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arXiv:1104.4963

Broadband polarization retarder

Andon A. Rangelov

Published Apr 26, 2011• 0 citations
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Abstract

We derive a new kind of effective broadband polarization device using the analogy between the equation for the polarization of light, propagating through an optically anisotropic medium, and the optical Bloch equation in adiabatic regime, which describes coherent laser excitation of a two-state atom.
DOI
10.48550/arxiv.1104.4963

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The propagation of optical waves in coupled waveguides can be described by the coupled-mode theory. This formalism is mathematically analogous to the one for the quantum dynamics of the population of coupled atomic states, which is described by the Schrödinger equation within the so called Rotating Wave Approximation (RWA). This analogy has been pointed out in recent years. It was applied to coupled waveguide systems with constant effective refractive indices, which are fully analogous to resonant coupled quantum systems. This work extends this kind of studies to optical systems possessing an additional control parameter: the longitudinal modulation of the waveguide propagation constants. This approach is analogous to quantum systems with time dependent non-resonant excitation. As the population transfer between atomic states can be controlled by means of the Rabi frequencies and the laser frequency detunings, the light transfer between coupled waveguides can be controlled by means of the coupling constants and the propagation constants.Several such analogies are studied and exploited in this thesis for the demonstration of robust (broadband) adiabatic light transfer and splitting. The first system is based on the recently introduced quantum process known as two-state STImulated Raman Adiabatic Passage (two-state STIRAP). This is implemented for the first time in classical optics with a set of two evanescently coupled waveguides with proper longitudinal modulation of the mode propagation constants and of the coupling coefficient between them. A broadband 50:50 beam splitter based on two-state STIRAP is theoretically proposed and experimentally demonstrated. The experiments are performed using reconfigurable and tuneable waveguide structures that are optically induced by a lateral illumination technique of a nonlinear photorefractive crystal. This experimental platform provides versatile guiding structures that can be erased and reconfigured to test various systems depending on the considered analogy.A second quantum analogy based on the process of Rapid Adiabatic Passage (RAP) is theoretically studied and experimentally implemented for a set of two waveguides for which the longitudinally varying detuning crosses zero at half propagation distance. The modulation of the detuning and of the coupling constant provide a very robust and highly achromatic mechanism for full light transfer between the waveguides (broadband directional coupler). This is analogous to the RAP-based robust inversion of two-level quantum systems.The above RAP-like transfer applies to systems containing only two waveguides. It is also shown theoretically and numerically that the same functionality can be obtained in systems containing N waveguides with N>2. This relies on a technique called adiabatic elimination. It consists in the formal elimination of the N-2 internal waveguide(s) who reduces the system to an effective two-waveguide system where RAP can be applied. This is relevant because it permits a light transfer between the outer waveguides without excitation of the middle one(s). In contrast to the already known technique based on the conventional STIRAP process, the technique studied here works in a symmetric way and for an odd and even total number of guides N. Adiabatic elimination is achieved by a strong detuning between the two outer waveguides and the remaining one(s). It can be concluded that the analogies of all the classical optical systems studied in this work with corresponding non-resonant quantum systems and processes give powerful tools to design new broadband photonic structures. Moreover, the present studies can pave the way for dealing with future novel functionalities in nonlinear optical waveguide systems, which involve in a natural way a spatial light-intensity-dependent variation of the waveguide propagation constants and detuning.
The formation of dark states under an interaction of degenerate atomic states with incoherent broadband radiation (white light) is discussed. A simple coupling scheme in a three level $\ensuremath{\Lambda}$ system, which allows both qualitative and quantitative analysis, is discussed. We found a stationary solution of the optical Bloch equations in a broad excitation line approximation that describes the dynamics of the atom-white light interaction and demonstrated its identity to a conventional dark state created with coherent laser fields. We than examine the efficiency of the population transfer induced by broadband radiation in a model $\ensuremath{\Lambda}$ system and revealed that high efficiency (attaining 100%) of stimulated Raman adiabatic passagelike processes can be achieved with certain temporal control of light polarization. The corresponding criterion of adiabaticity was formulated and justified by means of numerical simulations.