Multiplication of the drive signal frequency in a relativistic microwave amplifier with a rod slow-wave structure

A theory is developed for the one-dimensional nonlinear multimode simulation of a Cerenkov maser of special configuration (antenna-amplifier [1, 2]) where a tubular relativistic electron beam propagates along a circular waveguide with a dielectric rod. The operating mode is the fundamental azimuthally asymmetric HE ₁₁ mode. Harmonics at the input signal frequency can be amplified because they fall into the amplification bands for higher modes. At certain parameters, the output power at the second or third harmonic may considerably exceed that of the amplified signal at the fundamental frequency. The powers of output harmonics can be efficiently controlled by varying the point of electron beam extraction from the interaction region, as well as by varying the input frequency or by switching the polarization of the input signal from linear to circular.     

高Q法布里-珀罗腔中二阶串级非线性相移

在高Q值法布里珀罗腔中研究了二阶串级非线性相移.结果表明,通过改变入射光强,可以全光学控制基频光束的透射率和它的相移.基频透射光束的非线性相移相对入射光强的变化率被提高了腔精细度的平方.这可用作光子学开关器件 关键词： 二阶串级效应 法布里珀罗腔 非线性相移     

Nonlinear Phase Shifts by Cascaded Optical Rectification and Linear Electro-Optic Effect

Cascaded optical rectification and the consequent linear electro-optic effect have been investigated theoretically. Nonlinear phase shift of the fundamental beam caused by the cascading process was found to be proportional to the input intensity and the propagation length as in the Kerr effect. It is notable that the depletion of the fundamental optical pulse energy is negligible even for large nonlinear phase shifts.     

Efficient nonlinear phase shifts due to cascaded second-order processes in a counterpropagating quasi-phase-matched configuration

A counterpropagating quasi-phase-matched configuration is examined that is capable of efficiently producing second-order cascaded nonlinear phase shifts with minimal power lost to the second harmonic. For all-optical switching in a nonlinear Mach-Zehnder interferometer, the calculated minimum input power needed for switching (i.e., to yield a +/-pi/2 phase shift) is 40 times smaller than the power needed in the standard typeI copropagating configuration. The throughput of this counterpropagating device is 96% at the optimum switching point.     

Bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration with nonlinear left-handed metamaterials

We study the bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration containing left-handed metamaterials with self-focusing and self-defocusing Kerr-type nonlinearity. It is shown that the lateral shifts can be large and negative when the thickness of the middle metal film is smaller than the critical value. Taking the nonlinear effect into account, there exists a hysteretic response between the beam shift and the intensity of the incident light beam. These results suggest that the bistable and negative beam shifts can be modulated by nonlinear coefficients and intensity of incident beam, which might be used in integrated photonics and optical switches.     

Generation of large fifth-order nonlinear phase shifts by use of lossless χ~((2)) cascaded nonlinear processes

Theinherentthird-ordernonlinearityofmaterialc(3)isnormallyweak.Toaccumulatealargenonlinearphaseshift,highlaserintensityandlongopticalpathinmaterialareneeded.Whilethevalueofnonlinearitycouldbemadelargerneartheregionofabsorptionresonance,astronglosswillbeaccompaniedthroughtheprocessoftwo-photonabsorption.Inordertorealizestrongthird-ordernonlinearitywithcontrollableenergyloss,thec(2)(w;2w,-w)︰c(2)(2w;w,w)cascadingprocesshasbeenproposed,whichisequivalenttothethird-ordernonlinearityc(3)(w;w,w,-w)w…     

Generation of large fifth-order nonlinear phase shifts by use of lossless<Emphasis Type="Italic">χ</Emphasis><Superscript>(2)</Superscript> cascaded nonlinear processescascaded nonlinear processes

It is shown that the cascaded fifth-order nonlinear phase shifts will increase with energy loss in the cascaded processes. Essentially different from the multi-photon absorption accompanied with inherent material nonlinearities, the loss of fundamental wave in a cascaded process is controllable and suppressible. By introducing difference frequencies generated from the reaction between the fundamental and its second harmonic after the cascaded processes, the fundamental wave can be free of energy loss, while the large cascaded fifth-order nonlinear phase shift is maintained.     

Generation of large fifth-order nonlinear phase shifts by use of lossless χ(2) cascaded nonlinear processes

It is shown that the cascaded fifth-order nonlinear phase shifts will increase with energy loss in the cascaded processes. Essentially different from the multi-photon absorption accompanied with inherent material nonlinearities, the loss of fundamental wave in a cascaded process is controllable and suppressible. By introducing difference frequencies generated from the reaction between the fundamental and its second harmonic after the cascaded processes, the fundamental wave can be free of energy loss, while the large cascaded fifth-order nonlinear phase shift is maintained.     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

Approximately analytical optimization of Cherenkov cascading second order nonlinear effects in a dissipative waveguide

The coupled-mode equation in dissipative waveguides in Cherenkov configuration has been detailedly discussed for the first time, to our knowledge. Based on this equation, Cherenkov second harmonic generation (SHG) and Cherenkov nonlinear phase shift (NPS) caused by Cherenkov cascading second order nonlinear (CSON) effects have been analyzed and optimized comprehensively and systematically by an analytical method, taking into account both the conversion depletion and the waveguide loss, and the analytical expressions for Cherenkov SHG and NPS has been presented. The dependence of the NPS and the conversion efficiency on varied parameters, such as the waveguide thickness, the fundamental wavelength, the input fundamental power and the temperature, has been discussed completely. The results show that a large enough NPS (>10π) can be attained for nondissipative waveguides with a very small depletion of the fundamental power, at the same time, this Cherenkov CSON configuration has some advantages over the quasi-phase matching CSON configuration, e.g., the much looser tolerances of the waveguide parameters and the noncollinear feature of the fundamental wave and the second harmonic wave, these characteristics make the Cherenkov CSON configuration a promising direction to realize all-optical devices.     

Nonlinear computer-generated holograms

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.     

Trapped-ion quantum simulator: experimental application to nonlinear interferometers

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).     

级联二阶非线性法布里-珀罗谐振腔特性分析

在小信号近似下,得出了级联二阶过程的表达式。利用该式的有效三阶极化率的表达式,讨论了存在二阶非线性光学晶体的法－珀谐振腔的非线性光学特性。分析表明,由于谐振腔的存在,通过非线性晶体的功率密度超过入射功率密度几十倍以上,因而产生较大的、随相位失配变化的非线性相位漂移。当相位失配接近２π时,获得基叔光的最大相位漂移。该最大相位漂移对应的相位失配随着入射功率密度、非线性晶体的地阶极化率和晶体长度而变化。     

Mode Cooperation in a Submillimeter Wave FU Series Gyrotron

At certain gyrotron operating conditions, mode cooperation instead of mode competition takes place between a fundamental and a second harmonic mode. This means the phase bunching of a gyrating electron beam under the second harmonic operation reduces the starting current for the fundamental operation and increases total output power as well as beam efficiency. Such mode cooperation is observed in experiments and confirmed by computer simulations for submillimeter wave Gyrotron FU II.     

Giant and negative bistable shifts for one-dimensional photonic crystal containing a nonlinear metamaterial defect

In this Letter, we investigate giant and negative bistable lateral shifts for a light beam transmitted through a one-dimensional photonic crystal containing a nonlinear metamaterial defect. It is shown that there exists a typical S-shaped curve of the normalized input-output intensity. The hysteresis of lateral shift, resulting from the reshaping effect (constructive and destructive interferences of each plane wave components undergoing different phase shifts) is dependent on the nonlinear defect, the incident intensity and incidence angle. Numerical simulations are also made for the validity of stationary phase approach. All these phenomena lead to potential applications in integrated optics and optical switches.     

Analytical formulae for the optimization of the process of low-power phase modulation in a quadratic nonlinear medium

We show that using the approximation of fixed intensity analytical formulae, describing the process of induced phase modulation for the beams involved in second-order nonlinear optical processes can be derived. Expressions that allow the optimization of the phase shifts experienced by the fundamental and generated waves are presented for nonlinear quadratic processes, second-harmonic generation and sum-frequency mixing. In the case of seeding at the generated wavelength, the phase shift of the fundamental wave is due to two interactions: (i) a cubic one, based on coupled second-order processes (cascade cubic nonlinearity) and (ii) single quadratic interaction with participation of the seeding wave. By comparison with the exact numerical solution, we defined the input parameters of the beams for which this analytical approach is valid. It is shown that phase shifts exceeding /2 can be correctly predicted using the expressions obtained.     

Polarization-dependent colored conical emission in a quadratically nonlinear medium

Both supercontinuum conical emission (SCCE) and blue-green conical emission (CE) by means of second harmonic generation (SHG) were observed alternately in a β-barium borate (BBO) crystal induced by femtosecond laser pulses with vertical polarization state. Three theoretical models were analyzed to interpret the angular beam of SCCE. The experimental conical angles with different wavelengths in BBO crystal and BK-7 glass can be explained well by nonlinear X-wave model and Cerenkov type phase matching model other than four-wave mixing (FWM) model.     

基于衍射理论的大非线性相移Z扫描研究

以衍射理论为基础,建立了强非线性吸收下,非线性介质对高斯光束的衍射模型.数值计算表明,折射相移的增大使峰的透过率增强而谷的透过率趋于饱和;而吸收相移的增大使峰的透过率被抑制而谷的透过率增强.相移比值是决定谷-峰结构存在与否的关键.在一定的输入功率下,远场输出功率并不是完全随着非线性吸收系数的增大而增大.该理论的近似条件只要求是薄样品,具有更好的适用性.     

Nonlinear dynamics with higher-order modes in lithium niobate waveguide arrays

We present theoretical and experimental studies on nonlinear beam propagation in lithium niobate waveguide arrays utilizing higher-order second harmonic bands. We find that the implementation of the higher-order second harmonic bands leads to a number of new effects. The combined interaction of two second harmonic bands with a propagating fundamental beam can lead to a complete inhibition of nonlinear effects or to the formation of discrete spatial solitons, depending only on the wavelength of the fundamental wave. Furthermore we analyze the properties of discrete solitons, allowing for linear coupling of the second harmonic. Here we predict and demonstrate experimentally a power dependent phase transition of the soliton topology.