An improved time-domain beam propagation method for integrated optics components

Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides

“…For circularly symmetric fields, (5) can be rewritten as follows: (11) Note that the first derivative with respect to the direction appears in (11), as contrasted with (6). In this section, we present the detail derivation of the FD equations in cylindrical coordinates, paying attention to the treatment of the first and second derivatives in the direction.…”

“…Among them, the TD-BPM in which the SVEA is applied only to the time term has the advantage that reflection and diffraction can be evaluated by the BPM algorithm with slight coefficient changes [4]- [10]. With the use of the implicit scheme for discretization in time, a time step is chosen to be larger than that in the FD-TDM [4]- [6], [8]- [10].…”

A time domain beam propagation method based on a finite element scheme

“…(5) are neglected. Then, the basic equation for the TD-BPM based on the Fresnel equation can be obtained [5,6]. The Fresnel equation is effective for the spectral components near the carrier frequency.…”

“…Under this circumstance, the time domain beam propagation method (TD-BPM) [5,6], in which the time domain evaluation is simplified, has been developed. In this method, it is noted that the signal frequency in the optical wavelength region is sufficiently smaller than the carrier frequency, and the slowly varying envelope approximation (SVEA) is applied to the time terms of the wave equation, so that the restriction on the time step width is substantially relaxed.…”

Analysis of Ultra-Short Pulse Propagation in Nonlinear Optical Fiber

“…Thanks to the quantum structure of some semiconductor materials, quantum cascade (QC) lasers can generate ultra-short pulses by gain switching and active and passive mode-locking of this type of semiconductor lasers due to the short relaxation times of electrons and the photon lifetime; both are of the order of a picosecond in these lasers. On the other hand, due to the huge bandwidth and the high instantaneous power associated with ultra-short pulses, dispersion and nonlinearity represent critical issues for their practical applications [1][2][3][4][5][6][7][8][9][10].…”