光致折射晶体中高速调制光束传输和放大的理论研究

本文首次对高速调制光束在先致折射晶体中的耦合进行了理论研究,指出利用光致折射晶体中的双光束耦合可以实现高速调制光束的信息转换和放大,并为实验所证实.     

Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals

The amplification of the input signal beam in two-wave mixing experiments with photorefractive Bi₁₂SiO₂₀ crystals is achieved when an additional phase shift is established between the photoinduced index modulation (phase volume hologram) and the incident fringe pattern. This stationary phase shift is introduced by either moving the crystal or the interference fringes at a constant speed. The transferred intensity is measured versus the applied electric field, fringe spacing and crystal velocity. The crystallographic orientation and the relative displacement with respect to the applied electric field polarity determine the amplitude of the energy transfer. For the first time in this crystal, signal beam amplification is reached for an applied field E₀ > 8 kV cm^?1 and a crystal or fringe displacement speed around 5 μm s^?1 at the green line (λ = 514 nm) of an argon laser.     

Frequency detuning dependence of oscillation condition for a semilinear photorefractive optical resonator in a photorefractive material with reflection gratings

Frequency detuning dependence of four-beam coupling in a photorefractive crystal pumped with two counter-propagating waves for a semilinear coherent optical resonator on the oscillation conditions has been analyzed in the case of non-degenerate-wave mixing under the slowly varying amplitude approximation method. Self oscillation can be achieved when the gain arising from the four-beam coupling is large enough to overcome the cavity loss. The effects of frequency detuning (i.e., non-degeneracy), dielectric constant and photoconductivity of the photorefractive materials on the performance of the semilinear photorefractive coherent resonator with the reflection grating configuration have also been studied in detail. The phase-conjugate reflectivity of the pumped crystal and oscillation intensity has been calculated for different input pump beam intensity ratio, intensity reflectivity of the conventional mirrors, degenerate energy coupling strength of the interacting beams. It has been found that for the higher value of the photoconductivity σ_p(>2.0 pS/cm) of photorefractive crystal, the semilinear resonator can oscillate at almost any frequency detuning (Ω) of the oscillation beam with respect to the fixed frequency of the pump waves whereas for the lower value of photoconductivity σ_p(<0.1 pS/cm) oscillation occurs only when the frequency detuning is limited to small region around Ω = 0. But reverse of the case is found for dielectric constant (?), pump intensity ratio (p) and conventional mirror reflectivity (R).     

Highly efficient hologram enhancement in Bi12TiO20 fibre-type crystal

Experimental results for two-wave mixing experiments in a single Bi₁₂TiO₂₀ fibre-type crystal at a wavelength of 632.8 nm under transverse a.c. electric field are reported. An exponential gain factor =4.7 cm^-1, which is much higher than the absorption coefficient (0.6 cm^-1), is obtained. It is observed that the signal beam enhancement is in fact signal beam depletion for spatial frequencies higher than F _B, which is determined by fibre geometry. An unusually strong dependence of response time on the recording beams intensities ratio reflects the nonlinearities of the multi-two-wave mixing process.     

高速振幅调制光束在光折变晶体中的耦合理论

通过简化Kukhtarev方程,给出了适于连续光和高速振幅调制光在光折变晶体中的耦合方程.同时,还讨论了简化耦合方程组的适用条件及对调制速度的限制因表.     

Crystal orientation dependence of the SNR for signal beam amplification in photorefractive BaTiO3

In signal beam amplification by two-beam coupling in BaTiO₃ photorefractive crystals, beam fanning in the direction of the amplified signal reduces the signal-to-noise ratio (SNR). The dependence of the SNR and the signal beam gain on the crystal orientation are analysed using a HeNe laser. It is found that orientating the crystal for maximum gain gives poor signal-to-noise ratio. A compromise has to be made between the SNR and high gain for optimum signal amplification.     

Comparative Study of the Signal-to-Noise Ratio and Gain in Photorefractive Materials

We calculate the dependence of the signal-to-noise ratio and gain on the angle α between the pump and signal beams and the beam ratio β in Cu-doped potassium-sodium-strontium-barium niobate (Cu:KNSBN) crystal and compare them with the experimental results available in the literature. We find good qualitative agreement between the calculated and experimental results. Also we study variations of SNR and gain with α and β in BaTiO₃ crystal. Experimental data for this crystal are not available.     

Dynamics of refractive-index changes and two-beam coupling in resonant media

The dynamics of light-induced change in the refractive index of a resonant medium are examined. For illumination with weak fields, the two relevant relaxation times are T ₁, the population lifetime and T ₂, the dipole-dephasing time. The response time of the index change is determined by the slower relaxation time of the medium which is usually the time T ₁ taken by the excited system to relax back to its thermal equilibrium value. Illumination with two beams of the same frequency that intersect within the medium leads to the formation of a volume grating in the medium that is spatially local. Hence there is no exchange of energy between the beams that write the grating, each beam merely reducing the absorption experienced by the other beam. Illumination with a moving, spatially periodic intensity pattern leads to gain for one beam and additional absorption for the other beam as they propagate through the medium. A complete set of coupled equations describing the intensities and phases of the beams undergoing non-degenerate two-wave mixing in the resonant media is derived using third-order perturbation theory, and the solutions are studied numerically. In particular, the two-beam coupling constant for intensity is shown to depend on the frequency difference between the two beams and on the pressure-induced collisional relaxations in the system.     

Effect of photoconductivity and dielectric constant of the photorefractive materials on two-beam coupling gain and phase-shifts for a single unidirectional photorefractive ring resonator

Photoconductive dependence of two-beam coupling between the pump beam and the signal beam in photorefractive materials have been analyzed in case of non-degenerate wave mixing under the undepleted pump approximation method. During the two-wave mixing in photorefractive materials, steady state amplification of the signal beam and oscillation characteristics of a single unidirectional ring resonator has been studied. The domination of the two-beam coupling gain over the combined absorption and resonator losses such as Fresnel reflections from the crystal and imperfect mirrors builds up unidirectional oscillation. The buildup of such an oscillation leads to a saturation of the gain, which can be explained in terms of the photorefractive phase-shift. The existence of this phase-shift between the photorefractive index grating and the illumination intensity pattern, which is of characteristic of the photorefractive effect, leads to an energy transfer between the two beams. For a single unidirectional ring resonators, the effects of photoconductivity of the materials, two-beam energy coupling coefficient, dielectric constant, crystal thickness, and material's absorption coefficient on amplification of the two-beam coupling gain and photorefractive phase-shifts of the signal beam have also been studied in detail. It has been found that amplification of the signal beam and phase-shift can be enhanced by taking the photorefractive crystal having higher photoconductivity and lower dielectric constant, which improves performance of the resonators.     

高速调幅光束的光折变两波耦合的理论研究

对高速调幅光束的光折变两波耦合进行了理论研究，给出了复耦合系数为任意值时两波耦合方程的解析解，讨论了耦合系数对高速调幅光束的光折变两波耦合的影响。     

Magneto-elastic properties of Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> (TGG)

The temperature dependence of the elastic constants in Tb₃Ga₅O₁₂ was measured and analysed with a simple crystal field model. The magneto-elastic coupling constants have been deduced from this experiment. The coupling constant g_Γ5, related to the c₄₄ mode, is anomalously large. These coupling constants are important for the interpretation of the phonon Hall effect.     

Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals. Application to dynamic interferometry

The polarization properties of the volume gratings in photorefractive B₁₂SiO₂₀ crystals permit to increase the contrast and signal to noise ratio in the image plane of a large size vibrating object structure. The experiment is based on the nearly degenerate two wave mixing of a pump beam with a low intensity signal beam due to the object structure (moving grating recording with an externally applied field in the 110 crystallographic direction). For a correct orientation of the incident recording beam polarizations, the pump beam emerging from the crystal is linearly polarized, while the signal, after two beam coupling is elliptically polarized. The selective attenuation of the direct pump and scattered beams is obtained with a polarizer. Improved contrasts in the interferogram plane of the vibrating object are demonstrated.     

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d₁, diameters of outer core holes d₂ and hole to hole pitch Λ on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.     

Dependence of gain and phase-shift on crystal parameters and pump intensity in unidirectional photorefractive ring resonators

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material’s cavity length (crystal length) and modulation ratio have also been studied.      

Theory of Intensity Dependent Two Wave Mixing with High Speed Amplitude Modulated Beams in Photorefractive Crystal

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Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient (α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (ΔΓ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around ΔΓ=0). But reverse of the case is found for energy coupling coefficient (γ₀).     

Modeling the power of an optical parametric generator by discrete mode summation

An analytical expression for calculating the signal output power of an optical parametric generator (OPG) configuration was developed. The model is based on Heisenberg equations in space and radiation mode theory. A simple analytical expression can be obtained by assuming that all modes within the gain bandwidth of the nonlinear crystal have the same gain and the same interaction length. Another derivation considers the gain and interaction length of each individual mode. The model predictions are in excellent agreement with the measured signal power of OPGs based on 25- and 35-mm periodically poled LiNbO₃ crystal (with effective quadratic nonlinearity of ∼14.5 pm/V) and 47-mm periodically poled LiTaO₃ crystal (with effective quadratic nonlinearity of ∼9 pm/V). In addition, a comparison was made between the summation over discrete modes approach and the traditional approach of continuous integration over the beam parameters and pump frequency. We have found that the first approach, which is developed in this paper, predicts more accurately the output power of the OPG.     

Two-wave mixing and energy transfer in BaTiO3 application to laser beamsteering

Energy transfer between the two recording beams in a BaTiO₃ photorefractive crystal is analyzed as a function of the following parameters: incident beams ratio, spatial frequency, pump beam intensity. Exponential gain coefficients Γ ≈ 20 cm^-1 are reached for optimized holographic recording conditions. Application of the energy transfer to a new method of laser beam deflection is proposed.     

Photorefractive surface waves in a thin Bi12TiO20 crystal

A theoretical model considering total internal reflections of fanned beams from the side crystal surfaces and their coupling with the pump beam is proposed. The interaction of these beams results in the light intensity redistribution and in the generation of the photorefractive surface wave. An experimental observation of the light intensity self-concentration near the surface of a thin photorefractive Bi₁₂TiO₂₀ crystal is reported. It results in an acceleration of the photorefractive energy exchange process.     

Study on Optimum Incident Angles of Cross Polarized Four-Wave Mixing with a Photorefractive Crystal

We consider the optimum incident angles of cross polarized four-wave mixing with a photorefractive crystal. First, the phase matching angles are obtained for two operation modes: one in which the writing beams are ordinary rays and the reading beam is an extraordinary ray, we call this Mode 1. The other in which the writing beams are extraordinary rays and the reading beam is an ordinary ray, Mode 2. Next, practicable ranges of the incident angles are calculated considering of the total internal reflection of the phase conjugate beam in cases where the two writing beams illuminate the same surface of the BaTiO₃ crystal and where they illuminate the neighboring right-angled surfaces, respectively. Then, the coupling coefficient is determined as a function of the incident angle, and the optimum incident angles for effective beam interaction in Mode 1 and Mode 2 are estimated.