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Temporal reflection is a process where an optical pulse reflects off a moving boundary with different refractive indices across it. In a dispersive medium, this process creates a reflected pulse with a frequency shift that changes its speed. Such frequency shifts depend on the speed of the moving boundary. In this work, we propose and experimentally show that it is possible to probe the trajectory of the boundary by measuring the frequency shifts while changing the initial delay between the incident pulse and the boundary. We demonstrate this effect by reflecting a probe pulse off a short soliton, acting as a moving boundary that decelerates inside a photonic crystal fiber because of intrapulse Raman scattering. We deduce trajectory of the soliton from the measured spectral data for the reflected pulse.

A semi-analytic model of the amplification process is presented for Raman amplifiers made with graded-index multimode fibers. When the pump beam remains much more intense than the signal being amplified, it evolves in a self-similar fashion and recovers its initial width periodically. Using this feature, the width of the amplified signal is found to satisfy an equation whose form is similar to that of a damped harmonic oscillator. We use this equation to discuss the spatial beam narrowing occurring inside a Raman amplifier. In addition to oscillating with a period ∼1mm, the beam also narrows down during its amplification inside a graded-index fiber on a length scale ∼1m. The main advantage of our simplified approach is that it provides an analytic expression for the damping distance of width oscillations that shows clearly the role played by various physical parameters.

We use coherence theory to study how the focusing of an optical beam by a graded-index (GRIN) lens is affected when the incoming beam is only partially coherent. The Gaussian–Schell model is used to show that the intensity of a partially coherent beam exhibits self-imaging and evolves in a periodic fashion in a GRIN medium with a parabolic index profile. Spatial coherence of the beam affects a single parameter that governs how much the beam is compressed at the focal point. Our results show that the focal spot size depends on the fraction of the beam’s diameter over which coherence persists. Focusing ceases to occur, and the beam may even expand at the focal point of a GRIN lens, when this fraction is below 10%.

Doped and optically pumped graded-index (GRIN) fibers can be used to amplify an optical beam such that its spatial quality is improved at the output end of the fiber compared with that of the unamplified beam. We develop a simple model of the amplification process in such GRIN fiber amplifiers and show that the resulting equations can be solved analytically with suitable approximations. The solution shows that the width of the amplifying beam oscillates but also becomes narrower because of the radial dependence of the optical gain. The main advantage of our simplified approach is that it provides an analytic expression for the damping distance of beam-width oscillations that shows clearly the role played by various physical parameters.

We study temporal reflection of an optical pulse from the refractive-index barrier created by a short pump soliton inside a nonlinear dispersive medium such as an optical fiber. One feature is that the soliton’s speed changes continuously as its spectrum redshifts because of intrapulse Raman scattering. We use the generalized nonlinear Schrödinger equation to find the shape and spectrum of the reflected pulse. Both are affected considerably by the soliton’s trajectory. The reflected pulse can become considerably narrower compared to the incident pulse under conditions that involve a type of temporal focusing. This phenomenon is explained through space–time duality by showing that the temporal situation is analogous to an optical beam incident obliquely on a parabolic mirror. We obtain an approximate analytic expression for the reflected pulse’s spectrum and use it to derive the temporal version of the transformation law for the$q$parameter associated with a Gaussian beam.

Changing the frequency of light outside the laser cavity is essential for an integrated photonics platform, especially when the optical frequency of the on-chip light source is fixed or challenging to be tuned precisely. Previous on-chip frequency conversion demonstrations of multiple GHz have limitations of tuning the shifted frequency continuously. To achieve continuous on-chip optical frequency conversion, we electrically tune a lithium niobate ring resonator to induce adiabatic frequency conversion. In this work, frequency shifts of up to 14.3 GHz are achieved by adjusting the voltage of an RF control. With this technique, we can dynamically control light in a cavity within its photon lifetime by tuning the refractive index of the ring resonator electrically.