One-dimensional Nonlinear Photonic Crystal Research Articles

The transport of dipole solitons in a one-dimensional nonlinear photonic crystal

Quadratic χ(2) nonlinearity crystal provide an ideal stage for the researches of the transport of optical solitons. However, the transport of dipole solitons in a homogeneous χ(2) nonlinear medium is unstable. To solve this problem, a one dimensional nonlinearity photonic crystal is designed from a χ(2) nonlinearity crystal by quasi-phase matching technique. The duty cycle of the positive polarized in the transverse direction of the crystal is periodic modulated, so as to realize a stable transport of dipole solitons in it. Besides, relations of the transportation characteristics of the dipole soliton and the modulation parameters are researched in this letter numerically. Moreover, mobility and collision of these dipole soliton through the crystals are discussed through the paper. Some key parameters of the related experiment are also estimated.

Defect-doped one-dimensional nonlinear photonic crystals exhibit coherent perfect absorption with bistable properties

In this paper, the bistable phenomenon with the coherent perfect absorption properties are studied through the nonlinear transfer matrix method in one-dimensional nonlinear photonic crystals doped with a defect. The focus is on the influences of the relative phase of coherent light on the bistable coherent absorption intensity, and the tuning of the bistable threshold by parameters such as angle and wavelength of incidence. The simulated results show that the coherent absorption intensity is very sensitive to the relative phase of coherent incidence. As the phase decreases, the absorption intensity also decreases, varying from 1 to −1 when the phase change is within 180°. The tuning of the relative phase to the absorption intensity provides great convenience for the application of bistable, and parameters such as the incident angle can also achieve sensitive tuning of the bistable threshold. The larger the incident angle, the larger the threshold, and the more obvious the bistable phenomenon at TE mode. The application of nonlinear optical devices has been expanded in the fields of filters, optical switches, optical power threshold devices, etc.

Electro-optic properties of one-dimensional (1D) nonlinear perfect photonic crystals based on Lithium tantalate layer

Electro-optic properties of one-dimensional (1D) nonlinear perfect photonic crystals (PCs) based on Lithium tantalate (LiTaO3) layer and air were studied. Using transfer matrix method, we found that the resonance transmission peak induced by weak defocusing Kerr nonlinearity can be tuned to any wavelength when the 1D structure is subject to external electric field. We demonstrated numerically that the intensity of this localized mode either increases or decreases depending on both the magnitude and the direction of the applied electric field. In addition, the wavelength varies linearly with the applied external electrical field and depends on the incidence angle. For a critical nonlinearity strength |αc|, the single resonance peak splits into two resonances as the magnitude of the external electric field is increased. Moreover, the number of transmission resonance peaks with narrow FWHM, high Q factor and total transmission can be enhanced by increasing the intensity of the applied electric field. Results presented in the current study promote the application of our one-dimensional (1D) nonlinear perfect photonic crystal for electrically tunable narrow-band transmission multi-channel optical filters and some other optoelectronic applications.

Second Harmonic Generation in Generalized Ferroelectric Superlattices

The goal of the work presented in this investigation is to achieve the efficient parametric interaction of narrow beams (in particular second harmonic generation) using a nonlinear (ferroelectric-LiTaO3) photonic crystal tuned to self-collimation (nondiffractive) regimes. A numerical study of second harmonic generation (SHG) in one-dimensional nonlinear photonic crystals based on a full nonlinear system of equations, implemented by a combination of the method of finite elements and fixed-point iterations, is reported. This model is derived from a nonlinear system of Maxwell’s equations that partly overcomes the known shortcoming of some existing models that rely on the undepleted pump approximation. We derive a general solution of SHG in one-dimensional nonlinear photonic crystals structures. Numerical simulations also show that the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental wave are located at the photonic band edges or are assigned to the designed defect states.

Design of a tunable 8-channel DWDM covers all transmission windows using defect mode nonlinear photonic crystals

The effect of a defective mode layer of GaAs semiconductor material of one-dimensional nonlinear photonic crystal, which is a function of intensity as well as the wavelength, is numerically simulated using transfer matrix method. It is observed that the transmission efficiency of this defective layer increases with an increase in the wavelength of the material. At the first transmission window (820 to 910 nm), the transmittance is low, but at the second (1260 to 1360 nm) and third transmission windows (1530 to 1565 nm), it approaches 100%. At the first transmission window, the efficiency of the material approaches 100% with an increase in the intensity up to 140 GW / cm2. We have designed a tunable 8-channel dense wavelength division multiplexer for both (first and third) transmission windows and compared the quality factor and efficiency of the structure and found that the transmission efficiency of the defective layer of the third transmission window is better than first transmission window. We observed that the channel spacing for first and third transmission windows are 0.72 and 1.17 nm, respectively, which correspond to the International Telecommunication Union grid systems.

Recursive transfer-matrix method for second-harmonic generation in a one-dimensional nonlinear photonic crystal at arbitrary incidence angle

In this paper, we derive a recursive transfer-matrix method (RTMM) and use the method to analyse the problem of second-harmonic generation (SHG) in a one-dimensional nonlinear photonic crystal (1D-NPC) under oblique incidence of fundamental-frequency (FF) wave and nondepleted pump approximation. This method is very simple and useful for determining SHG conversion efficiency at various incident angles of FF wave and thicknesses of nonlinear layer. The RTMM calculation results show that a maximum SHG conversion efficiency can be produced by the strong local FF field confinement in 1D-NPC due to optimal incidence angle and nonlinear layer thickness.

Generalized nonlinear Snell's law at χ(2) modulated nonlinear metasurfaces: anomalous nonlinear refraction and reflection.

The generalized nonlinear Snell's law at the χ(2) modulation surface is deduced from the universal model of χ(2) processes in nonlinear photonic crystals (NPhCs). Based on the generalized nonlinear Snell's law, the anomalous refraction and reflection geometries are predicted and observed at crystal's inner boundary on nonlinear metasurfaces formed by one-dimensional NPhCs. The emitted second harmonic is observed, which obeys the law and appears to turn into multiple orders compared to that in a bulk crystal. Furthermore, the analysis shows a potential way to achieve nonlinear over-reflection by using submicron periodic χ(2) modulation in metasurfaces.

Time-reversed and reciprocal second-harmonic generation with pump depletion

The time-reversed second-harmonic generation in one-dimensional nonlinear photonic crystals has been theoretically studied without the undepleted pump approximation. A simple criterion has been deduced which determines the energy flow. Based on it, two kinds of structures with different symmetries are presented to realize the nonlinear time reversal effect. A completely reciprocal nonlinear response is also found in the same process. Furthermore, a multi-section-cascaded structure is proposed to realize the nonlinear time reversal at any given position.

Surface enhanced nonlinear Cherenkov radiation in one-dimensional nonlinear photonic crystal.

We study the configuration of efficient nonlinear Cherenkov radiation generated at the inner surface of a one-dimensional nonlinear photonic crystal, which utilizes the combination of both quasi-phase matching and total internal reflection by the crystal surface. Multi-directional nonlinear Cherenkov radiation assisted by different orders of reciprocal vectors is demonstrated experimentally. At specific angles, by associating with quasi-phase matching, the incident fundamental wave and total internal reflection wave format completely the phase-matching scheme, leading to great enhancement of harmonic wave intensity.

Third-harmonic signal generation and enhancement in nonlinear photonic crystals with an efficient continuation finite-element method

A computational study of the third-harmonic (TH) generation (THG) and enhancement through an χ(3) process in one-dimensional nonlinear photonic crystals is presented in this paper. We have introduced a canonical variational problem with a small increment factor to solve the THG problem. The problem with a large input pump intensity or strong nonlinear susceptibilities can be handled by a versatile and accurate method, which combines finite-element methods and a continuation fixed-point iteration algorithm. The TH signal generation and enhancement through the direct χ(3) process are displayed by two periodic structures. Numerical experiments show that the TH signal is significantly enhanced when the frequencies of the fundamental wave and the TH wave are turned to the corresponding photonic band edges to meet the phase-matching condition. Results of numerical experiments also indicate that our proposed method is computationally efficient and precise to handle strong nonlinearities, i.e., large values of input pump power.

Modulation of Kerr nonlinearity on spectral characteristics for one-dimensional nonlinear defective photonic crystals

Nonlinear reflectance spectra of one-dimensional photonic crystals with a Kerr defect layer are numerically studied in this paper. The laser intensity-dependent nonlinearity will cause the bending of the reflectance spectrum and the moving of the defect mode's location in a certain direction according to the sign of χ(3). The influence of incident intensity, polarization, and incident angle on the nonlinear reflectance spectra are discussed in detail. The reflectance spectra will show bistable characteristic when the incident intensity is larger than the threshold value. The possible application of the spectral characteristic in switchable filtering is discussed as well. These results will provide a valuable reference for the design and application of new filtering and switching devices.

VO2-like thermo-optical switching effect in one-dimensional nonlinear defective photonic crystals

A new approach to achieve VO2-like thermo-optical switching in a one-dimensional photonic crystal by the combination of thermo-optical and optical Kerr effects was proposed and numerically demonstrated in this study. The switching temperature and the hysteresis width can be tuned in a wide temperature range. Steep transition, high optical contrast, and low pumping power can be achieved at the same time. This kind of one-dimensional photonic crystal-based bistable switch will be low-cost, easy-to-fabricate, and versatile in practical applications compared with traditional VO2-type one.

Disorder-induced light trapping enhanced by pulse collisions in one-dimensional nonlinear photonic crystals

We use numerical simulations to study interaction of co- and counter-propagating pulses in disordered multilayers with noninstantaneous Kerr nonlinearity. We propose a statistical argument for existence of the disorder-induced trapping which implies the dramatic rise of the probability of realization with low output energy in the structure with a certain level of disorder. This effect is much more pronounced in the case of two interacting pulses than in the single-pulse regime and does not occur in the strictly ordered system at the same intensity of the pulses. Therefore it cannot be explained simply as a result of increase in strength of nonlinear light-matter interaction.

Giant enhancement of second harmonic generation in one-dimensional defective nonlinear photonic crystals

In this paper, the second harmonic generations in finite size one-dimensional defective nonlinear photonic crystals have been investigated. To calculate the conversion efficiency, fundamental and second harmonic wave propagation among four proposed structures, we use the transfer matrix method. In the designed defective nonlinear photonic crystal structures, the linear and nonlinear optical parameters are both periodically modulated and thus the second harmonic generation efficiency can be several orders of magnitude larger than in a conventional quasi-phase-matched nonlinear structure with the same sample length.

Photonic band structure in one-dimensional nonlinear crystal: Analysis of harmonic stability

We consider a one-dimensional nonlinear photonic crystal consisting of an infinite set of concentrated equidistant scatterers inserted in a linear dielectric medium. Each of the scatterers is made by a very thin layer of a nonlinear medium with high refractive index that we model by a delta function. We show that the nonlinear optical exact solutions of this system form an intensity dependent band structure. To analyze the stability of these solutions we consider a modulation harmonic perturbation of these solutions whose amplitudes are slightly above the instability threshold. We demonstrate that the nonlinearity gives rise to an oscillatory instability of the solutions, which is a localized version of the well-known modulational instability of the nonlinear Schrodinger equation. We show that the linear harmonic perturbation forms as well a band structure whose allowed bands coincide for some intervals with those of the nonlinear band structure of the solutions for which case the structures are unstable whereas in the region where both the linear and nonlinear bands do not coincide, the nonlinear waves are indeed stable so that they conform spatial solitons.

Propagation dynamic of a Gaussian in the inverted nonlinear photonic crystals

In this work, we study the evolution of a Gaussian beam inside a one-dimensional inverted nonlinear photonic crystals (INPC) with a Kerr nonlinearity. The INPC is a kind of virtual crystals which is generated by the optical induction via the electromagnetically induced transparency (EIT). The propagation dynamics of the Gaussian with different total power are identified. Four types of propagation behavior are found. They are collapse beam, breather beam, soliton and symmetry-breaking beam, respectively. The border between these four behavior types are given. For symmetry-breaking beam, an asymmetric profile of the beam is evolving from the symmetry Gaussian, which can be termed as a kind of dynamical symmetry breaking (DSB). The influences on the appearance of the symmetry breaking point are studied by varying input parameters of the Gaussian. The results of this work are both suitable in nonlinear optics and Bose-Einstein condensate (BEC).

Exact iterative solution of simultaneous second-harmonic and third-harmonic generation in nonlinear photonic crystals

A computational study on simultaneous second-harmonic and third-harmonic generation and enhancement through a χ(2) three-wave mixing process in one-dimensional nonlinear photonic crystals is presented. The mathematical model partly overcomes the shortcoming of some existing models based on the undepleted pump approximation, which is derived from a nonlinear system of Maxwell equations. We introduce not only a variational approach that combined the finite element method and the fixed-point iteration to study the nonlinear frequency conversion but also a continuation technique depends on the weak formulation of the incremental fields to ensure the convergence of the iterative procedure when the nonlinearity is very strong. Two designed photonic crystals matched the phase by utilizing and balancing the interplay of material dispersion and the geometrical dispersion are reported, as well as a tested photonic crystal to show the validity and efficiency of our approaches. Numerical experiments indicate that the conversion efficiencies of SH and TH generation can be significantly enhanced when the frequencies of fundamental and harmonic waves are tuned at the photonic band edges or are located to the defect states.

Čerenkov nonlinear diffraction of femtosecond pulses

Čerenkov nonlinear diffraction of femtosecond pulses in one-dimensional nonlinear photonic crystal of strontium tetraborate was studied theoretically and experimentally in both frequency and time domains. Spectral features of second harmonic radiation were measured in the course of mapping the nonlinear photonic crystal structure. The local second harmonic spectrum demonstrates complex angular behavior within the beam cross section. The spectral width of the second harmonic radiation is found to be fundamental beam size-dependent, and optimal focusing should be used for exact conversion of the fundamental spectrum into the second harmonic one. Experimental results are in excellent agreement with calculations. Maximum second harmonic generation efficiency was up to 2.1% at pumping by a femtosecond oscillator.

Effects of pulse collisions in a multilayer system with noninstantaneous cubic nonlinearity

Numerical simulations of an ultrashort pulse propagation in a one-dimensional nonlinear photonic crystal are carried out. It is known that the relaxation of cubic nonlinearity is the reason for the effect of pulse self-trapping in such a multilayer system. In this paper we study further implications of this effect. It is shown that the trapped light absorbs additional low-intensity pulses which cannot be self-trapped per se. On the other hand, such low-intensity pulses are subject to the so-called induced trapping when light becomes trapped due to a collision of two such pulses. We consider the conditions for this effect in cases of both co- and counter-propagating pulses.

Computational design for efficient second-harmonic generation in nonlinear photonic crystals

A computational study on the efficient second-harmonic generation (SHG) in one-dimensional nonlinear photonic crystals (PhCs) is presented. The design requirements are specified in terms of the corresponding fundamental wavelength of the incident wave, at which the maximum conversion efficiency of SHG occurs. The computational approach has developed a Newton-type local optimization method to optimize the fill factor and the period of a PhC. An optimal structure can be determined by controlling the band structure such that the frequencies of the fundamental and second-harmonic waves are precisely located at the lower edges of photonic bandgaps. The results of our numerical experiments show the optimal design problem can be solved efficiently based on crucial initial data given by some useful engineering intuitions. The SHG with high conversion efficiency is achieved by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure of the PhC precisely.