Nonlinear Directional Coupler Research Articles

Matrix coupled mode theory model of strongly-coupled multiwaveguide optical nonlinear directional couplers

This paper discusses an improved coupled mode theory model for the nonlinear directional coupler in the strong-coupling range. A new single-line matrix equation is derived for the multiwaveguide case. For the two-guide case, a new critical power formula and two exact identities are derived. Interrelation between the overlap integral and nonlinear cross-coefficients is demonstrated. It is shown that inconsistent inclusion of these terms in previous approaches leads to inaccuracies. Results obtained by consistent inclusion of these terms and our critical power formula show a great improvement in accuracy over previous analyses in strong-coupling.

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).

Light propagation in a directional coupler with saturable nonlinearity

The propagation of laser radiation in a nonlinear directional coupler with identical optical waveguides is studied theoretically. Account is taken of refractive index saturation. Bifurcations of the intensity distribution and transmission characteristic are revealed, and respective regions in the parameter plane are delineated. Two points of input intensity self-switching are found. A coupling length vs. normalized input intensity is investigated for different values of the nonlinearity parameter. Distinctive features of the coupler with saturated nonlinearity compared with Kerr-type couplers are highlighted.

Phase properties of the superposition of squeezed and displaced number states

We show that a nonlinear asymmetric directional coupler composed of a linear waveguide and a nonlinear waveguide operating by nondegenerate parametric amplification is an effective source of single-mode squeezed light. This is has been demonstrated, under certain conditions and for specific modes, for incident coherent beams in terms of the quasiprobability functions, photon-number distribution and phase distribution.

Full-vectorial finite-element beam propagation method for nonlinear directional coupler devices

A new full-vectorial beam propagation algorithm based on the computationally-efficient finite element method is presented which can accurately model nonlinear directional couplers. The robust perfectly matched layer boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The accuracy of the proposed vectorial propagation approach is demonstrated through comparison with other semivectorial approaches and the weaknesses of the commonly-used scalar approaches are highlighted. The proposed full-vectorial approach considers only two transverse components of the magnetic field without destroying the sparsity of the matrix equation, so it is numerically very efficient.

Theory of light propagation in three-core nonlinear directional couplers

An exact analytic solution is obtained for the problem of light propagation in a three-core nonlinear directional coupler with identical parallel fibres in the geometry of a regular triangle for an arbitrary dependence of the propagation constant on the light intensity.

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.

Analysis of soliton switching in dispersion-decreasing fiber couplers

We present an analytical and numerical investigation of the propagation and the switching of fundamental solitons in a two-core nonlinear fiber coupler constructed with dispersion decreasing fiber (DDF) with a variational method using the Lagrangian density formulation. The analytical solutions were directly obtained from the coupled nonlinear Schrödinger equations. Our simulations considering six different profiles, linear, hyperbolic, exponential, logarithm, constant and Gaussian. The transmission characteristics, the critical energy and the compression factor of first order solitons obtained by the analytical procedure agree well with the results from numerical analysis. Twin core nonlinear directional couplers that include loss are also examined. The inclusion of loss results in the increase of the critical power of the coupler and broadening of the switched pulses, while the switching characteristics deteriorate. To compensate for this worse behavior, associated to the loss, we have investigated the effect of the DDF profile on the performance of the coupler. We show that appropriate shaping of the DDF profile is quite effective to recover, almost completely, the original switching behavior associated to the lossless situation. It is concluded that the hyperbolic dispersion profile is nearly optimum to the recovery of the lossless switching behavior.

Nonlinear directional coupler in periodically poled lithium niobate

Nonlinear wave propagation was investigated experimentally in coupled waveguides by means of the cascaded nonlinearity in quasi-phase-matched second-harmonic generation. With a specially designed wave-vector-mismatch distribution along the propagation axis, cascading was optimized for low fundamental depletion. High-contrast, ultrafast all-optical switching with switching powers of tens of watts was observed.

Temporal soliton switching in a rectangular nonlinear directional coupler

We address the theory of temporal soliton switching in a planar geometry directional coupler constructed from silica and doped silica glass and operating at the central wavelength of 1.55 microm, significant for erbium-doped amplification. We formulate the field in the coupler in terms of the supermodes of the total structure and take account of the two transverse dimensions of the rectangular channels. In the case of the weak coupling between channels consistent with elimination of pulse breakup, the effect of the fields in the outer corner regions of the channels results in a switching intensity that differs significantly from that derived from coupled-mode theory on the basis of a slab model of the coupler.

Theory of nonlinear directional couplers

A method is proposed for obtaining exact analytical solutions for the system of nonlinear equations for the propagation of electromagnetic waves in directional couplers with an arbitrary nonlinearity in the propagation constant. The resulting solutions can be used to determine the operating characteristics of nonlinear directional couplers.

Numerical simulation of a passive twin-core fibre nonlinear coupler ring laser

Passive modelocking of a passive nonlinear directional coupler ring laser employing a near-half-beat-length passive twin-core fibre is numerically simulated by taking into account Raman self frequency shift and gain saturation. Raman self frequency shift is reduced by inserting two bandpass filters. Modelocking threshold condition and steady-state characteristics are investigated in extensive numerical experiments. It is found that, in addition to solitonic modelocking operation regime predicted by previous studies, non-soliton and chirped soliton operation regimes also exist in such a laser. The solitonic modelocking operation requires a proper balance of saturable amplification, bandpass filtering, nonlinear coupling and output coupling. The generation of transform-limited solitons with durations as short as 0.44 ps and pedestal extinctions of better than 40 dB is numerically demonstrated.

Application of the polyconjugated main chain polymer DPOP-PPV for ultrafast all-optical switching in a nonlinear directional coupler

The observation of ultrafast all-optical switching in a polyconjugated main chain polymer (DPOP-PPV), nonlinear directional coupler at a wavelength with an energy below two-photon resonances is reported. The effect responsible for the switching is clearly the nonresonant instantaneous intensity dependent refractive index change. To our knowledge these results represent the first demonstration of an ultrafast device using a polyconjugated polymer, where the switching is not drastically limited by absorption processes.

Soliton interaction and switching in a coupler with third order dispersion and Raman effect

The interaction and switching of optical solitons in a nonlinear directional coupler are investigated analytically and numerically. The influence of the coupling-coefficient dispersion, the third order dispersion and the Raman effect in fibers on these processes are reported. Coupled soliton states are found, and their stability is checked numerically. Switching characteristics of solitons in directional couplers are studied.

Switching dynamics of short optical pulses in a nonlinear directional coupler

It has been shown recently that the propagation of short optical pulses in a nonlinear directional coupler consisting of two parallel waveguides or fibers should be described more generally by a pair of coupled nonlinear equations that take into account the dispersion properties of the coupling coefficient. In this paper, we use the Fourier series analysis method to solve these equations, and study the effects of a dispersive coupling coefficient on the switching dynamics of short optical pulses in a nonlinear directional coupler. We demonstrate, with numerical examples, that a dispersive coupling coefficient could cause significant pulse distortion and affect the threshold switching intensity. The effects of introducing frequency chirps in the input pulses are also discussed.

Observation of Solitons on Nonlinear Directional Couplers by Finite Difference Method

An efficient procedure for solving the coupled nonlinear Schrodinger equations by finite difference method is proposed. The procedure is illustrated on the example of soliton propagation on nonlinear directional coupler (NLDC), what is described by a pair of coupled nonlinear Schrodinger differential equations. The numerical routine is implemented in the program for numerically solving the nonlinear Schrodinger equations. The analysis enables observation of solitons and includes losses and third-order dispersion. Graphical representation of soliton propagation in two and three dimensions is obtained. The energies in both channels of the directional couplers, at the coupling length, are presented.

Analysis of an Optically Controlled Nonlinear Directional Coupler

An optically controlled nonlinear directional coupler (NLDC) to be useful in optical integrated circuits has been analyzed. The optical control is achieved through the interactions between a laser beam and surrounding semiconductor medium. The effect of plasma density, laser beam wavelength and waveguide with on the performance of the coupler including critical power has been thoroughly investigated. A far better performance compared to a simple NLDC has been achieved.

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.

Nonlinear optical limiter and digital optical switch by cascaded nonlinear couplers: analysis

In this paper, an all-optical digital switch and a limiter are proposed and analyzed, both of which consist of several nonlinear directional couplers in series. These two devices utilize the nonlinear restraining effect of the nonlinear coherent coupler on its input power. In the devices, the OFF-ON extinction ratio, the output power fluctuation and the dynamic switching range all decrease with the number of the couplers in series increasing, and the output power level can be adjusted by varying the coupling length. The characteristics of these devices with different structures are discussed, and the numerical results show that the OFF-ON extinction ratio and the dynamic switching range of the optical switches can be less than -90 dB and 0.03P/sub c//100, respectively, and that the fluctuation of the limiting output power of the optical limiter can be less than 10/sup -7/P/sub c/.

All-fiber logical devices based on the nonlinear directional coupler

We have studied theoretically the transmission of lightwave through cascaded nonlinear directional couplers with two-input excitations. Various types of all optical logic operations including AND, OR, XOR, NOR, NXOR, and NAND are available in the same cascaded nonlinear fiber coupler structure.