Investigation of magnesium fluoride crystals for imaging acousto-optic tunable filter applications

Investigation of magnesium fluoride crystals forimaging acousto-optic tunable filter applications

Vitaly B. Voloshinov and Neelam Gupta

Results of an investigation of acousto-optic (AO) cells using single crystals of magnesium fluoride �MgF2�are presented. Two acousto-optic tunable filter (AOTF) cells for imaging application have been designedand tested in the visible and ultraviolet (UV) regions of the spectrum from 190 to 490 nm. The twoimaging filters were developed by using the wide-angle AO interaction geometry in the �010� and �11̄0�planes of the crystal. These filters were used to obtain spectral images at the shortest wavelengthsachieved so far. Advantages and drawbacks of this crystal are discussed and photoelastic, acoustic, andAO properties of MgF2 are examined. The investigation confirmed that MgF2-based AOTF cells can beused in the deep UV region up to 110 nm. © 2006 Optical Society of America

OCIS codes: 110.0110, 230.1040.

1. Introduction

The phenomenon of light diffraction by acousticwaves in crystals has been widely used in the designof modern instruments to control optical radiation.Acousto-optic (AO) modulators, deflectors, filters, andoptical information processing devices are used inmany applications in science and technology due totheir reliability, fast speed, and low drive powerrequirements.1–5 The operational range of modernAO instruments covers a wide spectral interval fromthe ultraviolet (UV) to the long wave infrared(LWIR). Recently there is more interest in extendingthe operational range toward shorter UV wave-lengths below 250 nm.6–8 This spectral region is usu-ally defined as the “vacuum UV” because theterrestrial atmosphere is not transparent to radiationat these very short optical wavelengths.7

One of the main practical motivations in the deepUV is a need to rapidly and precisely control coherentradiation of lasers.1–4 Another reason is to modulateparameters of beams propagating from noncoherent,especially broadband, sources of UV radiation. For

example, the excimer F2 laser radiating at 157 nmand the excimer KrF laser at 193 nm are both widelyused in lithography and ophthalmology. Also, radia-tion emanating from space, e.g., from the Sun, andfrom artificial sources used in spectroscopy and med-icine, such as xenon and mercury lamps, representthe traditional nonmonochromatic sources of the in-coherent UV light. As for the AO instruments, theacousto-optic tunable filters (AOTFs) are developingrather rapidly for applications in laser tuning, spec-troscopy, and hyperspectral imaging.5–18 Recentlysuch filters have demonstrated their capability tocontrol not only collimated rays but also to processdivergent and convergent UV optical beams includ-ing those forming images.8–13

A literature search on AO devices operating in theUV regime shows that only a few birefringent crys-talline materials may be useful to fabricate suchdevices.5–13,15–19 A list of birefringent crystals trans-parent at wavelengths shorter than 250 nm is in-cluded in Table 1 along with their crystal group,optical transparency range, and AO figure of meritM2.1–4 M2 values listed in Table 1 are for the aniso-tropic AO diffraction that yields the wide-angle inter-action geometry, utilized in the design of imagingfilters.5,8–14 It is clear from Table 1 that only quartzand MgF2 are transparent below 170 nm and thelatter is transparent down to 110 nm. In this regardMgF2 is a unique material to fabricate AO devicesoperating in the deep UV.1,13,15 Until now, the mostcommonly used crystal for developing UV AOTFs isquartz that has M2 � 0.59 � 10�18 s3�g, which is

V. B. Voloshinov ([email protected]) is with the Departmentof Physics, M. V. Lomonosov Moscow State University, 119992Moscow, Russia. N. Gupta ([email protected]) is with the U.S.Army Research Laboratory, 2800 Powder Mill Road, Adelphi,Maryland 20783-1197.

Received 12 April 2005; revised 12 September 2005; accepted 17September 2005.

0003-6935/06/133127-09$15.00/0© 2006 Optical Society of America

1 May 2006 � Vol. 45, No. 13 � APPLIED OPTICS 3127

roughly 2.5 times smaller compared to the value of M2for the case of the isotropic AO diffraction.1–4 Thevalue of M2 for the wide-angle interaction geometryin MgF2 has not been evaluated so far. Therefore oneof the goals of our research was to examine optical,acoustic, and AO characteristics of this material. Theother aim was to fabricate an AOTF in MgF2 that canbe used for imaging applications in the vacuum UV.

2. Physical Properties of MgF2 Single Crystals

The single crystal of MgF2 is a well-known opticalmaterial that has not found much application inAOs.1–6 Previously only one other group used thiscrystal to fabricate an AO device.15 Based on MgF2’scrystalline symmetry, birefringence, and transmis-sion in the deep UV, we decided to investigate its usein fabrication of imaging filters and AO deflectorsdespite the low M2 because no other known crystalcan transmit as low UV wavelengths as this crystal.To the best of our knowledge, no results on the in-vestigation of the wide-angle AO interaction geome-try in MgF2 are available in the literature; thereforewe had to treat this as a novel AO material and startfrom the first principles to understand and evaluateits optical, photoelastic, and acoustic properties.

A. Optical Properties

The single crystal of MgF2 belongs to the tetragonalclass of the uniaxial crystalline materials of the pointgroup 4�mmm.1,13 The optical material is positivebecause the refractive index for the extraordinarypolarized beam is larger than for the ordinary beam,i.e., ne � no. The birefringence of the material�n � ne � no � 0.012 is rather low and comparable toquartz.1–8,16–18,20,21 In particular, at 589 nm the val-ues of the refractive indices of MgF2 are ne � 1.389and no � 1.377. The material is transparent from theinfrared to the UV region of the spectrum down to110 nm.20,21

The birefringence �n of MgF2 is almost constant forthe wavelengths greater than 300 nm. On the otherhand, at the wavelengths close to the absorption edgeof the material (i.e., � � 200 nm), the absolute valuesof the refractive indices and those of the birefringenceincrease dramatically. For example, at 115 nm,ne � 1.742, no � 1.721, and �n � 0.021, which isalmost twice as large as the value for the visibleregion.

Another practical consideration in favor of usingMgF2 is that it is a common optical material and largecrystals with high optical quality are easily availablecommercially, and the growth process is simple andinexpensive. MgF2 is a hard crystal, which makes thetasks of cutting and polishing of crystal and weldingof transducers on it relatively easier. Also, unlikeKDP, MgF2 is not hygroscopic and does not requirespecial protective coating and storage.

B. Photoelastic Properties

The matrix of the photoelastic coefficients of the ma-terial, pij, includes seven coefficients that have non-zero values.1–3 Based on our extensive literaturesurvey, we concluded that so far only limited combi-nations of these coefficients have been measured,such as p11 � p12 � 0.892, p11 � p31 � 0.139, andp33 � p13 � 0.226.1 It is quite clear that the firstrelation has a mistake or misprint. As for the abso-lute values of the photoelastic coefficients, data ononly two of them were found in the literaturep44 � 0.0776 and p66 � 0.0448.1 Moreover, signs of allseven coefficients pij for MgF2 are unknown so far.Therefore, during the analysis, it was not possible toobtain reliable values of M2 in order to select an op-timal cut of the crystal. For this reason we had tocarry out our own measurement of the photoelasticcoefficients during this investigation.

C. Acoustic Properties

To evaluate the acoustic and AO properties of thematerial, it was necessary to calculate acousticphase velocities in the crystal for both the longitudi-nal and shear elastic waves. The Christoffel equationwas used to carry out these calculations in the tradi-tional manner.1–3 The following values of the elasticcoefficients of MgF2 have been used in these calcula-tions: c11 � 1.237 � 1012 dyn�cm2, c12 � 0.732� 1012 dyn�cm2, c44 � 0.552 � 1012 dyn�cm2, c33

� 1.77 � 1012 dyn�cm2, c13 � 0.536 � 1012 dyn�cm2,and c66 � 0.951 � 1012 dyn�cm2.22 The value of thedensity � � 3.18 g�cm3 was used for this material.

Since MgF2 has not been used much for AO devicefabrication, it was necessary to determine all valuesof acoustic phase velocity V in the three basic planes�001�, �010�, and �11�0� of the tetragonal crystal. Theresults of the calculations of the acoustic slowness

Table 1. Properties of Birefringent Crystals for UV Applications

Material FormulaCrystalGroup

Transparency� �nm�

Figure of MeritM2 � 10�18 s3�g

Quartz ��SiO2 32 150–4500 0.59Sapphire ammonium ��Al2O3 3m 170–6500 0.3

dihydrogenphosphate(ADP)

NH4H2PO4 42m 200–1200 5.1

Potassiumdihydrogenphosphate

(KDP)

KH2PO4 42m 200–1500 4.6

Magnesium fluoride MgF2 4�mmm 110–7500 –

3128 APPLIED OPTICS � Vol. 45, No. 13 � 1 May 2006

(defined as 1�V) for the longitudinal and fast andslow shear acoustic waves are shown in Figs. 1(a),1(b), and 1(c), respectively. The results of the calcu-lations are that the longitudinal acoustic mode hasphase velocities equal to 6.24 � 105 cm�s and 7.81� 105 cm�s along the directions �100� and �110�, re-spectively. The transverse acoustic wave in the XYplane propagates at 4.16 � 105 cm�s and it does notdepend upon the direction of propagation. On theother hand, the velocity of the slow shear acousticwave strongly depends on the propagation direction.For example, if the acoustic waves are generatedalong the X axis, then the magnitude of the slowshear velocity is 5.47 � 105 cm�s. The slowest acous-tic velocity in the crystal is 2.83 � 105 cm�s for theacoustic wave propagation along the �110� direction.

We focused our investigation on the slow shearelastic waves in order to utilize the anisotropic dif-fraction regime, which always involves a rotation ofthe optical polarization in the crystal. According tothe results of our calculations in the �010� plane of thecrystal, the velocity of the shear wave is 4.16� 105 cm�s � V � 5.47 � 105 cm�s. In the �11�0� planethe following analytical expression for the slow shearwave velocity containing the dependence on the prop-agation angle was used23:

V() � �V1102 cos2 V001

2 sin2 , (1)

where the angle � is measured with respect to the�110� axis, V110 � 2.83 � 105 cm�s, and V001 � 4.16� 105 cm�s. It should be noted here that in this planethe interaction geometry in MgF2 is quite similar tothat used in the design of AOTF cells based onTeO2.19 The only difference is that the acousticwalkoff angle in MgF2 is limited to 21° while it may begreater than 50° in TeO2. The acoustic walkoff angle�, i.e., the angle between the phase and the groupvelocities of ultrasound in the �11�0� plane of the ma-terial, is given by23

� � arctan�(V001�V110)2 tan � � . (2)

After solving Eqs. (1) and (2) we find that in the�11�0� plane, the value of � is �21°. In addition, atsmall values of the propagation angles, i.e., for � 10°, � � 15°. In other words, we can say that theelastic anisotropy of MgF2 is much smaller than thatof TeO2, and it may be neglected in the majority of AOcell designs.

The result of our analysis clearly establishes thatthe wide-angle regime of AO interaction can be ob-served in MgF2 if the slow shear waves are launchedin the �010� and �11�0� planes.13 It is clear that theinteraction taking place in the �010� plane of MgF2 issimilar to that used in KDP,11,12 while the diffractionin the plane �11�0� of the crystal corresponds to theinteraction in TeO2 as mentioned earlier.5,9,10,14,19 Itis well known that the value of M2 in a crystal de-

Fig. 1. Cross section of acoustic slowness (same as 1�V) surfacein the MgF2 crystal (a) in the �001� plane, (b) in the �010� plane, and(c) in the �11�0� plane.


creases as V�3.1–4 Consequently, it is reasonable toconclude that the cut of the MgF2 crystal includingthe �11�0� interaction plane with the acoustic wavespropagating close to the �110� axis is superior to the�010� cut in which the waves propagate close to the�100� axis. Since the magnitudes of the effective pho-toelastic coefficients peff in MgF2 were not known, itwas necessary to examine both interaction geome-tries in the crystal. It was also necessary to findwhich combination of the two effective photoelasticcoefficients and the phase velocity values should beused to obtain the largest value of M2. Therefore dur-ing this investigation two different designs of theAOTF cells based on the �11�0� and �010� AO interac-tion planes were used to fabricate working imagingdevices for characterization.13

3. Wide-Angle Acousto-Optic Interaction Geometry

A wave vector diagram illustrating the AO interac-tion in �010� or �11�0� planes of MgF2 is shown in Fig.2. The only difference in the two cases is the label ofthe axis that is orthogonal to the optical axis Z. Forexample, the �100� axis in Fig. 2 for interaction in the�010� plane should be substituted by the �110� axis forthe interaction in the �11�0� plane. It is clear from Fig.2 that the incident light wave vector, ki, the diffractedlight wave vector, kd, and the wave vector of ultra-sound, K, form a vector triangle, given by ki K� kd. The incident light wave in Fig. 2 has extraor-dinary polarization while the diffracted light wavehas an ordinary polarization. The magnitudes of thetwo optical wave vectors depend on the correspondingrefractive index as follows: ki � 2 ni�� and kd

� 2 no��, where no � ni � ne. The refractive index ofthe incident wave ni is related to the Bragg angle ofincidence of light �. The magnitude of the acousticwave vector K � 2 f�V�� depends on the acousticphase velocity V�� given by Eq. (2) and the acousticfrequency f. Figure 2 shows that the acoustic wavevector makes an angle � with the �100� axis. On theother hand, when the AO interaction is in the �11�0�plane, the tilt angle is measured with respect to the�110� axis.

For the two cases of AO interaction examined here,the refractive index of the incident beam ni is given bythe following expression:

ni �none

�no2 sin2(� ) ne

2 cos2(� ). (3)

Taking the cosine projection of the light wave vectorson the acoustic wavefront, we can write

ni cos � � no cos �d. (4)

Also, by using the sine projections we can obtain thetuning relationship for the filter that relates theacoustic frequency to the optical wavelength and theangle of incidence of light:

f �V()

�(ni sin � � �no

2 � ni2 cos2 �). (5)

In Eq. (5) the value of V�� should be selected tocorrespond to the chosen plane of the AO interaction.We can calculate the acoustic frequency dependenceof angles � and �d by solving Eqs. (4) and (5). It shouldbe noted that if the polarization of the incident lightis changed from the extraordinary to the ordinary,the frequency dependence ��f� for the ordinary polar-ized incident light will be given by the frequencydependence �d�f�.

4. Calculation of Bragg Angles of Incidence

The calculated frequency dependence of the angles ofincidence of light for the ordinary (o) and the extraor-dinary (e) polarized optical beams are plotted in Figs.3(a) and 3(b) by using the dashed and the solidcurves, respectively. On each of these figures the cor-responding measured data (which will be discussedlater) are shown by pluses (��) for the ordinarybeams and crosses (��) for the extraordinarybeams, respectively. The calculations for the AO in-teraction in the �010� and �11�0� planes of the crystalare shown in Figs. 3(a) and 3(b), respectively. In thesecalculations we used � � 633 nm, � 8°, no

� 1.377, and ne � 1.389.10,11

It is clear from Figs. 3(a) and 3(b) that the wide-angle regime of the AO interaction, needed to designan AOTF, is observed at Bragg angle � equal to 8.7°at an acoustic frequency f � 55.5 MHz for the �010�plane and at f � 29.3 MHz for the �11�0� plane, when

Fig. 2. Wave vector diagram for wide-angle AO interaction inMgF2. One of the cells is based on the plane defined by �100� and�001� axes and the second cell uses the plane containing �110� and�001� axes.


df�d� � 0.5,8–14 In each of these cases, the correspond-ing angle of diffraction of light �d is equal to 8.4°. Itmeans that the angular separation of the transmittedand the diffracted beams in the crystal �� d isequal to 0.3°. In air, �� 0.4°, which is approxi-mately 1.4 times larger due to the refractive indexvalue. This is an important parameter for an imagingfilter because it determines the angular aperture ofthe instrument2,3 and our calculations clearly showthat the maximum angular aperture of the imagingfilter in MgF2 with � 8° is limited to 0.4°. Also weshould point out that the difference in the calculatedacoustic frequencies for the two different planesarises due to the difference in the values of the acous-tic phase velocities along the �100� and �110� axes.From now on we will label the cell designed using theAO interaction geometry in the �010� plane as cell1and in the �11�0� plane as cell2.

5. Tuning Curves and Spectral Transmissionof the Filters

The theoretical tuning curves of the two AOTFs ob-tained by using Eq. (5) are plotted in Fig. 4.10–12

Curve 1 in this figure is for cell1 and curve 2 is forcell2. In carrying out the calculations for these twocurves, we took into account the dispersion of therefractive indices no�� and ne��. It is clear from thisfigure that the cells can be tuned in the UV regiondown to 200 nm with a corresponding tuning fre-quency equal to 100 MHz for cell2 and 200 MHz forcell1. If the filters are tuned to wavelengths of lessthan 200 nm (closer to the absorption edge of thematerial), the frequencies of ultrasound grow dra-matically. Based on such a consideration, cell2 is su-perior to cell1 due to the problems associated withdesigning an impedance matching network for thepiezoelectric transducer and the higher attenuationof ultrasound at such high frequencies.

The spectral transmission bandwidth of the filter��, with a transducer of length l, can be calculated byusing the following expression2–4,11,12:

�� 0.8 �2 cos �

�nl sin2(� ). (6)

For both filters discussed above with l � 1.4 cm, �� 230 A at � � 633 nm and �� 23 A at �� 200 nm, and the corresponding spectral resolution��2 � 570 cm�1.

6. Acousto-Optic Figure of Merit

The transmission coefficient T of an AO device isdefined by the ratio of the intensities of the diffracted�Id� and the incident �Io� light, i.e., T � 100% �Id�Io�. Itis given by the following equation1–4:

T � (100%)sin2�

� cos ��M2Pl

2d , (7)

where P is the acoustic drive power applied to the

Fig. 3. Frequency dependence of incidence angles in the crystal (a)in the �010� plane as in cell1 and (b) in the �11�0� plane as in cell2.

Fig. 4. AOTF tuning curves for the two cells: curve 1 is for cell1and curve 2 is for cell2.


transducer and d is the width of the transducer. M2depends on the indices of refraction, the effective pho-toelastic coefficient peff, density of the material �, andthe phase velocity V according to the following ex-pression1–4:

M2 �peff

2ni3no

3

�V3 . (8)

The effective photoelastic constant calculations werecarried out in the traditional manner.12,23 The diffrac-tion in MgF2 in the plane �010� is similar to that inKDP and in the �11�0� plane it is similar to that inTeO2.

Analysis of the AO interaction in MgF2 based on itscrystalline structure shows that the effective pho-toelastic coefficient in the �010� plane of the crystal isgiven by12

peff � p66 cos cos(� ) p44 sin sin(� ), (9)

while in the �11�0� plane of interaction it is given by23

peff � 0.5(p12 � p11)cos cos(� ) p44 sin sin(� ). (10)

As mentioned in Subsection 2.B, since measured datafor the full set of phoelastic coefficients is not avail-able, it is not possible to evaluate all effective pho-toelastic coefficients of MgF2. By using Eq. (9) withthe available values of p44 and p66 with � 8° and�� 16.7° for the wide-angle interaction geom-etry, we obtained peff � 0.046 in the �010� plane.1 Thisvalue of the effective photoelastic coefficient was ob-tained by assuming that both constants in Eq. (9) hadthe same signs. In the case of opposite signs, thecorresponding value of the effective photoelastic co-efficient was close to 20% lower. By using peff

� 0.046, V � 5.45 � 105 cm�s corresponding to thedirection of propagation with the tilt angle � 8°,no � 1.377, and ni � 1.378 in Eq. (8), we obtainedM2 � 2.8 � 10�20 s3�g in the �010� plane of MgF2.

To calculate M2 in the �11�0� plane, measurement ofthe photoelastic coefficients p11 and p12 was carriedout at � � 633 nm. The measurement was performedby using the traditional Dixon method.2,3 A longitu-dinal acoustic wave was propagated in the crystalalong the �010� axis, while the light wave traveledapproximately along the Z axis. Fused quartz wasused as the reference material in this experiment.The absolute magnitude of the coefficient p11 wasobtained when the optical radiation was polarizedalong the Y axis, i.e., along the acoustic wave propa-gation direction in MgF2. The measured absolutevalue of the photoelastic coefficient |p11| � 0.045� 10%. To measure the coefficient p12, light polarizedorthogonal to the Y axis was used and we obtained|p12| � 0.107 � 10%. By using these measurementresults in Eq. (10), we find that 0.026 � peff

� 0.075, depending on the relative signs of the coef-ficients p11, p12, and p44. To calculate M2 in the �11�0�plane of MgF2 in the manner described earlier for the�010� plane, we first use the upper limit of peff toobtain M2 � 5.1 � 10�19 s3�g, while the lower limitresults in an eight times lower value. This clearlyshows that the �11�0� plane of interaction in MgF2 issuperior to the �010� plane because it corresponds tothe higher value of the AO figure of merit even withthe most unfavorable combination of the photoelasticcoefficient values. Based on this analysis we concludethat the wide-angle diffraction in the �11�0� plane ofMgF2 should be chosen for the design of the mostefficient AOTF.

7. Fabrication of Acousto-Optic Tunable Filter Cells

Two AOTF cells were fabricated by using single crys-tals of MgF2 in the form of a prism. The configurationof the AOTF cells is shown in Fig. 5. The transducerfacet of the prisms forms the angle � 8° with theoptical axis �001� in the �010� or �11�0� planes, respec-tively. As discussed in Section 4, these cells are re-ferred to as cell1 and cell2. Thin-plate piezoelectrictransducers were fabricated by using a single crystalof X-cut LiNbO3. The size of the transducer for cell1was given by l � 2.1 cm and d � 0.7 cm, and for cell2the size of the transducer was l � 1.4 cm and d� 0.6 cm along the �11�0� axis. The transducers werebonded by using cold-indium vacuum welding tech-nology. After the welding, the transducers were pol-ished and divided into sections by cutting the LiNbO3plate into several sections connected in a series tomake it easier to design a broadband impedancematching circuit to connect the transducer to a driv-ing rf generator. For cell1 there were nine sections tomeet the high drive frequency requirement whilethere were only three sections for cell2. An electricalmatching network was used for each filter. In addi-tion to the electrical impedance matching, acousticimpedance matching was achieved by evaporation ofthin intermediate layers of indium and tin in the

Fig. 5. Geometry of AOTF cells in MgF2 single crystal.


acoustic bond between the prism of MgF2 and thepiezoelectric plate.

The input optical facet of each crystal formed anangle of 81.3° with the transducer facet. Conse-quently, the wide-angle Bragg interaction in the crys-tal was observed at normal incidence of theextraordinary polarized light on the input facet ofeach cell with the Bragg angle � � 8.7°. All opticalfacets of the two cells were antireflection coated toeliminate the Fresnel losses of 4% of light at eachfacet in MgF2. The total optical loss was reduced to0.5% for the entire cell as a result of applying theantireflection coating as measured at 250 and450 nm while at 300 nm the loss was only around0.1%.

The AOTF cells with the bonded transducers, thematching networks, and the acoustic absorbers wereplaced inside heavy metal boxes to protect the crys-tals from damage and to provide a heat sink. Whenthese cells were continuously operated at 2 W rfpower for a few hours, the temperature of the metalhousing increased only slightly compared to roomtemperature, showing that the heat sink was reason-ably effective.

8. Results of Experimental Characterization

To evaluate the efficiency of generation of ultrasoundin the filters, a detailed testing of the piezoelectrictransducers was performed by measuring the fre-quency dependence of the drive acoustic power. Themeasurement demonstrated that the voltage stand-ing wave ratio (VSWR), i.e., frequency dependence ofthe standing wave ratio that determines the electri-cal performance of the device, of better than 3 dB wasobtained for cell1 over the frequency interval of72–209 MHz and for cell2 from 42 to 110 MHz.The corresponding optical spectral range was190–490 nm for cell1 and 190–420 nm for cell2 asshown in Fig. 4. Based on these results we can con-clude that the tuning range of both devices was rel-atively wide because it exceeded an octave.

The measured frequency dependence of Bragg an-gles of incidence for the extraordinary and ordinarypolarized light in cell1 and cell2 at 633 nm are shownusing crosses (��) and pluses (��) in Figs. 3(a)and 3(b), respectively. It is clear from these figuresthat the measured and calculated values are in goodagreement, i.e., the measured value of the acousticfrequency of 29.1 MHz differed from its theoreticalprediction of 29.3 MHz by only approximately 1% forcell2. Also the measured and predicted values of theBragg angle at 8.7° are in complete agreement.

Figures 3(a) and 3(b) are used to find the measuredvalue of the angular aperture of each of the two filtersto be 0.4° in air. This value is roughly four timessmaller than the value of 1.5° obtained for a KDPfilter.11,12 The reason for the lower value of angularaperture in MgF2 as compared to KDP is due to itsrelatively lower value of birefringence.

The measured value of the transmission coefficientof cell1 was 0.19% at 633 nm with 1 W drive power.By substituting this value of T in Eq. (7) with the

same value of the other parameters as in Section 6,we obtain M2 � 5.1 � 10�20 s3�g as compared to thetheoretically predicted value of 2.8 � 10�20 s3�g. Thusthe agreement between the experimental and thetheoretical values is not close but could be consideredsatisfactory because they are within a factor of 2. Thereason for this discrepancy could be that the pho-toelastic coefficient p66 in MgF2 has a higher valuethan what is given in Ref. 1.

Characterization of cell2 demonstrated that thetransmission coefficient measured at 1.0 W acousticdrive power was 0.84%. It corresponds to M2 � 3.6� 10�19 s3�g, which is higher than in the �010� planeand close to the value of M2 in crystal quartz. Earlierwe had computed M2 � 5.1 � 10�19 s3�g or 4.4� 10�19 s3�g depending on the relative signs of thecoefficients p12 and p66. The 20% discrepancy betweenthe experimental and the calculated data is quitereasonable based on the experimental errors in mea-suring the transmission coefficient and the photoelas-tic coefficients and due to the loss of acoustic power asa result of imperfections in the electrical and acousticimpedance matching.

We would like to note that these experiments con-firmed the basic conclusion of our research that inMgF2 the �11�0� plane of AO interaction is superior tothe �010� plane for designing AOTF cells. Such aconclusion can be generalized to include AO deflec-tors as well.

Based on our measurement results we can predictthat the value of the measured transmission coeffi-cient at 200 nm would be 12%. Also, if the drivepower is increased from 1.0 to 2.0 W, the correspond-ing measured transmission coefficient would begreater than 20%. It is likely that tuning of the cell inthe vacuum UV will increase the transmission coef-ficients to 50%, due to the lower value of the wave-length and the dispersion of the refractive indices.These values of the transmission coefficient may beconsidered quite promising for many applications inspectroscopy and laser technology. It is also clear thatthe design of the cells with longer lengths of AOinteraction results in an improvement in practicallyall basic parameters of the imaging devices in MgF2.

The spectral bandpass �� of the filters was evalu-ated at 633 nm by measuring the change in acousticfrequency �f. The experimental value of �f was foundto be 1.32 MHz for cell1 and 1.24 MHz for cell2. Thecorresponding value of �� for cell1 is 146 Å and 270 Åfor cell2. Based on these measured values of thebandpass, we can extrapolate that near 200 nm thevalue of �� is 15 Å for cell1 and 27 Å for cell2. Themeasured value of the bandpass for cell2 is in goodagreement with the theoretical value of 23 Å calcu-lated by using Eq. (6) while for cell1 the differencebetween the theoretical and the experimental valuesof the bandpass was 20%.

9. Imaging Experiments

We carried out spectral imaging experiments by us-ing the MgF2 filters in the setup shown in Fig. 6. The


AOTF cell was placed between a pair of calcite Glan–Taylor polarizing prisms. A xenon lamp was thesource of the UV radiation and quartz lenses trans-mitted light. A quartz microscope slide with thinslices of a plant specimen (fir) was the object that wasimaged on an UV-enhanced CCD camera. Two irises(used as spatial filters) and a beam stop were neededto block light propagating outside the angular aper-tures of the filters. The frequency of the applied rfsignal was changed to obtain spectral images at var-ious wavelengths. Each spectral image was digitizedby a frame grabber and saved on a personal com-puter.

Filtered spectral images could be observed over theentire tuning range of the filters; however, most dis-tinct and sharp images were registered at wave-lengths in the interval from 250 to 440 nm. We couldnot observe spectral images for wavelengths shorterthan 200 nm because the polarizers were apparentlynot transparent in the short UV range. Four of thefiltered images obtained at 250, 285, 330, and 385 nmby using cell2 are shown in Fig. 7. The sample usedhas no specific spectral signatures at these wave-

lengths except the fact that that quartz is transpar-ent in this spectral region.

The number of resolvable spots N in a line or overa frame can be used to evaluate the optical quality ofa filtered image. For a linear dimension, N � ��,where �� is the angular aperture of the device and ��is the angular size of the smallest pixel resolved bythe filter.12 The number of spots can be evaluated bythe following expression:

N �1.25�nL

�sin2(� )cos �. (11)

This equation clearly shows that the number of re-solvable spots is inversely proportional to the opticalwavelength. Calculation using Eq. (11) at 350 nmgave N � 75 for cell1 and N � 50 for cell2, while at200 nm we obtained N � 135 for cell1 and N � 90 forcell2. Based on these results, we expected to obtaingood quality optical images by using these filters. Ourexperimental results confirmed the good quality ofimages as shown by the blur-free images in Fig. 7.Even though the image quality is good, it is poorerthan those obtained by a KDP filter designed with thesame geometry of AO interaction due to the smallerbirefringence of MgF2 as compared to the KDP crys-tal. The important fact about the MgF2 filters is thatat present it is the only material that can be used tofabricate filters for applications in the vacuum UVbelow 200 nm where KDP does not transmit light.

10. Conclusions

We carried out a detailed investigation of the optical,acoustic, and AO properties of MgF2. Our results un-doubtedly establish that so far it is the only birefrin-gent material that can be used to design and fabricateboth AO deflectors and filters operating down to110 nm in the vacuum UV range. Also our investiga-tion clearly demonstrated that the AO filters anddeflectors should be designed by using the wide-angleAO interaction geometry in the plane defined by thecrystal optical axis and the �110� axis by using ashear acoustic wave to create a phase grating in thematerial. The values of M2 for both MgF2 and crystalquartz are close. Even though M2 is relatively smallfor the imaging filter application, one can still obtainclose to 50% transmission coefficient values with a2 W drive power at the optical wavelengths corre-sponding to the vacuum UV.

Values of the spectral resolution and angular ap-ertures of imaging filters in MgF2 are lower comparedto the imaging devices in KDP, TeO2, Tl3AsSe3, etc.,due to its low value of birefringence. Nevertheless,our imaging experiments demonstrated that good op-tical quality spectral images can be obtained by usingMgF2 AOTFs. The choice of a crystal cut with theacoustic wave propagation direction in the �11�0�plane with a tilt angle of greater than 8° but less thanor equal to 19.5° improves the angular aperture andspectral resolution of the filter with wide-angle dif-fraction. In the case of the acoustic propagation along

Fig. 6. Block diagram of the imaging experimental setup usingUV light.

Fig. 7. Filtered images in the UV region of the spectrum at 250,285, 330, and 385 nm.


the direction with a tilt angle equal to 19.5°, close tooptimal diffraction geometry is obtained. It is pre-dicted that the spectral resolution and the angularaperture of filters in the optimal case may be im-proved by a factor of 2.5 as compared to the filtersexamined in our present investigation. Due to thesmall angular apertures these filters may be bestsuited in nonimaging applications (i.e., spectrome-ters) and in some imaging applications in the vacuumUV region due to the lack of a better AO material atthe present time.

References1. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).2. J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).3. A. Goutzoulis and D. Pape, Design and Fabrication of Acousto-

Optic Devices (Marcel Dekker, 1994).4. N. Gupta, “Acousto-Optics,” in Optical Engineer’s Desk Refer-

ence, W. Wolfe, ed. (Optical Society of America, 2003).5. I. C. Chang, “Tunable acousto-optic filters: an overview,” in

Acousto-Optics: Device Development�Instrumentation�Appli-cations, J. B. Houston, ed., Proc. SPIE 90, 12–22 (1976).

6. S. R. Gilleskie and J. W. Carnahan, “Ultraviolet acousto-optictunable filter wavelength selection for inductively coupledplasma atom emission spectrometry,” Appl. Spectrosc. 55,730–738 (2001).

7. V. B. Voloshinov and N. Gupta, “Tunable acousto-optic filtersfor monitoring of atmospheric ozone,” in Instrumentation forAir Pollution and Global Atmospheric Monitoring, J. O.Jensen, ed., Proc. SPIE 4574, 162–173 (2002).

8. G. C. Tang, J. T. Chen, A. Katz, E. J. Celmer, R. W. Krumm,and R. R. Alfano, “Ultraviolet visible acousto-optic tunablespectroscopic imager for medical diagnostics,” J. Biomed. Opt.3, 80–84 (1998).

9. D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acous-tooptic imaging spectropolarimetry for remote sensing,” Appl.Opt. 33, 7412–7424 (1994).

10. L. J. Cheng, J. C. Mahone, G. F. Reyes, and H. R. Suiter,“Target detection using an AOTF hyperspectral imager,” inOptical Pattern Recognition V, D. P. Casasent and D. Chao,eds., Proc. SPIE 2237, 251–258 (1994).

11. N. Gupta and V. Voloshinov, “Hyperspectral imager, from ul-

traviolet to visible, with a KDP acousto-optic tunable filter,”Appl. Opt. 43, 2752–2759 (2004).

12. V. Voloshinov and N. Gupta, “Ultraviolet-visible imagingacousto-optic tunable filters in KDP,” Appl. Opt. 43, 3901–3909 (2004).

13. N. Gupta and V. Voloshinov, “Tunable ultraviolet hyperspec-tral imagers,” in Proceedings of the Conference on Lasers andElectro-Optics and Quantum Electronics and Laser Science(Optical Society of America, 2003), paper CTHYG 6.

14. V. B. Voloshinov, “Imaging experiments based on applicationof non-collinear tunable acousto-optic filters,” in 27th AIPRWorkshop: Advances in Computer-Assisted Recognition, R. J.Mericsko, ed., Proc. SPIE 3584, 116–127 (1998).

15. I. C. Chang and J. Xu, “High performance AOTFs for theultraviolet,” Proceedings of the IEEE Ultrasonics Symposium(Institute of Electrical and Electronic Engineering, 1998), pp.1289–1292.

16. P. Katzka and I. C. Chang, “Non-collinear acousto-optic filterfor the ultraviolet,” in Infrared Technology for Target Detectionand Classification, P. M. Narendra, ed., Proc. SPIE 202, 26–32(1979).

17. I. B. Belikov, V. B. Voloshinov, A. B. Kasyanov, and V. N.Parygin, “Acousto-optic spectral filtration of radiation in theultraviolet region,” Sov. Tech. Phys. Lett. 16, 645–650 (1989).

18. V. B. Voloshinov, “Acousto-optic filtration of electromagneticradiation in the ultraviolet region,” in Physical Acoustics: Fun-damentals and Applications, O. Leroy and M. Breazeale, eds.(Plenum, 1991), pp. 665–670.

19. N. Gupta and V. Voloshinov, “Hyperspectral imaging perfor-mance of TeO2 AOTF in UV region,” Opt. Lett. 30, 985–987(2005).

20. A. Duncanson and R. Stevenson, “Some properties of MgF2

crystal from the melt,” Proc. R. Phys. Soc., London 72, 1001–1006 (1958).

21. P. Laporte, J. Subtil, M. Courbon, and M. Bon, “Vacuum-ultraviolet refractive index of LiF and MgF2 in the tempera-ture range 80–300 K,” J. Opt. Soc. Am. 73, 1062–1069 (1983).

22. H. Kandil, J. Greiner, A. Ayers, and J. Smith, “Single crystalelastic constants of MgF2 in the temperature range4.2–300 K,” J. Appl. Phys. 52, 759–765 (1981).

23. V. B. Voloshinov, “Anisotropic light diffraction on ultrasoundin tellurium dioxide single crystal,” Ultrasound 31, 333–338(1993).


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Investigation of magnesium fluoride crystals for imaging acousto-optic tunable filter applications