Nonlinear Directional Coupler Research Articles

Soliton switching and multi-frequency generation in a nonlinear photonic crystal fiber coupler

Soliton switching in nonlinear directional couplers implemented in photonic crystal fibers (PCF) examined here. A vector finite element method (FEM) has been developed to precisely calculate the dispersion along with coupling length of the guided modes. The PCF coupler geometry was carefully designed so that it can support soliton pulses. Soliton switching is demonstrated numerically at 1.55 microm for 100 femto-second (fs) pulses. Our theoretical results explain some of the key spectral features previously observed in the experiment.

Quantization of coupled 1D vector modes in integrated photonic waveguides

A quantum mechanical analysis of the guided light in integrated photonics waveguides is presented. The analysis is made starting from one-dimensional (1D) guided vector modes by taking into account the modal orthonormalization property on a cross section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry in order to quantize the 1D vector modes and to derive the quantum momentum operator and the Heisenberg equations. The results provide a quantum-consistent formulation of the linear and nonlinear quantum light propagations as a function of forward and backward creation and annihilation operators in integrated photonics. As an illustration, an application to an integrated nonlinear directional coupler is given, that is, both the nonlinear momentum and the Heisenberg equations of the nonlinear coupler are derived.

Soliton Switching in Fiber Coupler with Periodically Modulated Dispersion, Coupling Constant Dispersion and Cubic Quintic Nonlinearity

In this paper we present the soliton dynamics in a two port fiber nonlinear directional coupler with periodically modulated dispersion and coupling constant dispersion that arose due to the intermodal dispersion between symmetric and antisymmetric modes of the coupler. The fiber material possessed cubic quintic nonlinearity. The influences of the coupling constant dispersion, periodically modulated dispersion and quintic nonlinearity on the soliton switching dynamics have been comprehensively studied. The expressions for the transmission coefficient, cross talk and extinction ratio have been derived in the context of both quintic nonlinearity and periodically modulated dispersion. It has been found that an increase in the value of the quintic nonlinearity has detrimental influence on the soliton switching. Our analytical results have been supported by numerical simulation.

Soliton switching and propagation in two-core nonlinear fiber coupler with high order coupling coefficient

We use the variational approach (VA) and the split-step Fourier transforms (SSFT) to study the transmission and switching characteristics inside the fiber nonlinear directional coupler (NDLC). The results, based on the VA, indicate that the second-order coupling coefficient dispersion and initiative chirp all reduce the coupling length, and the second-order coupling coefficient dispersion makes the switching characteristics become sharper and threshold power become bigger under the case of not having initiative chirp. The outcomes, based on the SSFT, indicate that the first order intermodal dispersion coefficient make optical pulses splitting in the propagation of fundamental solitons, and the second-order coupling coefficient dispersion reduces the coupling length, sharpens the switching characteristics and increases the switching threshold power, the results agrees well with those from the VA.

Analysis of a Tunable Asymmetrical Nonlinear Directional Coupler Using Laser Beam Interaction with Semiconductor Medium

A tunable asymmetrical nonlinear directional coupler (NLDC) having interaction of a laser beam with the semiconductor medium of the coupler has been thoroughly analyzed. The analysis is based on the coupled-mode theory for coupled lines. Laser beam is used for achieving optical control over the nonlinear directional coupler. The effects of various parameters such as plasma density, waveguide width, laser beam frequency and laser spot position on the coupling of power, on an asymmetric coupler have been investigated and presented.

Coupling Theory of Asymmetric Photonic-crystal Waveguides

The physical properties of asymmetric photonic-crystal directional couplers are studied by using the tight-binding theory, which considers that the fleld distributions of photonic- crystal waveguides (PCWs) are localized around the periodic defects. From this model, the analytic formulas which describe the dispersion of the coupler and the eigenmode patterns were derived. By considering coupling up to the third nearest-neighboring between two PCWs, analytic expressions of the dispersion relations of asymmetric photonic crystal coupler are consistent with the results from the plane wave expansion method (PWEM). Due to the broken symmetry, two dispersion curves will never cross. Nevertheless, the eigenmode patterns switch their parity as the symmetric coupler does when wavevector k passes over the decoupling point. Photonic crystal waveguide (PCW) is a structure which introduces considerable quantities of point defects in the photonic crystal (PC). The electromagnetic (EM) wave is strongly conflned in the defect channel, allowing low-loss in Y-blanches and a sharp-bending. Furthermore, creating two line defects to form a directional coupler are used as add/drop fllters, switches and multiplexers. To design photonic crystal devices, the simulation tools such as the PWEM and the flnite difierence time domain method (FDTD) have often been used. However, there is no simple analytic for- mula to analyze physical properties of the coupled photonic crystal waveguides (PCWs), especially to analyze coupling between PCWs (1). Tight-binding theory (TBT) is widely used not only in condensed matter physics but also recently in the EM wave propagation in linear and nonlinear single line defects PCW analytically. They usually considered only coupling between the nearest- neighboring defects that may be good enough in the single PCW or conventional waveguides. Nevertheless, it is insu-cient to only consider the nearest-neighboring defects in the directional coupler made of two identical PCWs (2). The dispersion curves will always split or never cross if only the nearest-neighboring coupling is considered, but the dispersion do cross that was resolved by further considering coupling of the second nearest neighboring defects which causes a sinusoidal modulation to the dispersion curves. Similar to the extended TBT (2) which considers three nearby coupling coe-cients, in this paper, we flrstly derive an analytic solution to describe the dispersion of asymmetric coupled PCWs. This formula provides more generalized discussion and physical insight than what is derived for the case of symmetric coupled PCWs. Especially, the coupled identical PCWs should become asymmetric due to the intensity dependent index of refraction in the nonlinear photonic crystal directional coupler. Secondly, by using the analytic formulas, the phenomena of mode switching and mode patterns in the asymmetric PCWs are extensively analyzed. Finally, the simulation results of considering PCWs of triangular lattices are consistent with our theoretic results. 2. COUPLED EQUATIONS FOR ASYMMSTRIC PHOTONIC CRYSTAL WAVEGUIDES

Switching in three-core nonlinear fiber coupler with second order coupling dispersion coefficient

The propagation and switching of fundamental solitons in three-core fiber nonlinear directional coupler with three cores in an equilateral-triangle arrangement have been investigated with two methods. Firstly, by using variational method, we obtained the equation of transmission coefficient with respect to distance. Secondly, we used the split-step Fourier method (SSFM) to solve the nonlinear Schrdinger equations. The results of both variational method and SSFM indicate that the energy of optical pulses transfer periodically between the three cores and have sharp switching characteristics when the first order intermodal dispersion coefficient is small. Otherwise, the periodicity of the coupling transmission characteristics of optical solitons in fiber coupler and the sharpness of switching are destroyed. The second order intermodal dispersion coefficient and initiative chirp reduce the coupling length, shorten the periods of the energy transfer of optical pulses between the three cores, and increase the threshold switching power. Though the cross phase modulation coefficient has weaker impact on transmission characteristics, it increases the threshold switching power of couplers.

Analysis of an optical logic gate using a symmetric coupler operating with pulse position modulation (PPM)

In this paper we propose the operation of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) operating with a pulse position modulation (PPM). The performance of a symmetric NLDC realizing two-input AND/OR logical functions, which can be applied in transmission and processing of signals in all-optical form in TDM systems, is examined. This integrated symmetric NLDC logical gate operates with two ultrashort soliton light pulses (2ps), which are modulated in agreement with the technique of pulse position modulation (PPM). Initially, we evaluate the effect resulting of an increment in the PPM coding parameter offset (ε), for the temporal position of the output pulse, considering the anomalous group-velocity dispersion (GVD), nonlinear self phase modulation (SPM) and without loss propagation regime of input pulses, in the cores 1 and 2 of the NLDC. In this situation, we analyze the four possible situations for the two-input logical gate, modulating the 1 and 2 input pulses through temporal displacement and allowing a variation in the coding parameter offset. We can conclude that is possible to get AND/OR logical operations for the cores 1 or 2, without to insert PPM error, since a phase control (Δϕ) exists applied in agreement with the logical level of the input pulse in the core 1. Finally we define the truth table, considering the adequate phase difference and coding parameter offset for the stable operation of the AND/OR logical gate based in the symmetric NLDC.

Phase-induced soliton switching in fiber nonlinear directional couplers

A numerical study of femtosecond soliton switching by the relative phase change of a weak control pulse is carried out for a Kerr coupler with the simultaneous presence of intermodal dispersion, cross-phase modulation, third-order dispersion, self-steepening, and intrapulse Raman scattering. It is shown (numerically) that cross-phase modulation, though it appears as a very tiny parameter, plays a positive role in this mode of soliton switching and that these perturbative effects may lead to useful soliton switching if the relative phase of the control pulse is monitored judiciously.

Logic Gates Based in Asymmetric Couplers: Numerical Analysis

In this work, we present a numerical investigation of the transmission and switching of fundamental solitons in asymmetric nonlinear directional couplers, constructed with dispersion decreasing fibers (DDF). In this configuration, the coupler consists of two separated parallel fibers, one with a DDF profile and the other with a constant profile. We obtained the characteristics of transmission, extinction ratio, and compression factor of the device. The truth tables for the logic gates AND, OR, and XOR were obtained. We concluded that the device presenting a constant profile provided the best performance of the studied logic gates. Logic gates AND, OR, and XOR operating with extinction coefficient around 16.6 dB were obtained.

Switchable AlxGa1−xAs all-optical delay line at 1.55μm

The authors demonstrate an on-chip optical delay in AlxGa1−xAs that operates at room temperature and 1.55μm. A nonlinear directional coupler for optical switching and a 188ps long racetrack structure provide bit delays of >100 for picosecond pulses. In the linear regime the transmission ratio of the slow channel is 74%, which reduces to 40% with increasing peak intensity. (Meanwhile, the fast channel output increases from 26% to 60%.) Switching occurs due to a nonlinear detuning of the directional coupler, limited by three-photon absorption and time-averaging effects. This proof-of-principle device can operate at up to 5GHz and is promising for optical buffering applications.

Analysis of a gained nonlinear directional coupler pulse switch

We have investigated the switching performance of a gained (nonlinear directional coupler) NLDC switch in the presence of both 2nd and 4th order gain nonlinearities. In this system, we have achieved a nearly complete pulse switching at half beat length of the coupler which implies about 40% reduction in the switching length as compared to the switching length reported in Trillo et al. (1988). We have shown that at the half beat length the output energy of each branch is equal to that of the input energy and hence the gained NLDC switches have ability to be cascaded. Our initial investigations reveal that this gained NLDC switch has remarkable performance and potential to be used in ultra-fast optical communication systems.

Nonlinear directional coupler for polychromatic light

We demonstrate that a nonlinear directional coupler with special bending of waveguide axes can be used for all-optical switching of polychromatic light with a very broad spectrum covering all of the visible region. The bandwidth of the suggested device is enhanced five times compared with conventional couplers. Our results suggest novel opportunities for the creation of all-optical logical gates and switches for polychromatic light with white-light and supercontinuum spectra.

Design of an ultra-fast all-optical dark soliton switch in a nonlinear directional coupler (NLDC) made of chalcogenide glasses

We designed and simulated a nonlinear directional coupler switch by using dark soliton propagation in this coupler. We utilized the optical properties of chalcogenide glasses such as their high nonlinear refractive index and positive group velocity dispersion and designed a switch having a length of 1.2 mm and an ultra-fast pulse width of 10 fs with a 100 W power input pulse. The switching characteristic shows that complete switching is possible for different ranges of lengths and pulse widths, and by using the result of the simulation we find a relation between the length and the pulse width with respect to the necessary power for complete dark soliton switching. Also the effect of two photon absorption (2PA) on dark soliton switching was studied and it was shown that the 2PA puts some limitations on the switching action but, because of the low value of the 2PA figure of merit for chalcogenide glasses, it did not have any considerable effect on dark soliton switching.

Microwave nonlinear spin wave directional coupler

A nonlinear spin-wave directional coupler for the microwave range has been designed, constructed, and studied for the first time. Each of the four ports of the device can be used as the input or output for a microwave signal. The role of a control element in the coupler is played by a nonlinear spin wave shifter based on a thin ferromagnetic film. A distinctive feature of the proposed device is that an increase in the input power level leads to the signal switching from one to another output, which is caused by a power-dependent variation in the spin wave phase shift.

Power-dependent switching of microwave signals in a ferrite-film nonlinear directional coupler

The authors report the realization of a microwave nonlinear directional coupler based on a ferrite film. It is a passive device for direct signal processing at microwave frequencies. The power-dependent switching of microwave signals is demonstrated. The switching is achieved through a differential nonlinear phase shift of the operating spin waves propagating in the ferrite film.

Effects of third-order dispersion on soliton switching in fiber nonlinear directional couplers

The split-step Fourier method is used to study the energy switching characteristics of fiber nonlinear directional couplers with the third-order dispersion. The effects of the third-order dispersion increases with the third-order dispersion coefficient and input power and result in pulse shift and energy decreases. Adding high-order nonlinear can partly overcomes these effects.

Variational principles for coupled nonlinear Schrödinger equations

Via He's semi-inverse method, a variational principle is established for coupled nonlinear Schrödinger equations arising in nonlinear directional coupler. This Letter shows the effectiveness and convenience of the semi-inverse method.

Nonlinear optical pulse coupling dynamics

The pulse coupling dynamics in a nonlinear directional coupler (NLDC) is analyzed by using the new normalized coupled nonlinear Schro/spl uml/dinger equations. The operation of an NLDC can be divided into three regions according to L/sub D//spl kappa/: Region 1 (L/sub D//spl kappa//spl les/1), Region 2 (L/sub D//spl kappa/>50), and Region 3 (1<L/sub D//spl kappa//spl les/50). In region 1, an NLDC can exhibit a good switching performance. In region 2, both the pulse coupling and continuous-wave (cw) coupling in an NLDC show the similar energy transfer characteristics. In the case of L/sub D//spl kappa//spl ges/1000, even an ultrashort pulse coupling can be reduced to the cw coupling and follow Jensen's equations when certain criteria are met. Consequently, many of the applications of NLDC that are suggested under the condition of cw excitation can also be implemented under the condition of ultrashort pulse excitation. In region 3, pulses suffer from pulse compression and serious distortion. The conditions for a pulse following Jensen's equations are presented. A 0.8-ps pulse with a wavelength of 1.55 /spl mu/m in a silica coupler with a half-beat length of 50 mm follows Jensen's equation. To get a good switching performance, the input optical pulsewidth should be smaller than a certain maximum value. In addition, the intermodal dispersion including the contribution of the material dispersion is derived, and zero intermodal dispersion is predicted.

Pulse-width selective all-optical switching

The coupled nonlinear Schrödinger equations governing the optical pulse coupling in a nonlinear directional coupler are solved numerically. The numerical results show that the optical pulse can be coupled back and forth efficiently between the two-coupled waveguides by varying the input pulse duration. The energy transfer efficiency between the two-coupled waveguide can be greater than 90%. It implies that the pulse-width dependent all-optical switching can be realized in a nonlinear directional coupler.