Michael Scalora

A beam propagation method that handles reflections

Abstract We review the fast Fourier transform beam propagation method (FFT-BPM) that is commonly used to describe diffraction of electromagnetic waves and introduce a time-domain version that takes into account arbitrary longitudinal index profiles, as well as transverse effects. This method can describe all relevant aspects of paraxial propagation in linear or nonlinear media. That is, the technique can handle transmission, diffraction, and, in particular, reflection of electromagnetic waves.

Stimulated Raman scattering: diffractive coupling in transient and steady-state regimes

A numerical study is presented of the steady-state and transient regimes in stimulated Raman scattering, including diffractive coupling of the fields and detuning of the Stokes field from resonance. In the steady-state regime, ring formation in the laser output intensity is observed as well as a ring in the Stokes output intensity when it is detuned from resonance. In the transient regime a solitonlike pulse is initiated by modulation of the phase of the input Stokes field. For Fresnel numbers between 5 and 50, we observe a simultaneous maximum of the on-axis laser and Stokes intensities after a π phase shift is introduced on the Stokes seed. At the same time the transverse profiles of the fields are narrowed and the laser intensity displays a satellite ring. It is found that the soliton remains relatively stable, although diffraction eventually leads to its decay.

Quantum fluctuations and diffraction in stimulated Raman scattering

Abstract We investigate the statistics of Stokes emissions in stimulated Raman scattering. By using a full dynamical model that includes both pump depletion and diffraction effects we present numerical results for pulse energy statistics. We find that multi-mode operation along the transverse coordinate significantly alters energy distributions in both high and low Fresnel number limits and that average Stokes pulse energies are very sensitive to Fresnel number variations in the non-linear regime.

Transverse effects in intrinsic optical bistability

Electromagnetic wave propagation with one transverse dimension is investigated in a medium whose response is modeled by a nonlinear oscillator. We report results with transverse effects due to diffraction, which are controlled by varying the Fresnel number. We find that diffraction does not significantly reduce the bistable intensity characteristics either for the center of the beam intensity or in the intensity integrated across the transverse coordinate, although in the latter case the contrast is reduced; bistable behavior is found to persist even for a Fresnel number of order unity, and the switching intensity is not affected by the Fresnel number. These results are explained by simple physical arguments.

Blue and green light emission: new directions and perspectives of applications of one-dimensional photonic band gap structures

Nonlinear quadratic interactions near the band edge of a finite length photonic band gap structure are studied. A strong enhancement of the nonlinear response is found due to the essential role played by the electromagnetic density of modes and phase matching conditions. This open the door to a new generation of very compact nonlinear devices. The blue and green light emission conditions are discussed.

Transparent, conducting films based on metal/dielectric photonic band gaps

A transparent conductor has been developed based on 1D metal/dielectric photonic band gap structures. Laminated metal/dielectric filters containing 100 nm of silver have been fabricated with > 50% transmittance. Applications for transparent, conducting films include antennas embedded in windshields, electrodes on flat panel displays, electromagnetic shielding, and solar window panes.

Intrinsic optical bistability in a cavity.

We have investigated wave propagation through a nonlinear medium in a ring cavity. The medium is modeled by a collection of nonlinear harmonic oscillators, and transverse effects on the wave propagation are retained in the model. Previously, this model has been studied without a cavity, since it is a prototype example of an intrinsically bistable medium.1-3 Diffraction effects have predicted a wave-guiding effect for the light, and the bistable characteristics, such as the contrast and threshold intensities, are not sensitive to the Fresnel number, i.e., a measure of the Importance of the diffraction coupling between the adjacent light rays.

Beaming and filtering at terahertz frequencies in liquid crystal filled metallic grating

The increasing interest in the terahertz frequency range is motivated by the unique property of sub-millimeter waves to penetrate any nonmetallic materials such as fabric and plastic, and sense objects distinctive signatures. Furthermore, because of its low photon energy, terahertz radiation can be used in medical applications for accurate imaging without damaging tissues. For these reasons there is a growing need of devices dedicated to control the radiation in this frequency range. Current established technology uses non-tunable, mesh-like filters and mechanical mirrors to filter and manipulate THz radiation. We study electrically-controlled beaming and filtering abilities of sub-wavelength metallic gratings. The geometry consists of a finite array of slits in a metallic film separated by spacers and filled with liquid crystal (LC). We exploit the Fabry-Perot (FP) like resonances of the slits to filter THz radiation. We then simulate the application of an external voltage across the metallic grating in order to generate an electro-optic torque force on the LC molecules and change the dielectric constant inside the slits. This results in a large tuning effect on the FP resonances. We also predict that a linear voltage distribution across the grating induces a linear phase delay resulting in a beamsteering action for radiation incoming at grazing incidence.

Highly efficient parametric interactions in one-dimensional photonic band gap structures

Band edge effects such as increased density of modes, large field enhancement, and low group velocity will provide highly efficient parametric amplification if the proper phase matching conditions can be established. We derive the phase matching conditions for 1D-photonic band gap structures. Direct integration of Maxwells equations in the time domain confirms these conclusions, and show that parametric amplification in 1D-photonic band gap structures provide much larger conversion efficiencies compared with quasi-phase-matching.

Nonlinear dynamics of counter-propagating beams in epsilon-near-zero films

Epsilon-near-zero materials are ideal platforms for nonlinear optics. Extreme electric field enhancements are predicted when a transverse-magnetic polarized field impinges obliquely on a film of material whose real part of the dielectric permittivity approaches zero. Under these circumstances, the component of the electric field with polarization normal to the film surface is enhanced by a factor proportional to the inverse square root of the dielectric permittivity. Nonlinear processes benefit from such uniquely favorable field localization, whether the condition is achieved in natural or artificial materials. Nonlinear optical processes have also been shown to be affected by the interference mechanism that occurs when two counter-propagating beams/pulses interact. Counter-propagating pulse dynamics has been investigated for surface plasmons and guided beams, they have been used for direct characterization of ultra-short pulses, to control emission of high-harmonics and to indirectly measure the phase mismatch of waveguides. Finally, they have been studied also in one dimensional photonic crystals and negative index materials. However, all these examples rely on either phase-matching or the availability of photonic resonances. Here we demonstrate that, thanks to the ability of epsilon-near-zero materials to efficiently support nonlinear processes in the absence of phase-matching or resonant conditions, one can control harmonic generation process by altering the phase of two non-collinear counter-propagating beams. We investigate the dynamics of two non-collinear counter-propagating beams impinging on an epsilon-near-zero slab and evaluate the modulation of the second and third harmonic signals as a function of the phase difference between the two sources. The calculations are performed considering a 100nm-thick slab of indium-tin-oxide (ITO). The results confirm that epsilon-near-zero media are exceptional platforms for nonlinear optics, providing a novel path to control these processes, including the possibility to easily characterize optical pulses.