Three-wave mixing in chiral liquids

Second-order nonlinear optical frequency conversion in isotropic systems is only dipole allowed for sum- and difference-frequency generation in chiral media. We develop a single-center chiral model of the three-wave mixing (sum-frequency generation) nonlinearity and estimate its magnitude. We also report results from ab initio calculations and from three- and four-wave mixing experiments in support of the theoretical estimates. We show that the second-order susceptibility in chiral liquids is much smaller than previously thought.     

Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium

Using an example of a Raman active medium we describe how a common nonlinear process of four-wave mixing can be used to induce strong coupling between the spatial and temporal degrees of freedom in optical waves. This coupling produces several unexpected effects. Amongst those are cascaded excitation of multiply charged optical vortices, spatial focusing in a nonlinearly defocusing medium, and generation of helically shaped spatiotemporal optical solitons.     

Four-wave mixing of picosecond pulses in hollow fibers: Phase matching and the influence of high-order waveguide modes

The processes of third-harmonic and difference-frequency generation through the four-wave mixing of picosecond pulses in gas-filled hollow fibers are experimentally studied. Due to the improvement of phase-matching conditions with an appropriate choice of the gas pressure and optimal parameters of the hollow fiber, we were able to use hollow fibers with a large length (up to 30 cm) for difference-frequency generation, which resulted in a considerable increase in the power of the difference-frequency signal at the output of the fiber. Our experimental data reveal a considerable influence of high-order waveguide modes on four-wave mixing processes in a hollow fiber. It is shown that the waveguide regime of nonlinear optical interactions implemented in hollow fibers removes the limitations on the efficiency of third-harmonic and sum-frequency generation, which are characteristic of the tight-focusing regime in media with normal dispersion and which are due to the geometric phase shift arising in tightly focused light beams.     

Observation of interference between four-wave mixing and six-wave mixing

We report generation of four-wave mixing enhanced by electromagnetically induced transparency and optical pumping in a ladder-type atomic system. When two pumping laser beams are used to form a conjugate small-angle static grating, both four-wave and six-wave mixing processes are shown to exist at the same time. Interference between these two nonlinear wave-mixing signals is experimentally demonstrated.     

Confocal nonlinear optical microscopy for high-resolution measurement of absorptive objects

We demonstrate a new scheme to enhance the spatial resolution of a confocal optical microscope. Our scheme improves the spatial resolution in the direction of the optical axis. The confocal optical microscope, by use of a four-wave mixing geometry, can obtain optical information about weakly absorptive objects with organic dyes. Owing to the third-order nonlinear dependence of absorptive objects, the optical signal is confined to the focal region of the focusing incident beam.     

Real-time two-dimensional imaging in scattering media by use of a femtosecond Cr(4+):forsterite laser

An original femtosecond Cr(4+):forsterite laser source associated with a nonlinear optical correlator was used for imaging through scattering media with 1220-nm light. The system, which operates as an ultrafast optical gate by sum-frequency generation in a nonlinear crystal, was able to detect the light reflected from a resolution chart hidden in a turbid medium, at an attenuation of as much as 15 mean free paths. When the object was illuminated with a collimated beam, real-time two-dimensional images were obtained, with a maximum transverse resolution of ~20 microm.     

Spatial optical solitons resulting from multistep cascading

We introduce a novel class of parametric optical solitons supported simultaneously by two second-order nonlinear cascading processes, second-harmonic generation and sum-frequency mixing. We obtain analytical and numerical solutions for three-wave spatial solitons and show that the presence of an additional cascading mechanism can change dramatically the properties and stability of two-wave quadratic solitary waves.     

双光子荧光与相干反斯托克斯拉曼散射显微成像技术的实验研究

双光子荧光与相干反斯托克斯拉曼散射同属于三阶非线性效应,二者之间的差异与联系是一个值得研究的问题.本文基于自行搭建的超连续谱近红外宽带相干反斯托克斯拉曼散射显微成像系统进行光谱成像,同时通过理论与实验对比分析了双光子荧光与相干反斯托克斯拉曼散射图像存在差异的原因.结果表明,具有亚微米以上横向分辨率的相干反斯托克斯拉曼散射成像系统,可以使用较大尺寸的荧光珠进行双光子荧光成像,通过解卷积得到双光子荧光成像的系统分辨率,并将它近似等效于相干反斯托克斯拉曼散射成像系统的当下分辨率.如果需要得到相干反斯托克斯拉曼散射成像系准确的分辨率结果,就必须使用尺寸比相干反斯托克斯拉曼散射成像系统实际分辨率小的球形样品进行实验测量.     

Fifth-order attosecond polarization beats using twin color-locked noisy lights in cascade three-level system with Doppler-free approach

Fifth-order attosecond sum-frequency polarization beat (FASPB) is studied in a cascade three level system with the phase-conjugation fourth-order coherence function theory. An improved schematic diagram of geometry, which is different from that inducing fifth-order femtosecond different-frequency polarization beat(FFDPB), is used to obtain FASPB. By analyzing the cases that pump beams have either narrow or broad bandwidth, it is found that the temporal behavior of the sum-frequency polarization beat signal depends on the properties of the lasers and transverse relaxation rate of the atomic energy-level system. Finally,the cascaded four-wave mixing (FWM) processes and the difference between attosecond and femtosecond polarization beats have been discussed, it is found that cascaded or sequential lower processes can often obscure the direct fifth-order polarization beat processes.     

Optical chaos in multiple degenerate four-wave mixing

Spatial evolution has been studied of an ensemble of equal-frequency light waves involved in several four-wave mixing processes under linear photoabsorption. It is shown that this system may exhibit spatial chaos caused by competition of optical mixing processes with strong energy exchange between the waves. For pulsed radiation, the temporal envelopes of interacting waves undergo modulations which may also be of chaotic character. Also discussed are possible variants of identifying chaos in systems of interacting light waves experimentally and the role of accompanying photoprocesses (photoabsorption, self-action of radiation).     

Spatial interference between four- and six-wave mixing signals

We experimentally demonstrate spatial interference between simultaneously generated four-wave mixing (FWM) and six-wave mixing (SWM) signals in a multilevel atomic system. By tuning the relative phase between the FWM and SWM processes the relative strengths between these two high-order nonlinear optical processes can be investigated.     

在远离光子晶体光纤零色散波长的正常色散区入射飞秒脉冲产生四波混频及孤子效应的实验研究

在远离光子晶体光纤零色散波长的正常色散区入射飞秒脉冲,实验产生了一对由四波混频引起的信号波带和闲频波带,及一对由脉冲内拉曼散射和非孤子辐射引起的孤子和色散波带,并观察到功率饱和现象.利用有限元法理论模拟了光纤的色散和非线性特性,用四波混频的相位匹配条件模拟了光纤在满足相位匹配条件下所产生的信号波带和闲频波带出现的可能位置,并与实验结果符合得很好.结果表明:即使在光子晶体光纤的正常色散区抽运激光脉冲亦可以产生四波混频和孤子效应;研究发现四波混频的产生是由四阶色散参量引起的;并进一步从理论上解释了孤子及色散波的产生原因.     

Erasing distinguishability using quantum frequency up-conversion

The frequency distinguishability of two single photons was successfully erased using single photon frequency up-conversion. A frequency nondegenerate photon pair generated via spontaneous four-wave mixing in a dispersion shifted fiber was used to emulate two telecom-band single photons that were in the same temporal mode but in different frequency modes. The frequencies of these photons were converted to the same frequency by using the sum-frequency generation process in periodically poled lithium niobate waveguides, while maintaining their temporal indistinguishability. As a result, the two converted photons exhibited a nonclassical dip in a Hong-Ou-Mandel quantum interference experiment. The present scheme will add flexibility to networking quantum information systems that use photons with various wavelengths.     

Multistep cascading in periodically poled directional couplers

We suggest a novel scheme for multistep cascaded parametric processes based on a periodically poled nonlinear directional coupler and derive the conditions for simultaneous phase matching of the second-harmonic generation and sum-frequency mixing processes. We predict an efficient wavelength conversion by the cascaded third-harmonic generation from the third optical communication window (1.53-1.56 microm) to visible in a LiNbO3 poled waveguide coupler.     

Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.     

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.     

Evolution of first-order sidebands from multiple FWM processes in HiBi optical fibers

The generation of two idler waves inside a high birefringent (HiBi) optical fiber through three four-wave mixing (FWM) processes is studied theoretically. The coupled-equations for the field amplitudes are derived and analytically solved, in the co-polarized and orthogonal polarization schemes. The obtained solutions take into account the delayed Raman response of the medium. The polarization sensitivity of the generation of the idler waves is analyzed. Results show that the stimulated Raman scattering does not change the efficiency of the idler wave generation in the co-polarized scheme, whereas in the orthogonal polarization scheme that nonlinear process decreases the efficiency of the four-wave mixing processes. Results also show that this set of multiple four-wave mixing processes is physically quite different from the typical single or dual pump four-wave mixing configurations. Findings show that the power transfer from the pumps to the idler fields can lead to a monotonous growth, or a periodic evolution of the sidebands along the fiber. Results show that the process efficiency varies greatly with the angle between the two pump polarizations.     

四波混频在长距离相干光纤传输中的影响

本文研究光纤非线性现象之一的四波混频对长距离相干多路光纤传输系统的影响.通过对一条长度为550km,采用9个掺铒光纤放大器的频分复用系统的实验,清楚地观察到了四波混频这一光纤非线性.实验的结果符合对四波混频的理论分析与计算.结果表明:对信息容量在每秒10~9bit数量级,采用常规的不归零码作信号方式的多路传输,光纤中的四波混频现象将严重地影响其传输性能.     

Nonlinear excitation of surface plasmon polaritons by four-wave mixing

We demonstrate nonlinear excitation of surface plasmons on a gold film by optical four-wave mixing. Two excitation beams of frequencies omega(1) and omega(2) are used in a modified Kretschmann configuration to induce a nonlinear polarization at a frequency of omega(4wm)=2omega(1)-omega(2), which gives rise to surface plasmon excitation at a frequency of omega(4wm). We observe a characteristic plasmon dip at the Kretschmann angle and explain its origin in terms of destructive interference. Despite a nonvanishing bulk response, surface plasmon excitation by four-wave mixing is dominated by a nonlinear surface polarization. To interpret and validate our results, we provide a comparison with second-harmonic generation.     

Transient sum-frequency mixing with temporally tailored laser pulses

We discuss the possibility of using temporally tailored pump laser pulses to control the temporal width and shape of optical pulses generated in a process of transient sum-frequency mixing in crystals with second-order nonlinearity. Specific calculations performed in a model crystal in the case of fifth-harmonic generation are presented.