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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Thermal Expulsion As A New Mechanism For Optical Bistability In Prism Coupling Into Planar Wavegaides

P. Pirani, V. Briguet, W. Lukosz

Published Jan 1, 1987• 1 citation
Publisher

Abstract

We investigated theoretically and experimentally a new type of cptical bistability (0B) in prism coupling into absorbing planar waveguides. Origin of this (B is the thermal expansion of the substrate (and the waveguiding film) and of the prism, due to heating by the part P = P of the incoupled power which is absorbed in the incoupling region. This expansion causes a reduction in the width d of the air gap between the prism coupler and the waveguide in the ompling region. Since the incoupling efficiency is a function of d, positive feedback, and therefore as, can occur. At the same input power Pa, the system has two bistable states, which differ in gap width d, in absorbed power Pa, and consequently in output (reflected) power PR. (see Fig. 1).

DOI
10.1117/12.967216

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We investigated theoretically and experimentally a new type of cptical bistability (0B) in prism coupling into absorbing planar waveguides. Origin of this (B is the thermal expansion of the substrate (and the waveguiding film) and of the prism, due to heating by the part P = P of the incoupled power which is absorbed in the incoupling region. This expansion causes a reduction in the width d of the air gap between the prism coupler and the waveguide in the ompling region. Since the incoupling efficiency is a function of d, positive feedback, and therefore as, can occur. At the same input power Pa, the system has two bistable states, which differ in gap width d, in absorbed power Pa, and consequently in output (reflected) power PR. (see Fig. 1).
We have identified photothermal displacement as a mechanism for optical bistability (OB) in prism coupling into absorbing planar waveguides: heating by the absorbed incoupled power causes a buckling of the waveguide, a reduction in air-gap width, and thus an increase in incoupling efficiency and a positive feedback. We developed a theory of this OB that qualitatively agrees well with experimental results obtained by coupling argon-laser light into indium-tin oxide layers as strongly absorbing waveguides. This new OB is quite different from dispersive OB in prism or grating couplers caused by a power-dependent effective guide index.
Self-pulsing optical systems produce at constant input power P an output power PR (t)varying periodically with time t. Self-pulsing (SP) in nonlinear Fabry Perots and hybrid systems is well known. We reported the first known observation of SP in prism coupling into planar waveguides [1]. Recently we identified the physical mechanism of the SP and we shaved that SP occurs in a wider class of waveguide materials [2]. We also demonstrated that the same prism-waveguide system can exhibit SP, optical bistability (0B), and a special form of bistability (0B/SP), where at the same constant input power P the output power P is either constant in time or self-pulsing. In the present paper we present more experimental material and discuss the physical effects determining the system's behaviour.
The salient question which arises when light is coupled via a grating or a prism into a waveguide exhibiting an intensity-dependent refractive index is whether switching occurs with or without bistability under appropriate detuning conditions. There are two prevailing theories. In the first1, a plane wave input is assumed leading to a uniform optically induced index change in the coupling region. In the second2, a finite width incident beam is assumed and the growth of the guided field under the coupler leads to an index change proportional to the local guided wave intensity. The first approach leads to optical bistability under certain detuning conditions, whereas the second results in switching only. Although it is known that plane wave analyses are inadequate when dealing with linear-nonlinear interfaces, bistability has been observed experimentally with nonlinear prism couplers3. Fundamentally the finite beam theoretical approaches are unable to predict bistability because no longitudinal feedback is included. Recently we showed that when non-locality is introduced into the optically induced refractive index change, longitudinal feedback occurs and bistability is predicted for the growing mode case4. However, the model used for the non-locality was artificial and resulted only in qualitative predictions. In this paper the nonlocality is modelled by the same equation used to describe heat transfer and carrier diffusion, leading to a quantitative estimate of the minimum diffusion length required for bistability.
The 'external' grating coupler is a diffraction grating pressed against the planar waveguide in a similar way as a prism coupler. Such couplers have, to the best of our knowledge, not been used in integrated optics. The couplers normally used are surface relief gratings on the waveguide. We report on a new type of optical bistability (OB) which occurs only with external but not with normal grating couplers. The air gap of width d, where 0≤d≤λ, plays an essential role in the OB mechanism.