Nonlinear Finite-difference Time-domain Research Articles

Optimization of an All-Optical Photonic Crystal NOT Logic Gate Using Switch Based on Nonlinear Kerr Effect and Ring Resonator

In this paper, the use of the Kerr effect in a two-dimensional square lattice of In0.82Ga0.18As0.40P0.60 rods in photonic crystal proposes an ultra-compact all-optical NOT logic gate. The main device operation is based on the concept of all the optical switches. In our work, the novelty lies in the design of a new simple nonlinear ring based on the combination of silicon nano-crystal "Si–Nc/In0.82Ga0.18As0.40P0.60" materials that can be used. The contrast ratio and delay time for the proposed NOT logic gate are respectively 25.52 dB and 0.66 ps. The structure size is equal to 168 μm2. Designed logic gates are characterized by low energy consumption, high-speed response, compactness and easy integration. All simulations are based on Non-Linear-Finite Difference Time Domain (NL-FDTD) and Plane Wave Expansion (PWE) numerical methods.

An Extensive Finite-Difference Time-Domain Formalism for Second-Order Nonlinearities Based on the Faust-Henry Dispersion Model: Application to Terahertz Generation

A nonlinear finite-difference time-domain (FDTD) formalism is developed to model dispersive second-order nonlinear effects in photonic arrangements and optical devices. The dispersion of the second-order nonlinear susceptibility, χ(2), is based on the Faust-Henry model, which makes no implicit assumption on the relationship between the linear and nonlinear dispersion. Unlike other models for χ(2) dispersion, the Faust-Henry model accurately describes a broad range of crystal classes, including the $$ \overline{4}3m $$ crystal class, which is essential to generating radiation in the terahertz frequency regime. As such, the developed formalism based on the Faust-Henry dispersion model overcomes limitations imposed by previous FDTD methods for modelling second-order nonlinear effects.

Unconditionally stable FDTD algorithm for 3-D electromagnetic simulation of nonlinear media.

For the first time, an unconditionally stable finite-difference time-domain (FDTD) method for 3-D simulation of dispersive nonlinear media is presented. By applying a new adopted alternating-direction implicit (ADI) time-splitting scheme and the auxiliary differential equation (ADE) technique, the time-step in the FDTD simulations can be increased much beyond the Courant-Friedrichs-Lewy (CFL) stability limit. Thus, in comparison to the classical nonlinear FDTD method, the computational time for the proposed approach is decreased significantly while maintaining a reasonable level of accuracy. Numerical examples are presented to demonstrate the validity, stability, accuracy and computational efficiency of the proposed method.

A polarization- and direction-independent phase-matching for third harmonic generation

We proposed a nearly perfect phase-matching for third harmonic generation (THG) in photonic crystals (PhCs), which is independent of the polarization and propagation direction of the fundamental wave. Taking an AlN-like Kerr medium as an example, equal effective refractive indices of the fundamental and the triple frequencies were achieved for both the TM and TE modes simultaneously by fabricating this dispersive medium into a two-dimensional square-lattice PhC. Furthermore, the THG conversion efficiency were numerically calculated by using the nonlinear finite-difference time-domain method to simulate Gaussian pulses with TM and TE polarizations propagating along the high-symmetry directions of the PhC (ΓX and ΓM), respectively. The simulation results show that all THG conversion efficiencies increase with the propagation length like a parabola regardless of the polarization and the propagation direction of the incident fundamental wave, indicating a nearly perfect phase matching.

Optimizing the Nonlinear Optical Response of Plasmonic Metasurfaces.

Controlling the nonlinear optical response of nanoscale metamaterials opens new exciting applications such as frequency conversion or flat metal optical elements. To utilize the already well-developed fabrication methods, a systematic design methodology for obtaining high nonlinearities is required. In this paper we consider an optimization-based approach, combining a multiparameter genetic algorithm with three-dimensional finite-difference time domain (FDTD) simulations. We investigate two choices of the optimization function: one which looks for plasmonic resonance enhancements at the frequencies of the process using linear FDTD, and another one, based on nonlinear FDTD, which directly computes the predicted nonlinear response. We optimize a four-wave-mixing process with specific predefined input frequencies in an array of rectangular nanocavities milled in a thin free-standing gold film. Both approaches yield a significant enhancement of the nonlinear signal. Although the direct calculation gives rise to the maximum possible signal, the linear optimization provides the expected triply resonant configuration with almost the same enhancement, while being much easier to implement in practice.

A nonlinear relaxation formulation of the p-curl problem modelling high-temperature superconductors: A modified Yee's scheme

We propose a new tool for the study of the parabolic p-curl problem modelling the magnetic field in a high-temperature superconductor (HTS), a problem involving an operator ∇×(|∇×H|p−2∇×H) analogous to the p-Laplacian. This so-called nonlinear p-curl problem is computationally expensive in three space dimensions because sharp fronts in the magnetic field develop near the surface of HTS. The proposed technique is a relaxation model of the p-curl problem which is shown to provide a consistent and stable approximation according to first, an inner/outer layer analysis and secondly, according to a time scale expansion. The relaxation model leads to monotone approximations of the front because of the presence of anisotropic diffusion. Most importantly, it can be used to develop new schemes that inherit the properties of the relaxation model.In order to demonstrate the relevance of the relaxation model, this paper applies the approximation to the construction of a second-order nonlinear finite-difference time-domain (FDTD) method, similar to Yee's scheme. It is shown that the natural discretization of the p-curl inspired by Yee's scheme leads to an unstable scheme, while a discretization based on the relaxation model is stable. We propose two numerical discretizations that are respectively first and second order in time, but both second-order in space. The linear and nonlinear stability of the schemes is studied and it is demonstrated that the schemes are both discrete divergence free. We verify the numerical schemes using manufactured solutions and Mayergoyz's moving-front solution in both one and two space dimensions, as well as on a magnetization of a typical HTS.

High efficiency all-optical plasmonic diode based on a nonlinear side-coupled waveguide–cavity structure with broken symmetry

An all-optical plasmonic diode, comprising a metal–insulator–metal waveguide coupled with a stub cavity, is proposed based on a nonlinear Fano structure. The key technique used is to break structural spatial symmetry by a simple reflector layer in the waveguide. The spatial asymmetry of the structure gives rise to the nonreciprocity of coupling efficiencies between the Fano cavity and waveguides on both sides of the reflector layer, leading to a nonreciprocal nonlinear response. Transmission properties and dynamic responses are numerically simulated and investigated by the nonlinear finite-difference time-domain method. In the proposed structure, high-efficiency nonreciprocal transmission can be achieved with a low power threshold and an ultrafast response time (subpicosecond level). A high maximum transmittance of 89.3% and an ultra-high transmission contrast ratio of 99.6% can also be obtained. The device can be flexibly adjusted for working wavebands by altering the stub cavity length.

All-optical bistable switching, hard-limiter and wavelength-controlled power source

In this paper, an all-optical bistable switching operation of resonant-tunneling devices with ultra-small photonic crystal cavity was demonstrated. The whole structure was based on a square lattice photonic crystal formed by rods of refractive index nr= 3.4 in an air background. The cavity was surrounded by eight nonlinear rods of refractive index nL0= 3.1 and nonlinear Kerr coefficient n2= 9 × 10–17 W/m2. Nonlinear finite difference time domain method was used to get a bistability hysteresis loop. Next, all-optical wavelength controlled power source (WCPS), hard-limiter and switching operation based on optical nonlinearity were shown. And that small cavity structure has a small length of 12 mm. Considering the numerous applications and small length, this proposed structure has various potential function in all-optical circuits. Keywords

Nonlinear terahertz frequency conversion via graphene microribbon array

By exploiting the interesting trait of graphene to have electrically tunable first- and third-order conductivities besides its capability to support plasmonic resonances at terahertz frequencies, here, through the nonlinear finite-difference time-domain numerical technique we developed, we demonstrate a noticeable improvement in the conversion efficiency of third-harmonic generation (THG) from a graphene microribbon array by more than five orders of magnitude compared to an infinite graphene sheet, under normal illumination of terahertz waves. As the Fermi level and period length of the ribbon array increase, the transmission obviously manifests a blue shift but denotes a red shift with an increase in ribbon width. The quality factor of resonance (and so the THG efficiency) also shows improvement with an increase in graphene Fermi level, carrier mobility and period length and is degraded by an increase in ribbon width. Generating new frequencies, terahertz signal processing, spectroscopy and so on are among the plethora of valuable potential applications envisioned to be developed based on the findings reported here.

A novel single control all-optical switching and routing in nonlinear photonic crystals

A novel simple control all-optical switching and routing mechanism using two nonlinear photonic crystal (PC) cavities and a T-branch waveguide has been presented. It has been shown that using a single control signal, the input power can be switched with a high-contrast ratio and routed to any of the two output ports. The performance of the proposed device has been investigated through the use of temporal coupled-mode theory (CMT) and two-dimensional (2D) nonlinear finite-difference time-domain (FDTD) simulations in PCs of square lattice.

All-optical controllable channel-drop filters in two-dimensional square-lattice photonic crystals

A novel all-optical controllable channel-drop filter in photonic crystals (PC) of square lattice is presented. We show that using a resonant-cavity-based add-drop filter with a wavelength-selective reflection feedback and a single-control switching module which is based on nonlinear PC microcavities, the dropped channel can be routed to the drop port or returned to the bus waveguide. Using the temporal coupled-mode theory and two-dimensional nonlinear finite-difference time-domain method, the performance of the proposed device is investigated and the simulation results show the validity of the proposed design.

Nonlinear Manipulation of Surface Plasmon Polaritons in Graphene-Based Bragg Reflector

Here, we take the advantage of the strong electromagnetic field of surface plasmon polaritons (SPPs) on graphene to design a tunable terahertz plasmonic Bragg reflector by the intensity of propagating SPP wave. A periodic variation in the effective mode index of SPPs in the direction of their propagation on a graphene layer, required for Bragg scattering, is created by a properly designed silicon\silicon dioxide substrate. A small change in the applied voltage between the graphene sheet and the substrate leads to a noticeable tuning of the stopband region of the reflector. Deposition of a Kerr nonlinear medium on the substrate and in the immediate vicinity of the graphene layer is employed to control the propagation characteristics of SPPs by their intensity. Our numerical simulation results via a developed nonlinear finite difference time domain method reveal that by increasing the SPP wave intensity up to 0.9 ${\bf MW}/{\bf cm}^2 $ which is below the damage threshold of graphene, a red shift in the Bragg frequency up to 220 GHz is achievable. Valuable potential applications can be envisioned for this Bragg reflector as filters and switches due to its fast and high level of tunability with applied gate voltage and the intensity of propagating SPP wave.

Plasmon gap mode-assisted third-harmonic generation from metal film-coupled nanowires

A numerical investigation on the third-order nonlinear optical properties of a plasmonic system composed by metal film-coupled nanowires is reported. The linear and nonlinear optical characteristics are studied by finite-difference time-domain (FDTD) method. To substantially improve the nonlinear effect, the geometric parameters of the system are carefully engineered to excite strong plasmon gap resonance with dramatically enhanced electric field intensity at the gap between the nanowires and the film. The third-harmonic generation (THG) property is examined by nonlinear FDTD simulation. It shows that the THG efficiency estimated from the nonlinear optical absorption can be ∼1 × 10−5 under an incident power density of 5.2 GW/cm2. Plasmonic resonance is necessary to achieve highly efficient THG since the system on resonance shows the THG intensity 4 orders of magnitude higher than that of an off-resonance system.

High-efficiency degenerate four-wave mixing in triply resonant nanobeam cavities

We demonstrate high-efficiency, degenerate four-wave mixing in triply resonant Kerr $\chi^(3)$ photonic crystal (PhC) nanobeam cavities. Using a combination of temporal coupled mode theory and nonlinear finite-difference time-domain (FDTD) simulations, we study the nonlinear dynamics of resonant four-wave mixing processes and demonstrate the possibility of observing high-efficiency limit cycles and steady-state conversion corresponding to $\approx 100$% depletion of the pump light at low powers, even including effects due to losses, self- and cross-phase modulation, and imperfect frequency matching. Assuming operation in the telecom range, we predict close to perfect quantum efficiencies at reasonably low $\sim$ 50 mW input powers in silicon micrometer-scale cavities.

Plasmonic Slot Waveguides with Core Nonlinearity

We analytically study the interplay between group velocity dispersion and material dispersion due to femtosecond ultrafast pulse inside plasmonic slot waveguides with nonlinear dielectric core. The analytic investigation of the role of the core nonlinearity on pulse propagation has been investigated. Interestingly, our model shows that the focusing and defocusing effects of the material can be revered if the material is confined inside the core of a plasmonic slot. We confirm our analytical results with nonlinear finite difference time domain (FDTD) simulations.

Experimental and Numerical Analysis of Temperature Rise in Phantom Caused by High-Intensity Focused Ultrasonic Irradiation

For the safe usage of ultrasonic diagnosis, it is important to research the temperature rise in the human body caused by ultrasonic irradiation. The temperature increase in the human body has been estimated by numerical analysis and an experiment using a tissue-mimicking phantom. In this study, we developed a method for the three-dimensional nonlinear simulation of temperature rise caused by intense ultrasonic irradiation. The sound fields and thermal distributions were calculated by the nonlinear finite difference time domain (FDTD) method and heat conduction equation (HCE) method, respectively. The sound fields and waveforms in water were measured using a hydrophone. The thermal distributions caused by ultrasonic irradiation in the phantom were measured using a thermal camera. The simulation and experimental results of the sound field and thermal distribution were in good agreement. The maximum temperature increase caused by focused ultrasonic irradiation in the phantom was accurately estimated.

Nonreciprocal bistability in nonlinear fractal Fibonacci photonic crystals

It is investigated that the interplay of fractal resonant states and Kerr nonlinearity in the presence of the intrinsic asymmetry of fractal Fibonacci photonic crystals (FFPC) leads to nonreciprocal bistability. Finite element analysis of the 1D nonlinear Helmholtz equation and the nonlinear finite difference time domain are used to study both stable and dynamic electromagnetic behaviors of nonlinear FFPC and nonreciprocal transmission is interpreted through coupled mode theory.

Time-Domain Modeling of Nonlinear Optical Structures With Extended Stability FDTD Schemes

Two numerical methodologies based on the finite-difference time-domain (FDTD) technique are formulated and applied to model optical structures with Raman and Kerr type nonlinearities. The first scheme is based on the alternating-direction implicit finite-difference time-domain (ADI-FDTD), while the second one is based on a recently introduced spatially filtered FDTD method. Both methods are able to extend FDTD time steps beyond the conventional Courant-Friedrichs-Lewy stability limit. It is demonstrated that both methods are significantly faster than the standard nonlinear FDTD, while maintaining its level of accuracy. Their potential as design and analysis tools for nonlinear periodic structures is demonstrated with the study of a 1-D problem involving a nonlinear Bragg reflector.

Fluorescent microscopy using localized excitation source with gold nanotriangles: A computational study

A new method for fluorescent microscopy has been proposed. Proposed method uses indirect excitation of fluorophores with nanometer localized illuminating source. Localized source is created at corners of gold nanotriangles which are deposited on glass substrate. Actually the combination of gold nanotriangle (deposited on glass) acts as active substrate (where species will be placed) for our proposed method. The structure will be scanned with a focused beam of laser (or combination of beams). Due to electric field enhancement in corners and edges of nanotringle (because of surface plasmons), third order nonlinear effect will be enhanced accordingly. Enhancement in third order nonlinearity will give the chance to third harmonic generation and four wave mixing at hot spots. Enhancement in nonlinear process will give the chance of localized source creation for excitation of fluorophores in near field region. In order to prove our claim, we have numerically analyzed interaction of light with gold nanotriangle deposited on glass substrate. Our method is based on solving Maxwell's equation in three dimensions, considering dispersion behaviour of permittivity and third order nonlinear susceptibility by nonlinear finite difference time domain method. Simulation results show that generated light is highly localized and its wavelength can be tuned by changing the excitation wavelength. As a result of omitting background noise and space dependency of excitation source, enhancement in spectral and spatial resolution of imaging system will result.

NOVEL METHOD FOR CANCER CELL APOPTOSIS BY LOCALIZED UV LIGHT WITH GOLD NANOSTRUCTURES: A THEORETICAL INVESTIGATION

A novel approach for phototherapy is proposed. The proposed method is based on cell apoptosis according to halting activation of cancer cell membrane receptor by exposure to UV light pulses without any side effect. In the proposed method, gold nanoparticles are directed to cancerous cells by conjugating their surface with specific ligands. UV light is created locally adjacent to cells around the gold nanoparticles. UV light is generated due to nonlinear interaction of visible light with gold nanoparticles because of enhancement in third order nonlinear effects. For example, by using 780 nm laser, 260 nm UV will be generated around the nanoparticle because of third harmonic generation process. As the generated UV is localized around the cell, there will be no side effect for other cells. We have numerically analyzed the proposed method by solving Maxwell's equation considering third order nonlinear susceptibility and dispersion behavior of permittivity by 3D nonlinear finite difference time domain using Newton–Raphson method. Simulation results for different geometries show that UV light will be generated around gold nanoparticle and it is maximum in hot spots where electric field enhancement occurs. Simulation results illustrate that there is neither UV irradiation side effect to healthy cells, nor harmful temperature rise.