Using a variational method, we have developed an approximate model of the dynamics of soliton coupling described by coupled nonlinear Schrodinger equations. The results are analytical and can be recast into a suggestive particlelike description providing a physical insight into the problem.The particular case of the nonlinear coherent coupler is emphasized, and an estimate of the soliton switching peak power is obtained. A symmetry-breaking instability is also described, in a simple way, with the potential-well picture.

We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm 2 . Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm. In a typical configuration, a waveguide array of MachZehnder interferometers (MZIs) with increasing path differences are used to implement the SHS concept [9,10]. For such a geometry, the source power spectrum and the output interferogram are related by the cosine FT. A similar MZI array geometry, including phase-correction circuits using independent heaters for each MZI, has also been demonstrated [13]. However, when long optical path delays are required for high spectral resolution, similar configurations yield prohibitively large devices.In this Letter, we present a compact FT spectrometer chip, in which a high spectral resolution of 40 pm with a compact device size is achieved by using tightly coiled spiral waveguide structures in an MZI array. Furthermore, a spectral retrieval algorithm with phase and amplitude error compensations is demonstrated for the first time to the best of our knowledge, obviating the need for dedicated phase correction circuits. The FT spectrometer is implemented as an array of N MZIs in silicon-on-insulator (SOI) waveguides (Fig. 1). Each MZI comprises a reference arm of constant length and a delay arm with a spiral waveguide. The length of the delay arm, i.e., spiral length, linearly increases by ΔL across the array. The high refractive index contrast of the SOI platform and the waveguide bend radius of ∼5 μm readily allows the making of spirals with geometrical lengths of over a centimeter within an area only a few hundred micrometers in diameter.For a given input spectral distribution, the dispersive property of the MZI array results in a wavelengthdependent spatial interferogram at the outputs of the array. The relation between the input spectral distribution and the interferogram Ix i is unambiguous within

Concept, theory and simulations of a new type of waveguide device, a multiaperture Fourier-transform planar waveguide spectrometer, are presented. The spectrometer is formed by an array of Mach-Zehnder interferometers generating a wavelength dependent spatial fringe pattern at the array output. The input light spectrum is calculated using a discrete Fourier transformation of the output spatial fringes. The multiaperture input significantly increases the optical throughput (étendue) compared to conventional single input spectrometers. Design rules for the arrayed spectrometer are deduced from performance specifications such as wavelength range and spectral resolution. A design example with spectral resolution 0.025 nm and range 2.5 nm is presented, where the optical throughput is increased by a factor of 200 compared to a single input device.

We performed a systematic analysis of exact solutions for the higher-order nonlinear Schrodinger equation iP~+Prr=a, g~t(t~'+azg~P~+ia, (P~P~')r+(a4+ia, )P(~g~')r that describes wave propagation in nonlinear dispersive media. The method consists of the determination of all transformations that reduce the equation to ordinary differential equations that are solved whenever possible.All obtained solutions fall into one of the following categories: "bright" or "dark" solitary waves, solitonic waves, regular and singular periodic waves, shock waves, accelerating waves, and selfsimilar solutions. They are expressed in terms of simple functions except for few cases given in terms of the less-known Painleve transcendents.