Linear Schrödinger equation with temporal evolution for front induced transitions.

The nonlinear Schrödinger equation based on slowly varying approximation is usually applied to describe the pulse propagation in nonlinear waveguides. However, for the case of the front induced transitions (FITs), the pump effect is well described by the dielectric constant perturbation in space and time. Thus, a linear Schrödinger equation (LSE) can be used. Also, in waveguides with weak dispersion the spatial evolution of the pulse temporal profile is usually tracked. Such a formulation becomes impossible for optical systems for which the group index or higher dispersion terms diverge as is the case near the band edge of photonic crystals. For the description of FITs in such systems a linear Schrödinger equation can be used where temporal evolution of the pulse spatial profile is tracked instead of tracking the spatial evolution. This representation provides the same descriptive power and can easily deal with zero group velocities. Furthermore, the Schrödinger equation with temporal evolution can describe signal pulse reflection from both static and counter-propagating fronts, in contrast to the Schrödinger equation with spatial evolution which is bound to forward propagation. Here, we discuss the two approaches and apply the LSE with temporal evolution for systems close to the band edge where the group velocity vanishes by simulating intraband indirect photonic transitions. We also compare the numerical results with the theoretical predictions from the phase continuity criterion for complete transitions.

Ewald sphere construction for structural colors.

Disordered structures producing a non-iridescent color impression have been shown to feature a spherically shaped Fourier transform of their refractive-index distribution. We determine the direction and efficiency of scattering from thin films made from such structures with the help of the Ewald sphere construction which follows from first-order scattering approximation. This way we present a simple geometrical argument why these structures are well suited for creating short wavelength colors like blue but are hindered from producing long wavelength colors like red. We also numerically synthesize a model structure dedicated to produce a sharp spherical shell in reciprocal space. The reflectivity of this structure as predicted by the first-order approximation is compared to direct electromagnetic simulations. The results indicate the Ewald sphere construction to constitute a simple geometrical tool that can be used to describe and to explain important spectral and directional features of the reflectivity. It is shown that total internal reflection in the film in combination with directed scattering can be used to obtain long wavelength structural colors.

Nonlinear distortion of optical pulses by self-produced free carriers in short or highly lossy silicon-based waveguides.

An explicit analytical solution for the asymmetric attenuation of optical pulses by self-produced free carriers in silicon waveguides is derived. It allows us to quantify the pulse distortion and to calculate explicitly the free-carrier density and the nonlinear phase shifts caused by the Kerr effect and by free-carrier refraction. We show that omitting two-photon absorption (TPA) as a cause of attenuation and accounting only for free-carrier absorption (FCA) as done in the derivation appropriately models the pulse propagation in short or highly lossy silicon-based waveguides such as plasmonic waveguides with particular use for high-energy input pulses. Moreover, this formulation is also aimed at serving as a tool in discussing the role of FCA in its competition with TPA when used for continuum generation or pulse compression in low-loss silicon waveguides. We show that sech-shaped intensity pulses maintain their shape independently of the intensity or pulse width and self-induced FCA may act as an ideal limiter on them. Pulse propagation under self-induced free-carrier absorption exhibits some features of superluminal propagation such as fast or even backward travelling. We find that input pulses need to have a sufficiently steep front slope to be compressible at all and illustrate this with the FCA-induced pulse broadening for Lorentzian-shaped input pulses.

Measurement of nonreciprocal spontaneous Raman scattering in silicon photonic wires.

We report on measurements that show the strength of the spontaneous Raman scattering in strongly confining silicon waveguides to depend significantly on the propagation direction of the amplified signal wave with respect to the pump wave. Furthermore, the strength of this nonreciprocity depends on the orientation of the waveguide with respect to the crystallographic axes. We find that when changing the orientation from ˂011˃ to ˂001˃, the Raman-induced nonreciprocity increases by almost a factor of 3.

Photonic glass for high contrast structural color.

Non-iridescent structural colors based on disordered arrangement of monodisperse spherical particles, also called photonic glass, show low color saturation due to gradual transition in the reflectivity spectrum. No significant improvement is usually expected from particles optimization, as Mie resonances are broad for small dielectric particles with moderate refractive index. Moreover, the short range order of a photonic glass alone is also insufficient to cause sharp spectral features. We show here, that the combination of a well-chosen particle geometry with the short range order of a photonic glass has strong synergetic effects. Using a first-order approximation and an Ewald sphere construction the reflectivity of such structures can be related to the Fourier transform of the permittivity distribution. The Fourier transform required for a highly saturated color can be achieved by tailoring the substructure of the motif. We show that this can be obtained by choosing core-shell particles with a non-monotonous refractive index distribution from the center of the particle through the shell and into the background material. The first-order theoretical predictions are confirmed by numerical simulations.

Self-imaging silicon Raman amplifier.

We propose a new type of waveguide optical amplifier. The device consists of collinearly propagating pump and amplified Stokes beams with periodic imaging of the Stokes beam due to the Talbot effect. The application of this device as an Image preamplifier for Mid Wave Infrared (MWIR) remote sensing is discussed and its performance is described. Silicon is the preferred material for this application in MWIR due to its excellent transmission properties, high thermal conductivity, high damage threshold and the mature fabrication technology. In these devices, the Raman amplification process also includes four-wave-mixing between various spatial modes of pump and Stokes signals. This phenomenon is unique to nonlinear interactions in multimode waveguides and places a limit on the maximum achievable gain, beyond which the image begins to distort. Another source of image distortion is the preferential amplification of Stokes modes that have the highest overlap with the pump. These effects introduce a tradeoff between the gain and image quality. We show that a possible solution to this trade-off is to restrict the pump into a single higher order waveguide mode.

Analysis of Raman lasing characteristics in silicon-on-insulator waveguides.

Numerical analysis predicts that continuous-wave Raman lasing is possible in silicon-on-insulator (SOI) waveguides, in spite of the detrimental presence of two-photon absorption and free-carrier absorption. We discuss in particular the dependence of the lasing characteristics of SOI Raman lasers on the effective lifetime of the free carriers generated by two-photon absorption. It is shown that the pump-power-dependent cavity losses lead to a rollover of the output-power characteristics at a certain pump-power level and that there exists an upper shutdown threshold at which the laser operation breaks down.

Comment on "Nonreciprocal light propagation in a silicon photonic circuit".

We show that the structure demonstrated by Feng et al. (Reports, 5 August 2011, p. 729) cannot enable optical isolation because it possesses a symmetric scattering matrix. Moreover, one cannot construct an optical isolator by incorporating this structure into any system as long as the system is linear and time-independent and is described by materials with a scalar dielectric function.