Combined Effects Of Self-phase Modulation Research Articles

Spectral broadening in lithium niobate in a self-diffraction geometry using ultrashort pulses

We report on broadband light generation in the impulsive regime in an un-doped lithium niobate (LiNbO3) crystal by two femtosecond laser pulses (36 fs) from a Ti-sapphire laser amplifier. We systematically investigate the role of incident intensity on spectral broadening. At relatively low incident intensity (0.7 TW cm−2), spectral broadening in the transmitted beam occurs due to the combined effect of self-phase modulation and cross-phase modulation. At higher incident intensity (10.2 TW cm−2), we observe generation of as many as 21 anti-Stokes orders due to coherent anti-Stokes Raman scattering in self-diffraction geometry. Moreover, we observe order-dependent spectral broadening of anti-Stokes lines that may be attributed to the competition with other nonlinear optical effects like cross-phase modulation.

A Comprehensive Study of Actively Mode-Locked Fiber Optical Parametric Oscillators for High-Speed Pulse Generation

We perform a comprehensive study on the implementation of active harmonic and rational harmonic mode-locking of a fiber optical parametric oscillator (FOPO). In particular, the effect of pump parameters and cavity designs on the characteristics of the generated pulses are analyzed. Two methods of frequency multiplication in FOPOs are discussed and compared and we show that we can generate optical pulses with very high-repetition-rate (up to 240 GHz) using rational harmonic mode-locking. We find that optical pulses with short duration can be obtained using pump pulses with small duty cycle, large pump power, and an intra-cavity optical filter with proper bandwidth. In addition, optical pulses with low root-mean-square timing jitter are achievable when no pump phase modulation is applied and hybrid gain of erbium-doped fiber amplifier and parametric amplifier is used. High supermode noise suppression ratio is achieved by taking advantage of the fast parametric gain and the combined effect of self-phase modulation and spectral filtering. We conclude that synchronous-pumping of an actively mode-locked FOPO offers many advantages in terms of reducing the cavity loss, increasing the modulation frequency, enabling rational harmonic mode-locking, and applications to all-optical clock recovery.

Spectral broadening and self-compression of negatively chirped visible femtosecond pulses in fused silica

This paper describes a new effect: spectral broadening and self-compression of negatively chirped visible femtosecond pulses as a result of nonlinear interaction of large-aperture beams with fused silica. We assume that the likely mechanism of the observed spectral broadening is the combined effect of self-phase modulation and four-wave mixing.

Soliton solutions via auxiliary function method for a coherently-coupled model in the optical fiber communications

A coherently-coupled nonlinear Schrödinger system in the optical fiber communications, with the mixed self-phase modulation (SPM), cross-phase modulation (XPM) and positive coherent coupling terms, is studied through the bilinear method with an auxiliary function. Solutions for that system are found to be of two types: singular and non-singular ones, and the latter appear as the soliton-typed. Vector bright one- and two-solitons are derived with the corresponding phase-shift parameter constraints. In virtue of computerized symbolic computation and asymptotic behavior analysis, elastic collision mechanisms of such vector solitons are investigated. With the aid of graphical simulation, vector solitons are displayed to be of the single- or double-hump profiles. The formation and collision mechanisms of the vector bright solitons for that system are generated based on the combined effects of SPM, XPM and coherent coupling. Only elastic collisions of the vector solitons occur for that system, which is a distinctive feature amid those of other coherently-coupled nonlinear Schrödinger systems.

Vector bright soliton behaviors associated with negative coherent coupling

With the introduction of an auxiliary function, a genuine bilinear system (in contrast to the published trilinear forms) is obtained for the two-coupled nonlinear Schrödinger equations with negative coherent coupling in the optical fiber communications. With symbolic computation, degenerate and nondegenerate vector solitons are derived associated with the corresponding phase-parameter constraints. In virtue of asymptotic analysis and graphical simulation, vector solitons of the single-hump, double-hump, or flat-top profiles are displayed, and the collision mechanisms of such vector solitons are revealed as well; namely, the collisions among degenerate solitons and among nondegenerate solitons are both elastic. The only possible inelastic collision, the collision in the degenerate-nondegenerate case, is pointed out, where a degenerate soliton interacts with a nondegenerate one. Results in this paper may be useful for the optical switching with the combined effects of self-phase modulation, cross-phase modulation, and negative coherent coupling.

Modulation instability in lossy silicon optical waveguide

Taking into account the small linear loss of silicon-on-insulator(SOI) waveguide, conditions and gain spectra of modulation instability(MI) induced by combined effects of self-phase modulation and waveguide dispersions are investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically. Results show that strong MI takes place even in the existence of low light power. The MI peak gain is 2 to 3 orders of magnitude larger than that achieved in optical fibers with the same light power. The linear loss of waveguide impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain, peak gain frequency and bandwidth of gain spectra decrease to 66.828%, 41.683% and 41.6879% of their maxima at propagation distance z = 5mm, respectively.

Modulation instability in silicon optical waveguide considering linear loss

Taking into account the linear loss of silicon-on-insulator (SOI) waveguide, modulation instability (MI) induced by combined effects of self-phase modulation and waveguide dispersions is investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically, and direct numerical simulation of nonlinear Schroedinger equation is performed as well. Results show that strong MI takes place even in the existence of low light power. The linear loss of waveguide obviously impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain frequency and bandwidth of gain spectra decrease to 41.683% and 41.6879% of their maximum at propagation distance z = 5 mm, respectively.

Influence of the Channel Number on the Optimal Dispersion Map Due to XPM in WDM Links

The influence of the channel number on the optimal dispersion map (ODM) due to cross-phase modulation (XPM) in wavelength division multiplexed links is assessed using an analytical method. The analytical method is validated by comparison with numerical simulation using two different methods: the pump-probe method and a realistic method in which all channels are digitally modulated carriers. It is shown that there are usually, at least, two local ODMs due to XPM: one characterized by negative residual dispersion per span (RDPS) and another characterized by positive RDPS. These two local ODMs due to XPM lead to similar XPM-induced degradation. However, the local ODM with negative RDPS shows always much higher tolerance to the dispersion map (DM) variation. Furthermore, as the ODM due to the combined effect of self-phase modulation and group-velocity dispersion is characterized by negative RDPS when reduced and moderate power levels are used, the use of the local ODM due to XPM with negative RDPS is recommended. This local ODM due to XPM remains approximately the same as long as, at least, 8 channels are transmitted when 100 or 50 GHz channel spacings are used and 12 channels are transmitted when 25 GHz channel spacing is used. However, the high XPM tolerance to the DM variation for 25 GHz channel spacing leads to the conclusion that the ODM for 8 channels is the recommended DM in case of an arbitrary number of channels, independently of the channel spacing. These outcomes are independent of the power level, number and length of spans and transmission fiber type.

Optimal loop length of a nonlinear optical loop mirror in switching solitons

The optimal loop length of a nonlinear optical loop mirror (NOLM) for switching solitons was investigated numerically for the case where the wavelengths of the control pulse and signal soliton straddle the dispersion zero. In our analysis, the Raman effect is also included because the wavelength difference between the control and signal pulses is within the Raman gainband. It was found that the control pulse not only imposes phase shift on the copropagating signal, but also transfers part of its energy to the signal. Furthermore, the broadening of the control pulse due to the combined effect of self-phase modulation and group velocity dispersion increases the switching power of the control pulse significantly. The broadening of the control pulse also introduces more uniform phase shift to the signal, thus resulting in a higher switching efficiency. Finally, our results show that the pulse distortion is minimal if a loop length equivalent to one soliton period is employed.