Search results for "Dispersion"

Switching Dynamics of Dark Solitons in Kerr Microresonators

2019

Dissipative Kerr solitons (DKS) are localized structures in optical resonators that arise from a double balance between dispersion and Kerr effect, and linear loss and parametric gain [1]. The periodic nature of DKS corresponds to frequency combs. DKS can be generated in high-Q microresonators for diverse applications, from coherent communications to precision frequency synthesis [1]. Most studies of DKS have focused on microresonator cavities operating in the anomalous dispersion regime, where the waveforms correspond to bright soliton pulses. Coherent microresonator combs can also be formed in the normal dispersion regime [2]. The time-domain waveform corresponds to a localized dark-pulse…

Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation

2007

The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…

Configurational entropy of microemulsions : The fundamental length scale

1993

Phenomenological models have been quite successful in characterizing both the various complex phases and the corresponding phase diagrams of microemulsions. In some approaches, e.g., the random mixing model (RMM), the lattice parameter is of the order of the dimension of an oil or water domain and has been used as a length scale for computing a configurational entropy, the so‐called entropy of mixing, of the microemulsion. In the central and material section of this paper (Sec. III), we show that the fundamental length scale for the calculation of the entropy of mixing is of the order of the cube root of the volume per molecule—orders of magnitude smaller than the dimension of such a domain…

“Nonlocal” dispersion cancellation with classical light

2009

Nonlocal dispersion cancellation [1] is a quantum phenomenon that relies on the use of a quantum light source, e.g., spontaneous parametric down-conversion (SPDC), providing temporally entangled photon pairs. Each photon in the pair propagates through a dispersive medium [see Fig. 1 (a)]. Under suitable conditions the dispersion of one photon cancels out the dispersion of the other photon, so that their intensity coincidence probability remains unchanged. Nonlocal dispersion cancellation has been experimentally demonstrated [2] and this phenomenon has subsequently triggered important applications in quantum information science, such as quantum-optical coherence tomography, distant clock syn…

Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"

2016

A recent paper [Phys. Rev. E 91, 022925 (2015)PRESCM1539-375510.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrodinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc c…

An optical pulse modulator based on an all-fiber mirror

1996

Vector description of higher-order modes in photonic crystal fibers

2000

We extensively study the propagation features of higher-order modes in a photonic crystal fiber (PCF). Our analysis is based on a full-vector modal technique specially adapted to accurately describe light propagation in PCF's. Unlike conventional fibers, PCF's exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCF's are characterized by the constancy of the number of modes below a wavelength threshold. An explicit verification of this property is given through a complete analysis of the dispersion relations of higher-order modes in terms of the structural parameters of this kind of fiber. The transverse irradiance distributions for some of these high…

Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical f…

1998

Four-photon mixing in a low-birefringence fiber is strongly influenced by the orientation of the pump and signal waves with respect to the fiber axes. We experimentally investigated the dependence of the modulational gain spectra on pump power and polarization by mixing orthogonal pump and probe light beams in a birefringent optical fiber. With a pump on the fast fiber axis, a cascade of sidebands was generated in the regime of normal fiber dispersion. These sidebands are shown to correspond to 0.2–0.3-THz trains of pulses with complex polarization profiles. The analysis reveals that, at particular values of the input pump and probe powers and signal frequency detuning, trains of dark-solit…

Quantized separations of phase-locked soliton pairs in fiber lasers

2003

Quantized separations of phase-locked soliton pairs in fiber lasers were presented. The relation between the Kelly sidebands and the quantized separations between solitons was confirmed. Simulation results showed that the solitons can see each other at relatively larger distances than they would in the absence of radiation.

Role of Polarization Mode Dispersion on Modulational Instability in Optical Fibers

2001

We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we give the explicit form of the effective matrix and numerically compute the maximal eigenvalue. In the anomalous dispersion regime, polarization dispersion widens the unstable bandwidth. Depending on the type of variations of the birefringence parameters, polariza…