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  • Electrooptic sideband generation at 72 GHzR. Kallenbach, B. Scheumann, C. Zimmermann, D. Meschede, and T. W. Hnsch

    Citation: Applied Physics Letters 54, 1622 (1989); doi: 10.1063/1.101324 View online: http://dx.doi.org/10.1063/1.101324 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/54/17?ver=pdfcov Published by the AIP Publishing

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  • Electro~optic sideband generation at 72 GHz R. Kallenbach, B. Scheu mann, C. Zimmermann, D. Meschede, and T. W. Hansch Max-Planck-Institut fur Quantenoptik, D-8046 Garciling, Federal Republic of Germany (Received 9 December 1988; accepted for publication 23 February 1989) Sidebands are observed at 72 GHz off an optical carrier at 633 nm. The laser beam is phase modulated in a LiNb01 crystal which is exposed to a mm-wave field inside a Fabry-Perot resonator. Under optimum phase-matching conditions we obtain a modulation index of 5% derived from 200 m W microwave power. Phase matching is obtained by guiding the light beam on a zig-zag path under internal total reflections. For this unconventional type of phase matching, the optical wave fronts travel at twice the speed of the modulating wave along the resonator axis.

    We describe a novel type of electro-optic light modula-tor which we have used to generate optical sidehands 72 GHz off the carrier frequency of a 633 nm He-Ne laser. This modulation frequency is several times higher than previous-ly demonstrated with cw electro-optic modulators. I An elec-tro-optic crystal is placed as a resonant etalon in an open microwave Fabry-Perot resonator (Fig. 1), and the laser beam follows a zig-zag path inside the crystal under total internal reflections so that phase matching is achieved and transit time limitations are overcome. A rdated technique has been used by Kaminov et al. 2 to mix the 0.96 THz hydro-gen. cyanide laser with optical radi3.tion.

    We believe that this modulator can operate at any mi-crowave frequency from a few ten GHz up, limited only by the availability of mm-wave sources. The applicability of phase-modulated optical waves is hence extended signifi-cantly, for example, in high-resolution FM spectroscopy,3 for optical frequency synthesis;1 or also for optical commu-nications.

    Phase modulation of the HeNe laser is proportional to the electro-optic coefficientS r33 = 3 X 10- 11 m/V of the thin parallel-plate LiNbO, crystal with optical z axis parallel to the polarizations of both optical and microwave radiation. A Fabry-Perot cavity, which is formed by two 25-mm-diam ccpper mirrors of 100 mm radius at a separation of 3ii. mm = 12.6 mm, serves to enhance the microwave field strength. The resonator is driven by the 200 m W output of a reflex klystron. A Q of about 10 000 is measured for the empty cavity.

    The thickness of the wafer is chosen as 1 microwave-length, d = Ammlnmnt = O.S mm, for an index of refraction flmn' = 5.5. Insertion of the crystal reduces the Q factor to values between 100 and 2000 depending on its position. Therefore, the losses of the resonator are dominated by crys-tal absorption and almost all the power coupled into the resonator is delivered to the crystaL For small losses per single pass the microwave field amplitude ED is related to the power P absorbed in a crystal volume V through the imagi-nary part of the complex dielectric function cmm :

    P IV = AnEo fm(Emm )E~, (l) Outside the crystal, the field strength depends on the

    position of the crystal, however. The ratios are h~1Ut / E,n = 1 for crystal surfaces positioned at anti nodes of the microwave

    field, EpuJEill = nmrn = [Re(Emm)] 1/2 at nodes.6 The lat-ter case corresponds to the maximum total energy stored in the resonator and hence the maximum Q value. In our exper-iment the LiNb03 etdon is adjusted to this configuration since it is favored by the weak coupling of a dipole antenna 7 that allows some mechanical tunability of the coupling strength in our apparatus. Residual resonator reflection is about 20%, so that most of the incident microwave power is, in fact, used for the refractive index modulation.

    The node location of the crystal surfaces furthermore requires an optical path for which the projection of tile opti-cal phase velocity on the resonator axis (Fig. 2), c' = ccos ()/noPt (nOP1 = 2,2),istwicethemicrowavephase velocityemm = c/nmm as is explained in Fig. 3. The corre-sponding angle is e = 38, wen beyond the critical angle (270 at 633 nm) for the LiNb03 , and the laser beam undergoes 30 reflections on passing the 20 mm crystal length.

    After passing the laser beam through the LiNbO; eta-lon, it is analyzed by means of a monochromator with 10 GHz resolution. Symmetric sidebands are observed (Fig. 4) in phase with the mm-wave radiation, which is chopped at 300 Hz. From the sidehand to carrier intensity ratio, S / C = 2.5 X 10-" we estimate a modulation index b = 5%, where the phase-modulated sine wave is given by eo"t = eo sin r ult + {5 ( (3) sin !1t- 50]' and to is a time-depen-dent phase offset due to the total internal reflections.

    FIG, L Electro-optic modulator.

    I "electro -

    optic crystal

    1622 Appl. Phys. Lett 5

  • 'i ./td

    2j.3

    2j .2 Jd, ~(j : (,\ ; e ! 2H t cos S/nopl

    ~ Q!;ao

    2 x C/l'lmm 2j

    FIG. 2. Wave propagation in the LiNbO, crystal.

    The He-Ne laser heam is focused into the modulator crystal so that its beam waist has a spot size of 0.1 mm, corresponding to a Rayleigh range of 100 mm. The laser beam diameter remains thus well below AmnJ2 along the entire beam path so that the phase modulation across the beam is approximately uniform. The angular walk-off of the sidebands remains below 10-4 rad and is unimportant for the same reasons.

    For a theoretical estimateS of the modulation index 15, we can assume an infinitely long crystal because the trans-verse field distribution of the microwave with spot size 100 = 6 mm, E(y) = (Eol[ii)exp - (ylw() 2, is concentrat-ed in a volume small compared to the crystal length. The

    b

    c

    FIG. 3. Phase-matching conditions. Across the width of the crystal the mi-crowave amplitude is shown vs time. Positive lldds symholiz.e an increased index of refraction for the laser light, and the zig-zag lines show the propa-gation of an optical wave front experiencing maximum retardation. (a) For a crystal of width Am", and with antinodes at the surfaces, optimum phase matching is achieved for c' ~= Cnnn or e ~~ 66'. With nodes at the surfaces no net phase modulation is obtained for fI = 66'. Optimum phase matching is achieved in this case for c' .~c 2eo'", or {J ,~, 38'.

    1623 Appl. Phys. Lett., VoL 54, No.17, 24 April 19S9

    f ' , ,

    ~! ~~~~ L.----

  • The sensitivity of the method with respect to angle mis-match and crystal thickness variations is also given by Eq. (5), indicating a half-width of 1j = 3% for thickness varia-tions and of 88 = 10 for angle dctunings. These estimates show that the method is reasonably stable against technical im perfections.

    The modulation index can be increased by using a high-er microwave field strength or a longer interaction time 7",. Even a simple triple pass of the light beam would give an immediate ninefold enhancement of the sideband intensity. A modulation index of 10 or more may ultimately be possi-ble.

    We gratefully acknowledge lending of microwave equipment by M. Munich of the Institute for Plasmaphysics (lPP) at Garching, FRG. Crystals were polished by M. Os-wald, also at the IPP. L. Eft} manufactured the resonator mirrors.

    1624 Appl. Phys.lett., Vol. 54, No. 17,24 April 1989

    '1'. F. Gallagher, N. H. Tran, and J. P. Watjcn, AppJ. Opt. 25, 510 (1986). cI. P. Kaminov, T. J. Bridges, and M. A. Pollack, App!. Phys. Lett. 16,416 (1970); reprinted in, I. P. Kaminov, An Introduction to Electrooptic De-vices (Academic, New York, 1974).

    -'G. C. Bjorklund, Opt. Lett. 5,15 (1980). 4K. M. Evenson, O. W. Day, J. S. Wells, and L O. Mullen. App!. Phys. Lett. 211,133 (1972).

    'The rf value for the electro-optic coefficient is used here. To our knowledge il has not been measured for the very high frequencies employed in our experiment. The index of refraction is nearly constant for frequencies between 65 MHz and 7 THz. See Ref. I and L P. Kaminov and E. H. Turner, Froc. IEEE 54,1374 (1966).

    6A simple arugment explains this behavior: At an antinode the tangential electric field is continuous and hence the field strength inside and outside. At a node the tangential magnetic field is maximum and continuous; its amplitude lS related to the electric .field by the index of refraction, IHI = /liEI, from which the ratio of the electric field strengths inside and outside follows.

    7U. Harbarth, J. Kowalski, R. Neumann, S. Noehte, K. Scheffzek, and G. zu Putlitz, J. Phys. E 20,409 (1987).

    K A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

    Kallenbach et al. 1624

    This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:164.125.41.50 On: Thu, 10 Sep 2015 01:41:50