Asymmetric Nonlinear Directional Coupler Research Articles

Modulational Instability in Linearly Coupled Asymmetric Dual-Core Fibers

We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. Using coupled-mode equations for this system, we identify MI conditions from the linearization with respect to small perturbations. First, we compare the MI spectra of the asymmetric system and its symmetric counterpart in the case of the anomalous group-velocity dispersion (GVD). In particular, it is demonstrated that the increase of the inter-core linear-coupling coefficient leads to a reduction of the MI gain spectrum in the asymmetric coupler. The analysis is extended for the asymmetric system in the normal-GVD regime, where the coupling induces and controls the MI, as well as for the system with opposite GVD signs in the two cores. Following the analytical consideration of the MI, numerical simulations are carried out to explore nonlinear development of the MI, revealing the generation of periodic chains of localized peaks with growing amplitudes, which may transform into arrays of solitons.

Interaction dynamics of bright solitons in linearly coupled asymmetric systems

We present an extensive numerical investigation on the interaction dynamics of optical bright solitons in asymmetric nonlinear directional couplers taking into account the effects of group velocity mismatch, phase-velocity mismatch and differences in group velocity dispersions and effective mode areas between two cores. We also numerically explore the stability of bright solitons in the presence of harmonic infinitesimal perturbation, which is seeded in the form of uniform white noise. To have a comprehensive picture, we finally emphasize the influence of every individual asymmetric parameters on the soliton interaction in asymmetric nonlinear directional couplers.

Numerical investigation of dark soliton switching in asymmetric nonlinear fiber couplers

Switching characteristics of dark soliton in asymmetric nonlinear directional couplers are numerically studied. Every individual effect, responsible for producing asymmetry in nonlinear directional coupler, has been analyzed in detail. It is found that group-velocity mismatch and the difference in group-velocity dispersions between the two cores have no impact on dark soliton, which can be specified as an advancement over the bright solitons. The effects of phase velocity, the difference in effective mode areas and the linear coupling coefficient on the dark soliton switching are also investigated.

All-optical logic gates based on cross-phase modulation in an asymmetric coupler

In this paper we propose an operation of an all-optical logical gate based on an asymmetric nonlinear directional coupler operating with the cross-phase modulation. Two-input OR and XOR gates and a new logical operation based on an asymmetric nonlinear directional coupler, which can be applied to transmission and processing of signals in all-optical systems, are examined. Initially, we evaluate the effect of the pump power on switching. We import a pulse into the nonlinear directional coupler, meanwhile adding a pump light via wavelength division multiplex in order to take advantage of Kerr effect and produce the cross-phase modulation. In this situation, we analyze two possible situations for the two-input logical gate, and draw a switching characteristic curve via Matlab. Finally, we define the truth table and it is clear that OR and XOR logic gates and a new logical operation can be realized by changing the pump power. Next the investigation also indicates that to change the input pulse's phase switching can be realized. In the same way, we define the truth table and it can be observed that different logic gates are realized.

Switching and enhanced bistability in an asymmetric nonlinear directional coupler with a metamaterial channel

We numerically simulate the propagation and switching of ultra-short pulses in a metamaterial nonlinear directional asymmetric coupler where one of the guides is a conventional medium with a positive refraction index having a decreasing Kerr nonlinearity. The second guide is based in a metamaterial. A complete study of the nonlinear dynamics of ultra-short pulses propagation and switching in this new nonlinear directional coupler, including the transmission characteristics, bistability, critical power, compression factor and extinction coefficients are presented and compared to those of a conventional coupler. We conclude that the conventional coupler has higher transmission efficiency and extinction rate when compared with the metamaterial coupler. However the metamaterial coupler presents bistability which opens the possibility of such device to be used in a large variety of optical switching, storage and logical gates. We show that the input power range leading to bistability can be optimized by controlling the profile of the nonlinear refraction index of the conventional channel.

Thermal stability analysis of nonlinear optical switch based on asymmetric three-core nonlinear directional coupler with variable Gaussian coupling coefficient

We analyze the thermal stability of the power transmission efficiency and the extinction ratio in an asymmetric three-core silicon-on- insulator nonlinear directional coupler with variable Gaussian coupling coefficient. Because the refractive indices of Si and SiO2 materials are subject to temperature change, the effective refractive index of the non- linear coupler varies correspondingly. When ratio (LC/b) andT change, the relative transmission efficiency error (� ) values and relative change of extinction ratio (η) values are obtained. It can be easily shown that vari- ation ofand η are negligible under LC/b ≤ 1/2. Therefore, we can set LC/b ≤ 1/2 andT ∈ (-100 K, 100 K) in order to make the power transmis- sion efficiency and the extinction ratio work steadily. This is significant in guiding an actual nonlinear optical pulse switch fabrication. C � 2011 Society

Study of the Performance of an All-Optical Half-Adder Based on Three-Core Non-Linear Directional Fiber Coupler Under Delayed and Instantaneous Non-Linear Kerr Responses

Recently, much attention has been given to the influence of the relaxation process of the non-linear response, because the usual assumption of instantaneous non-linear response fails for ultra-short pulses, and additional contributions coming from non-linear dispersion and delayed non-linearity have to be taken into account. This article presents a numerical analysis of the symmetric planar and asymmetric planar three-core non-linear directional fiber couplers operating with a soliton pulse, where effects of both delayed and instantaneous non-linear Kerr responses are analyzed for implementation of an all-optical half-adder. To implement this all-optical half-adder, eight configurations were analyzed for the non-linear directional fiber coupler, with two symmetric and six asymmetric configurations. The half-adder is the key building block for many digital processing functions, such as shift register, binary counter, and serial parallel data converters. The optical coupler is an important component for applications in optical-fiber telecommunication systems and all integrated optical circuit because of its very high switching speeds. In this numerical simulation, the symmetric/asymmetric planar presents a structure with three cores in a parallel equidistant arrangement, three logical inputs, and two output energy. To prove the effectiveness of the theoretical model for generation of the all-optical half-adder, the best phase to be applied to the control pulse was sought, and a study was done of the extinction ratio level as a function of the Δ > parameter, the normalized time duration, and the Sum and Carry outputs of the (symmetric planar/asymmetric planar) non-linear directional fiber coupler. In this article, the interest is in transmission characteristics, extinction ratio level, normalized time duration, and pulse evolution along the non-linear directional fiber coupler. To compare the performance of the all-optical half-adders, the figure of merit of the logic gates was used. All results were obtained numerically, considering a simple model for generation of an all-optical half-adder.

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.

All-optical limiting using nonlinear directional couplers composed of a self-focusing and a self-defocusing waveguide

We numerically demonstrate the all-optical limiting features in a mismatched nonlinear directional coupler (NLDC) composed of a self-focusing and a self-defocusing waveguide for both continuous wave and pulse cases. The working conditions required are analyzed. To obtain the limiting feature, the propagation constant of the self-focusing waveguide should not be larger than that of the self-defocusing waveguide. Cascaded asymmetric NLDCs are investigated to improve the limiting characteristics. The limiting threshold and the limiting output power can be adjusted by varying the coupler length or the ratio of the nonlinearity coefficients of the self-defocusing and self-focusing waveguides. Analytical solutions are presented in the case of a continuous wave. For the pulse case, numerical solutions show that the top part of the output pulse, if it exceeds the limiting threshold, will be tailored, while the rising and falling edges of the output pulse are almost the same as the input pulse. There is almost no pulse breakup. The influence of the second order dispersion and the intermodal dispersion on the limiting characteristics are analyzed.

All optical logic gates based on an asymmetric nonlinear directional coupler

The performance of three different asymmetric dual core nonlinear directional couplers which includes an increasing and a decreasing self-phase modulation profile (SPM) was investigated. The asymmetry is associated to the SPM profile of one of the channels. Looking at the transmission characteristics of the device, through the direct- and cross-channel, we did a study of the extinction ratio (Xratio) of the devices. It was observed that in the operation of the three couplers, the performance of AND, XOR and OR gates are dependent on the nonlinearity profile of the coupler. For all configurations, an AND port with gain was observed. We can conclude that to operate the asymmetric coupler as a logic gate one has to control the nonlinearity profile to optimize the transmission characteristics thorough the extinction rate coefficient (Xratio).

The Calculation of Switching Power of Symmetric and Asymmetric Nonlinear Directional Couplers With Variable Coupling Coefficient

It is proposed that the switching power of symmetric one-coupling-length nonlinear directional couplers (NLDC) with variable coupling coefficient (VCC) can be calculated as the weighted average of the local critical power of the coupler. Further, it is shown that the switching characteristics of a one-coupling-length VCC NLDC are determined mainly by the first half of the coupler and the switching power of an asymmetric VCC NLDC can be calculated as the weighted average of the local critical power over the first half of the coupler. Both symmetric and asymmetric examples are presented.

Realization of All-optical Ultrafast Logic Gates using Triple Core Asymmetric Nonlinear Directional Coupler

Article Realization of All-optical Ultrafast Logic Gates using Triple Core Asymmetric Nonlinear Directional Coupler was published on April 1, 2001 in the journal Journal of Optical Communications (volume 22, issue 2).

Multistable all-optical switching behavior of the asymmetric nonlinear directional coupler

Asymmetric dual core nonlinear directional couplers that include an increasing self phase modulation profile are examined. The asymmetry is associated with the self phase modulation profile of one of the channels (direct channel). Looking at the transmission characteristics of the device, through the direct channel, one observes that, when pumping in the direct channel, there is a decrease in the critical power which is lower compared with the symmetric coupler, and the critical power is a single-value function of the nonlinearity. For the pump power in the cross channel the transmission function of the coupler presents regions of multistability, where the coupler presents more than one critical power for certain values of the self phase modulation profile index. It was also observed that all the profiles under study, with increasing self phase modulation profile, present this behavior. For the studied profiles, one region of multistability was observed where three possible critical powers were observed. However, for the exponential profile, a second region was observed for a higher value of the self phase modulation profile parameter. It is concluded that to operate the asymmetric coupler in a single-value region for the critical power, the exponential self phase modulation profile presents the best behavior for the profiles under study.

Optical Multistability on the Asymmetric Nonlinear Directional Coupler

Asymmetric dual core nonlinear directional couplers that include an increasing self phase modulation profile are examined. The asymmetry is associated to the nonlinear refractive index profile of one of the channels (direct channel). Looking at the transmission characteristics of the device, through the direct channel, one observe that, when pumping in the direct channel, there is a decrease in the critical power which is lower compared with the symmetric coupler, however the critical power is a single valued function of the nonlinearity. For the pump power in the cross channel the transmission function of the coupler present regions of multistability, where the coupler presents more than one critical power for certain values of the self phase modulation index. For the studied profiles one region of multistability was observed, where three possible critical powers were seen. It is concluded that the asymmetry leads the coupler to operate in a multivalued function of the critical power for certain values of the nonlinear parameter. To operate the asymmetric coupler in a single valued region for the critical power one has to avoid the multistable region of the device.

Coupled-mode analysis of an asymmetric nonlinear directional coupler

A coupled-mode analysis of an asymmetric planar nonlinear directional coupler (NLDC) is presented by using the singular perturbation technique. The NLDC consists of a nonlinear waveguide with the core of Kerr-like medium and a linear waveguide situated parallel to each other. The effects of linear coupling and nonlinear modification of refractive index are treated to as small perturbations, and the modal fields of isolated linear waveguides are employed as the basis of propagation model. The self-consistent coupled-mode equations governing the power transfer are derived in analytically closed form. The representative numerical result for the input/output characteristics demonstrates that the asymmetric NLDC is useful for constructing a band-pass power-filter or a band-reject power-filter.

Switching power reduction in asymmetrically designed nonlinear directional couplers

An asymmetric nonlinear directional coupler, where the switching of a signal controlled by a strong pump, is investigated, in order to reduce the necessary switching power. It is shown that the switching power is reduced by 67% when the control wavelength is located in the vicinity of the signal wavelength.

Role of the asymmetry in a third-order nonlinear directional coupler

The behaviour of an asymmetric third-order nonlinear directional coupler is discussed. The operation of such devices is strongly influenced by the choice of the channel for the input, the linear or the nonlinear one. When input linear excitation is considered and no saturation is present in the other nonlinear arm, a power switch in a half-beat length coupler with excellent functional characteristics is found. When saturation is included, the initial excitation in the linear core gives a critical nonlinear saturation value to achieve effective power switching larger with respect to the nonlinear core input excitation.

Optically induced grating in a directional coupler

An optically induced grating in an asymmetric nonlinear directional coupler, formed by the interference of two strong external fields in a nonlinear medium, is analyzed. The grating constant and the amplitude of the grating depend on the parameters of the external waves, and thus they can be varied during coupler operation. As a result external-power-controlled coupling of a chosen pair of normally mismatched guided modes can be realized.

Numerical analysis of an asymmetric nonlinear directional coupler

AbstractThe power transfer characteristics of an asymmetric nonlinear directional coupler (NLDC), which consists of a nonlinear waveguide with a core of Ken‐like medium and a linear waveguide, are analyzed using the beam propagation method. The numerical results demonstrate that the asymmetric NLDC is useful for constructing an optical power filler. © 1994 John Wiley & Sons, Inc.

All-optical ultrafast logic gates that use asymmetric nonlinear directional couplers

All-optical ultrafast AND, OR, and XOR logic functions that use asymmetric nonlinear directional couplers are numerically demonstrated. In such an asymmetric coupler, different Kerr effects are generated when the same power is launched into two waveguides. The output power tends to appear in the waveguide of stronger Kerr effect when only one waveguide is excited. When both waveguides are excited, the output power contrast between the two waveguides depends on the relative phase of the two input signals. The parameters of fiber couplers are used to demonstrate the logic functions.