Effect Of Pump Depletion Research Articles

Degenerate four-wave mixing in Kerr media in the presence of nonlinear refraction, pump depletion and linear absorption

We present a theoretical study of degenerate four-wave mixing in Kerr media when the effects of nonlinear refraction, pump depletion and linear absorption are included. The phase conjugate reflectivity and the transmissions of the probe and the pump beams are obtained simultaneously using a method that does not require the determination of the first integrals of the coupled nonlinear differential equations. It is therefore applicable to the study of many other related phenomena. Another advantage of using this method is that the effect of linear absorption can be incorporated in the theory in a straightforward manner.

Effect of Strong Pump Depletion on Two-beam Coupling in Photorefractive BaTiO3at 442 nm

Abstract Photorefractive BaTiO3 crystal illuminated at 442 nm gives a large initial scattering level, which leads to strong pump depletion into beam fanning. Studies on the time development of beam fanning show a temporal shift of the fanned beam maximum towards the c-axis direction. The effect on the signal beam amplification of the strong pump depletion into beam fanning has been investigated, revealing different temporal development of the amplified signal for various cross-angles. Our observations on beam fanning in the presence and in the absence of a signal reveal that there is appreciable coupling between the fanned beam and the signal.

Quantum fluctuations and diffraction in stimulated Raman scattering

We investigate the statistics of Stokes emissions in stimulated Raman scattering. By using a full dynamical model that includes both pump depletion and diffraction effects we present numerical results for pulse energy statistics. We find that multi-mode operation along the transverse coordinate significantly alters energy distributions in both high and low Fresnel number limits and that average Stokes pulse energies are very sensitive to Fresnel number variations in the non-linear regime.

Two- and four-wave mixing with saturable absorption and gain

An exact solution to a model of two- and four-wave mixing in photorefractive media with saturable gain and absorption is presented. Pump depletion effects are accounted for, and the procedure for matching two-point boundary conditions is given. Possibilities of multistable solutions are investigated, and procedures on how to deal with such situations are outlined. It is found that the energy transfer between waves is less effective in the nonsaturated regime as compared to the saturated regime. It is also established that the nonsaturated system is more stable than the saturated under the same conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Theory of dressed-state lasers. III. Pump-depletion effects.

We present further developments in the theory of dressed-state lasers, i.e., lasers that operate on inverted transitions between the dressed states of a coupled atom-field system. We take into account the quantum character of the driving field, and consider the effect of its depletion. We derive effective Hamiltonians appropriate for the analysis of both one- and two-photon dressed-state lasers, and then discuss the stability and statistics of such lasers. We show that pump-depletion effects tend to reduce the degree of squeezing found in dressed-state-laser output while simultaneously introducing small squeezing effects into the depleted pump field.

Theory of a synchronously pumped optical parametric oscillator in steady-state operation

A single nonlinear differential equation describing a cw synchronously pumped, singly resonant optical parametric oscillator is derived. This equation accounts for the important effects associated with this kind of ultrashort tunable-pulse generation, including the effects of phase mismatch, pulse walk-off, group-velocity dispersion, cavity-length detuning, and pump depletion. The various effects are investigated in detail through numerical solutions. The formalism is general enough that the results obtained are applicable to a wide variety of systems.

Angle dependence of the PCR in the simultaneous operation of reflection and transmission gratings in photorefractives

We consider phase conjugation via degenerate four-wave mixing (DFWM) in photorefractive crystals when reflection and transmission gratings are simultaneously operative. The role of the angle of incidence on the phase conjugate reflectivity (PCR) in the two-grating operation has been studied numerically. We include the effects of pump depletion, absorption and unequal average (linear) refractive index in different regions. Results are compared with the case when only the pure reflection grating is present. It is found that there exists a beneficial influence of the angle of incidence on the PCR in the behaviour of two-grating operation.

Growth and stabilization of a laser ripple on laser beam in a collisionless unmagnetized plasma

In this paper we have studied the growth and stabilization of a radially symmetric ripple superimposed on a laser beam in a collisionless unmagnetized plasma. The saturation of the growth rate is due to pump depletion effect. On acoount of the nonuniform intensity distribution of the main beam, a d.c. component of the ponderomotive force becomes finite and it redistributes the carriers in the plasma in a plane transverse to the beam propagation. We have set up and solved the wave equations for main beam and ripple by using the WKB and paraxial ray approximations. As the ripple grows in the plasma, it draws energy from the background laser field. It is seen that the relative intensity of the laser ripple becomes critical due to the counteracting behaviour of the self-focusing and depletion of the main beam.

Investigations of optical feedback used to enhance stimulated scattering

The technique of using optical feedback to enhance the phase-conjugation process of stimulated Brillouin scattering is experimentally and theoretically investigated. Several feedback arrangements are experimentally studied and demonstrate the ability to reduce significantly the threshold power requirement, enhance the efficiency, and improve the phase-conjugate fidelity of the Brillouin process. Steady-state analytical solutions for the interactions, including the effects of laser pump depletion, are derived. Numerical modeling is used to introduce the more complete transient effects. Good agreement between the experimental results using a pulsed Nd:YAG laser system and the numerical simulations is achieved. The results are applicable, with modification, to other forms of stimulated scattering and also to self-pumped photoreflection.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phase conjugation via unequal amplitude multiple gratings in photorefractives: A simple shooting method for numerical solution

We present a simple shooting method to obtain numerical solutions of the nonlinear coupled-wave equations for degenerate four-wave mixing in photorefractive crystals when four different types of the index gratings of unequal amplitudes are responsible for phase-conjugation. Our analysis includes the effects of pump depletion and absorption in the medium. Intensities of the four beams, both inside and at the output surface, are obtained as a function of four unequal coupling strengths and absorption coefficient. Intensity of the generated phase-conjugate beam is shown as a function of both the small and wide ranges of signal beam intensity. It is found that the multigrating operation with a careful choice of coupling constants and their combinations may improve the phase-conjugate wave generation. Also the presence of absorption reduces the phase-conjugate intensity more significantly when all the gratings are operative than when a single grating is allowed. Numerical results obtained from the computer calculations are presented in graphical form.

Effects of cross-phase modulation and pump depletion on Stokes pulse dynamics in stimulated Raman scattering

An investigation is made of the effects of cross-phase modulation and pump depletion on pulse dynamics in the stimulated Raman scattering process. It is shown that cross-phase modulation may significantly affect the frequency chirp of the pulse even to the point of reversing the sign of the chirp. As a consequence, solitonlike pulse compression using Raman amplification may become impossible with the Stokes pulse in the anomalous-dispersion regime. The chirp reversion effect is weakened by pulse walk-off, which, if strong enough, retains the frequency characteristics of the inherent self-phase modulation.

Four-photon parametric mixing in optical fibers: effect of pump depletion

The analytical solutions to differential equations governing nonlinear four-photon mixing in optical fibers are presented for the general case of depleted pump power. The expressions reduce to those derived earlier with the assumption of nondepleted pump power. We find that the maximum power available for conversion from the pump waves to the signal waves resulting from a third-order nonlinearity depends on the index mismatch and that the index mismatch required for achieving maximum possible power transfer is a function of the frequency shift.

Solitonlike Stokes pulses in stimulated Raman scattering

An analytical solution for compressed solitonlike Stokes pulses created by Raman amplification is presented in the limit where the relative velocity between a wide pump pulse and the Stokes pulse is large and pump-depletion effects can be neglected. The concomitant deviations from the classical soliton shape are shown to be harmless for optical communication purposes. In the opposite limit, where pump depletion becomes important, cross-phase modulation between the pump and the Stokes pulse destroys the conditions for compression during Raman amplification.

Limiting factors in an inverse free electron laser

The main problems connected with the optimum design of an inverse free electron laser are discussed. Particular attention has been paid to the diffraction and pump depletion effects.

Laser Acceleration of Particles with the Plasma Vector-Soliton

The closed, energy conserving system of electromagnetic-plasma equations describing the classical beat wave accelerator are shown to lead to an intrinsic limit on the acceleration efficiency due to the pump depletion effect producing an intense trail of plasma waves. We propose and analyze with theory and simulations a wakeless accelerating structure composed of a nonlinear vector soliton. The solitary wave speed u o f the vector soliton can be greater than the group velocity of the electromagnetic pulse as determined by the laser intensity a0 = e E0/m ω0 c through the soliton dispersion relation. Combining the triple soliton structure with a weak plasma density depression of radius (c/ωp) (ω0/ωp)1/2, we compute an accelerating structure with Ep &lt;̰ me ωp c/e moving at the speed of light and limited in length only by the conditions set by beam loading or plasma nonuniformities.

Analytical theory of four-wave stimulated Brillouin scattering in the saturation regime

An analytical solution of the enhanced stimulated Brillouin scattering arranged in a four-wave mixing configuration is presented. The theory includes the effect of pump depletion and is able to demonstrate the reflectivity, efficiency, and field variations in the saturation regime.

Non-frequency-shifted phase conjugation by Brillouin-enhanced four-wave mixing

We present a theoretical treatment of four-wave mixing (FWM) in a Brillouin-active medium for the case in which the pump waves differ in frequency by approximately twice the Brillouin frequency shift of the medium and in which the probe-wave frequency is approximately the arithmetic mean of the frequencies of the two pump waves. Under these conditions, the conjugate wave produced by the FWM process has the desirable property of being at the same frequency as the probe. We derive the coupled amplitude equations describing this interaction. We solve these equations analytically in the limit of negligible pump depletion and find that large phase conjugate reflectivities are readily achievable. The coupled amplitude equations are solved numerically for the general case, and it is found that large power transfer from the pumps to the output wave is possible. The output wave is shown to be a nearly perfect phase conjugate of the probe wave, even far into the regime where pump depletion effects are important. Our formalism predicts the existence of a parametric instability in the propagation of the pump waves, but good performance is predicted before the onset of this instability.

Theory of modulational instability in optical fibers

The theory of modulational instability is presented which takes into account the nonlinear terms neglected in the usual linearized theory. When the pump depletion is introduced, the theory predicts the threshold behavior of the phenomenon due to the counteracting effect of pump depletion on the perturbation growth, in accordance with the recent experimental observations of Tai et al.

Pump-depletion effects in noncollinear degenerate four-wave mixing in Kerr media

This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.

Exact solution to the stationary holographic four-wave mixing in photorefractive crystals

An exact solution to the stationary holographic degenerate four-wave mixing in both transmission and reflection geometry for photorefractive media is obtained. The effects of pump depletion and light absorption in the non-linear dynamic medium are rigorously taken into account. The case of the transmission geometry is treated in more detail, with an emphasis on the energy transfer. The numerical steps in the procedure are reduced to the solution of one simple first-order differential equation, or are absent altogether for the case of no absorption.