal axis. Although this prioi art arrangement is preferable to that in which the phase velocity vector of the acoustic wave is aligned with the optical wave in such anisotropic media, it still provides a tilted acoustic wave front in the filter and, except foi instances in which the optical beam is collimated to high degree, the bandwidth of the filter is undesirablj broadened. It is desirable to increase the usable optica aperture angle and to improve the resolution, i.e., narrow the bandwidth, of such acousto-optical filters.

A first approach is to utilize a filter medium in which the phase velocity vector and the group velocity vectoi of the acoustical wave are in alignment such that both of these acoustic vectors will be aligned with the optica wave traveling through the medium. In the case of quartz crystal, an important filter medium in that it ma] be used in both the visible and ultraviolet regions of the spectrum, the phase and group velocity vectors of th acoustic wave traveling therethrough will be collineai when the direction of travel is aligned with the X-axii of the crystal structure. In this instance, the acoustic wave employed is a longitudinal wave as contrastec with the shear wave utilized with a Y-bar quartz crysta filter such as that described in U.S. Pat. No. 3,687,521 A filter utilizing such a longitudinal mode is handi capped by the need for relatively high acoustic fre quencies since the longitudinal acoustic velocity is ap proximately twice that of the shear acoustic velocity. Ii addition, since the acoustic power required to operat the filter is substantially proportional to the acoustic velocity cubed, the power requirement is increased b; about a factor of eight. Thus, by utilizing an X-bar crys tal orientation in lieu of a Y-bar orientation, an increased optical aperture and a narrower bandwidth are obtained only with a sacrifice in power and acoustic frequency. In addition, when utilizing the shear mode 5 and reflecting off the input face into collinearity with e the optical beam, essentially a percent conversion of the acoustic wave is obtained. In a filter employing the longitudinal mode acoustic wave, the conversion t efficiency is about half and thus an even higher acous-a tic power input is required. In quartz, therefore, it is desired to operate with a shear acoustic wave with the optical and acoustic waves being directed along a Y-bar c orientation of the crystal, and some other approach is e needed for improving the optical and acoustic wave in-y teraction.

In the present invention a novel method and apparatus is provided for utilizing a crystal orientation for the i. anisotropic medium in an acousto-optic filter whereby i, enhanced resolution and improved optical aperture angles are obtained and wherein reasonable values of J acoustic frequency and power are required.

In general, it is desired to employ a crystal orientah tion in the Y-Z plane so that the shear acoustic wave y may be employed rather than the longitudinal wave. The orientation desired is such that the phase velocity D vector and the group velocity vector of the acoustic t wave along the particular orientation approach collin-s earity so that the problems encountered with a tilted wave front are substantially eliminated. It has been ;- found, however, that in approaching this idealized ori-g entation in a quartz filter medium, the optical birefrin-> gence of the filter medium varies rapidly with the light n propagation direction, thereby seriously degrading the r resolution, i.e., increasing the bandwidth for all but e very small optical aperture angles. Thus, although one e gains from the collinearity of the acoustic phase and ve-s locity vectors, one loses by the change in birefringence, r and thus optimum results are not obtained.

It has been discovered, however, that certain crystal y orientations exist where the effect of the birefringence il change is cancelled out by the effect due to acoustic anisotropy so that an acousto-optical filter with im-proved high resolution and relatively large optical aper-h ture angles is obtained. For example, in the case of a r quartz filter, excellent results have been obtained with fi the optical and acoustic energy being propagated il through the quartz cut with its major axis in the Y-Z a plane and oriented in a direction at an angle approxi-y mately 11.2 to the Y-axis.

Referring now to FIG. 1, there is shown in schematic form a typical acousto-optic filter of the type described in the above-cited U.S. Pat. No. 3,687,521. This filter comprises a suitable anisotropic medium 11, for example, a birefringent quartz crystal, provided with angled input and output end surfaces 12 and 13, respectively. The medium 11 is oriented with the longitudinal axis through the filter aligned with the Y-axis of the quartz crystal, the Z-axis of the quartz crystal extending in a vertical direction.

The optical beam 14 from a source 15, for example, ultraviolet light in the case of the quartz medium, is transmitted into the body 11 through the input surface 12, the input surface being preferably cut at Brewster s angle to minimize transmission reflection losses. The optical beam passes along the Y-axis of the body 11 and exits through the output end 13. This light is polarized in a first direction along the Z-axis by a vertical linear polarizer 16. A horizontal linear polarizer 17 is located at the output to separate the light exiting with polarization along the Z-axis from the orthogonally polarized light produced by the diffraction in the medium 11.

An acoustical transducer 18 is mounted in intimate contact with the crystal 11 and is connected to a suitable signal generator or source 19 such as a voltage tunable oscillator, the frequency of which can be varied by varying the input voltage applied thereto. The transducer 18 may be of any suitable type, for example, an X-cut lithium niobate transducer. The RF output of the voltage tunable oscillator 19 is fed via an adjustable attenuator 21 to the acoustic transducer 18 for generating an acoustic shear wave which is internally reflected from the input face 12 of the crystal 11 and propagated collinearly along the Y-axis of the crystal 11 with the optical wave.

For a particular combination of light wave and acoustic wave frequencies, there is found to be a strong interaction between the light and the acoustic wave in which the acoustic wave diffracts the light wave from the polarization orientation of the input beam into the orthogonal polarization. This yields a narrow pass band of light of orthogonal polarization which is then separated from the input light beam by horizontal linear polarizer 17. This narrow pass band of light is a function of the applied acoustical frequency and can therefore be varied in frequency by varying the frequency of excitation supplied by the voltage tunable oscillator 19. The acoustic shear wave is reflected off the end face 13 and absorbed by acoustic absorber 22.

This collinear diffraction occurs as a cumulative effect for a very narrow band of light frequencies, and il is noncumulative by incremental self-cancellation foi other frequencies. The cumulative diffraction effect occurs when the momentum vectors of the incident light and acoustic waves satisfy the relation that their sum equals that of the output light beam. This condition is called "phase-matching" and occurs when the diffraction-generated polarization travels at the same velocity as the free electromagnetic wave. A narrow band of frequencies satisfying this relation and diffracted into the orthogonal polarization is then passed by the output polarizer 17 while the light of the initial polarization is blocked. If desired, the output polarizer 17 may be polarized in the Z direction to pass the non-5 diffracted light and block the diffracted light.

Diffraction into the orthogonal polarization occurs : via the photoelastic effect, and is only cumulative if: ka 1 ke = ka where the subscripts o, e, and a denote the or-r dinary light wave, the extraordinary light wave, and the - acoustic wave, respectively. This will be the case if the 1 light and acoustic frequencies/, and/a are related by:

where c/V is the ratio of the light velocity in vacuum to i the acoustic group velocity in the medium, and An is the birefringence of the crystal.

As more fully described in the above-cited U.S. Pat.

No. 3,687,521, the face angle of input surface 12 is so : chosen that the group velocity vector V, of the acoustic i wave is aligned with the longitudinal axis of the crystal, . whereas the phase velocity vector Vp extends off at an 1 angle thereto. Aligning the group velocity vector with the optical beam enhances the interaction between the two waves through the medium. - However, because of the tilted wave front of the phase velocity vector Vp, the incoming optical beam must be well collimated to obtain the desired resolu-i tion. As the optical aperture angle increases, the bandwidth of the filter increases and thus resolution is de-; graded. In order to improve the resolution of the filter and to increase the usable optical aperture, it is desir-; able that the phase velocity and the group velocity of i the acoustic wave be brought into closer collinearity and it would thus appear that the proper approach \ should be to determine a crystal cut wherein the group ; velocity and phase velocity vectors are collinear along the longitudinal axis of the filter. This approach leads to various problems with the birefringence of the filter i as more fully described below and requires additional i modifications. As stated above, it is most desirable to ; work with the shear mode of the acoustic wave for acoustic frequency and power considerations and thus the crystal orientation selection is made with this condition in mind. i Referring to FIG. 2, there is shown an illustration of the acoustic propagation in the Y-Z plane of the quartz crystal, the ellipse forming the envelope of the inverse f phase velocity vectors, the direction of the vectors de-i fining the direction of the phase velocity, and the mag-r nitude of the vectors being 1/VP. The group velocity i vectors are normal to the tangent of the elliptical envelope at any selected point on the ellipse, and thus the i group velocity vectors are parallel to the phase velocity i vectors along the major and minor axes of the ellipse i and at an angle thereto at all other points. The major axis of the ellipse is located approximately +32.3 from the Y-axis of the quartz crystal. This would suggest that t if a filter body were cut from a quartz crystal such that r the longitudinal axis of the filter body lies in the Y-Z t plane of the quartz crystal and along a direction +32.3 t from the Y-axis of the crystal, the group velocity vector r and phase velocity vector would travel collinearly with the optical beam along the longitudinal axis of the filter : body. This collinearity of optical beam and group and 5 phase velocity of the acoustic wave should result in the / enhanced resolution and increased optical aperture desired.

However, in operating at this new crystal cut, a problem is encountered with birefringence and this can be understood by referring to FIG. 3 which is a diagrammatic illustration of the indices of refraction for quartz, the outer ellipse representing the index of refraction, nt, for the extraordinary light wave and the center circle representing the index of refraction, na, for the ordinary light wave. The diagram is not to scale since the indices n, and n0 are substantially closer together than shown, the ratio of n, to being approximately 1.006, The rates of change of the indices of refraction are represented by the tangents to the envelopes shown The rate of change of the birefringence of the crystal is equal to the difference in the rates of change of the indices of refraction, and, hence, to the difference ol the slopes of the tangents to the envelopes. It is seen that on the Y-axis the tangents to the two curves are parallel and, hence, have the same slope. Therefore, foi this orientation, the rate of change of the birefringence is zero, and there is no further degrading of the operation of the filter due to birefringence effects.

However, at an angle of +32.3 from the Y-axis, ii can be seen that the tangents are no longer parallel bui indeed are widely divergent so that the rate of change with angle of the birefringence is quite high and so thai very small changes in the optical angle of incidence ai this particular crystal cut result in relatively large changes in birefringence. This results in large changes in the optical bandpass as the input optical aperture angle 13 increased. For example, in one version of this orientation constructed and tested, the bandpass foi collimated, monochromatic light from a He-Ne laser a 6,328 A was approximately 4 A wide. When the angu lar aperture was opened up from essentially zero tc 1 -W, the bandwidth increased to A due to the bire fringence change mentioned above.

Thus, while the selected orientation provides the de sired collinearity between acoustic group and phase ve locity vectors, the optical birefringence varies rapidl; with the light propagation direction, thereby cancelling any gain achieved by the improved acoustic collinearit; and degrading the resolution for all but a very small ap erture angle. It is therefore most desirable to determine a crystal orientation for the filter body which takes intc account the desire to move toward collinearity betweer the acoustic group and phase velocity vectors while a the same time avoiding the effect of variation in bire fringence with light propagation direction, hopefull] obtaining an orientation where the two effects will bal ance each other out, rendering a high resolution filtei usable with relatively wide optical aperture angles.

Consider the variation of the acoustic frequency foi a fixed optical wavelength as the direction of the inpu light vector (ku) is varied. Referring to FIG. 4, the k vector matching conditions (for the light vector 1?L coilinear with the acoustic group velocity vector \a. can be written as:

ku = kLt cos B0 + ka cos Bm and ku sin = ka sin Bm where kLl and kL2 represent the input and output ligh rays, which are orthogonally polarized. For all cases o: interest kit and ku are very nearly coilinear so that d, is extremely small, as seen from Equation (3). There fore, cos at 1, and Equation (2) becomes kLl " ku + ka cos Om (4)

giving COS flro (5)

where kvac 2ir/A, X = optical wavelength in vacuum, ka = 2irfaIVp,fa = acoustic frequency, Vv acoustic phase velocity, and 10/i) and 2 are the indices of refraction for the input and output plane polarized light waves. Therefore, Equa-tion 5 can be rewritten as fi = P/COS flap (AA) (6)

f 1 5 where An = nt n2 = the effective birefringence, which n is a function of the particular orientation. s First consider varying the input light direction through a small angle a, in the plane formed by the s acoustic group and phase velocity vectors, as shown in .- FIG. 5. The k- vector matching condition now leads to / = Fp/cos .(, + a,) [A/ifaO/A (7)

Now consider varying the input light direction e through a small angle a2 perpendicular to the plane of it the acoustic group and phase velocities, as shown in .t FIG. 6, where kL2 kL2 cos fl0 and ka = ka cos flw. e Here, kL1 and ka are the projections of kL1 and ka in the s plane that contains KLl and that is and orthogonal to e the plane of FIG. 4. For phase matching s icu> - ku cos Q + ka cos a2 = kit cos B0 cos 0 + ka cos & cos 2 it Using the following approximations i- cos = 1 and 6 < 2/500 so that 3 cos 0 = 1 for reasonable values of at gives kLl = kLl + ka cos flap cos o2 i- In the limit (1 cos a2) (1 cos 6m)

giving ku = kLt + ka cos flOT

Therefore, to the first order, the angle between the acoustic and optical k-vectors does not change, leading i- to the equation:

fa Kp/cos Om A/j(a2)/A (8) o n 45 Note that in both Equations (7) and (8) the acoustic it phase velocity, Vp, remains constant independent of the angle a, or a2.

The optimum orientation is that which allows the I- light direction to be moved through small angles around the acoustic group velocity direction, while keeping the acoustic frequency fixed (for a given light >r wavelength), i.e., it SfJSa I x /ix d = 0 . For the case of the light direction varying in the "acoustic plane," Equation (7) leads to 8/B/6a, = VJK [A/i(a,) 6/8a, ( I/cos (0BP + a,)) + I/cos ,n Therefore SfJSa, I x . cmut. = 0 i ) leads to (I/An) S/8oti [An(a,) =- tan Bm (io>

f Similarly, for the case of the light direction varying > perpendicularly to the "acoustic plane," one gets :- 6/801, [A/i(aj) = 0 (ii)

To satisfy Equations (10) and (11) requires specifn expressions for the birefringence as a function of ligh propagation direction and for the angle, 6m, betweei the acoustic group and phase velocity vectors as a func tion of the acoustic group velocity direction.

To evaluate the birefringence, the indices of cefrac tion must be expressed as a function of crystal geome try and light propagation direction. For biaxial crysta (tricltnic, monoclinic, orthorhombic), the conventioi for defining the X Y Z axes is that nx < nu < n,.

With this convention, there are two optic axes sym metric to the Z-axis and lying in the X-Y plane, a shown in FIG. 7, with /3 given by tan /3=+/-

l _L___L

For a light k-vector propagating in a general direc tion, there are two linearly polarized normal modes with indices of refraction given by: Mn +/- 2 = & [(llnj + 1/n,2) + (1/n2 - 1/n,2) cos (6 +/-02)1 where 61 and 02 are the angles between the light k vector, ift, and the two optic axes. These angles are de fined by:

cos <9, =[(kL)xlkL sin /3 + ((kL),lkL cos ft cos 02 = -[(t)x/J sin /3 +((kL)JkL cos /3 For the cases of interest in constructing tunable fil ters, the indices are approximately equal, and Equatioi (13) can be reduced to give A/i = n+ n_ ". (n, nx) sin 0, sin 6t .(M

For uniaxial crystals, ft = 0 and 0, = 02; therefore Equation (13) reduces to: 1 In,1 = sin2fl/ne + cos20/n0 ; 1 /n02 = 1 /n02 <i s where 6 is the angle between KL and the Z-axis, and n and ne are defined as the ordinary and extraordinary indices, respectively. Similarly, Equation (14) be comes:

ul,i " (n, na) sin20 Equations (10) and (11) must be solved using the ex pressions for An versus angle given above. Since Equa tion (11) is not concerned with the acoustic properties it can be considered now. Equation (11) means that th direction of k must be varied with An remaining fixei to first order. For the biaxial case both 0t and 0, mus remain fixed, indicating that the k-vector must lie in th X-Y plane, with the angular variation, <2, being per pendicular to the X-Z plane. For the uniaxial case, th< angular variation, a,, must be tangent to a cone aroum the Z-axis, i.e., perpendicular to the plane formed by and the Z-axis.

Now the solution to Equation (10) must be consid ered in light of the above restrictions. Specifically Equation (10) must be solved for motion of the ligh 4-vector in the plane formed by kL and Z, with the addi ional restriction in the biaxial case that kL lie in th< X-Z plane.To now evaluate the angle, 0flp, between the acoustic it group and phase velocity vectors, one must consider n the acoustic equations of motion. As an example, con-;- sider the uniaxial crystals quartz (SiOs) and lithium ni-5 obate (LiNbO3), which have -trigonal symmetry. For :- both crystals, the pure shear mode in the Y-Z plane . can be considered, giving the "slowness" equation il A-Jo>= Vp (Cm sin2 6 + C44 cos2 0P + C14 sin2 0,,)-"12 n A (17)

where Ov = angle between ka and Z-axis and p = den-j. sity. For quartz, piezoelectric effects alter Equation ts (17) slightly, and the effect on the final result will be mentioned below. The group velocity is defined by Va = X (8<u/8/t) + Y (Sot/Ska) + Z(8<a/Skj) < ig)

In the Y-Z plane, Sta/dkj. = 0, and Equation (18) leads to 0B = tan-1 [(8W8/tv)/(8W8,) ( 19)

20 Substituting Equation (17) into Equation (19) yields an expression for the angle, 0fl, between the group velocity vector and the Z-axis shown in FIG. 8: 0a = tan-1 [(CM tan 0P + Cu,)l(C + CH tan 0J(20)

25 Inverting Equation (20) gives 0P = tan1 [(CV, tan 0e - C)l(Cm - C14 tan 0fl) 1 0TO = 0, - 0P = 0, - tan- [[C tan 0fl - C,4)/(C66 - Cu 3) tan 0e) (2i)

c" For the uniaxial case Equations (16) and (21) can be J" substituted in Equation (10). Now A(a,) = (ne - n0)

cos2 !, and evaluating the derivative in Equation (10)

at = Oe gives 1- 35 (7T.

i fc tau-C\-[!VerticalLine!] tan U-C14tanJJ

3. Equation (22) can now be solved for 09 using the specific constants for quartz. At 4,000 A, 0 = 1.56, 5) no = 1.57, C44 = 5.79 x Nt/m2, Cu = - 1.81 x Nt/rn2, and C56 = 4.06 X Nt/m2. 0U is found < to be - 101.13; or- 1 1.13 from the Y-axis Includ-"y ing piezo-electric terms gives a more exact_answer - "of "Ti .20, a! shown in FTG 9. This angle is found to be relatively independent of wavelength in the 5) region of crystal transparency.

Referring now to FIG. 10, there is shown a quartz fil-4" ter body 11 for use in the filter of FIG. 1, this body " being oriented in a direction approximately 11.20 s> relative to the Y-axis. In the nomenclature adopted by IEEE in The Standards on Piezoelectric Crystals, IEEE d 176-1 949, this direction is designated (zyw) - 1 1 .20.

In actual practice, good results are obtained when the 16 crystal cut lies within the range of (zyw) 1 1.10 to r" (zyw) - 11.30.

j As described in detail in the above-cited U. S. Pat.

60 No. 3,687,521, the face angley of the Quartz crystal 11 CL (i.e. the angle between the input face normal and the longitudinal axis of the crystal) may be calculated from the following equation: y cos y = ( VJVn) sin (y + 8 ) (23)

i- where Vfl is the phase velocity of the acoustic wave in ie the crystal 11 along the path between the acoustical transducer 18 and the input face 12 of the crystal, Vvi <HR>3,7: 9 is the phase velocity of the acoustic wave in the crystal along the longitudinal axis of the crystal, and 8 is the walk-off angle between the group and phase velocity vectors of the acoustic wave as shown in FIG. 1 of this application. Substituting the values of KPi, Vpt, and 8 for the orientation shown in FIG. of this application in equation (23) gives:

cos y = (4.36 x 10s cm/sec/3.62 X cm/sec) sin (y + 21.79)

From this expression it may be determined that y= 26.-

Thus, the face angle for quartz, if cut at approximately 26.26 will result in the group velocity vector for the acoustic wave lying along the longitudinal axis of the quartz body, rendering optimized interaction with the optical wave.

With this orientation, the effect of the variation in birefringence cancels the effect due to acoustic anisot-ropy, and high resolution is obtained with the filter even at large aperture angles. For example, in one embodiment of the invention constructed and tested, the quartz filter operated at 6,328 A with a bandwidth of approximately 3 A and with an optical aperture angle of 4. This compares very favorably with a prior form of optical filter shown in FIG. 1 with the propagation down the Y-axis of the crystal wherein at 6,328 A the bandwidth obtained was A for an aperture angle of 1.

For a lithium niobate crystal utilizing light in the IR region, a crystal cut is chosen such that the longitudinal axis of the body 11 along which the group velocity vector of the acoustic wave is directed extends along the direction of approximately 4.0 from the Y-axis of the crystal, i.e., (zyw) 4.0. The phase velocity vector extends along a direction of approximately 3.6. The face angle is cut at approximately 51.6.