Interaction of nonlocal incoherent spatial solitons

We investigate numerically the interaction of nonlocal incoherent spatial solitons in strongly nonlocal kerr media based on the coherent density approach. Numerical simulations show that the incoherent soliton position is very similar to the case of coherent soliton, and show that the incoherence plays an important role in the soliton interaction, while the role of other parameters such as the phase difference, the separation, the extent of nonlocality and the input power play in the interaction is very similar to the case of nonlocal coherent soliton. Some interesting numerical examples are presented to illustrate their interaction behavior further. Pertinent physics features are addressed.     

Phase effects at second harmonic generation in the layer media

An analysis is made of quasi-phase-matched interaction at second harmonic generation in a regular domain structure with accounts for losses and change of phases of all the interacting waves. The constant-intensity approximation of basic radiation is applied for this purpose, not to regular domain structure as a whole, but to each separately taken domain. It allows to carry out more strict analysis of quasi-synchronous interaction during the frequency conversion to the polydomain consisting of n layers, forming “grating” periods of modulation of the nonlinear susceptibility. With this, the values of complex amplitudes of basic radiation and second harmonic wave at the outlet of each domain are entrance values of the corresponding complex amplitudes to the following domain. The analytical expression is given for the case of n domains and the factors limiting the efficiency of the process of frequency conversion are analyzed. In the constant-intensity approximation, in contrast to the constant field approximation, the coherent length of domain depends on pump intensity. With increasing pump intensity the optimum length decreases. In a regular domain structure at frequency conversion from a layer to a layer, intensity of the basic radiation changes. Also the optimum length of domains at which conversion efficiency is maximal therefore changes. Thus, it is possible to obtain the high values of conversion frequency at the outlet of a regular domain structure by choice of optimum parameters of a task (length of domains, phase mismatch, pump intensity), as well as using the layers-domains of high quality.     

Interaction of Nonlocal Incoherent White-Light Solitons

The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.     

Nonlinear refraction in photo-induced anisotropic states of azo-dye containing materials

The optical anisotropic states in the azo-dye Disperse Red 13 doped poly(methyl methacrylate) polymeric film are induced by polarized light and the nonlinear refractive index in these states are studied by the Z-scan technique. It is found that the n₂ of the sample can be controlled by changing both the polarization direction and the intensity of the 514 nm light. Photo-induced isomerization and reorientation of azo chromophores in polymer matrices are used to explain the results.     

Wavefront study in a Gaussian beam passed through a nonlinear optical medium

We present a numerical model to study the wavefront of a Gaussian laser beam propagated through a nonlinear Kerr media. The model is based on the Gaussian decomposition method. The interaction between a laser beam and a self-focusing or self-defocusing media is discussed from the viewpoint of wavefront distortion. The method is useful for simulation of the wavefront of the beam next to the sample. We also compare our results with those obtained from z-scan method. There is a quite good agreement between data from z-scan method and our results.     

Photorefractive mutually pumped phase conjugation with partially coherent beams

We investigate the mutually pumped phase-conjugation process in photorefractive media with partially coherent pump beams. We consider the effects of transmission, reflection, and 2k-reflection gratings as well as the depletion of both pump beams. The theoretical results can be employed to qualitatively explain the experimental observations.     

Incoherent solitons in strongly nonlocal media: The coherent density theory

We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum θ₀ as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic harmonic oscillation.     

Optical beams in lossy non-local Kerr media

It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions.     

Nonlinear optical and optical power limiting studies on a new thiophene-based conjugated polymer in solution and solid PMMA matrix

An experimental investigation of the third-order nonlinear optical properties of new poly{2-{5-[3,4-ditetradecyloxy-5-(1,3,4-oxadiazol-2-yl)thiophen-2-yl]-1,3,4-oxadiazol-2-yl}pyridine} (P) in tetrahydrofuran (THF) solution and in solid poly(methylmethacrylate) (PMMA) matrix, by Z-scan technique is reported. The Z-scan traces reveal that the composite films exhibit large negative nonlinear refractive index of the order 10⁻¹⁰ esu. The excited-state absorption cross-section was found to be larger than the ground-state absorption indicating that the operating nonlinear process is reverse saturable absorption (RSA). The new polymer P exhibits good optical power limiting properties in the nanosecond regime in solution and as well in solid PMMA matrix.     

β-BaB2O4 deep UV monolithic walk-off compensating tandem

The generation of watt-level cw narrow-linewidth sources at specific deep-UV wavelengths corresponding to atomic cooling transitions usually employs external cavity-enhanced second-harmonic generation (SHG) of moderate-power visible lasers in birefringent materials. Among the oxo-borate materials, barium borate (β-BaB₂O₄ or BBO) combines the highest UV band edge and largest nonlinearity but suffers from large walk-off angles that limits the nonlinear interaction length. Alternative quasi-phase-matched (QPM) ferroelectrics are hardly suited for cavity-enhanced operation due to their much larger UV absorption and associated photo-refractive and thermal lensing effects, in addition to the difficult fabrication of fine-pitch domain gratings for short UV coherence lengths. In this work, we investigate an alternative approach to cw deep-UV generation by employing the low-loss BBO in a monolithic walk-off compensating structure [J.-J. Zondy, Ch. Bonnin, D. Lupinski, J. Opt. Soc. Am. B 20 (2003) 1675] to simultaneously enhance the effective nonlinear coefficient while minimizing the UV beam ellipticity under tight focusing. As a preliminary step to cavity-enhanced operation, and in order to apprehend the design difficulties stemming from the extremely low acceptance angle of BBO, we investigate and analyze the single-pass performance of a L_c = 8 mm monolithic walk-off compensating structure made of 2 optically-contacted BBO plates cut for type-I critically phase-matched SHG of a cw λ = 570.4 nm dye laser. As compared with a bulk crystal of identical length, a sharp UV efficiency enhancement factor of 1.65 has been evidenced with the tandem structure, but at ∼−1 nm from the targeted fundamental wavelength, highlighting the sensitivity of this technique when applied to a highly birefringent material such as BBO. Solutions to angle cut residual errors are identified so as to match accurately more complex periodic-tandem structure performance to any target UV wavelength, opening the prospect for high-power, good beam quality deep-UV cw laser sources for atom cooling and trapping.     

Mirrorless coherent oscillation due to vectorial four-wave mixing in LiNbO3

Mirrorless coherent oscillation in a four-wave mixing arrangement with two phase-conjugate counterpropagating pump waves is studied in a LiNbO₃:Fe crystal. Oscillation waves are observed within a wide, but limited angular window where the gain factor takes its maximum value. The spatial structure and the intensities of particular oscillating components vary continuously in time.     

Metallic nonlinear magnetooptical nonreciprocal isolator

In advanced optical fiber communication systems where reflection light might cause degradation of the signal quality, optical waveguide isolators play an important role. The effect of a metal layer with negative permittivity on the behavior of nonlinear-magnetooptic isolator is studied. The isolator consists of metal film, nonlinear cladding, and magnetooptic substrate. It is found that difference between forward and backward propagation for TM₀ mode increases with increasing the absolute value of the tuning parameter which is the permittivity of the metal film, ?_f. It is also found that the maximum cut-off thickness of the isolator occurs in self-defocusing case around η = 0.65 and at the highest assumed value of ?_f = −8. These results are helpful in fabricating an isolator with high performance.     

Quantum phase properties of the field in a two-photon micromaser

In this paper, we study the quantum phase properties of the field in a two-photon micromaser, including the effects of the finite detuning of the intermediate level. For initial coherent state of the cavity field and atoms initially in their excited state multipeak phase structure appears which eventually leads to the randomization of the cavity field phase. However, the approach towards the randomization depends upon the detuning. If the atoms are injected in a coherent superposition of their upper and lower atomic states then the phase distribution evolves into two-peak structure. For initial thermal state and atoms in polarized state, cavity field acquires some phase. We also consider the effect of finite Q of the cavity, random injection of the atoms and fluctuations in the interaction time.     

Self-deflection of partially spatially incoherent beams and solitons in photovoltaic photorefractive crystals

By considering the effect of background light and diffusion, the self-deflection process of partially spatially incoherent (PSIC) beams and photovoltaic (PV) solitons in open-circuit PV photorefractive crystals has been investigated by employing numerical method and the perturbation technique, respectively. The results from the two approaches are in good agreement: the center of PSIC PV solitons moves on a parabolic trajectory, which is similar to those of coherent solitons. In addition, we also discuss that the dependence of self-deflection effect on the coherent parameter θ₀ and find it is slight relative to θ₀ for quasi-soliton but decreases monotonously with θ₀ for PSIC beam.     

The role of the longitudinal component of the electric field vector in two-wave mixing in photorefractive BaTiO3

It is shown that for waves incident with a polarisation in the plane of the grating the component of the electric field in the direction of propagation must be included in the calculations. Coupled differential equations for both the transverse and longitudinal components are derived for wave interaction in photorefractive BaTiO₃. Analytic solutions for the electric field of the signal wave are obtained under the assumption that the pump wave is undepleted. For the parameters considered the longitudinal component is shown to be negligible.     

Quantum non-demolition measurement of photon number using weak nonlinearities

We propose an alternative method for the quantum non-demolition measurement of photon numbers wherein weak cross-Kerr nonlinearities are to be used. The usual approach to quantum non-demolition measurements of quantum number involves encoding the photon number, through a cross-Kerr interaction, into a phase shift of a probe coherent state which is then detected through balanced homodyning. Weak nonlinearities produce small phase shifts which are difficult to detect and distinguish. In the method we propose, unbalanced homodyning acts as a displacement operator on the probe beam coherent state such that the cross-Kerr interaction encodes the photon number into the amplitude of a new coherent state. The value of the photon number can be determined by inefficient photon counting on the new coherent state. Our proposed method requires fewer resources than does the usual approach.     

High optical gain using counterpropagating beams in iron and terbium-doped photorefractive lithium niobate

Exceptionally high values of photorefractive gain coefficient of up to 100 cm^-1 have been observed in Fe-doped and Fe/Tb-doped crystals of photorefractive lithium niobate. It is believed that these are the highest observed coefficients of any crystalline photorefractive medium. Accurate measurements of gain coefficient have been possible for the first time by using a specially cut triangular crystal which allows the use of short interaction lengths and the complete elimination of surface reflections by having the beams incident at Brewster’s angle. Experimental results are consistent with a simple model of photorefractive beam coupling up until the onset of noise which is observed to deplete the pump for interaction lengths longer than 1 mm. Received: 28 September 1998 / Revised version: 8 January 1999 / Published online: 31 March 1999     

Holographic scattering lines observed with photorefractive BaTiO3

We investigate holographic scattering processes in BaTiO₃ pumped by two coherent copropagating waves. Four lines are observed on a screen behind the sample. The experimental results are well described by a model taking into account parametric mixing of four copropagating waves and limitations of optically induced space charge fields because of the finite trap density.     

Z-scan measurements of optical nonlinearity in acid blue 29 dye

The third order nonlinear optical properties of acid blue 29 solutions have been studied using Z-scan technique. Experiments are performed using a CW He–Ne laser at 632.8 nm wavelength and 3 mW power. The linear absorption coefficient α₀, nonlinear absorption coefficient β, nonlinear refractive index n₂, Re χ³, and Im χ³ are measured at three different concentrations. Our results show that higher concentration gives better nonlinear optical properties. Also, it was found that there is an increasing trend in the value of the nonlinear refractive index n₂ as the concentration increases.     

Enhanced third harmonic reflection and diffraction in Silicon on Insulator photonic waveguides

Enhanced third harmonic (TH) generation from Silicon-On-Insulator (SOI) planar waveguides as well as SOI photonic crystal (PhC) slabs is studied in different angular configurations, both in the visible and infrared energy ranges. In the SOI planar waveguide, the multilayer structure causes the optical properties such as TH reflection to be different from those of bulk silicon samples. This behavior is well reproduced by calculations of TH reflectance.Measurements of third-harmonic reflection and diffraction from one-dimensional PhC slabs etched in the SOI waveguide are also reported. The angular positions of TH peaks at various diffraction orders agree well with those calculated from a nonlinear grating equation. Both reflection and diffraction processes contribute to enhanced TH generation efficiency in the PhC slabs.TH reflectance measurements performed on PhC slabs in the near infrared show a resonant interaction between the incident beam and the photonic structure, dependent on the angle of incidence. This leads to a nonlinear conversion efficiency which is strongly enhanced with respect to that of the SOI waveguide, due to the excitation of strong local fields associated with the presence of photonic modes in the PhC slab.