Mode Matching Conditions Research Articles

An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg--de Vries Solitons

Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a linear equation coupled to the Korteweg--de Vries (KdV) equation. The model has one parameter, a coupling constant $\kappa$. For one value of the coupling constant, $\kappa=1$, the linear equation becomes the linearized KdV equation, for which the linear waves can indeed be trapped by solitons and, moreover, for which the initial value problem for the linear waves has been solved exactly by Sachs [S83] in terms of quadratic forms in the Jost eigenfunctions of the associated Schrodinger operator. We consider in detail a different case of weaker coupling, $\kappa=1/2$. We show that in this case linear waves may again be trapped by solitons, and like the stronger coupling case $\kappa=1$, the initial value problem for the linear waves can also be solved exactly, this time in terms of linear forms in the Jost eigenfunctions. We presen...

Stable propagation of non-Gaussian beams in a multiple-pass cell

To apply annular output beams emitted from an unstable resonator to a multiple-pass cell (MPC) for Raman conversion, we studied the mode-matching condition of non-Gaussian beams to a MPC using beam propagation analysis based on Laguerre-Gaussian functions. During transits of the MPC, the radial profile of an annular beam changes between annular and Airy patterns. Although such behavior indicates that it is impossible to achieve complete mode matching of an annular beam, we found a quasi-mode-matching condition under which the variation of beam size was minimized. The above theoretical analysis was verified experimentally using a CO(2) laser beam prepared for a para-hydrogen Raman laser.

Cavity ring-down spectroscopy with Fourier-transform-limited light pulses

We have investigated the implications of using a pulsed, nearly Fourier-transform-limited, single-mode light source for cavity ring-down spectroscopy (CRDS) in the mid-infrared spectral range. We show that in the case where the coherence time and duration of the light pulse exceeds the cavity roundtrip time, mode beating generates oscillations in the ring-down waveform. When the period of the oscillations is comparable to the ring-down time, it becomes difficult to obtain meaningful decay constants. This situation can be avoided by careful choice of cavity geometry and mode matching conditions together with suitable electronic filtering.

Transverse structures in a sodium-filled Fabry-Pérot resonator—I. Experimental results: Symmetries and the role of the incoupling conditions

Transverse patterns occurring in a sodium-filled Fabry-Pérot resonator are studied in a carefully controlled experiment. The transitions among them, observed as a function of cavity tuning, can be continuous or discontinuous (Transverse Optical Bistability), depending on the experimental parameters. For a variety of suitably chosen input conditions, in which only a few excited modes participate in the interaction, the classification of the patterns according to their topological characteristics reveals underlying symmetries in the sign of the nonlinearity, the plane of observation, and, most importantly, the mode-matching conditions. We show that the crucial parameters controlling the structures are the phase coefficients of the resonator modes excited by the input beam. The properties of the nonlinear cavity spectrum are also used to characterize further the observations.

Second Harmonic Generation in Ion Implanted Lithium Niobate Planar Waveguides

Abstract We report the first demonstration of second harmonic generation (SHG) in ion implanted lithium niobate optical waveguides. For both ordinary and extraordinary index profiles a computer program was developed to simulate the positions of the modes within the optical well. With the help of this program the theoretical possibility of SHG using mode matching conditions within the guide was then studied as a function of the guide depth and temperature, and from these predictions, practical guides were constructed. Initially, SHG Cerenkov radiation was observed with leaky single implanted guides. Mode matched SHG from m = 0 to m = 2 was subsequently achieved by means of a multiple energy implant which was able to confine both fundamental and harmonic waves. Allowing for coupling and transmission losses, the corrected conversion efficiency is 0–018% W−1 which compares favourably to a theoretical prediction for this guide of 0–020% W−1. In this case a wide temperature tuning range was obtained.

Optimum approximate modes of strain-hardening beams

Summary The effects of using various mode forms and various types of matching conditions on the accuracy of a mode approximation method for strain-hardening structures is examined. Although accuracy is improved by increasing the complexity of the approximation, good results are obtained for the simplest practical formulation provided the choice of the best combination of mode shape and matching condition is made.

Mode-matching Techniques as an Aid to Laser Cavity Alignment

Improvement of the alignment accuracy of an experimental, curved mirror, laser cavity by mode matching of the alignment laser beam to the experimental cavity parameters is discussed. It is shown that the use of a two-lens telescope, giving beam magnification, allows the mode-matched condition to be readily obtained for a wide variety of cavity configurations, and that a particular matching condition optimizes the mirror alignment accuracy, giving equal alignment sensitivity for each mirror of the experimental cavity. The mode-matching procedure avoids the need for large distances to provide high angular sensitivity, and compact alignment systems, suitable for building in to experimental lasers are readily designed. As an example, the alignment of an atomic iodine laser is discussed.

Experimental determination of cw dye laser parameters by loss variation

The behavior of a cw dye laser under variation of the output coupling has been investigated. By studying the dependence of laser threshold, output power and slope efficiency on the degree of outcoupling, numerical values for macroscopic and microscopic laser parameters have been obtained. The macroscopic data comprise values for internal cavity losses and mode matching conditions, the microscopic data refer to molecular parameters of the dye used, such as cross-sections for stimulated emission and triplet-triplet absorption.