Search for: All records

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.

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.

We investigate the impact of the finite rise time of a spatiotemporal boundary inside a dispersive medium used for reflection and refraction of optical pulses. We develop a matrix approach in the frequency domain for analyzing such spatiotemporal boundaries and use it to show that the frequency range over which reflection can occur is reduced as the rise time increases. We also show that total internal reflection can occur even for boundaries with long rise times. This feature suggests that spatiotemporal waveguides can be realized through cross-phase modulation even when pump pulses have relatively long rise and fall times.

We reveal the crucial role played by the frequency dependence of the nonlinear parameter on the evolution of femtosecond solitons inside photonic crystal fibers (PCFs). We show that the conventional approach based on the self-steepening effect is not appropriate when such fibers have two zero-dispersion wavelengths, and several higher-order nonlinear terms must be included for realistic modeling of the nonlinear phenomena in PCFs. These terms affect not only the Raman-induced wavelength shift of a soliton but also impact its shedding of dispersive radiation.

We show that the temporal analog of a Fabry–Perot resonator (FPR) can be realized by using two moving temporal boundaries, formed by intense pump pulses inside a dispersive medium (such as an optical fiber). We analyze such FPRs using a transfer-matrix method, similar to that used for spatial structures containing multiple thin films. We consider a temporal slab formed using a single square-shape pump pulse and find that the resonance of such an FPR has transmission peaks whose quality ($Q$) factors decrease rapidly with an increasing velocity difference between the pump and probe pulses. We propose an improved design by using two pump pulses. We apply our transfer-matrix method to this design and show considerable improvement in the$Q$factors of various peaks. We also show that such FPRs can be realized in practice by using two short pump pulses that propagate as solitons inside a fiber. We verified the results of the transfer-matrix method by directly solving the pulse propagation equation with the split-step Fourier method.