Showing papers on "Four-wave mixing published in 1996"
TL;DR: In this article, the Born-Oppenheimer approximation is used to separate the motional part of the response functions from coordinate independent electronic hyperpolarizabilities, and the theory of these nonlinear optical processes is given for electronically nonresonant optical interactions up to fifth order in the electric field.
Abstract: Low‐frequency intermolecular dynamics in liquids is studied by ultrafast four‐ and six‐wave mixing. The theory of these nonlinear optical processes is given for electronically nonresonant optical interactions up to fifth order in the electric field. The Born–Oppenheimer approximation is used to separate the motional part of the response functions from coordinate independent electronic hyperpolarizabilities. A large variety of experiments, involving far‐infrared absorption, ordinary Rayleigh–Raman or hyper Rayleigh–Raman scattering is covered by this theory. The response in nonresonant six‐wave mixing comprises four dynamically different processes. It is shown that one of the terms contains information on the time scale(s) of intermolecular dynamics, that is not available from lower‐order nonresonant experiments. For instance, homogenous and inhomogeneous contributions to line broadening can be distinguished. The optical response of harmonic nuclear motion is calculated for nonlinear coordinate dependence of the polarizabilities. Results for level‐dependent and level‐independent damping of the motion are compared. It is shown that level‐dependent damping destroys the interference between different quantum mechanical pathways, yielding an extra contribution to the fifth‐order response that has not been discussed before. When two or more nuclear modes determine the optical response, their relative contributions to the four‐ and six‐wave mixing signals are in general different. These contributions are determined by the coordinate dependence of the electronic polarizability, which is usually not fully known. Model calculations are presented for the dynamic parameters of liquid CS2. The theory of this paper will be employed in Part II, to analyze experimental results on femtosecond four‐ and six‐wave mixing.
141 citations
TL;DR: In this article, a theoretical model for analyzing the propagation of densely spaced WDM optical signals through a cascade of erbium-doped fiber amplifiers and single-mode optical fibers with nonuniform chromatic dispersion is presented.
Abstract: A theoretical model is presented for analyzing the propagation of densely spaced WDM optical signals through a cascade of erbium-doped fiber amplifiers and single-mode optical fibers with nonuniform chromatic dispersion. By combining a numerical solution for the EDFA and an analytical expression for FWM components generated through the cascade, the model allows a realistic system analysis which includes gain peaking effect, amplified spontaneous emission accumulation and the effect of dispersion management on the four-wave mixing efficiency. The FWM power distribution at the end of the multi-amplifier transmission link is computed taking into account the phase relation between FWM light amplitudes generated within different sections of the link. The transmission of many WDM channels, evenly spaced around 1547.5 nm, has been analyzed for various dispersion management techniques and propagation distances. Numerical results point out the importance of such a model for a realistic design of WDM optical communication systems and networks. A proper choice of chromatic dispersion, amplifier characteristics, span length, input signal powers and wavelengths, combined with the use of gain equalizing filters, allows to maximize the transmission distance ensuring acceptable signal-to-noise ratio (SNR) and limited SNR variation among channels.
96 citations
TL;DR: A unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale is presented and the results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute.
Abstract: We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many-particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (-FWM) shows biexcitonic or bound excitonic contributions under various experimental conditions, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through. \textcopyright{} 1996 The American Physical Society.
92 citations
TL;DR: Numerical simulation shows that this growth in four-wave mixing fields from soliton-soliton collisions can be eliminated through the use of fiber whose dispersion is tapered, either continuously or in steps, in conformity with the fiber loss curve.
Abstract: In a soliton transmission system using lumped amplifiers, pseudo phase matching allows four-wave mixing fields from soliton–soliton collisions to grow uncontrollably and inflict severe penalties. Through numerical simulation, we show that this growth can be eliminated, or at least greatly reduced, through the use of fiber whose dispersion is tapered, either continuously or in steps, in conformity with the fiber loss curve.
91 citations
TL;DR: Polarization-independent all-optical time division demultiplexing is demonstrated in this article with < 0.5 dB polarisation dependency based on four-wave mixing in depolarized TE and TM modes in a traveling-wave semiconductor laser amplifier.
Abstract: Polarisation-independent all-optical time-division demultiplexing is demonstrated up to 200 Gbit/s with <0.5 dB polarisation dependency based on four-wave mixing in depolarised TE and TM modes in a travelling-wave semiconductor laser amplifier.
72 citations
TL;DR: The use of DFWM as an ultrafast time gate for the detection of ballistic light in optical mammography appears to hold great promise for improving the current state of the art.
Abstract: Optical imaging through turbid media is demonstrated using a degenerate four-wave mixing correlation time gate. An apparatus and method for detecting ballistic and/or snake light while rejecting unwanted diffusive light for imaging structures within highly scattering media are described. Degenerate four-wave mixing (DFWM) of a doubled YAG laser in rhodamine 590 is used to provide an ultrafast correlation time gate to discriminate against light that has undergone multiple scattering and therefore has lost memory of the structures within the scattering medium. Images have been obtained of a test cross-hair pattern through highly turbid suspensions of whole milk in water that are opaque to the naked eye, which demonstrates the utility of DFWM for imaging through turbid media. Use of DFWM as an ultrafast time gate for the detection of ballistic and/or snake light in optical mammography is discussed.
65 citations
07 Jun 1996
TL;DR: A novel technique based on four-wave mixing (FWM) in fibers is introduced, which has the potential for achieving unit conversion efficiency and involves only spectrum translation, not inversion or phase conjugation.
Abstract: Summary form only given. Wavelength conversion has been the subject of much research in recent years. Various methods have been studied with use of optical nonlinearities in either semiconductors or fibers. We introduce a novel technique based on four-wave mixing (FWM) in fibers, which has the potential for achieving unit conversion efficiency. It involves only spectrum translation, not inversion or phase conjugation. It is widely tunable and can, in principle, shift wavelengths by tens and even hundreds of nanometers. It can also perform a novel optical function, namely, complete exchange of optical power between two wavelengths.
56 citations
TL;DR: Four-wave mixing in wavelength-division-multiplexed soliton systems with damping and amplification is studied and an analytical model is introduced that explains the dramatic growth of the four-wave terms.
Abstract: Four-wave mixing in wavelength-division-multiplexed soliton systems with damping and amplification is studied. An analytical model is introduced that explains the dramatic growth of the four-wave terms. The model yields a resonance condition relating the soliton frequency and the amplifier distance. It correctly predicts all essential features regarding the resonant growth of the four-wave contributions.
55 citations
TL;DR: In this article, an efficient continuous resonant frequency mixing ω4 = ω1 − ω2 + ω3 in Na2 has been realized, where the bichromatic field (λ 1 = 488 nm, λ 2 = 525 nm) generated by an Ar+-laser-pumped Na2 Raman laser, and radiation at λ 3 = 655 nm from a dye laser interact resonantly with corresponding transitions X1∑g+(υ=3,J=43) → B1Πu(6,
Abstract: Efficient continuous resonant frequency mixing ω4 = ω1 − ω2 + ω3 in Na2 has been realized. A bichromatic field (λ1 = 488 nm, λ2 = 525 nm), generated by an Ar+-laser-pumped Na2 Raman laser, and radiation at λ3 = 655 nm from a dye laser interact resonantly with corresponding transitions X1∑g+(υ=3,J=43) → B1Πu(6, 43) → X1∑g+(13,43)→A1∑g+(24,44) in a test Na2 heat pipe. For input powers of 200, 25, and 400 mW an output beam of as much as 0.2 mW at λ4 = 599 nm has been observed. Measured parameter dependences indicate an influence of interference effects. This is directly related to the discussion of lasing without inversion.
54 citations
TL;DR: In this article, the authors report on high efficiency frequency-conversion obtained by four-wave mixing in a single traveling-wave optical amplifier for frequency conversion up to 2 THz.
Abstract: We report on high efficiency frequency‐conversion obtained by four‐wave mixing in a single traveling‐wave semiconductor optical amplifier. Efficiency in excess of 0 dB is demonstrated for frequency conversion up to 2 THz. Measurements of the signal to the amplified spontaneous emission background ratio are also presented.
50 citations
TL;DR: In this paper, the authors used four-wave mixing to measure the resonant nonlinear optical response to C 60 by fitting the line-shapes resulting from interference between a standard and sample.
TL;DR: In this article, the first analysis of heterodyne experiments that includes the propagation along the waveguide is given, under the assumption that the material polarization is adiabatically eliminated.
Abstract: We give the first analysis of heterodyne experiments that includes the propagation along the waveguide. Under the assumption that the material polarization is adiabatically eliminated we derive simple analytic expressions for the coherent coupling term, exact for Gaussian pulses and a good approximation for other shapes. We find that the measured signal does not display any phase dependence close to zero pump–probe delay. A four-wave mixing band is identified in the heterodyne signal, and a new class of experiments is proposed by analogy with the spatial case.
TL;DR: In this paper, the effect of nonlinear loss on four-wave mixing (FWM) conversion efficiency was analyzed and it was shown that the maximum FWM conversion efficiency is geometry independent and is equal to e−2|χ(3)/Im{χ (3)}|2 when non-linear loss dominates.
Abstract: We analyze the effect of nonlinear loss on four‐wave mixing (FWM) conversion efficiency. Maximum conversion efficiency is geometry independent and equal to e−2|χ(3)/Im{χ(3)}|2 when nonlinear loss dominates. Optimum device length and operating conditions are obtained and theoretical results are verified with a picosecond pulse FWM experiment.
TL;DR: In this article, a general expression for the polarization dependence of the four-wave mixing (FWM) efficiency in the dual-pump configuration was given, along with some general properties of the FWM susceptibility tensor, and a simple scheme to generate a nearly (1.5-dB variation) polarization independent FWM converted signal.
Abstract: We give a general expression for the polarization dependence of the four-wave mixing (FWM) efficiency in the dual-pump configuration. This expression, along with some general properties of the FWM susceptibility tensor, is used to propose a simple scheme to generate a nearly (1.5-dB variation) polarization independent FWM converted signal. The viability of this scheme is verified in a wavelength conversion experiment at 2.5 Gb/s.
TL;DR: In this paper, the effects of the probe-pulse chirp on time-resolved dispersion relations are studied, and the temporal evolution of the optical Kerr response in CS2 is projected into DPS.
Abstract: We measure difference phase spectra (DPS) over the whole visible spectrum by frequency-domain interferometry (FDI), using chirped femtosecond continuum pulses. The effects of the probe-pulse chirp on time-resolved dispersion relations are studied. Because of the correspondence between time and frequency in the chirp, temporal evolution of the optical Kerr response in CS2 is projected into DPS. In addition, it is found that the chirped continuum shows unexpected frequency shifts owing to induced phase modulation even when the continuum has a flat spectrum. The chirp character can be readily obtained from the projected traces, and the potential application to the single-shot pulse-shape measurement by FDI is discussed. It is shown that the delay-time-corrected spectra satisfy the Kramers–Kronig relations if the continuum has a flat spectrum and does not have higher chirp than the linear chirp but that the distortion caused by the induced modulation of the continuum remains unremoved in the corrected spectra.
TL;DR: In this article, the complete polarization state of the degenerate four-wave mixing signal from a GaAs/AlxGa1-xAs multiple quantum well is determined by time resolution of all four of its Stokes parameters as a function of the relative angle between the two linear input polarizations.
Abstract: The complete polarization state of the degenerate four-wave mixing signal from a GaAs/AlxGa1-xAs multiple quantum well is determined by time resolution of all four of its Stokes parameters as a function of the relative angle between the two linear input polarizations. The degree of ellipticity and the orientation of the polarization ellipse are both observed to vary dramatically in time, and the temporal evolution is found to depend strongly on the orientation of the input polarizations. These time-resolved results are shown to be consistent with previous measurements of the time-integrated Stokes parameters and to provide new constraints for physical models. The results are shown to be qualitatively consistent with a phenomenological model requiring the inclusion of both many-body interactions and biexcitonic effects.
TL;DR: A novel interference effect in transient four-wave mixing is demonstrated based on phase-controlled Liouville-space pathways interference and observed in the heterodyne-detected stimulated photon echo.
Abstract: A novel interference effect in transient four-wave mixing is demonstrated. The phenomenon is based on phase-controlled Liouville-space pathways interference and observed in the heterodyne-detected stimulated photon echo. Changing the phase difference between the first two excitation pulses from $\ensuremath{\pi}/2$ to 0 leads from no signal to maximum echo signal. A Brownian oscillator dynamical model is successfully used to analyze the effect and simulate the experimental data. The relation between this time-domain interference effect and dephasing-induced resonance in four-wave mixing spectroscopy is elaborated.
TL;DR: In this article, the influence of pump separation on polarization dependence and on conversion efficiency in a fiber-based optical phase-conjugator with two orthogonal pump waves at different wavelengths was studied.
Abstract: We study the influence of pump separation on polarization dependence and on conversion efficiency in a fiber-based optical phase-conjugator with two orthogonal pump waves at different wavelengths. The polarization dependence is found to be minimized when the pump wavelength separation is small. Furthermore, both theory and experiments show that the efficiency is maximized if the signal wavelength is located close to one of the pumps.
TL;DR: In this article, the effects of gain saturation, gain asymmetry, and pump/probe depletion on the conversion efficiency of four-wave mixing (FWM) in semiconductor optical amplifiers are studied analytically and numerically.
Abstract: The effects of gain saturation, gain asymmetry, and pump/probe depletion on the conversion efficiency of four-wave mixing (FWM) in semiconductor optical amplifiers are studied analytically and numerically. The power dependence of FWM coupling coefficients and ultrafast relaxation-related gain mechanisms are included in the model. By studying the FWM efficiency in the transition from unsaturated to strongly saturated regions, it is seen that gain asymmetry results in deviation from small-signal models when the pump-probe detuning and pump powers are small. At high pump injection or gain conditions, it is also shown that the small-signal model breaks down even for relatively large detuning frequencies. Probe depletion is also seen to be critical under saturated conditions and an upper bound is derived for ranges of input pump power, pump-probe detuning, and gain for a given amplifier under which the small-signal model is valid.
TL;DR: In this paper, an analytical solution of the four-wave mixing problem including gain dispersion and saturation effects is given, and it is shown that the linear gain factors for the different waves and the nonlinear susceptibilities associated with the different nonlinear effects must be characterized by different carrier densities at transparency.
Abstract: This paper addresses four-wave mixing (FWM) in semiconductor laser amplifiers from the point of view of a propagation problem. The gain dispersion effect, i.e., the difference of the gain factors for the pump, probe and signal waves is shown to be significant in the case of large detunings >1 THz. It is given an analytical solution of the FWM problem including gain dispersion and saturation effects. Considering the saturation behaviour, it is shown that the linear gain factors for the different waves and the nonlinear susceptibilities associated with the different nonlinear effects must be characterized by different carrier densities at transparency. A comparison of our theory with a numerical model, with previous approaches and with experimental data is given.
TL;DR: In this paper, the authors performed four wave mixing experiments on GaN epilayers using 13 ps pulses at 532 nm and found that the absolute scattering efficiency was 1×10−3 cm2/GW which is greater than an order of magnitude larger than the expected value.
Abstract: Pulsed probe degenerate four wave mixing experiments were performed on GaN epilayers using 13 ps pulses at 532 nm. Intensity and time response of the scattering efficiency was studied. Intensity dependence of the observed signal suggests carrier generation by both single and two photon effects. The absolute scattering efficiency was measured and related to pump‐induced nonlinear index change. The nonlinear refractive coefficient found was 1×10−3 cm2/GW which is greater than an order of magnitude larger than the expected value. Time response of the signal was found to be dictated by carrier lifetimes. Double‐exponential decays to trap levels with lifetimes of 100 ps and 1.1 ns are suggested as the dominant recombination processes.
TL;DR: In this article, a femtosecond four-wave mixing technique was used to measure the ultrafast coherent dynamics of the optical polarization in semiconductor optical amplifiers, and the dephasing time close to the transparency point is on the order of 100 fs.
Abstract: A femtosecond four‐wave mixing technique is used to measure the ultrafast coherent dynamics of the optical polarization in semiconductor optical amplifiers. A heterodyne detection scheme enables us to measure a background‐free quasi‐degenerate four‐wave mixing signal even without spatial separation of the pump and probe beam. First results indicate that the polarization dephasing time close to the transparency point is on the order of 100 fs.
25 Feb 1996
TL;DR: In this paper, a simple polarisation independent (PI) all-optical TDM demultiplexer was proposed that utilizes the ultrafast four-wave mixing (FWM) process of both TE and TM modes in a semiconductor laser amplifier (SLA) in which input pump and signal pulses are deliberately depolarized to suppress polarization coupling.
Abstract: Summary form only given. All-optical time-division demultiplexing (TDM) is one of the most fundamental functions in future Tbit/s all-optical networks. This paper proposes a simple polarisation independent (PI) all-optical TDM demultiplexer that utilizes the ultrafast four-wave mixing (FWM) process of both TE and TM modes in a semiconductor laser amplifier (SLA) in which input pump and signal pulses are deliberately depolarized to suppress polarization coupling.
TL;DR: In this article, a model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime, and the effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed.
Abstract: A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.
TL;DR: In this article, the influence of electron-electron scattering processes on the time evolution of four-wave mixing signals for ultrashort excitation in the vicinity of the band edge is investigated.
Abstract: The influence of electron–electron scattering processes on the time evolution of four-wave mixing signals for ultrashort excitation in the vicinity of the band edge is investigated. The validity of a Markovian approximation is carefully analyzed. The Markovian relaxation of the one-particle distribution is compared with non-Markovian results obtained from the solution of quantum-kinetic equations for two-point functions. In the non-Markovian case relaxation processes are slowed down.
TL;DR: It is experimentally demonstrated that wave-front reversal of picosecond optical signals can be efficiently achieved with low-gain parametric amplification with the use of a KTP crystal.
Abstract: Revisiting the pioneering work of Avizonis et al. [Appl. Phys. Lett. 31, 435 (1977)], we experimentally demonstrate that wave-front reversal of picosecond optical signals can be efficiently achieved with low-gain parametric amplification. The use of a KTP crystal permits forward phase conjugation of radiation with high divergence (40 mrad) and a broad spectrum (20 nm). The potential application of this technique to compensate for the group-velocity dispersion of standard optical fibers in the 1.55-μm window is discussed.
TL;DR: In this paper, an InGaAsP-InP quantum-well waveguides were used to achieve -20 dB conversion efficiency over the erbium-doped fiber-amplifier gain band with /spl ap/18dBm CW pump power.
Abstract: Results on wavelength shifters based on four-wave mixing that operate in the 1.5-/spl mu/m regime are reported. These devices utilize the near-bandedge resonant enhancement in the third-order nonlinearity in passive InGaAsP-InP quantum-well waveguides. Over the erbium-doped fiber-amplifier gain band approximately -20 dB conversion efficiency was obtained with /spl ap/18-dBm CW pump power. The conversion efficiency was nearly constant for wavelength shifts up to /spl ap/26 nm (3.3 THz), limited by the phase-matching bandwidth of the 8.5-mm-long device.
TL;DR: In this paper, the authors measured four-wave mixing in several geometries to evaluate the direct contribution of the third-order polarizabilities and the cascaded contribution, and showed experimentally that the cascading effect is large and that contributing polarization gratings must be transversely polarized.
Abstract: In a crystal without inversion symmetry there exist two-step indirect contributions to third-order nonlinear optical processes (cascading). Contributions to optical four-wave mixing occur through optical rectification and linear electro-optic effects. In contrast to cascading by second-harmonic generation, which has to satisfy strict phase-matching conditions, optical rectification is always allowed. In polar KNbO3 crystals we measured four-wave mixing in several geometries to evaluate the direct contribution of the third-order polarizabilities and the cascaded contribution. We present a theoretical model and show experimentally that the cascading effect is large and that contributing polarization gratings must be transversely polarized.