Coupling Coefficient Dispersion Research Articles

Effects of coupling coefficient dispersion on the Fermi-Pasta-Ulam-Tsingou recurrence in two-core optical fibers

In a two-core optical fiber (TCF), the linear coupling coefficient between the two cores in general varies with the optical wavelength, a phenomenon known as coupling coefficient dispersion (CCD). Here we study the effects of CCD on the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena in a TCF. Modulation instability tends to be a precursor in the formation of breathers. The subsequent decay of breathers and re-emergence of modulation instability lead to FPUT type periodic patterns. For the symmetric or antisymmetric continuous-wave (CW) state of a TCF, CCD does not affect the modulation instability gain spectra. However, if asymmetric perturbations are applied to a symmetric CW state, CCD can drastically modify FPUT. In the anomalous dispersion regime, without CCD, only FPUT dynamics without energy transfer between the two cores occurs. With CCD effects, FPUT dynamics with strong energy transfer between the two cores can arise. As CCD increases, FPUT dynamics without energy transfer never vanishes, but the corresponding number of FPUT cycles can be drastically reduced to only one. In the normal dispersion regime, no FPUT dynamics with energy transfer between the two cores occurs. The major CCD effect is to significantly decrease the FPUT cycles, and only one FPUT cycle can be observed at relatively large magnitude of CCD values. As the magnitude of CCD increases further, more FPUT cycles arise again. Moreover, larger CCD will lead to higher (lower) propagation speed of the wave patterns in the anomalous (normal) dispersion regime respectively. To enhance theoretical insight, we perform a Floquet analysis for the linearized stability equations with periodic coefficients based on the FPUT dynamics in the normal dispersion regime. The monodromy matrix and eigenvalues can be computed explicitly. Larger eigenvalues correlate with stronger instability and more rapid disintegration of the periodic patterns, agreeing well with the trends of the numerical simulations.

Modulation instabilities in twin-core fibers with self-steepening effects

Effects of self-steepening (SS) on modulation instabilities (MIs) are systematically studied in twin-core optical fibers with the asymmetric continuous wave (CW) state. In anomalous dispersion, there is one MI band. SS can reduce the instability gain significantly, shrink the MI band dramatically, and move the instability band to low frequency. MI never vanishes for any incident total powers above a required minimum total power, being contrary to the case in single core fibers that MI disappears at total powers above a threshold value in relation to SS. In normal dispersion, there are two MI bands. With SS, the high frequency band vanishes for incident total powers above a threshold value, and the low frequency band enhances with gain increasing and moves to the lower frequency. We also discover that SS can significantly suppress (enhances) the high frequency band that appears due to coupling coefficient dispersion and fourth-order dispersion (Raman scattering).

Solitary wave solutions in two-Core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity

In this paper, we studies chirped solitary waves in two-Core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct chirp soliton, the couple of nonlinear Schrödinger equation which describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, the exact analytical solutions of the GNSE were obtained by using three relevant mathematical methods namely the auxiliary equation method, the modified auxiliary equation method and the Sine-Gordon expansion approach. Lastly, the behavior of the chirped like-soliton solutions were discussed and some contours of the plot evolution of the bright and dark solitons are obtained.

The effects of fourth-order dispersion on modulation instabilities in two-core optical fibers with asymmetric CW state

The effects of fourth-order dispersion (FOD) on modulation instabilities in the twin-core optical fibers with the asymmetric CW state are studied systematically. When the product of the group velocity dispersion and FOD is negative, in the anomalous dispersion regime, two new MI bands in the high frequency are generated with one band either having the equivalent gain with that of original band or dominating the MI depending on the FOD value; in the normal dispersion, a new dominant MI band in the high frequency is always generated, and the original MI bands vanish in the presence of FOD at total power above a critical value. When the product of the group velocity dispersion and FOD is positive, the main effect of FOD is to shift the MI band to the low frequency and reduce the bandwidth simultaneously with minor effects on the instability gain. We also find that the effects of linear coupling coefficient dispersion can be significantly suppressed in the presence of FOD especially for the case of negative product of the group velocity dispersion and FOD. Finally, the effects of FOD on MI are verified numerically by launching continuous waves with the wave propagation method. Our results should provide very benificial information for successfully observing MI in TCFs or MI related applications with TCFs.

Impact of fourth order dispersion on modulational instabilities in asymmetrical three-core optical fiber

In this paper we investigate the impact of linear coupling coefficient and coupling coefficient dispersion on modulational instability (MI) in the presence of fourth order dispersion (FOD) in an asymmetric three core optical fiber under normal and anomalous dispersion regime. In addition, we also considered the impact of symmetric and asymmetric power ratio on MI characteristics. It is found that there is significant influence by linear coupling coefficient and coupling coefficient dispersion (CCD) on MI under different dispersion regimes. In anomalous dispersion regime, at β4 < 0 the generation of smaller MI secondary side bands were observed at higher frequencies while at normal dispersion the effect of FOD leads to breaking of MI gain at different values of coupling coefficient. Though the appearance of the MI gain at different frequencies is highly controlled by FOD, but the amplitude of MI gain found to be reduced with increasing FOD under each dispersion regimes. In case of CCD, the impact of FOD found to be quite insensitive and found no MI gain in the absence of CCD under symmetric power ratio under both dispersion regimes.

The complexity of surface acoustic wave fields used for microfluidic applications

Using surface acoustic waves (SAW) for the agitation and manipulation of fluids and immersed particles or cells in lab-on-a-chip systems has been state of the art for several years. Basic tasks comprise fluid mixing, atomization of liquids as well as sorting and separation (or trapping) of particles and cells, e.g. in so-called acoustic tweezers. Even though the fundamental principles governing SAW excitation and propagation on anisotropic, piezoelectric substrates are well-investigated, the complexity of wave field effects including SAW diffraction, refraction and interference cannot be comprehensively simulated at this point of time with sufficient accuracy. However, the design of microfluidic actuators relies on a profound knowledge of SAW propagation, including superposition of multiple SAWs, to achieve the predestined functionality of the devices. Here, we present extensive experimental results of high-resolution analysis of the lateral distribution of the complex displacement amplitude, i.e. the wave field, alongside with the electrical S-parameters of the generating transducers. These measurements were carried out and are compared in setups utilizing travelling SAW (tSAW) excited by single interdigital transducer (IDT), standing SAW generated between two IDTs (1DsSAW, 1D acoustic tweezers) and between two pairs of IDTs (2DsSAW, 2D acoustic tweezers) with different angular alignment in respect to pure Rayleigh mode propagation directions and other practically relevant orientations. For these basic configurations, typically used to drive SAW-based microfluidics, the influence of common SAW phenomena including beam steering, coupling coefficient dispersion and diffraction on the resultant wave field is investigated. The results show how tailoring of the acoustic conditions, based on profound knowledge of the physical effects, can be achieved to finally realize a desired behavior of a SAW-based microacoustic-fluidic system.

Pressure sensing with zero group velocity lamb modes in self-supported a-SiC/c-ZnO membranes

The propagation of the Lamb modes along a-SiC/c-ZnO thin supported composite structures was simulated for different ZnO and a-SiC layer thicknesses and electrical boundary conditions. The phase and group velocity, the field profile and the electroacoustic coupling coefficient dispersion curves of the Lamb modes travelling along the composite plate were calculated for different layers thicknesses. Zero group velocity (ZGV) points were identified which group velocity vanishes while the phase velocity remains finite, at specific layers thickness values. ZGV resonators (ZGVRs) were designed that consist in only one interdigital transducer and no grating reflectors at its sides. The finite element method analysis was performed to investigate the strain, stress and internal pressure the a-SiC/ZnO plate experiences when subjected to an external uniform differential pressure in the 1–10 kPa range. The ZGVR pressure sensitivity, i.e. the relative frequency shift per unit pressure change, was found to be mostly affected by the change in the membrane thickness induced by the pressure. A pressure sensitivity of 9 ppm kPa−1, in the 4–10 kPa range, was predicted for the a-SiC(1 µm)/ZnO(1 µm) ZGV-based pressure sensor. The feasibility of high-frequency micro-pressure sensors based on a-SiC and ZnO thin film technology was demonstrated by the present simulation study.

Modulation instabilities in equilateral three-core optical fibers for isosceles-triangle symmetric continuous waves

Modulation instability (MI) of the isosceles-triangle symmetric continuous wave in equilateral three-core fibers (ETCFs) is studied in detail. The so-called isosceles-triangle symmetric continuous wave state is the planar wave where the fields in its two cores are identical but different from the field in the third core, and the premise of its existence is that the total power (P) exceeds a minimum value (Pmin) that depends on the linear coupling coefficient and nonlinear coefficient of ETCFs. For a given total power P (P ≥ qslant Pmin), set the power in one core to be P1, and the powers in the other two cores to be P2 (P=P1 + 2P2), then two kinds of filed distributions will be found. The first kind is for P1 &gt; P2 with P1 becoming more and more large as total power P increases. By the linear stability analysis method, the main characteristics of MI in ETCFs are found which are quite similar to those of the asymmetric continuous wave states in two core optical fibers (TCFs). The other kind is that P1 becomes more and more small and P2 becomes more and more large as total power P increases. Through the same method, the main characteristics of MI in ETCFs are found which are distinctively different from those of the asymmetric continuous wave states in TCFs. On the one hand, MI can be generated in both normal and anomalous dispersion regimes without perturbations. In addition, the zero-perturbation frequency corresponds to the largest gain of MI in the normal dispersion regime. On the other hand, the coupling coefficient dispersion, which can dramatically modify the spectra of MI in TCFs, plays a minor role in both normal and anomalous dispersion regimes in ETCFs. In practical application, the findings in this paper are of guiding significance for studying the nonlinear effects of mode-division multiplexing system based on the multimode or multicore optical fibers.

Impact of higher order dispersion and nonlinearities on modulational instability in a dual-core optical fiber

In this investigation, we examine theoretically modulational instability (MI) in a dual-core optical fiber with higher order dispersion as well as higher order nonlinear effects. For dual-core or multicore optical fiber the investigation of MI analysis extends with parameters like linear coupling coefficient and coupling coefficient dispersion using extended coupled nonlinear Schrodinger equation. We analyze the impact of these parameters on MI gain spectrum at anomalous and normal dispersion regime along with higher order parameters. Our results show that the combined effect of higher order dispersion like fourth order dispersion and nonlinear parameter like self-steepening effect due to cubic–quintic nonlinearity, stimulated Raman response which is inevitable for the study of ultrashort pulse propagation and generation of the soliton. The study reveals that the frequency selection of MI gain is primarily controlled by the dispersion parameters while nonlinear parameters restrict the intensity and bandwidth of the MI gain. Though most of the distinguishable effects are observed in anomalous dispersion regime due to the presence of higher order parameters decent gain is also visible in the normal dispersion regime.

Modulation instability in collinear three-core optical fibers

Modulation instability (MI) in a collinear three-core optical fiber, namely, an optical fiber that consists of three identical cores aligned symmetrically along a straight line, is analyzed in detail for the symmetric and antisymmetric continuous-wave (CW) states in the normal and anomalous dispersion regimes. The symmetric CW state, where the fields in the two side cores are identical, exists only with certain combinations of powers in the side cores and the center core within a limited range of total power, and these characteristics are governed by the linear coupling and the nonlinear coefficient of the fiber. The symmetric CW state generates MI characteristics not observed previously. In the anomalous dispersion regime, as the total power increases from a threshold value, three MI bands are generated and then merge rapidly into a single band, and the MI gain is insensitive to the linear coupling coefficient and the coupling-coefficient dispersion (CCD) of the fiber. In the normal dispersion regime, the generation of MI depends critically on the CCD. Two MI bands are generated from the CCD at a total power smaller than a critical value that depends on the linear coupling, the dispersion, and the nonlinear coefficient of the fiber. No MI can be generated without CCD. The antisymmetric CW state, where the fields in the two side cores have equal amplitudes of opposite signs and the field in the center core is zero, exists at any power. For this state, the MI characteristics are qualitatively similar to those of an equilateral three-core fiber. The study also includes direct numerical verification of the MI analysis with wave propagation simulation.

Influence of Glass Fiber Nonlinearity and Dispersion on Light propagation in Double Core Optical Fiber

Influence of coupling and intermodal dispersion coefficient on pulse splitting in double core optical fibre was investigated by using solutions of normalized coupled nonlinear Schrödinger equations. It was found that if coupling coefficient and intermodal dispersion coefficient was small, and then nonlinearity cannot balance intermodal dispersion effect. Consequently, pulse was distorted. Furthermore, if intermodal dispersion coefficient was large enough, then pulse splitting occurred. Increasing coupling coefficient avoids pulse splitting and the pulse was stable.

Modulation instabilities in equilateral three-core optical fibers

Modulation instabilities (MIs) of the continuous-wave (CW) states in equilateral three-core fibers are analyzed in detail. For the equilateral-triangle symmetric CW state where the fields in the three cores are identical, conventional MI characteristics similar to those of two-core fibers are obtained. For the antisymmetric CW state where the fields in two of the three cores have equal amplitudes of opposite signs and in the third core it is zero, new MI characteristics are found. In the normal dispersion regime, there are in general two MI bands, one of which is generated above a critical total power and quickly becomes the dominant band as the total power increases. This critical power is insensitive to the group-velocity dispersion, increases (decreases) with the coupling coefficient (the nonlinear coefficient) almost linearly, and decreases rapidly to almost zero as the coupling-coefficient dispersion (CCD) increases. In the anomalous dispersion regime, there are two significant MI bands, which are governed by two separate dispersion relations. The lower-frequency band, which is similar to the MI band of a single-core fiber, is not affected by the coupling coefficient and the CCD, while the higher-frequency band is sensitive to these two parameters. The lower-frequency band always has a higher gain than the higher-frequency band, which converges to the lower-frequency band as the coupling coefficient and the CCD approach zero. For the isosceles-triangle symmetric CW state where the fields in two of the three cores are equal, the MI characteristics are qualitatively similar to those of the asymmetric state of two-core fibers. Simulation results based on solving the nonlinear coupled-wave equations agree well with the MI analysis.

Love-Mode MEMS Devices for Sensing Applications in Liquids.

Love-wave-based MEMS devices are theoretically investigated in their potential role as a promising technological platform for the development of acoustic-wave-based sensors for liquid environments. Both single- and bi-layered structures have been investigated and the velocity dispersion curves were calculated for different layer thicknesses, crystallographic orientations, material types and electrical boundary conditions. High velocity materials have been investigated too, enabling device miniaturization, power consumption reduction and integration with the conditioning electronic circuits. The electroacoustic coupling coefficient dispersion curves of the first four Love modes are calculated for four dispersive coupling configurations based on a c-axis tilted ZnO layer on wz-BN substrate. The gravimetric sensitivity of four Love modes travelling at a common velocity of 9318 m/s along different layer thicknesses, and of three Love modes travelling at different velocity along a fixed ZnO layer thickness, are calculated in order to design enhanced-performance sensors. The phase velocity shift and attenuation due to the presence of a viscous liquid contacting the device surface are calculated for different thicknesses of a c-axis inclined ZnO layer onto BN half-space.

Spatial, temporal, and spatio-temporal modulational instabilities in a planar dual-core waveguide

We investigate modulational instability (MI) in a planar dual-core waveguide (DWG), with a Kerr and non-Kerr polarizations based on coupled nonlinear Schrödinger equations in the presence of linear coupling term, coupling coefficient dispersion (CCD) and other higher order effects such as third order dispersion (TOD), fourth order dispersion (FOD), and self-steepening (ss). By employing a standard linear stability analysis, we obtain analytically, an explicit expression for the MI growth rate as a function of spatial and temporal frequencies of the perturbation and the material response time. Pertinently, we explicate three different types of MI—spatial, temporal, and spatio-temporal MI for symmetric/antisymmetric continuous wave (cw), and spatial MI for asymmetric cw, and emphasize that the earlier studies on MI in DWG do not account for this physics. Essentially, we discuss two cases: (i) the case for which the two waveguides are linearly coupled and the CCD term plays no role and (ii) the case for which the linear coupling term is zero and the CCD term is nonzero. In the former case, we find that the MI growth rate in the three different types of MI, seriously depends on the coupling term, quintic nonlinearity, FOD, and ss. In the later case, the presence of quintic nonlinearity, CCD, FOD, and ss seriously enhances the formation of MI sidebands, both in normal as well as anomalous dispersion regimes. For asymmetric cw, spatial MI is dependent on linear coupling term and quintic nonlinearity.

Analytical study of the propagation of fast longitudinal modes along wz-BN/AlN thin acoustic waveguides.

The propagation of the fundamental symmetric Lamb mode S0 along wz-BN/AlN thin composite plates suitable for telecommunication and sensing applications is studied. The investigation of the acoustic field profile across the plate thickness revealed the presence of modes having longitudinal polarization, the Anisimkin Jr. plate modes (AMs), travelling at a phase velocity close to that of the wz-BN longitudinal bulk acoustic wave propagating in the same direction. The study of the S0 mode phase velocity and coupling coefficient (K2) dispersion curves, for different electrical boundary conditions, has shown that eight different coupling configurations are allowable that exhibit a K2 as high as about 4% and very high phase velocity (up to about 16,700 m/s). The effect of the thickness and material type of the metal floating electrode on the K2 dispersion curves has also been investigated, specifically addressing the design of an enhanced coupling device. The gravimetric sensitivity of the BN/AlN-based acoustic waveguides was then calculated for both the AMs and elliptically polarized S0 modes; the AM-based sensor velocity and attenuation shifts due to the viscosity of a surrounding liquid was theoretically predicted. The performed investigation suggests that wz-BN/AlN is a very promising substrate material suitable for developing GHz band devices with enhanced electroacoustic coupling efficiency and suitable for application in telecommunications and sensing fields.

Quasi-Linear Polarized Modes in Y-Rotated Piezoelectric GaPO4 Plates

The propagation of both surface and flexural acoustic plate modes along y-rotated x-propagation GaPO4 piezoelectric substrates was studied for several y-cut angles: the phase velocity and coupling coefficient dispersion curves were theoretically calculated for two different electroacoustic coupling configurations. The investigation of the acoustic field profile across the plate thickness revealed the presence of thin plate modes having polarization predominantly oriented along the propagation direction, and hence suitable for operation in liquid environment. These modes include the linearly polarized Anisimkin Jr. and the quasi longitudinal plate modes, AMs and QLs, showing a phase velocity close to that of the longitudinal bulk acoustic wave propagating in the same direction. The temperature coefficient of delay (TCD) of these longitudinal modes was investigated in the −20 to 420 °C temperature range, in order to identify thermally stable or low TCD cuts. The power flow angle, i.e., the angle between the phase and group velocity vectors, was also estimated to evaluate the substrate anisotropy effect on the acoustic wave propagation. The GaPO4 intrinsic properties, such as its resistance to high temperature and its chemical inertness, make it especially attractive for the development of acoustic waves-based sensors for applications in harsh liquid environment.

Dark soliton switching in nonlinear fiber couplers with gain

Abstract In this paper, we present a study of numerical simulations for all-optical dark soliton switching in nonlinear directional couplers with gain additions in two waveguides whilst considering intermodal dispersion and its higher-order effects. The effects of possible combinations of gain addition in the bar channel as well as in the cross channel of the nonlinear couplers are theoretically presented. In addition, the consequence of second-order coupling coefficient dispersion based on coupled mode theory for dark soliton switching is numerically depicted.

Switching of ultrashort pulses in nonlinear high-birefringence two-core optical fibers

We analyze the switching characteristics of ultrashort pulses in a nonlinear high-birefringence two-core optical fiber by solving a set of four generalized coupled nonlinear Schrödinger equations. In such a fiber, the critical power required for activating switching changes significantly with the polarization angle of the input pulse and, as a result, a pulse at a proper power level can be switched between the two cores of the fiber by changing the input polarization angle. This provides a simple mechanism of achieving optical switching with the fiber. We also study the effects of the group-delay difference (GDD) between the two polarization components and the coupling-coefficient dispersion (CCD) in the fiber on the switching characteristics. The GDD tends to break up the two polarization components in the input pulse and thus leads to an increase in the switching power. A larger GDD, however, can give a sharper switching contrast when the input polarization angle is varied. The CCD tends to break up the input pulse and cause pulse distortion, regardless of the polarization, so it also leads to an increase in the switching power. Unlike the GDD, a large CCD always reduces the switching contrast. To achieve high-quality switching, the fiber should have a small CCD.

Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber

The modulational instability of a dual core optical fiber under the combined effect of coupling coefficient dispersion (CCD) and relaxation of nonlinear response is presented. The effect of wavelength dependence of coupling coefficient is effectively included in the pair of generalized linearly coupled nonlinear Schrödinger equation (CNLSE). In order to account for the finite response time, a time dependent nonlinear response is incorporated in the system of CNLSE using the Debye relaxation model. The results from the linear stability analysis show that in anomalous dispersion regime for any finite relaxation time, the nonlinearity becomes complex and there exist two unstable modes. In the normal dispersion regime, a single unstable band at higher detuning frequency is observed which is identified as the Raman band. In symmetric case the CCD is found to be immaterial, whereas in asymmetric case the CCD is found to be crucial and brings new spectral bands. A critical value of CCD is predicted where the dynamics evolve dramatically in different manners. Thus in this paper, the MI dynamics of a dual core optical fiber is fully explored and the interplay between CCD and relaxation is clearly highlighted.

Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion

Modulational instability (MI) in a twin-core optical fiber with the combined effect of saturation of nonlinearity (SNL) and coupling coefficient dispersion (CCD) is presented. The CCD does not dramatically modify the spectrum of the symmetric or antisymmetric continuous wave (CW) case, but the SNL on the other hand behaves in a perceptible manner such that the gain and the unstable region inherently decrease. In the anomalous dispersion region, the gain of the instability spectrum increases (decreases) monotonously with power (coupling coefficient). The effective nonlinearity and the power threshold for the sustained CW solution becomes a function of power for the SNL case. The so-called nonlinear factor behaves in a unique way such that there exist two powers for the same value of nonlinear factor. The interplay between CCD and SNL is emphasized, where any nonzero value of CCD leads to new instability bands and the saturation on the other hand suppresses the gain of the instability band. We identified a pair of power corresponding to the constant value of the nonlinear factor, where the system becomes invariant, such that the number of instability bands, the gain, and the range of the unstable region are all preserved. In the case of the normal dispersion case, the MI is achieved purely by means of the coupling coefficient. In both cases, a critical CCD is predicted, where the system evolves dramatically in a different manner.