Negative Index Material Channel Research Articles

Impact of higher order dispersions and nonlinearities on instability criterion of oppositely directed coupler in the presence of negative index material channel

This paper intends to investigate the modulational instability (MI) criterion of two core positive-negative index coupler channel setup from the obtained analytical dispersion relation for MI gain profile. The governing equation, the modified nonlinear Schrodinger equation (MNLSE) is studied for the role of higher order dispersion (HOD) and higher order nonlinearity (HON) on instability spectra of two core positive indexed coupler (PIM) and negative indexed coupler (NIM) arrangement. The HOD comprises of the second, third, fourth and fifth order linear dispersion terms and HON is inclusive of cubic, quintic, septic, cubic-quintic-septic-self-steepening (SS), and cubic-quintic-septic-intrapulse Raman scattering (IRS). Our study reveals that it is the 6th order linear dispersion term which brings in the considerable changes of MI gain spectrum in both normal and anomalous dispersion regimes. In particular, the combined effect of septic SS and IRS in two core directional coupler with NIM channel proves to be very crucial in the generation of instability gain spectra. This study has higher prospects in generation of solitary wave in two core directional system for optical fiber communication.

Modulational instability in oppositely doubled-doped directed couplers with a non-kerr-like nonlinear refractive-index change

We theoretically investigate modulation instability (MI) in a two-core nonlinear oppositely directed coupler with a negative-index material channel in the presence of a non-kerr-like nonlinear refractive-index change. Using linear stability analysis, we obtain an expression for the instability gain. It is found that the MI in the nonlinear two-core oppositely directed coupler is significantly influenced by the ratio of the forward- to backward-propagating wave power, nonlinearity, power and saturation. In the normal dispersion regime, the septic nonlinearity is found to suppress the MI by reducing both the gain and width of the instability nonlinearity. But in anomalous dispersion regime, the situation is different because septic nonlinearity enhances the MI by increasing both the gain and width of MI. The increase of septic nonlinearity both in normal and anomalous dispersion regimes increases the gain of the instability nonlinearity. Thus, we report new ways to generate and manipulate the MI and solitons in two-core oppositely directed couplers with a particular emphasis on a negative-index material (NIM) channel in presence of septic nonlinearity.

Role of higher order nonlinearities in the instability spectra of two core oppositely directed saturated coupler

We theoretically investigate the impact of modified form of saturable nonlinearity in the modulational instability (MI) spectra of an opposite directed two core coupler with a negative index material channel. Particularly, our emphasize is on the interplay between the nonlinear saturation and the higher order nonlinear effects in fibers such as self-steepening and intrapulse Raman scattering. Using the modified nonlinear Schrödinger equation we appropriately model the light propagation in the two core opposite coupler with saturation of nonlinearity. A standard approach like the linear stability analysis was used to derive the dispersion relation pertaining to the MI. For a comprehensive picture, we consider both the normal and the anomalous dispersion regimes and special attention is paid to understand the influence of system parameters such as the power, coupling coefficient, saturation parameter, and nonlinear coefficient on the MI. Effect of different combinations of self-steepening as well as the contribution of intrapulse Raman scattering are discussed and its role on the instability bands are highlighted. Thus we report new ways to generate and manipulate the MI in two core oppositely directed couplers with the effect of saturation of nonlinearity.

Analyzing the effect of higher order nonlinearity on dispersion relation and optical multistability generation in oppositely directed coupler

We report the influence of higher order nonlinearity on dispersion relation and multistability in oppositely directed coupler with negative index material channel. The study shows that the high intensity electric field shifts the photonic bandgap down in energy. When the positive index material channel of the coupler is influenced by quintic nonlinearity the group velocity of upper branch of dispersion curve (δ–q curve) falls to zero in positive q region and the loop in the lower branch shifts to positive q region. But the minima in upper branch and loop in the lower branch are observed at negative q region when the negative index material channel is influenced by χ(5) nonlinearity. As the curvature of the dispersion relation determines the group velocity dispersion the study report the possibility for dispersion engineering in oppositely directed coupler. Also we observed that the quintic nonlinearity enhances formation of multi stable states.

Multistability and switching in oppositely-directed saturated coupler

We investigate theoretically the optical multistability that takes place in a two-core oppositely-directed saturated coupler (ODSC) having negative index material (NIM) channel. The dynamics are studied using the Lagrangian variational method, and analytical solutions are constructed with Jacobi elliptic functions. The ODSC exhibits a bandgap as a consequence of the effective feedback mechanism due to the opposite directionality of the phase velocity and the Poynting vector in the NIM channel. Depending on the strength of the nonlinear saturation, the system admits multiple stable states. Considering the additional degrees of design freedom with respect to conventional nonlinear couplers, the ODSC could become an attractive choice for all-optical switching. The existence of multiple transmission resonance windows could also facilitate the realization of gap solitons.

Effects of higher-order nonlinear dispersions on modulational instability in a three-core coupler with negative index material channel and saturable nonlinearity

A theoretical investigation on the impact of high-order nonlinear dispersions of the modulation instability (MI) spectra in the three core triangular oppositely directed coupler with negative index material channel is carried out. A keen attention was paid to find out the influence of self-steepening (SS), intrapulse Raman scattering (TR), second-order nonlinear dispersion (SOND) as well as saturable nonlinearity (SNL) on the MI spectra. Gain spectra has been investigated for both anomalous group velocity dispersion (GVD) and normal GVD regime. Particularly, our results show that in the normal GVD regime, the instability gain exists even if the perturbation frequency (Ω) is zero; and the instability gain at Ω=0 is nil when the dispersion is anomalous. We also find that the magnitude and sign of SOND exert strong influences on MI sideband. Furthermore, by adjusting various parameters such as SS, intrapulse Raman scattering, and SOND, we observe the occurrence of new instability regions. The MI sidelobes, as well as its bandwidth, have also been affected by the SNL. Finally, the SNL may influence considerably the number of wave trains induced by MI. These results can help to understand the generation of soliton-like excitation in nonlinear three-core oppositely directed couplers with a particular attention on a negative-index material channel.

Optical Bistability and Switching in Oppositely Directed Coupler

We report the optical bistability in two core oppositely directed coupler with negative index material channel. Using Langrangian variational method and Jacobi elliptic functions, we construct the solutions of the coupled nonlinear Schrodinger equations. The bistability arises due to the effective feedback mechanism as a result of opposite directionality of the phase velocity and energy flow in the negative index material channel. We report the various ways to control and manipulate the bistability threshold and hysteresis loop, which could be useful in the design and development of fast and low-threshold optical switches.

A theoretical study on threshold conditions of modulation instability in oppositely directed couplers

We theoretically investigate threshold conditions to observe modulation instability (MI) in a two-core nonlinear oppositely directed coupler (ODC) with a negative-index material (NIM) channel. Using linear stability analysis, we obtain an expression for the instability gain. The analysis shows, with two discrete instability regions, that the band at lower values of f (ratio of the backward to forward-propagating waves amplitude) is a result of the nonlinear positive index material (PIM) channel while the broader range band is a consequence of the nonlinear NIM channel. Both bands are highly sensitive to system parameters. We demonstrate that MI has a threshold-like condition in the normal dispersion regime. This study also shows that gain increases proportionally to power increases and the two instability regions approach each other, thereby narrowing the stability region. Furthermore, we report that the effect of pump power and the coupling coefficient on instability gain have an opposite relationship. Similarly, study of the influence of the nonlinear coefficient on critical power (Pc) shows that Pc gradually decreases as the nonlinear coefficient increases. Thus, a comprehensive study on the influence of various physical effects on MI is reported in this paper.

Influence of birefringence in the instability spectra of oppositely directed coupler with negative index material channel

A theoretical investigation on the influence of birefringence in the modulational instability (MI) spectra of an oppositely directed coupler (ODC) with a negative index material (NIM) channel is presented. We study the effect of birefringence on MI in linear and circular birefringent ODCs for both normal and anomalous dispersion regimes. It is found that besides the instability band due to nonlinear positive index material (PIM) and negative index material (NIM) channels, new symmetric instability regions are observed as a result of birefringent effects. Also defocusing nonlinearity suppresses the NIM band in the normal dispersion regime, but in the anomalous dispersion regime the defocusing nonlinearity enhances the gain of the NIM band. In contrast to the case of linear birefringence, in terms of MI gain from circular birefringence, only two birefringent bands dominate: the inherently PIM and NIM bands. This preponderance is attributed to the fact that the cross-phase modulation effect for the case of circular birefringence is stronger, thus allowing a better coupling between the beams, which results in the enhancement of the gain. Therefore, the manipulation of MI and solitons in an ODC is better performed when the birefringence is circular rather than linear. Here we report how to generate and manipulate MI and solitons in birefringent ODCs with a particular emphasis on a NIM channel.

Modulation instability in a triangular three-core coupler with a negative-index material channel

A theoretical investigation of the modulation instability (MI) in the three core triangular oppositely directed coupler with negative index material channel is presented. This class of couplers have an effective feedback mechanism due to the opposite directionality of the phase velocities in the negative and positive index channels. It is found that the MI in the nonlinear three core triangular oppositely directed coupler is significantly influenced by the ratio of the forward- to backward-propagating wave power and nonlinearity. Also, in the case of the normal dispersion regime a threshold-like behavior is observed, whereas this behavior is not identified in the anomalous dispersion regime. For the asymmetric case (), two pairs of instability bands are observed for both the nonlinear NIM and PIM channels, while a single pair of instability bands is noted for the symmetric case (h = 1). In the normal dispersion regime, the defocusing nonlinearity is found to suppress the MI by reducing both the gain and width of the instability band, whereas the MI is enhanced in the anomalous dispersion regime due to the defocusing nonlinearity. Thus we report new ways to generate and manipulate the MI and solitons in three-core triangular oppositely directed couplers with a particular emphasis on a negative-index material (NIM) channel.

Modulation instability in the oppositely directed coupler with a quadratic nonlinearity

We investigate modulation instability (MI) in a nonlinear oppositely directed coupler with a quadratic nonlinearity, where one channel is made from a positive-index material (PIM) and another channel is fabricated from a negative-index material (NIM), trying to identify the different MI properties from those in a conventional parametric gap system with grating. Both the analytic continuous wave (CW) solutions and dispersion relation are obtained. By using standard linear instability we in detail discuss how the ratio of the backward to forward propagating wave’s power, the phase mismatch, and the coupled coefficient influence the dynamical behavior of MI. Large stable regions are found if the fundamental harmonics (FH) falls in the normal dispersion when compared to the case in the conventional Bragg grating with a quadratic nonlinearity where the CW solutions are unstable in most cases. In addition, we also observe the large stable regimes of the CW solutions even when the coupled strength for the second harmonics (SHs) is weaker than that of the FH. These findings suggest that the oppositely directed coupler with a NIM channel provides more ways to manipulate the MI and soliton.

Theoretical investigation of modulation instability in a three-core coupler with negative index material channel

Abstract We investigate the modulation instability (MI) in a three-core oppositely-directed coupler with a particular emphasis on a negative index material (NIM) channel. In order to give a comprehensive picture, we consider the normal and the anomalous dispersion regimes. Special attention is paid to investigation of the influence of system parameters such as the power and the coupling coefficient on the MI. We also analyze the impact of different nonlinear configurations of coupler channels on MI.

Modulation instability in an array of positive- and negative-index waveguides

The dispersion relation and modulation instability (MI) of an array of alternating positive-index material (PIM) and negative-index material (NIM) waveguides are investigated. It is found that the transverse wave vector of the stability wave solution has modulation on the linear part of the dispersion relation, which leads to the dispersion relation being linear in the staggered case. The MI region for the staggered case is larger than the unstaggered case, which is the same as that of a conventional waveguide array. Whether in the staggered case or the unstaggered case, the self-focusing or self-defocusing nonlinear property of PIM and NIM channels affects the gain value of the array, and the gain structure of the array for the unstaggered case has an important dependence on the nonlinear property of PIM and NIM channels, but is not affected by the nonlinear property of the channels for the staggered case. It is also found that in addition to the nonlinear property of the channels, the interaction of the nonlinear effects of the channels also has great influence on the generation of the MI. These findings indicate that we can manipulate MI in an array of positive- and negative-index waveguides with the controllability of a NIM channel.