Backward Pump Beam Research Articles

Exact time-periodic solutions and nonlinear polarization attraction

We find exact time-periodic solutions to the nonlinear equations that describe the polarization interaction of two intense counter-propagating beams in a randomly birefringent fiber, expressed in terms of the forward and backward beam Stokes vectors. The overlap function between the forward signal beam and the backward pump beam has an exact expression in terms of an elliptic integral and varies periodically along the fiber. For specific parameters, this overlap function takes the form of a soliton, with an almost constant value at all points on the fiber except for a pulse located at the soliton center. In the soliton configuration, the system displays polarization attraction for any beam intensities and arbitrary fiber lengths. We show how to solve the vector equations for the forward and backward beam Stokes vectors, using a shooting method to implement the endpoint boundary conditions, and plot the trajectories on the Poincare sphere.

Demonstration of CNOT gate with Laguerre Gaussian beams via four-wave mixing in atom vapor.

We present an experimental study of controlled-NOT (CNOT) gate through four-wave mixing (FWM) process in a Rubidium vapor cell. A degenerate FWM process in a two level atomic system is directly excited by a single diode laser, where backward pump beam and probe beam are Laguerre Gaussian mode. By means of photons carrying orbital angular momentum, we demonstrate the ability to realize CNOT gate with topological charges transformation in this nonlinear process. The fidelity of CNOT gate for a superposition state with different topological charge reaches about 97% in our experiment.

Time Character of Nanosecond Phase-Conjugate Signals in an Erythrosin B-Doped Polymer Film

The generating mechanisms of nanosecond phase-conjugate (PC) signal and the time delay of a backward pump beam, at which the maximum diffraction efficiency of the PC signal can be obtained, are investigated using degenerate four-wave mixing in an erythrosin B-doped polyvinyl alcohol film. The influence of the coherence time of a pulse source on the measurement of the mechanisms of the PC signal generation is also examined. The population gratings due to saturable absorption of dye molecules mainly contribute to the PC signal generation rather than thermal gratings. The maximum diffraction efficiency is obtained at zero time delay of the backward pump beam, at which the coherence peak is observed.

Efficient phase conjugation via two-photon coherence in an optically dense crystal

We demonstrate efficient phase conjugation in an inhomogeneously broadened rare-earth doped crystal using electromagnetically induced transparency. The observed frequency conversion efficiency of the phase conjugate in energy over a backward pump beam is as high as 10% with \ensuremath{\sim}1/4 of maximal Raman coherence. This efficient phase conjugation has potential applications of nonlinear optical processes such as frequency up-conversion and Raman excited spin-echo optical memory.

Bistable phase-conjugate reflectivity controlled by a forward pump beam

One of the typical methods to generate the phase-conjugate beam is four-wave mixing with a photorefractive crystal. It is known that the phase-conjugate reflectivity shows the bistability in some cases. Analyzing the temporal property of four-wave mixing, we offer a new method to control the bistable phase-conjugate reflectivity, and we perform an experiment of the bistability control by the method. An equation to obtain the threshold value of the coupling strength for showing the bistability is derived by a steady-state analysis of four-wave mixing, and the temporal property of four-wave mixing is studied with two different initial conditions that are used for letting the phase-conjugate reflectivity R converge to an off state (R=0) or to an on state (R>0). The initial condition for the converging off state is that the forward pump beam is turned off throughout. The condition for the converging on state is that the forward pump beam is turned on in advance, and after enough time passes, it is turned off. In both conditions, the backward pump beam and the probe beam continue to illuminate throughout. Whereas both optical arrangements are equivalent after setting up these initial conditions, each phase-conjugate reflectivity converges to different stationary values, R=0 and R>0. Besides, an experiment is performed and we actually control the bistability by this method. Furthermore, the temporal and the spatial variation of the refractive-index grating in the photorefractive crystal is investigated, and the process of the bistability is explained.

Ultrafast relaxation times of metalloporphyrins by time-resolved degenerate four-wave mixing with incoherent light

We present experimental results on the measurement of the population-relaxation times of the excited states of some metalloporphyrins such as zinc meso-tetra-phenylporphyrin (ZnmTPP), zinc meso-tetra (p-methoxyphenyl) tetrabenzporphyrin (ZnmpTBP), tetratollylporphyrin (TTP), cobalt tetratollylporphyrin (CoTTP) and nickel tetratollylporphyrin (NiTTP) with time-resolved degenerate four-wave mixing with the incoherent emission of a nanosecond pumped-dye laser. The experiments are carried out in the counterpropagating geometry (k4=k1+k2-k3), where k1 and k2 are counterpropagating to one another and k3 is at angle θ (<90° with respect to k1). Excited-state and ground-state relaxation times are calculated based on the theoretical formalism developed by Hiromi Okamoto [J. Opt. Soc. Am. B, 10, 2353, 1993]. The signals are recorded by delaying the probe beam (k3) for different fixed delays of the backward pump beam (k2). We observe strong signal at a second peak owing to the coherence of beams k2 and k3 for samples exhibiting excited-state absorption and a narrow peak corresponding to the coherence of beams k1 and k3 for samples that do not exhibit excited-state or reverse-saturable absorption. The nonlinear absorption is studied with the Z-scan technique. From the experimental data, we estimate the relaxation times of excited states.

Detection of CN by degenerate four-wave mixing

The detection of CN, an important intermediate in the nitrogen oxidation chemistry of hydrocarbons, in the B2∑+ –X2∑+ electronic band by degenerate four-wave mixing is reported. The radical source consisted of a H2/O2/N2/C2H2/NO atmospheric-pressure premixed flame. We estimate a detection limit of 3 × 1013 CN molecules/cm3 and a rotational temperature of 920 K. A tilted backward pump beam degenerate four-wave mixing geometry is investigated, and results show an order-of-magnitude increase in the signal-to-noise ratio over the conventional counterpropagating pump beam geometry.

Phase-conjugation and self-oscillation with copropagating cross-polarized beams

We present the result of an experiment on optical phase conjugation made with a probe beam propagating in the same direction as the forward pump beam but having an orthogonal polarization. Using the difference of polarization, we separate the reflected beam from the backward pump beam. Is is shown that the amplitude of the reflected beam is the sum of two components, one proportional to the conjugate of the probe and one proportional to the amplitude of the probe. The experiment is done in sodium vapor and reflectivities larger than 350% have been observed near the D 1 transition. Weaker reflectivities due to a less efficient optical pumping are obtained near the D 2 line. We also describe the characteristics of the cw oscillation that appears between the Na cell and a mirror.

High-accuracy, high-reflectivity phase conjugation at 106 μm by four-wave mixing in photorefractive gallium arsenide

We have used a 20-kHz ac square-wave electric field to enhance the beam-coupling gain and the degenerate four-wave mixing reflectivity of photorefractive GaAs at 1.06 μm. The largest measured four-wave mixing reflectivity in the steady state was 15% at a grating period of 9 μm and an applied voltage of 3.2 kV across 0.4 cm. Theoretical results predict substantially higher reflectivity values for a field of 8 kV/cm; the origin of this discrepancy is thought to be space-charge effects that prevent us from obtaining the full field inside the crystal. We have also measured a transient reflectivity of 510% during the switch on of the backward pump beam. Finally, we have determined the accuracy of wave-front reversal through measurements of piston-error correction and conjugation fidelity.

A simple analytic approach to degenerate four-wave mixing by comparison with real-time holography

A simple analytic theory for degenerate four-wave mixing (DFWM) is presented. From the fundamental relationship between real-time holography and DFWM simple expressions for the DFWM signal are developed. The basic assumption in our approach is that the four waves are coupled only by the grating created by the forward-probe interference and that the intensities of the forward beam and the probe beam are not affected by the four-wave interaction. In general, this is only true when the backward pump beam intensity is much smaller than both the forward beam intensity and the probe beam intensity. However, within this restricted parameter range we obtain simple analytic expressions for the DFWM signal including the effects of linear losses in the nonlinear medium. For thin nonlinear media the signal intensity is determined by a squared Bessel-function of first order, and for thick nonlinear media the signal intensity is determined by a squared sine-function. The theory is restricted to small values of the signal reflectivity. Finally, we have investigated the DFWM signal from a CdS-sample with a Q -switched frequency doubled Nd:YAG laser. At a sample temperature of 375 K we obtain a third-order susceptibility of \chi^{(3)} = 4.4 \cdot 10^{-7} ESU. We apply the theory to these experiments.

Theory of phase-conjugation by four-wave mixing in a waveguide

We show that one can generate the time-reversed replica of an monochromatic, image-bearing beam by coupling it into a waveguide where it interacts with counterpropagating multimode waves of the same frequency. The nonlinear electric polarization density that is third order in the propagating electric fields in the guide medium generates the replica by the process of four-wave mixing. We show also that the input beam can serve simultaneously as its own pump beam. If the frequency ν of the backward pump beam is different from the frequency ω to of the input beam, then the to the input is generated at the entrance plane to the guide, and this radiates a replica of the input field, magnified by \omega/\nu , back along the input beam. The pump power required per resolution element to phase-conjugate a beam in a waveguide is orders-of-magnitude less than for the corresponding process with free (unguided) waves interacting in an infinite medium. Unlike the requirements for free waves, the pump waves do not need to be well aligned or single-mode to produce high fidelity in the replication process. Neither does the guiding structure or enclosed medium have to be precise in dimension or uniformity; the main requirements on the guiding structure being that it not attenuate the waves too heavily. Formulas are derived for the replication efficiency and fidelity in the various guided configurations. We also show how the process can be used: 1) to make a narrowband optical filter with a large acceptance solid angle; 2) to perform image-frequency conversion; 3) to obtain Raman and two-photon spectra of small samples; and 4) to achieve broadband optical amplification. We examine the conditions under which phase conjugation and these applications can be performed at several frequencies simultaneously. Limitations placed by the power-dependence of propagation constants are derived.