Observation of polarization-controlled spatial splitting of four-wave mixing in a three-level atomic system

We report experimental observations of intensity modulation and spatial splitting of four-wave mixing (FWM) signal beams which can be effectively controlled by the polarization states of the pumping laser beams. Due to the periodic change of the pumping beam’s polarization states, the intensity of the FWM beam also evolves periodically. The periodic spatial splitting phenomenon has been observed in both x- and y-directions. The cases with/without the dressing beams are compared. Such studies can be very useful in better understanding the formation of spatial solitons and for signal processing applications, such as spatial beam splitter, routing, and switching.     

Enhancement and Suppression of Four-Wave Mixing in a Four-Level Atomic System

We report observations of the enhancement and suppression of four-wave mixing （FWM） in an electromagnetically induced transparency window in a Y-type ^85 Rb atomic system. The results show the evolution of the dressed effects （from pure enhancement to partial enhancement/suppression, and finally into pure suppression） in the degenerate-FWM processes. Moreover, we use the perturbation chain method to describe the FWM process. Finally, we observe the polarization dependence of the enhancement and suppression of the FWM signal.     

Observations of Autler-Townes spatial splitting of four-wave mixing image

We report the self- and external-dressed Autler-Townes (A-T) splittings of the images of the generated four-wave mixing signal (FWM) and electromagnetically induced transparency (EIT) of probe images in cascade three-level atomic system. Such spatial properties of probe and FWM signals are induced by the enhanced cross-Kerr nonlinearity. We demonstrate the controlled electromagnetically induced spatial dispersion (EISD), splitting and focusing of probe and FWM signals images by adjusting self- and external-dressing fields. Studies on such controllable A-T spatial splitting and spatial EIT effect can be very useful in applications of spatial signal processing and optical communication.     

Enhancing and suppressing four‐wave mixing in electromagnetically induced transparency window

We demonstrate the enhancement and suppression of four‐wave mixing (FWM) in an electromagnetically induced transparency (EIT) window in Y‐type ⁸⁵Rb atomic system. The generated two‐photon FWM signal can be selectively enhanced and suppressed via an EIT window. The EIT of probe as well as the enhancement and suppression of FWM signals can be modified by the sequential‐cascade double dressing. The influence of different probe polarization configurations is also studied. Different polarization states of the probe laser can select different transitions among Zeeman sublevels and different dressing strengths. Copyright © 2010 John Wiley & Sons, Ltd.     

Angular momentum conversion of elliptically polarized beams focused by high numerical-aperture phase Fresnel zone plates

Based on the vectorial Debye theory, we investigate the tight focusing of elliptically polarized light beams by high numerical-aperture (NA) phase Fresnel zone plates (FZP). The conversion of the spin angular momentum (SAM) and the orbital angular momentum (OAM) in the tight focusing of the elliptically polarized beams is investigated in great detail. It is shown that the direction and magnitude of the OAM can be directly modulated by the input polarization, providing effective evidence that the SAM carried by an elliptically polarized light beam is converted into OAM in the tight focusing process. The properties of phase retardation between x and y components of the focused field are also investigated. It is found that focused field of x and y components still keeps its original elliptical polarization state, indicating that the focused field composed of x and y components still carries SAM, whereas the focused field of z component is changed into carrying OAM. The influences of the total zone number and the phase difference of binary phase FZPs with high NA on the intensity distribution in the focal plane are also investigated.     

Polarization enhancement and suppression of four-wave mixing in multi-Zeeman levels

Polarization dependence of the enhancement and suppression of four-wave mixing (FWM) in a multi-Zeeman level atomic system is investigated both theoretically and experimentally. A dressing field applied to the adjacent transition can cause energy level splitting. Therefore, it can control the enhancement and suppression of the FWM processes in the system due to the effect of electromagnetically induced transparency. The results show that the pumping beams with different polarizations select the transitions between different Zeeman levels that, in turn, affect the enhancement and suppression efficiencies of FWM.     

Generation of superpositions of coherent states of the motion of a trapped ion

We propose a method for preparing superpositions of coherent states of the motion of an ion in an anisotropic two-dimensional trap, in which the ion is tightly bound in the y direction. In the scheme the ion is excited by two resonant laser beams with equal amplitude, propagating along the x and y directions, respectively. In the Dicke-Lamb limit, an initial coherent state of the ion motion can be converted into a superposition of several coherent states on a circle through the laser-ion interactions and state-selective measurements on the ion. Received: 30 May 1997 / Revised: 29 July 1997 / Accepted: 22 October 1997     

Effects of notches on the order of flux-closure state formation in bi-rings by micromagnetic simulation

The effects of the number and the location of notches on the formation of flux-closure states in bi-rings with fields applied in the x direction (i.e., along the short axis direction of bi-rings) and y direction (i.e., along the long axis direction of bi-rings) are investigated using micromagnetic simulation. For the bi-rings with one notch and the bi-rings with two notches symmetric about y axis, the order of flux-closure state formation in each ring can be controlled. But the flux-closure state forms simultaneously in each ring for the bi-rings with two notches symmetric about x axis. For the bi-rings with two notches that are symmetric neither about x axis nor about y axis, only one ring can form a flux-closure state in the y-direction field and no flux-closure state can be found in rings in the x-direction field. Therefore, logic states can be defined by controlling the order of flux-closure state formation, which can be utilized in future logic devices.     

Dual-dressed four-wave mixing and dressed six-wave mixing in a five-level atomic system

We study the co-existing four-wave mixing (FWM) process with two dressing fields and the six-wave mixing (SWM) process with one dressing field in a five-level system with carefully arranged laser beams. We also show two kinds of doubly dressing mechanisms in the FWM process. FWM and SWM signals propagatingalong the same direction compete with each other. With the properly controlled dressing fields, the FWM signals can be suppressed, while the SWM signals have been enhanced.     

Spatial Splitting and Intensity Suppression of Four-Wave Mixing in V-Type Three-Level Atomic System

We illustrate our experimental observation of coexisting the controllable spatial splitting and intensity suppression of four-wave mixing （FWM） beam in a V-type three-level atomic system. The peak number and separation distance of the FWM beam are controlled by the intensities and frequencies of the laser beams, as well as atomic density.     

Generation and Manipulation of Spin-Orbit Coupling mode via Four-Wave Mixing with Quantum Interference

Recently, the vectorial nonlinear optical processes driven by spin-orbit coupling (SOC) light have come to the fore, leading to striking optical phenomena and important applications both in classical and quantum optics. However, research on the SOC-mediated light-atom interactions is still in its infancy. Here, the generation and manipulation of SOC mode through a vectorial four-wave mixing (FWM) process in ⁸⁵Rb vapor is demonstrated. Under the excitation of two SOC pump beams, multiple FWM paths can be simultaneously established due to the rich atomic Zeeman sublevels coupling with different circularly polarized components of SOC fields. A higher-order cylindrical or more general SOC FWM signal is observed in the vectorial FWM process, which obeys angular momentum conservation and Gouy phase matching. In particular, quantum interference between different FWM paths plays a crucial role in manipulating the SOC mode of the generated FWM signal, revealing that the conversion of SOC mode is intrinsically quantum. This work provides a pathway toward deeper insight into the vectorial nonlinear optical processes and may advance technology for shaping spatially structured light, which is essential in applications such as nonlinear polarization imaging and the optical communication realm.     

On the Theory of Gravitational Field in Finsler Spaces - II

Continuing the last paper [1], more detailed considerations are made on the spatial structure of the Finslerian gravitational field: firstly, a unified field between the external (x)-field and the internal (y)-field is constructed from a vector bundle-like standpoint, where the intrinsic behavior (i.e., δy) of the internal vector variable y is taken into account; secondly, the connection structure and the metrical structure are determined by setting the base and dual base properly in the unified field; thirdly, a compactification process of the internal field (i.e., a mapping process of the (y)-field on the (x)-field) is considered in order to realize a four-dimensional Finslerian structure.     

A theory for the enhancement of the photoacoustic signals by volatile liquids

It has been shown experimentally that photoacoustic signals can be enhanced by introduction of a volatile liquid into the cell. Korpiun developed a theory which predicted the enhancement to be proportional to the mole fraction of the volatile component (y ₀) in the gas phase. His theory is, however, based on a species conservation equation valid for dilute solutions only. We present a rigorous theory for predicting the enhancement of potoacoustic signal. Our theory shows the enhancement to be proportional toy ₀/(1–y ₀) which compares well with observations of Ganguly and Somasundaram.     

Self-consistent method for calculation of reflection coefficients of the interface with the dielectric tensor’s rotation

We give an interface between two same media whose orientation of optical axis, however, is rotated, and describe a method in detail to show how to calculate reflectance coefficient in this interface. We also give the theoretical simulation of the reflectance coefficient and discuss the effect of the rotation angle and the direction of electron vector on the reflectance coefficient. For the un-polarized lights the theoretical calculated results show that the reflectance coefficients (r _x1 and r _y1) are very small when the rotated angle is small, and they arrive at the maximum value as the rotation angle is equal to a decided value. For the polarized light, when the rotation angle is small, the reflectance coefficients (r _x1 and r _y1) are also small. Only when the rotation angle increases to a certain extent, they can reach the maximum values and be strongly affected by the direction of electronic vector. However, this effect on the reflectance coefficient in the direction of the maximum refraction is different from that in the direction of minimum refraction.     

Coherence vortex properties of partially coherent flat-topped vortex beams

The analytical propagation expression of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived, and it then is used to investigate the coherence vortex properties of partially coherent flat-topped vortex beams in the Fourier transform and fractional Fourier transform systems. It is shown that in the Fourier transform system the coherence vortex depends on the flat-topped beam order N, spatial coherence parameter α and position (x ₁,y ₁) of the reference point, whereas in the fractional Fourier transform system the flat-topped beam order N does not affect the spectral degree of coherence. Furthermore, in both transform systems, depending on the choice of the reference point, the zero value point of the spectral degree of coherence may be present or absent. In particular, if x ₁=y ₁=0 is selected, the phase at the zero value point of the spectral degree of coherence may be determinate; thus the coherence vortex does not exist.     

Rotational Raman gain suppression in H2

We report measurements of rotational Raman gain suppression in H₂ in the transient regime. Quantitative information about the dependence of the amount of the gain suppression on the pump energy and the propagation angle relative to the pump beam is obtained from angularly resolved measurements of the small signal amplification. These measurements, along with qualitative observations of the Stokes spatial distribution under gain conditions, demonstrate that the gain suppression is confined to a narrow region around the phase matching angle for collimated beams with relatively low gain per unit length. For focused beams with higher gain per unit length the suppressed region can extend to the forward direction, resulting in a two- to three-fold estimated increase in the Raman threshold.     

Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading

Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load, which can be expanded in terms of sinusoidal series. For plane stress problems, the stress function is assumed to consist of two parts, one being a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (y), and the other a linear polynomial of x with unknown coefficients depending on y. The governing equations satisfied by these y-dependent functions are derived. The expressions for stresses, resultant forces and displacements are then deduced, with integral constants determinable from the boundary conditions. While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness, the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness. The present analysis is applicable to beams with various boundary conditions at the two ends. Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters. Supported by the National Natural Science Foundation of China (Grant Nos. 10472102, 10432030, and 10725210)     

Coexisting four-wave mixing and six-wave mixing in three-level atomic system

We demonstrate the coexisting four-wave mixing (FWM) signal and six-wave mixing (SWM) signal which can be enhanced both by electromagnetically induced transparency (EIT) and optical pumping effect in a common three-level and open four-level inverted-Y type systems of ⁸⁵Rb. We also analyze the effect of optical pumping in different energy level systems by arranging laser beams and comparing the strength of the increased and reduced absorption caused by optical pumping.     

Strain-assisted spin manipulation in a quantum well

We show that the efficiency of manipulating electron spins in semiconductor quantum wells can be enhanced by tuning strain strengths. The combined effects of intrinsic and strain-induced spinorbit couplings vary for different quantum wells, which provide an alternative route to understand the experimental phenomena brought in by the strain. The contribution to the electron-dipole-spin-resonance intensity induced by the strain can be changed through adjusting the direction of the ac electric field in the x-y plane of the quantum well and tuning the strain strengths.     

N5B五能级系统中重复缀饰四波混频研究

从理论上研究了N5B五能级系统中一个激光场重复缀饰四波混频过程.结合能级图分析,从它特殊的Autler-Town分裂峰中可以非常清晰地看出其重复缀饰的作用.还研究了在强Probe场和强耦合场下N5B五能级下缀饰四波混频信号的抑制增强现象.采取独特的处理方法——独立作用法,研究结果表明一个激光场作用于N5B五能级系统时存在两次缀饰,并形成缀饰能级的二重分裂或者三重分裂,不同于多个耦合场对原子的多重缀饰作用.应用于非线性光谱术中对多峰结构的研究. 关键词： 四波混频 电磁感应透明 重复缀饰