Mixing Gain Research Articles

Dynamic solutions of the photorefractive two-wave coupling at large modulation depths

An analytical solution of the dynamic coupled wave equations as a function of time in a photorefractive medium at large modulation depths is presented by using the empirically corrected function introduced by Kawk et al. [Optics Commun. 105 (1994) 353–358]. The expiression for the response time of two-wave coupling at large modulation depths is also presented. It shows that the response time is dependent on both the material parameters and experimental parameters. The dynamic two-wave mixing gain for large modulation index is developed. The theoretical analysis shows good agreement with the experimental results in the doped KNSBN crystal for the whole range of modulation m.

Perturbative analytical solution of two-wave coupling in photorefractive materials at large modulation depth

We apply directly a perturbative expansion to the hopping model of Feinberg. The first three harmonics of the space-charge field are presented, considering the contributions from the higher-order terms at large modulation depth. The dependence of the harmonics on spatial frequency, modulation depth and applied field strength are discussed. An analytical solution of the two-wave coupling equations is given in this case. The mixing gain γ is also discussed.

Influence of zinc on the photorefractive behaviour of Cd 1− xZn xTe:V

Recent studies of the photorefractive characteristics of CdTe:V compound have demonstrated this material to provide high two wave mixing gain in the 1–1.5 μm wavelength range. However due to its high figure of merit, larger two wave mixing gain could be expected. We present some results about the influence of the zinc content in these materials which could explain such a reduction. In particular, we show that crystals can be ranked in two different classes following their photorefractive properties. This classification is essentially based on the absence (or existence) of a resonant intensity-temperature effect with the crystals with zinc (respectively without zinc). We also present some physico-chemical parameters obtained on these crystals by secondary ionic mass spectroscopy (SIMS) and electron paramagnetic resonance (EPR) experiments. The difference of photorefractive properties between the two classes would imply an evolution in the V 2+ V 3+ ratio which is not compatible with the EPR results. As to clarify this problem we will propose a new model of two deep levels in the gap of the material.

Design of multiwavelength optical communication systems based on an integrated waveguide amplifier compensator

We theoretically analyze the performance of longhaul multichannel optical communication systems based on an integrated WDM power level compensator. By placing an array of Er/sup 3+/-Yb/sup 3+/ co-doped silica waveguides in parallel between a demultiplexer/multiplexer pair and preceeding it by an EDFA, we demonstrate the possibility of transmitting eight unequally spaced WDM channels over long distances, without electronic regenerators and using span lengths as high as 50 km. This technique allows substantial reduction of both four-wave mixing crosstalk and gain peaking.

Numerical analysis of photorefractive InP:Fe at large fringe contrast

A finite difference method is used to analyze the behavior of photorefractive InP:Fe at high fringe contrast under externally applied field. The evolution with increasing fringe contrast m of the electron-hole resonance, which occurs in the presence of a continuous field, is studied. As m increases, the field tends to concentrate in a small zone and reaches very large local values. On the other hand, the resonance loses height and widens. For illuminations closed to the resonance, the two-wave mixing gain presents the usual aspect of a decreasing function of m. However, for other illuminations, it can be larger at a small pump-to-probe ratio than at a large one. When an ac field technique is used, nonlinearities drastically reduce the two-wave mixing gain, even at small fringe contrast. As m increases, the space-charge field tends to take a square shape. Even for rather small m values (0.1), the gain presents a maximum near the dc field resonant illumination, which is not predicted by the linear theory. Finally, when drift is the dominant process for the grating formation, the applied field limits the amplitude of the space-charge field, independently of an optimized dopant concentration which allows high gain in the small m approximation.

Two-wave mixing and fanning effect in Bi<inline-formula><sub><roman>12</roman></sub></inline-formula>TiO<inline-formula><sub><roman>20</roman></sub></inline-formula> under an alternating electric field

Numerical calculation of the two-wave mixing gain factor for arbitrary orientation of the holographic grating vector using the coupled wave theory developed for optically active electro-optic crystal enabling pump-beam depletion is presented. Two-dimensional angular dependencies of the gain factor are measured in Bi₁₂TiO₂₀ photorefractive crystal under an alternating external electric field using the fanning effect. It is found experimentally that the angular ditribution of fanning light is independent of the polarization state of the pump beam. This fact could not be explained by the existing theory.

Nearly-degenerate frequency technique for simultaneous measurement of n(2) and α(2), and four-wave mixing gain coefficients in waveguides

We describe an experimental technique that allows the simultaneous measurement of the nonlinear refractive index n (2) and the nonlinear absorption coefficient α (2) in waveguides. With minor modifications in the experimental setup, the four-wave mixing gain coefficient can also be measured. Measurements are demonstrated in AlGaAs waveguides.

Photorefractive two-wave mixing in semiconductors of the 4-bar3m space group in general spatial orientation.

The photorefractive two-wave mixing gain coefficient \ensuremath{\Gamma} of GaAs:Cr and InP:Fe, cut with different crystallographic orientations, was determined using a cw Nd:YAG (neodymium doped yttrium aluminum garnet) laser at 1064 nm. The polarization and orientation dependence of the gain coefficient \ensuremath{\Gamma} are calculated from the pertinent interaction matrix elements. Results are discussed with respect to the contactless determination of crystallographic parameters via the photorefractive effect.

Very high-gain two-wave mixing in BaTiO_3 with a self-bent pump beam

We propose a two-wave mixing interaction between a self-bent pump beam and a signal beam in a BaTiO3 crystal. This new configuration exhibits two-wave mixing gain values as high as Gsat = 1.5 × 105, corresponding to an enhancement of 40× in comparison with a conventional two-wave mixing geometry. Application to coherent image amplification with such a high gain combined with a very good signal-to-noise ratio is demonstrated.

Low-noise preamplifier for multistage photorefractive image amplification

We present a two-beam coupling configuration in photorefractive BaTiO(3) that provides a low-noise amplification of the signal to be detected. A two-wave mixing gain of 100 is reached, in conjunction with very low beam fanning background in the signal direction. The extensions of this configuration to photorefractive heterodyne detection and to multistage image amplif ication are theoretically and experimentally studied.

Theoretical study on effects of stimulated photorefractive backscattering in self-pumped phase conjugators

Effects of stimulated photorefractive backscattering (SPB) interactions in both stimulated photorefractive backscattering and four-wave mixing (SPB-FWM) and total internal reflection (TIR) self-pumped phase conjugators have been analyzed theoretically. SPB interactions in the four-wave mixing regions are neglected. Calculations show that the operational threshold and the phase conjugation reflectivity of both phase conjugators are very sensitive to the backscattering two-wave mixing gain coefficient of the crystals. From these results the mechanism transition phenomenon of a self-pumped phase conjugator between SPB-FWM and TIR can be explained if the backscattering gain coefficient of the crystal varies with doping concentration or with wavelength.

Two-Wave Mixing in Resonant Photorefractive GaAs/AlGaAs Semi-insulating Multiple Quantum Wells

We have observed the two-wave mixing of the photorefractive GaAs/AlGaAs semi-insulating multiple quantum wells fabricated by film lift-off approach and protonimplanting technique. Under the non-optimized condition, we have obtained the two-wave mixing gain larger than 180 cm-1 at wavelength near 784 nm for a field of 10 kV/cm. Energy transfer is also observed when the applied field is perpendicular to the grating vector.

Theory of the photorefractive effect for multiple-quantum-well structures in perpendicular field ref lection grating geometry

The theory of photorefractive grating formation in a semi-insulating GaAs/AlGaAs multiple-quantum-well structure (MQWS) with an electric field applied across the layers and for counterpropagating writing beams is presented. The gain and the response time demonstrate a resonant behavior with respect to variations in both the applied field and the light’s wavelength. For a semi-insulating MQWS such an interaction geometry could provide the highest two-wave mixing gain, as much as 104 cm−1, which exceeds the linear absorption.

Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO 3 crystal

The intensity-dependent two-wave mixing gain at large modulation depth is measured in a BaTiO 3 crystal. We derive an expression of nonlinear space-charge field from Kukhtarev's materials equations for single charge carrier without assuming the linear recombination of free charge carriers. The experimental results are interpreted by taking into account both an empirical correction function at large modulation depth [Refregier et al., J. Appl. Phys. 58 (1985) 45] and intensity-dependent factor of the space-charge field, which is caused by nonlinear recombinations of free charge carriers.

High-gain nondegenerate two-wave mixing in Cr:YAlO_3

A gain of 22 times was obtained by nondegenerate two-wave mixing in Cr:YAlO(3). To our knowledge, this is the largest cw two-wave mixing gain obtained in a bulk solid-state nonphotorefractive material. The measured gain appears to be limited by beam breakup that is due to spatial nonuniformities in the nonlinear refractive-index change that are the result of inhomogeneities in the crystal. Predictions based on our data indicate that gain in excess of 200 times should be possible in Cr:YAlO(3) if a homogeneous crystal can be obtained.

Photorefractive effect applied to flatten Gaussian beam profiles of near infrared lasers

The resonant behaviour of the two-wave mixing gain as a function of the intensity in photorefractive InP:Fe crystals is applied to flatten the Gaussian profiles of a beam emitted by a Nd:YAG laser at λ=1.06 μm. This can be extended efficiently to other wavelengths in the spectral range where InP:Fe is photosensitive.

Characterization of photorefractive CdTe:V: high two-wave mixing gain with an optimum low-frequency periodic external electric field

We present two-wave mixing results obtained with CdTe:V photorefractive crystals under an external dc or low-frequency square-shaped periodic electric field. The majority photorefractive carriers are holes at 1.32 and 1.54 μm, whereas electrons dominate slightly at 1.048 μm. At this wavelength an intensity-dependent resonant gain enhancement is observed in the presence of a dc field. The effective trap densities are near 1015 cm−3. The highest gains (to as high as 11 cm−1 for a field amplitude of 15 kV/cm at 1.32 μm) are obtained with a square-shaped periodic field at an optimum frequency F0. The dependence of F0 on the different experimental parameters is presented. A two-level model in which the secondary level has a thermal emission rate much larger than the principal one qualitatively describes this nonstandard frequency behavior.

Photorefractive effect in InP:Fe dominated by holes at room temperature: influence of the indirect transitions

Iron-ion concentrations have been determined from measurements of the photoinduced-grating erasure times. We checked the accuracy of this method by performing two-wave mixing experiments at λ = 1.32 μm without an applied field. After verifying the fit of the extended single-defect model with indirect transitions and the two-wave mixing gain data at λ = 1.06 μm, we conclude that the indirect transitions involving the excited state of Fe2+ can induce a reduction of the photorefractive effect in InP:Fe when the dominant photocarriers are holes at room temperature.

Self-pumped phase conjugation of KLTN crystal

Potassium lithium tantalate niobate (KLTN) crystals were grown using the flux pulling method. The two-wave mixing gain coefficient of a KLTN:Fe crystal was measured to be 2.7 cm −1. Using this crystal, a “cat” self-pumped phase conjugator has been demonstrated, for the first time. A reflectivity of 14% and a response time of the phase conjugator of 3 s at 3 W/cm 2 was measured using a frequency-doubled Nd:YAG laser.

Second harmonic generation and two-wave mixing in ion-implanted KNbO3waveguides

Abstract We report on nonlinear optical and photorefractive effects in KNbO3 waveguides produced by He+ ion implantation. Optical frequency doubling from the near infrared into the blue spectral range has been investigated in two configurations: (i) guided mode phase-matched and (ii) Cerenkov-type second harmonic generation where the second harmonic is radiated into the substrate. Up to 12 mW of blue light is generated with -200 mW of fundamental power in a channel waveguide of 1.1 cm length. Photorefractive two-wave mixing experiments have been performed in Fe-doped KNbO3 planar waveguides at visible and near infrared wavelengths. We measured two-wave mixing gain coefficients of up to 8 cm−1 at 514 nm and typical response times of about 40 μ at a power level of 10 mW.