Pulse Response of Nonlinear Multimode Interference Couplers

Abstract

The switching dynamics of short optical pulses in a multimode interference (MMI) coupler made of Kerr materials are numerically investigated using generalized nonlinear Schrödinger equations. These propagation equations contain four-wave mixing (FWM) as well as self-phase and crossphase modulation and dispersion of different orders to properly describe the nonlinear propagation in the multimode waveguide section. The FWM effects are more dominant than those of selfphase and cross-phase modulation, which cause power exchange among the modes in the waveguide. In numerical modeling, a 2 × 2 MMI coupler is treated to operate as a nearly two-mode interference (TMI) coupler. For long TMI couplers, multiple switching takes place in a relatively narrow range of input powers. It is also found that the transmitted pulse becomes unstable because of the interplay between the modal dispersion (i.e., the group-delay difference) and the FWM effect when the duration of the input pulse is extremely short (typically sub-picoseconds). In general, the switching characteristics of the nonlinear TMI coupler are similar to those of a nonlinear directional coupler.

All-Optical Signal Processing by Nonlinear Multimode Interference in Ta2O5 Waveguides

“…In the theoretical framework, nonlinear MMI have been intensively studied for their spectral and spatial properties; , however, in the experimental framework, nonlinear MMI have been described in mode-locking fiber lasers, which were possible due to the improved interaction length in a laser cavity and the precisely tuned refractive index sensors due to the nonlinear Kerr effect . All-optical power-dependent switching had never been experimentally demonstrated prior to this work.…”

“…As the incident power increases, the phase shift caused by the nonlinearity alters the accumulated phase differences and consequently leads to a state change represented by the transmission detected at port 2 and port 3. The detailed operation of the nonlinear MMI effect modeled by NCME in eq 2 was proposed by Ogusu et al in 2014 31 and included the effects of SPM, XPM, and especially FWM. The NCME were used to simulate the spatial temporal dynamics of an optical pulse propagating in a nonlinear MMI coupler.…”

“…A simple explanation for the operation of this MMI coupler is the interference between finite modes in the MMI section. The length of the MMI section is particularly designed to be either odd multiples of L π or even multiples of L π such that the wrapped accumulated phase difference of the two main guided modes in the linear domain is π or 2π, , and thus significant optical power is coupled into either port 2 or port 3, respectively. As the incident power increases, the phase shift caused by the nonlinearity alters the accumulated phase differences and consequently leads to a state change represented by the transmission detected at port 2 and port 3.…”

“…They include linear dispersion and nonlinear SPM, cross phase modulation (XPM), and four-wave mixing (FWM), , which describe the temporal dynamics of the modes involved. The NCME can be easily applied to study the spatial feature associated with the output characteristics of a nonlinear MMI waveguide coupler. , For single-polarized guided modes constrained either by the excitation or by the multimode waveguide structure, the phasor representation of the electric fields in the waveguide is E normalM normalM normalI = ∑ p = 0 N − 1 F p ( x , y ) A p ( z , t ) .25em normale i β 0 , p z − i ω t where ω is the angular frequency, F p ( x , y ), A p ( z , t ), and β 0, p are the transverse modal distribution, the spatiotemporal modal envelope, and the propagation constant of p th mode in the MMI section. The modal envelope satisfies the NCME expressed by ∂ A p false( z , t false) ∂ z + β 1 , p ∂ A p false( z , t false) ∂ t = ∑ n ≤ 2 i n + 1 n ! ∂ n …”

“…The NCME can be easily applied to study the spatial feature associated with the output characteristics of a nonlinear MMI waveguide coupler. 31,32 For single-polarized guided modes constrained either by the excitation or by the multimode waveguide structure, the phasor representation of the electric fields in the waveguide is…”