Self-trapping of weak optical beams in photorefractive materials

Intensity-independent self-trapping of optical beams in photorefractive crystals was found recently. But we show that due to the existence of dark conductivity in some photorefractive materials or coherent and non-coherent background irradiance, the self-trapping of weak optical beams in photorefractive materials, such as SBN, becomes intensity dependent. The threshold condition of the applied external de electric field for self-trapping is determined as function of the material parameters as well as the initial transverse sizes and relative intensities of the beams.     

半导体光折变介质中光束传输的自囚禁及周期调制

推导了光束在半导体光折变介质的光子晶格中演化的二能级形式, 给出了光束在其中传播时二能级方程的经典正则形式. 解析计算出了经典正则方程的不动点并对其稳定性作了分析, 计算出了拓扑结构变化的临界值. 根据二能级方程的经典正则形式做出了空间相图, 进一步分析了半导体光折变介质中光束传输的自囚禁现象, 发现有两种形式的自囚禁: 1)能级中的布居数差和相对相位都在平衡点附近振动; 2)能级中的布居数差在平衡点附近振动, 而相对相位单调变化. 分别从高频、低频、中频三个方面研究了外加周期调制对自囚禁的影响, 发现在高频调制中发生自囚禁现象的相变参数能够被周期场非常有效的调制, 使得光束在半导体光折变介质中传输时, 在非线性效应影响较小时也能够发生自囚禁. 关键词： 半导体光折变介质 自囚禁 二能级形式 周期调制     

Study of second harmonic generation by non-linear crystals with phase conjugation

We present the correction of the phase distortion which occurs during the second harmonic generation by non-linear crystals, such as KDP and KTP at high average power laser. This is due to the optical quality and thicknesses of the crystals which in turn influence the quality of the incident laser beam. This phase distortion is corrected by reflecting back the laser beam into the crystal using a phase conjugate mirror. It is found that the conversion efficiency of second harmonic generation without phase conjugation is more than that with phase conjugation. Far field pattern shows that the distortion of the laser beam can be corrected by using the phase conjugate mirror. Fidelity of the beam profile increases significantly with phase conjugation in the case of KDP crystal.     

Transmission behavior in a photorefractive polymer film

When a p-polarized beam propagates through a high-performance photorefractive polymer composite, poly dimethyl-4-(4^′-nitrophenylazo)benzene, its transmission behavior is influenced by three effects: the electroabsorption, the photorefractive coupling with the reflected beam from the rear surface, and the amplified scattering. From the measurements on the incidence angle dependence as well as the applied-electric-field dependence of the three effects, some conclusions are obtained. At a small incidence angle with a low applied electric field, both the amplified scattering and the electroabsorption are small whereas the coupling between the incident beam and the reflected beam plays a principal role. At a large incidence angle or with a high poling electric field, the transmission is influenced mainly by the amplified scattering and the electroabsorption. A poling electric field asymmetric loss to the amplification scattering is also observed. Received: 18 November 1998 / Revised version: 10 February 1999 / Published online: 12 April 1999     

The effect of a high external electric field on a photorefractive ring phase conjugator

It is shown that a high external electric field often used to enhance the efficiency of photorefractive beam coupling and to decrease the photorefractive response time, may cause mode switching in photorefractive ring phase conjugator leading to a significant drop in the phase conjugate reflectivity.     

Photorefractive mode coupling between two unidirectional ring oscillators

We consider the coupling between two photorefractive unidirectional ring resonators. The first resonator is driven by an external laser beam via photorefractive two-wave mixing. The internal oscillating beam is then employed to drive the second ring resonator via the same mechanism. Closed form solutions for the oscillation intensities and frequencies are given, and their numerical results are presented and discussed.     

Nonlinearity of a response in photorefractive crystals with a square-wave applied field

The space-charge-field formation in a photorefractive crystal illuminated by a one-dimensional light pattern is studied when an alternating square-wave electric field is applied to the crystal. We derive the general nonlinear equation for the time-averaged distribution of the space-charge field and employ the simplified versions of this equation to analyze the space-charge-field formation in the case of a Gaussian beam and interference light pattern. The borders of the applicability of simplified equations and analytic expressions to describe a self-action of light beams and the large modulation effects under two-beam coupling are estimated from the numerical calculations. Received: 18 November 1998 / Revised version: 26 January 1999 / Published online: 12 April 1999     

Detection of higher nonlinear harmonics of volume photorefractive gratings in reflection geometry

A comprehensive technique has been used to detect diffraction from the second and the third nonlinear spatial harmonic components, along with the fundamental harmonic of volume photorefractive gratings recorded in a channel waveguide in a LiNbO₃ substrate. For the first time to our knowledge, efficient diffraction from the higher spatial harmonic components of a photorefractive grating has been detected in reflection geometry. The dependence of a Bragg wavelength shift on the order of nonlinearity is also reported.     

Instabilities in coupled photorefractive ring cavities and self-pumped phase conjugators

We investigate the temporal instabilities of mode intensities in two coupled unidirectional photorefractive ring resonators. The first resonator is driven by an external laser beam via photorefractive two-wave mixing. The internal oscillating beam is then employed to drive the second ring resonator. The second ring resonator provides a nonlinear loss mechanism for the coupled system. Complete spatial-temporal equations for describing the coupled system are derived and mean-field approximation is employed to simplify the transient analysis. The results of linear stability analysis indicate that the coupled system exhibits instability in the off-state and steady-state operation. The instability is explained in terms of competition between nonlinear gain and loss. The results are presented and discussed.Part II on Numerical Results will be published in a forthcoming issue of Applied Physics B     

Femtosecond third-harmonic generation:. self-phase matching through a transient. Kerr grating and the way to ultrafast computing

The third harmonic of 810-nm 100-fs pulses at 130 μJ is generated very efficiently when ultrashort pulses from two noncollinear beams interfere in an optical medium to create an instantaneous transient grating via the optical Kerr effect. The grating couples two pathways for third-harmonic generation, each taking two photons from one beam and one photon from the other beam, respectively. The coupling enables self-phase matching in the complete process, resulting in a conversion efficiency of ≈3%. Scattering an independent beam at the transient grating confirms a lifetime limited by the pulse duration, with a reaction on the order of one optical cycle. Using the second harmonic of a Ti-sapphire laser at 405 nm, it is shown that the generation of the transient Kerr grating is a general feature, requiring less than 20 μJ/pulse. By introducing a third femtosecond beam we are able to emulate various digital logic units with femtosecond response. Received: 16 October 2001 / Published online: 6 June 2002     

Photorefractive two-wave mixing in the presence of an incoherent beam

We present the numerical results of the photorefractive two-wave mixing in the presence of an incoherent beam by considering the influence of the ratios of the intensities and the light-excitation cross sections of the incoherent beam to the coherent beams on the space-charge field and the effective coupling coefficient. The results show that the incoherent beam can control the intensity of the coherent beams effectively. The experimental results agree with the theory well. One application is demonstrated to obtain the positive and negative coherent replicas of an incoherent image. The coherent images have a resolution of 80.6 line pairs/mm. Received: 2 March 1999 / Revised version: 26 July 1999 / Published online: 20 October 1999     

Electric-field enhancement of beam coupling in Sn2P2S6

The influence of an external field on photorefractive recording in Sn₂P₂S₆ (SPS) crystals is studied. A large gain factor of more then 15 cm^-1 is achieved for a grating spacing of 12 μm at λ=0.9 μm. For an applied field exceeding ±200 V/cm a switching of the beam coupling direction is detected, exhibiting a pronounced hysteresis. Received: 25 October 2000 / Revised version: 18 January 2001 / Published online: 21 March 2001     

Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm

We demonstrate experimentally the operation of an adaptive two-wave mixing interferometer with no field applied to a photorefractive crystal in which the quadrature condition is introduced by an external π/2 phase step. To achieve high signal to noise ratio the counter-propagating geometry for grating recording is used with a CdTe:Ge crystal, ensuring effective recording of reflection holograms. It is demonstrated that the interferometer with a photorefractive semiconductor crystal provides good sensitivity without the adverse effects that are normally associated with an applied field.     

Orientational photorefractive effects observed in poly(vinyl alcohol)/liquid crystal composites

60 ) as a photoconductive sensitizer under an applied dc field. Orientational photorefractivity was demonstrated by observing Raman–Nath diffraction beams with an external dc field. The photorefractive gratings were partially memorized even in the absence of the applied dc field. Received: 12 January 1998/Revised version: 2 February 1998     

Dynamical tunneling of counterpropagating beams mediated by an optical photonic lattice

In a numerical study, we demonstrate the dynamical tunneling (DT) of two counterpropagating (CP) mutually incoherent beams in a two-dimensional photonic lattice, recorded in a photorefractive (PR) crystal. The beams are launched head-on from the opposite faces of a PR crystal in which an optically induced two-dimensional photonic lattice is established. The DT is caused by the spontaneous symmetry breaking of CP beams, which is induced by the nonlinear interaction between the beams and is mediated by the lattice. To observe DT we found no need to introduce a specific external tilt potential, as is done in the conventional Zener tunneling; the tilting is provided by the repulsive interaction between the beams, which causes ejection of one beam from the launching region of the other. As the beams propagate, they move laterally in real time, causing the leakage of radiation from the first Brillouin zone to the second and higher zones. In the process the beams also tunnel from the first photonic band zone to the higher zones, which by definition is the DT.     

Holographic solitons in photorefractive dissipative systems

A new kind of holographic soliton is proposed for a photorefractive dissipative system consisting of a biased photorefractive crystal and a strong pump beam with a uniform spatial distribution in both transverse dimensions. The self-trapping beam in the system can evolve into a spatial soliton when it couples coherently with the pump beam by two-wave mixing. Unlike the holographic solitons recently proposed by Cohen et al. [Opt. Lett. 27, 2031 (2002)], the most unique features of the present solitons are that they have a fixed amplitude and width that are determined completely by the system parameters and that their existence conditions are independent of the polarity of the bias field. Numerical simulations show that these solitons are stable relative to small perturbations.     

Modulational instability of optical beams in photovoltaic and photorefractive media due to two-photon photorefractive effect under open circuit condition

The modulational instability of broad optical beams in two-photon photorefractive (PR) photovoltaic materials under open circuit conditions has been investigated. Under linear stability framework, the one dimensional modulational instability growth rate has been estimated by considering the space charge field. Gain of the instability is shown to exist only when the photovoltaic fields orients in the same direction with respect to the optical c-axis of the medium. It is found that the behavior of the gain spectrum is different in low and high power regions. We have found by numerical simulations that the evolution of the soliton induced by the modulational instability at low photovoltaic field show the dynamical behaviors similar to those of the localized beam as the initial profile. However, it has been shown that increasing photovoltaic fields produce traveling, breathing, and mutually interacting solitons.     

Adaptive correlation filters for speckle patterns in photorefractive crystals

The experimental study of the in-plain vibration of the speckle pattern in photorefractive GaP and BTO crystals using the polarization self-modulation effect are presented. The simple model based on the propagation of the Gaussian beam through the crystal with recorded space-charge field is proposed to explain main features of the experiment. It is shown that these results allow designing a linear sensor of the speckle-pattern displacement in an effective way. The optical system is very simple and does not include any reference or readout beam. The sensitivity of this system is the same as that of an interferometer. Received: 27 November 1998 / Revised version: 26 January 1999 / Published online: 12 April 1999     

Second-harmonic generated by self-squeezed light in isotropic medium. The role of light intensity-dependent effects and molecular-statistical structure

An isotropic medium with electrically removed centre of symmetry in which a fundamental wave at frequency generates the second harmonic at 2 is considered. The two waves give rise to self-acting effects modifying the refractive indices at and/or 2 (selfinduced ellipse rotation, optical Kerr effect). For this physical situation, an effective interaction Hamiltonian is introduced involving nonlinear coupling parameters, discussed versus the dc electric field and temperature as well as the density, concentration and molecular structure of the medium. The solutions of the respective quantum equations for the field operators at and 2 permit, in particular, the calculation of the variances for a novel process of second-harmonic generation by light, self-squeezed in an isotropic medium. It is shown that squeezing in the out-of-phase component of the second harmonic beam follows, with some delay, after self-squeezing in the in-phase component of the fundamental beam.Sponsored by the Polish Academy of Sciences, Project CPBP 01.12     

Solitonlike beam propagation along light-induced singularity of space charge in fast photorefractive media

We investigate light beam propagation in a fast photorefractive medium placed in an alternating electric ac field to enhance the nonlinear response. It is shown that the joint action of the optical and material nonlinearities leads to formation of a narrow singularity of the light-induced space charge at the intensity maximum and to self-trapping of the light energy near the corresponding discontinuity of the index profile. Owing to the strong saturation of the material nonlinearity, the trapped beam propagates over long distances with only a weak loss of its power.