Effects of higher order nonlinearities on second-order frequency mixing

Equations are presented here which describe second-order nonlinear frequency mixing under conditions where third-order non-linearities significantly alter the phase-matching relations. The coupled amplitude and phase equations illustrate that additional phase mismatch of the second-order process can be expected due to third-order nonlinearities. These nonlinearities include refractive index changes for a wave at one frequency due to waves at other frequencies. Growth of off-axis weak waves (small scale self-focusing) is described in terms of four-wave mixing in the presence of the second-order frequency mixing. It is shown that in at least some cases growth of off-axis waves is enhanced by second-order frequency mixing.     

Quantitative nonlinear spectroscopy: a direct comparison ofdegenerate four-wave mixing with cavity ring-down spectroscopy appliedto NaH

Cavity ring-down spectroscopy and degenerate four-wave mixing have been applied for spectroscopic studies, temperature determination, and measurement of relative dipole transition moments of photochemically produced sodium hydride. In our experiment, NaH was formed within a heat-pipe oven after 3p excitation of sodium in a hydrogen atmosphere with a second dye laser. The reaction product NaH was probed in the near ultraviolet part of the spectrum at 382 nm with 1-4-μs delay to the excitation pulse using both a linear and nonlinear spectroscopic technique with a pulsed dye laser source (pulsewidth 15-ns full-width half-maximum). The strengths and limitations of these two spectroscopic techniques are discussed. Since the two processes depend on different parameters and the image-forming beams have different properties, it is difficult to define a single criterion for comparison. But our measurements indicate that cavity ring-down spectroscopy is a powerful tool with a sensitivity better than 10⁹ particles per cm³ and quantum state which is comparable to degenerate four-wave mixing in our case     

简并四波混频中相位共轭波强度的振荡特性研究

一、引言 文献1中用波长为0．53μm，脉宽为35ps的激光脉冲作泵浦源，以对称激励的形式，研究了透明以及可饱和吸收介质的筒并四波混频（DFwM）中后向相位共轭波能量E与读出光束相对于写入光束延迟到达非线性介质的时间△t之间的关系，     

钾蒸气中双光子共振四波混合的差频效应

在钾蒸气中观察到了双光子共振四波混合的差频效应。YAG:Nd~(3+)激光器的红外光波(ω_3)和 YAG:Nd~(3+)激光的二次谐波泵浦的可调谐染料激光器的可见光波(ω_1)用作入射波。当染料激光的两个光子的能量等于钾原子高激发态13s 和基态4s 间的能量差时,产生了一个新的波长为4052的相干光波(ω_4=2ω_1-ω_3)。     

Four-wave mixing in traveling-wave semiconductor laser amplifiers

Nondegenerate four-wave mixing (NDFWM) effects on simultaneous amplification of copropagating and counterpropagating waves with a frequency spacing of a few gigahertz in a 1.5-μm nonresonant near traveling-wave semiconductor laser amplifier are discussed. Experimental results are in qualitative agreement with a theoretical model assuming the NDFWM process is mainly due to carrier pulsation produced by the beating of copropagating waves in the amplifier. The amplification of a phase-modulated wave is considered. Time-reversal properties of four-wave mixing are demonstrated     

Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser

We demonstrate intracavity degenerate four-wave mixing in the saturable gain medium of a dye laser. The dye laser is a synchronously pumped bidirectional ring laser that produces pulses of 4 ps duration. The dynamics of the interaction provides information on the phase coherence of the pulses. A simple theory of transient degenerate four-wave mixing is presented that accurately describes the measurements.     

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.     

A statistical description of stimulated Brillouin scattering beamcombination efficiency

The mutual coherence between two stimulated Brillouin signals produced by undepleted pump beams that are partially overlapped is studied. The mutual coherence of the stimulated-Brillouin-scattered beams determines the efficiency with which the two beams can be combined. The statistical properties of the mutual coherence are calculated. The mechanism for coupling of two stimulated-Brillouin-scattering outputs is four-wave mixing. Mutual coherence is found to depend on the pump beam's pulse duration, the medium's phonon lifetime, and the degree of overlap between the laser pump beams     

Frequency comb generation by four-wave mixing and the role of fiberdispersion

A fiber-optic frequency comb generator utilizes four-wave mixing (FWM) to expand a modulated continuous wave (CW) lightwave into a comb of discrete, equispaced frequencies. The sign and magnitude of the fiber dispersion are shown to control comb expansion by affecting the interference among different four-wave mixing interactions at particular comb frequencies. Positive dispersion initiates comb expansion while zero and negative dispersions suppress expansion. Dispersion mapping engineers fiber links for maximum comb bandwidths. By managing dispersion in a 35 km link of dispersion-shifted fiber, a frequency comb spanning 1.1 THz is experimentally demonstrated. Promising applications include pulse train synthesis affording low-chirp, arbitrarily profiled, short pulses     

Nondegenerate four-wave mixing in a homogeneously broadened two-level system with saturating pump waves

The formulation of phase conjugation via nondegenerate four-wave mixing in a homogeneously broadened resonant medium is generalized to include saturating pump waves. An ultrahigh-Qoptical filter is predicted, showing both gain and a bandwidth less than the homogeneous linewidth of the atom. The dependence of the filter function on the ac Stark effect and on the use of asymmetric pump wave intensities is discussed. In addition, several new phenomena are shown which manifest themselves as a dip in the degenerate reflectivity at line center.     

Effect of fiber nonlinearity on long-distance transmission

The effect of the weak refractive-index nonlinearity of optical fibers on pulse shape is investigated using computer simulations of long-distance transmission. Fiber losses are canceled by periodically spaced optical amplifiers whose spontaneous emission noise is, however, not included in the simulations. The analysis is confined to normal pulses and does not consider solitons. Several conclusions are drawn. (1) If wavelength division multiplexing (WDM) of two channels is used in a uniform fiber without dispersion fluctuations, catastrophic buildup of four-wave mixing occurs if one primary channel is located at the zero-dispersion wavelength. (2) If two pulses with different carrier frequencies collide in a uniform fiber with no gain or loss discontinuities, their four-wave mixing products reach a peak during complete pulse overlap, but this spurious power dies away as the pulses separate. (3) Two-channel WDM transmission of light modulated in amplitude-shift keying format appears feasible at 2.5 GB/s over distances of 7500 km     

A novel method for polarization insensitive four-wave mixing in semiconductor optical amplifiers

A new method for obtaining polarization insensitive four-wave mixing with phase inversion in a semiconductor optical amplifier is proposed. The method uses the simplest configuration with co-propagating pump and signal waves. The possibility of polarization insensitive four-wave mixing is shown for a tensile quantum well. Polarization insensitivity can be obtained by the right detuning of the pump wavelength from the gain peak.     

Influence of the Stimulated Raman Scattering on the Four-Wave Mixing Process in Birefringent Fibers

The influence of the stimulated Raman scattering in the four-wave mixing process in high birefringent fibers is theoretically analyzed. We consider the dual pump configuration in both co-polarized and orthogonal polarization schemes and treat simultaneously the stimulated Raman scattering and the four-wave mixing processes. The obtained results are valid even when the shift between the pumps and signal lies inside the Raman band. Results show that when the phase-matching condition is achieved the generation of the idler wave is mostly dependent on the real part of the fiber nonlinear response function, whereas the amplification of the signal wave is mostly dependent on the imaginary part. Results also show that when the phase-matching condition is satisfied the optical power evolution of the signal and idler waves for small frequency detunings are mostly described by the anisotropic Raman response of the fiber, whereas for high frequency detunings the isotropic response dominates. Our analysis also shows that the stimulated Raman scattering can increase the efficiency of the four-wave mixing process, for certain frequency detunings.     

Degenerate four-wave mixing with guided waves

The theory, experimental implementation, and applications of degenerate four-wave mixing with guided waves are reviewed.     

Four-wave mixing in a semiconductor laser amplifier

Reports on nearly degenerate four-wave mixing (NDFWM) of two copropagating light waves inside a travelling wave amplifier (1.3 μm) at input light powers of less than 10 μW. It describes the first experimental determination of the range of frequency spacing of the two light waves for efficient NDFWM and of the dependence on the state of polarisation     

Polarization dependence of phase-conjugate reflectivities in solidfilms containing randomly oriented saturable dyes

The properties of polarization-dependent phase-conjugate (PC) reflectivities by degenerate four-wave mixing in saturable-dye-doped films are investigated on the basis of a four-level model including an excited-state absorption. Numerical calculations are carried out by taking account of the effect of molecular orientation as well as of pump propagation under the assumption that optically anisotropic dye molecules are rigidly fixed in a solid matrix without any positional and orientational order, in which a PC wave can be generated even in the case of a probe wave perpendicularly polarized to pump waves. Two cases of the polarization state are employed, where the polarization direction of the probe wave is either parallel or perpendicular to that of the parallel linearly polarized pump waves. Numerically calculating the PC reflectivities as a function of the pump intensity, we show how the polarization properties of the PC-reflectivity curves depend on saturation parameters, and clarify the influences of the molecular orientational and the pump propagation effect. The numerical results are compared with the experimental results obtained by using eosin-Y-doped polyvinyl alcohol films as saturable absorbers     

Contradirectional four-wave mixing in 1.51 mu m near-travelling-wave semiconductor laser amplifier

Experiments on contradirectional nondegenerate four-wave mixing (NDFWM) in a 1.51 mu m nonresonant near-travelling-wave semiconductor laser amplifier are presented. Experimental results are in qualitative agreement with a theoretical model assuming the NDFWM process is mainly due to carrier pulsation at the beat frequency of copropagating waves in the amplifier.<>     

氟化锂晶体F3^＋色心四波混频研究

利用简并四波混频技术观测到LiF晶体中F_3~+色心的非线性光学相位共轭效应,以脉冲染料激光为泵浦光得到最大相位共轭反射率约为0.1%,根据LiF晶体F_3~+色心的能级特点从理论上阐明了F_3~+色心系统非线性饱和吸收和四波混频的物理起源。     

四波混频原理及其应用

本文给出了四波混频的原理及特点,理论上推导了四波混频的产生,并给出了四波混频在光纤通信的密集波分复用、相位共轭波产生、四波混频实时光学检测中的应用.本文的研究目的旨在较为全面地掌握四波混频这一典型的非线性光学效应的应用方向,通过总结四波混频在已经较为成熟的研究领域的具体应用及研究方法,借此寻找四波混频更广泛的应用领域.