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Journal of Nonlinear Optical Physics & Materials

FOUR-WAVE MIXING IN LEFT-HANDED MATERIALS

Shiming Gao, Sailing He

Published Dec 1, 2007• 4 citations
Publisher

Abstract

The four-wave mixing (FWM) effect in a so-called left-handed material (LHM) with a third-order nonlinear response is studied. The theoretical models for the wavelength conversion (WC) and parametric amplification (PA) based on the FWM in the LHM are established when the signal falls in the frequency range of backward or forward wave. Analytical formulas for the WC efficiency and PA gain are derived. The influences of the pump powers, the phase mismatch, and the interaction length on the performances of the WC and PA are analyzed. The phase-match dependence of the performance is reduced by carefully controlling the pump powers.

DOI
10.1142/s0218863507003901

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The four-wave mixing (FWM) effect in a so-called left-handed material (LHM) with a third-order nonlinear response is studied. The theoretical models for the wavelength conversion (WC) and parametric amplification (PA) based on the FWM in the LHM are established when the signal falls in the frequency range of backward or forward wave. Analytical formulas for the WC efficiency and PA gain are derived. The influences of the pump powers, the phase mismatch, and the interaction length on the performances of the WC and PA are analyzed. The phase-match dependence of the performance is reduced by carefully controlling the pump powers.
A systematic study of degenerate two-wave mixing in the stationary regime in thin nonlinear local-response media is presented. The model is based on the coherent interaction of four waves, the two incident beams, and the two main diffracted waves. Analytical results are obtained in all cases investigated under the assumption of weak-beam amplification. It is demonstrated that the energy transfer arises only from the forward degenerate four-wave mixing terms. In particular, the theoretical results show two new features: (1) the gain factor of the interaction is substantially reduced because of the phase change associated with the two-wave mixing terms and (2) a phase mismatch can compensate for this phase change, leading to an appreciable gain enhancement. Moreover, the general case is solved numerically. Particular attention is given to the influence of separate two-wave and forward degenerate four-wave mixing terms. Self-diffraction effects and the gain dependence versus the ratio of the pump-beam intensity to the signal-beam intensity are investigated.
A strong pump-power dependence of the four-wave mixing (FWM) signal for an aqueous solution of Malachite green is reported. The characteristics of the pump-power dependence of the nonlinear signal are reproduced by a theoretical model based on the coupling between pump-probe, considering signal fields and propagation effects. The effect of the intramolecular coupling on the nonlinear intensity of the FWM signal is studied using a model molecule consisting of two-coupled harmonic curves of electronic energies with minima displaced in energy and nuclear positions. Two-vibrational states are considered while including non-adiabatic effects for the two-state model. Moreover, the coupling among the field components, as well as the propagation effects, are studied by considering a constant pump-intensity. Our calculation scheme, considering both the intramolecular coupling effects in the description of the molecular structure and the effects produced by the propagation of the FWM signal along the optical length, allows the exponential dependence of the latter, as the intensity of the pumping beam increases. Our treatments do not require the inclusion of other non-resonant processes outside the RWA approximation, due to the consideration of an adiabatic basis.
Four wave mixing (FWM) holds great promise as a tool to perform signal processing of classical light as well as of quantum states. However, typically FWM require use of high power pumps and as a consequence, the FWM process is accompanied by spontaneous Raman scattering as well as spontaneous FWM. In addition, FWM is also very sensitive to changes in the phase matching along propagation, caused by fluctuations in the core geometry of the fiber. In this work, we review recent progress in predicting and measuring the conversion efficiency and noise figure of wavelength conversion using FWM and we show consequences due fluctuations in the core geometry.
A configuration for wavelength conversion and optical amplification by parametric interaction using a nonlinear optical device is proposed. It enables pump generation through second harmonic generation (SHG), difference frequency generation (DFG), and optical parametric amplification (OPA) using a multiple-quasi-phase-matched (M-QPM) LiNbO3 waveguide in a bidirectional manner. Wavelength conversion for the 1.4–1.6 µm band is experimentally demonstrated. In addition, it is demonstrated that the parametric gain band can be changed using various detunings between the pump and QPM wavelengths used for the DFG/OPA process. The proposed method would be useful for enabling high-capacity optical transmission outside the 1550-nm band.
Efficient frequency conversion of photons has important applications in optical quantum technology because the frequency range suitable for photon manipulation and communication usually varies widely. Recently, an efficient frequency conversion system using a double- Λ four-wave mixing (FWM) process based on electromagnetically induced transparency (EIT) has attracted considerable attention because of its potential to achieve a nearly 100% conversion efficiency (CE). To obtain such a high CE, the spontaneous emission loss in this resonant-type FWM system must be suppressed considerably. A simple solution is to arrange the applied laser fields in a backward configuration. However, the phase mismatch due to this configuration can cause a significant decrease in CE. Here, we demonstrate that the phase mismatch can be effectively compensated by introducing the phase shift obtained by two-photon detuning. Under optimal conditions, we observe a wavelength conversion from 780 to 795 nm with a maximum CE of 91.2 % ± 0.6 % by using this backward FWM system at an optical depth of 130 in cold 87 Rb atoms. The current work represents an important step toward achieving low-loss, high-fidelity quantum frequency conversion based on EIT.
By applying a strong coupling field between a lower state and the upper state of an allowed transition to ground, an enhancement of nondegenerate four wave mixing (NDFWM) with a resonantly enhanced third-order nonlinear susceptibility in a rare-earth doped fiber can be obtained. We have derived an expression for the third-order nonlinear susceptibility using quantum theory and discussed the conversion efficiency for NDFWM. The theoretical result shows that the conversion efficiency has a maximum value while the third-order nonlinear susceptibility shows constructive interference at the Rabi frequency Ω 23 = ±√Γ 2 Γ 3 . On account of phase-mismatch, the frequency conversion efficiency has a maximum value over a certain small range of frequency separation (such as 0 < Δ f < 30 GHz at the wavelength λ c = 1.55 μm), and the frequency conversion range increases with increase of the third-order nonlinear susceptibility.