RAPID COMMUNICATIONS This section was established to reduce the lead time for the pub­lication of Letters containing new, significant material in rapidly advancing areas of optics judged compelling in their timeliness. The author of such a Letter should have his manuscript reviewed by an OSA Fellow who has similar technical interests and is not a member of the author's institution. The Letter should then be submitted to the Editor, accompanied by a LETTER OF ENDORSF-

Controlling the self-frequency shift and intensity of oscillations with photorefractive crystals

Shmuel Sternklar, Shimon Weiss, and Baruch Fischer Technion—Israel Institute of Technology, Department of Electrical Engineering, Haifa 32000, Israel. Received 6 July 1985. Sponsored by A. A. Friesem, Weizmann Institute of Science. 0003-6935/85/193121-02$02.00/0. © 1985 Optical Society of America. In a previous Letter1 we described a new type of optical

interferometry based on photorefractive four-wave mixing in a ring cavity and its use as a new optical gyroscope. We showed that frequency detuning of the oscillating beams re­sults from a nonreciprocal phase in the ring and depends on the optical loss in the ring, the beam intensities, and the effi­ciency of the mixing crystal. In that study, the effect of an applied dc electric field on the crystal was not explicitly ac­counted for. Here we report on the means for controlling the frequency shift and intensity of the oscillating beams using an applied electric field and an application as an optical fre­quency tuner. This field modulates the coupling constant γ of the mixing crystal and renders it complex. In this case, the oscillating beams interact with a moving grating which implies a frequency detuning of the beams.

The basic configuration for the ring passive phase conju-gator (PPC) with the addition of an electric field in the mixing crystal is shown in Fig. 1. We make use of the equations which describe the ring PPC operation1-2 and incorporate an applied electric field into the coupling constant γ, so that

7o is the value of the constant for the zero applied field1-2 and depends on material parameters and the specific four-wave mixing configuration of the crystal:2-3

E0 is the applied electric field parallel to the grating wave vector in the crystal. Eμ = σpd/(μkg), Ed = kBTkg/e, and Ep = epd/(εkg), where pd is the density of traps in the material, σ is the recombination coefficient of electrons or holes with traps, μ is electron or hole mobility, kB is Boltzmann's con­stant, T is temperature, e is the electron charge, ε is the per­mittivity of the material, kg is the grating's wave number, and τ0 is the zero field time response of the crystal, which is ap­proximately inversely proportional to the total power density of the beams.2 δ is the frequency detuning of beams 3 and 1 in the ring with respect to the input beam 2.4

MENT ΓROM THE OSΛ FELLOW (who in effect has served as the ref­eree and whose sponsorship will be indicated in the published Letter), A COMMITMENT FROM THE AUTHOR'S INSTITUTION TO PAY THE PUBLICATION CHARGES, and the signed COPYRIGHT TRANSFER AGREEMENT. The Letter will be published without further refereeing. The latest Directory of OSΛ Members, including Fellows, is published in the August 1985 issue of Optics News.

Fig. 1. Scheme of the ring PPC with applied electric field on the mixing crystal.

Inserting Eqs. (l)-(3) into Eq. (7) of Ref. 1 results in solu­tions for δ and the reflectivity of the device. In the nearly linearly operating region of this device,1 the following ex­pression is obtained for the detuning δ as a function of the nonreciprocal phase in the ring and applied electric field EQ in a crystal of width l:

where

The reflectivity of the ring PPC is taken to be equal to the intensity transmittance M of the ring in this oper­ating region (valid for large γ0l), and E0EP and E2

0 « Ed (Ed + EP). For the usual case of Ep » Ed, the slope of the δ vs E0 curve is dominated by Ed so that β ≈ 1/Ed.

As in the ring PPC gyroscope, the detuning is mea­sured by interfering the reflected beam 1 with the ref­erence beam at detector D. Note that for zero nonre­ciprocal phase, there is no dependence in the linear re­gion on γo of the crystal or M of the ring.

Since the counterpropagating beams in the ring are a phase-conjugate pair, a multimode fiber can be used as the ring cavity, and there is no inherent detuning in the crystal due to the reciprocal phase in the ring. However, an internal electric field such as that due to the photovoltaic effect will have a similar role on the grating dynamics in the crystal as that of an applied field. This property of self-detuning was observed in other passive devices with similar characteristics.4-6

Besides simple frequency detuning purposes an applied electric field can be used to shift the operating point of

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Fig. 2. Frequency detuning vs nonreciprocal phase in the ring for EQ = 0 (solid line), 0.1 kV/cm (lower dashed line), and -0.1 kV/cm

(upper dashed line). (γ0l) = 4 and M = 0.25.

this device when used as a gyroscope. In Fig. 2, (τ0δ) vs nonreciprocal phase in the ring is plotted in the region approximated by Eq. (4) for EQ = 0 and ±0.1 kV/cm. Here Ed = 1,Ep = 15, and Eμ = 25 (in units of kV/cm); these are typical values for the photorefractive crystal BaTiO3. This device is quite linear in this op­erating region. In this manner, any detuning due to internal fields or undesired nonreciprocal phase can be eliminated.

Other configurations with photorefractive materials such as the unidirectional or double-directional ring have similar detuning properies,1 the main differences being that the detuning also depends on reciprocal phases due to the optical path of the ring and a stricter coherence requirement.1

Finally, it should be noted that these same physical mechanisms will allow control of the optical power al­location (or modulation) between mixing beams using an applied electric field and the control of reflectivity or oscillation intensity in these devices with an applied optical phase in the light path.

To summarize: It has been shown that application of a dc electric field on the mixing crystal results in frequency detuning of the oscillating beams. Besides its use as an optical frequency tuner, it can shift the device's operating point when used as a gyroscope. The frequency tuning is also controllable by the ring's optical loss and the mixing crystal's efficiency and time con­stant. Controlled intensity modulation is also possible with an applied electric field on the crystal or optical phase in the light path.

This work was supported by the Technion VPR— Harris Fund.

References 1. B. Fischer and S. Sternklar, "New Optical Gyroscope Based on the

Ring Passive Phase Conjugator," Appl. Phys. Lett. 47, 1 (1985). 2. M. Cronin-Golomb, B. Fischer, J. 0. White, and A. Yariv, "Theory

and Applications of Four-Wave Mixing in Photorefractive Media," IEEE J. Quantum Electron. QE-20, 12 (1984).

3. M. Cronin-Golomb, "Light Nonlinearities in Four-Wave Mixing in Photorefractive Crystals," Ph.D. Thesis, Caltech (1983), un­published.

4. M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, and A. Yariv, "Nondegenerate Optical Oscillation in a Resonator formed by Two Phase Conjugate Mirrors," unpublished.

5. W. B. Whitten and J. M. Ramsey, "Self-scanning of a Dye Laser due to Feedback from a BaTiO3 Phase-Conjugate Reflector," Opt. Lett. 9, 44 (1984).

6. J. Feinberg and G. D. Bacher, "Self-Scanning of a Continuous-Wave Dye Laser Having a Phase-Conjugating Resonator Cavity," Opt. Lett. 9, 420 (1984).

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