Brent W. Plansinis

What is the Temporal Analog of Reflection and Refraction of Optical Beams

It is shown numerically and analytically that when an optical pulse approaches a moving temporal boundary across which the refractive index changes, it undergoes a temporal equivalent of reflection and refraction of optical beams at a spatial boundary. The main difference is that the role of angles is played by changes in the frequency. The frequency dependence of the dispersion of the material in which the pulse is propagating plays a fundamental role in determining the frequency shifts experienced by the reflected and refracted pulses. Our analytic expressions for these frequency shifts allow us to find the condition under which an analog of total internal reflection may occur at the temporal boundary.

Temporal waveguides for optical pulses

Temporal total internal reflection (TIR), in analogy to the conventional TIR of an optical beam at a dielectric interface, is the total reflection of an optical pulse inside a dispersive medium at a temporal boundary across which the refractive index changes. A pair of such boundaries separated in time acts as the temporal analog of planar dielectric waveguides. We study the propagation of optical pulses inside such temporal waveguides, both analytically and numerically, and show that the waveguide supports a finite number of temporal modes. We also discuss how a single-mode temporal waveguide can be created in practice. In contrast with the spatial case, the confinement can occur even when the central region has a lower refractive index.

Spectral Splitting of Optical Pulses Inside a Dispersive Medium at a Temporal Boundary

We show numerically that the spectrum of an optical pulse splits into multiple, widely separated, spectral bands when it arrives at a temporal boundary across which the refractive index suddenly changes. At the same time, the pulse breaks into several temporally separated pulses traveling at different speeds. The number of such pulses depends on the dispersive properties of the medium. We study the effect of second- and third-order dispersion in detail but also briefly consider the impact of other higher order terms. A temporal waveguide formed with two temporal boundaries can reflect the temporally separated pulses again and again, increasing the number of pulses trapped within the temporal waveguide.

Cross-phase-modulation-induced temporal reflection and waveguiding of optical pulses

Cross-phase modulation (XPM) is commonly viewed as a nonlinear process that chirps a probe pulse and modifies its spectrum when an intense pump pulse overlaps with it. Here we present an alternative view of XPM in which the pump pulse creates a moving refractive-index boundary that splits the probe pulse into two parts with distinct optical spectra through temporal reflection and refraction inside a dispersive nonlinear medium. The probe even undergoes a temporal version of total internal reflection for sufficiently intense pump pulses, a phenomenon that can be exploited for making temporal waveguides. We investigate the practical conditions under which XPM can be exploited for temporal reflection and waveguiding. The width and shape of the pump pulses as well as the nature of the medium dispersion at the pump and probe wavelengths (normal versus anomalous) play important roles. The super-Gaussian shape of a pump pulse is particularly helpful because of the relatively sharp edges of the super-Gaussian shape. When the pump wavelength lies in the anomalous-dispersion regime, the pump pulse can form a soliton, whose unique properties can be exploited to our advantage. We also discuss a potential application of XPM-induced temporal waveguides for compensating for timing jitter.

Single-pulse interference caused by temporal reflection at moving refractive-index boundaries

We show numerically and analytically that temporal reflections from a moving refractive-index boundary act as an analog of Lloyd’s mirror, allowing a single pulse to produce interference fringes in time as it propagates inside a dispersive medium. This interference can be viewed as the pulse interfering with a virtual pulse that is identical to the first, except for a π-phase shift. Furthermore, if a second moving refractive-index boundary is added to create the analog of an optical waveguide, a single pulse can be self-imaged or made to produce two or more pulses by adjusting the propagation length in a process similar to the Talbot effect.

Temporal Analog of Reflection and Refraction at a Temporal Boundary

We show numerically and analytically that an optical pulse that crosses over a temporal boundary in a dispersive medium acts as a temporal analog of the spatial reflection and refraction at a dielectric interface.