Nonlinear Phase Shift by Parametric Amplification in Leaky Waveguides

In this article, the cascaded second-order nonlinear phase shifts induced in the signal wave are studied using the three-wave parametric interaction in a four-layered QPM leaky waveguide configuration in Z-cut LiNbO 3 . In this interaction, the pump-andsignal waves are guided modes and the idler is radiated into the substrate. We have analyzed the nonlinear phase shifts induced in the signal wave due to cascaded second-order effects, as a function of different waveguide parameters. These studies should find application in realizing practical all-optical signal processing devices.     

二次谐波产生的非线性相移的解析研究

给出一种分析二阶非线性级联效应的解析方法，对Ⅱ型二次谐波产生的非线性级联效应进行了详细的理论研究和分析。结果表明倍频晶体中正交输入两个振幅不相等的基波分量时，在近相位匹配下二阶非线性级联效应能够产生大的相移。利用本文的解析方法可以对任意二阶非线性相移产生的过程进行优化，从而以最小的需求输入功率来获得特定的相移。还对由非线性相移诱导的且与光强有关的偏振旋转效应和一种基于偏振旋转效应的全光偏振开关进行了分析和讨论。本文的结果对于建立一种基于Ⅱ型倍频晶体中非线性相移诱导偏振旋转效应的新全固化被动锁模飞秒激光装置具有十分重要的意义。     

用光谱分辨的双光束耦合方法测量χ（2）:χ（2）级联非线性相移

针对重要的χ^(2):χ^(2)级联非线性相移,在理论上论证了可以用光谱分辨的双光束耦合方法来测量χ^(2)：χ^(2)级联非线性相移,在实验上研究了飞秒时域级联非线性相移随波矢失配置的变化规律。这一新疑的测量方法灵敏度高,实际使用简单,应用低能量的飞秒激光振荡器,就能方便地测量微弱χ（2）晶体的级联非线性相移。     

Coupled mode analysis to study cascading in the QPM Cerenkov regime in waveguides

In this paper we use the coupled mode analysis to study nonlinear phase shifts of the fundamental beam caused by cascaded second order nonlinear effects in the Quasi Phase Matched Cerenkov (QPMC) configuration in waveguides. Under the no-pump depletion approximation which is valid for low conversion efficiencies, we obtain the nonlinear phase shift as a function of length of interaction and grating period. It is observed that the nonlinear phase shift of the fundamental beam can be maximized by choosing a grating period for which the phase matched second harmonic radiation mode is radiated parallel to the film-substrate interface, i.e., for zero Cerenkov angle. Although the phase shifts are smaller than in the case of all guided geometry, QPM Cerenkov configuration is expected to have greater tolerance towards various waveguide parameters and the fundamental wavelength.     

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。     

基于周期极化反转铌酸锂光波导高速非归零码到归零码的转换

研究了基于周期极化反转铌酸锂光波导级联二阶非线性效应实现非归零码到归零码高速全光码型转换的新方案,使用的是马赫-曾德尔干涉仪结构.转换原理是非归零码信号光在级联倍频和差频过程中受到的放大作用引起马赫-曾德尔干涉仪的不平衡,进而通过干涉相消产生归零码信号光输出.首先从耦合波方程出发,数值模拟了非归零码到归零码码型转换过程.然后分析了波导长度、光功率、相对时延对消光比的影响并对码型转换进行了优化设计.最后分析了转换带宽,模拟计算表明信号光在90nm的3dB带宽内可调谐,进而可以实现多信道的同时转换. 关键词： 码型转换 级联倍频和差频 周期极化反转铌酸锂 马赫-曾德尔干涉仪     

基于周期极化反转铌酸锂光波导高速非归零码到归零码的转换

研究了基于周期极化反转铌酸锂光波导级联二阶非线性效应实现非归零码到归零码高速全光码型转换的新方案，使用的是马赫-曾德尔干涉仪结构.转换原理是非归零码信号光在级联倍频和差频过程中受到的放大作用引起马赫-曾德尔干涉仪的不平衡，进而通过干涉相消产生归零码信号光输出.首先从耦合波方程出发，数值模拟了非归零码到归零码码型转换过程.然后分析了波导长度、光功率、相对时延对消光比的影响并对码型转换进行了优化设计.最后分析了转换带宽，模拟计算表明信号光在90nm的3dB带宽内可调谐，进而可以实现多信道的同时转换.     

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…     

Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides

Simultaneous wavelength conversion and pulse compression are proposed and demonstrated exploiting cascaded second-order nonlinear processes in periodically domain-inverted LiNbO₃ waveguides. The influences of initial pulse widths and waveguide length on the conversion efficiency and converted pulse compression are theoretically analyzed. Tunable wavelength conversion is performed for the signal pulse with the temporal width of 7.5 ps and repetition rate of 40 GHz. Conversion efficiency of more than −24 dB is obtained for 35-nm conversion span under average signal power of 10 dBm when a CW control wave is adopted.     

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.     

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.     

二阶非线性串级效应及其全光晶体管作用

二阶非线性串级效应,特别是基频光波通过串级过程（二次谐波产徨过程和随后的频率下转换过程）获得的相移,是实现全光信号处理的一条非常有希望的途径。文章对二阶非线性串级效应的物理原理和基于此的全光晶体管的研究进行了综合介绍。     

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.     

Theoretical research on terahertz wave generation from planar waveguide by optimized cascaded difference frequency generation

A novel scheme for high-efficiency terahertz(THz)wave generation based on optimized cascaded difference frequency generation(OCDFG)with planar waveguide is presented.The phase mismatches of each-order cascaded difference frequency generation(CDFG)are modulated by changing the thickness of the waveguide,resulting in a decrement of phase mismatches in cascaded Stokes processes and an increment of phase mismatches in cascaded anti-Stokes processes simultaneously.The modulated phase mismatches enhance the cascaded Stokes processes and suppress the cascaded anti-Stokes processes simultaneously,yielding energy conversion efficiencies over 25%from optical wave to THz wave at 100 K.     

Analysis of difference frequency generation and cascaded second-harmonic generation and difference frequency generation in lossy quasi-phase-matched semiconductor waveguides

The analytical expressions of converted wave power for difference frequency generation (DFG), cascaded second-harmonic generation and difference frequency generation (cSHG/DFG) processes have been obtained under the non-depletion approximation in lossy waveguides. It is shown that the analytical results and the numerical simulation with depletion agree very well for lossy waveguides. Employing the analytical solutions, the formulas of optimized waveguide lengths in lossy waveguides are obtained for DFG and cSHG/DFG processes. After designing an AlGaAs quasi-phase-matched ridge waveguide, we investigate and compare the characteristics of the second-order nonlinear effects with and without waveguide loss, such as conversion efficiency, conversion bandwidth, pump wavelength tolerance and temperature stability in detail.     

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.     

Long wave-short wave resonance in nonlinear negative refractive index media

We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.     

Self-induced transparency and self-induced darkening with a nonlinear frequency-doubling polarization interferometer

It is shown that the system polarizer-frequency-doubling crystal(s)-analyzer has a nonlinear transmission for the fundamental wave. The intensity-dependent transmission of this device is due to the nonlinear phase shift that the fundamental beam obtains in the nonlinear crystal as a result of cascaded second-order processes. Depending on the mutual orientation of the polarizer and the analyzer such effects as self-induced transparency and self-induced darkening can be realized.     

Retiming of picosecond pulses by a cascaded second-order nonlinear process in quasi-phase-matched LiNbO3 waveguides

A new technique for reducing timing jitter by using a cascaded second-order nonlinear process in quasi-phase-matched (QPM) LiNbO3 waveguides is proposed. It was found that the timing jitter of a signal at QPM wavelength is not transferred to the converted pulses during cascading in a 30-mm-long LiNbO3 QPM waveguide. Timing-jitter transfer characteristics in QPM LiNbO3 waveguides are evaluated by calculation of pulse evolution, and retiming of 1.5-ps pulses in 10- and 30-mm-long waveguides is demonstrated experimentally.     

Active control of light based on polarization-coupling cascading

In this letter, we proposed a novel method for optical manipulation based on polarization-coupling cascading in MgO-doped periodically poled lithium niobate crystal. Polarization-coupling cascading, a series of energy exchanges between two orthogonally polarized beams close to phase matching condition, can also lead to phase shifts, in analogy with that in cascaded second-order nonlinearities. In addition, the parameters of light such as phase, amplitude, and group velocity can be modulated by changing the relative power ratio of the incident continuous wave beams. The phase control was demonstrated by Newton’s rings experiment, which was in good agreement with the theoretical prediction.