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Journal of Modern Optics

Classical simulation of coherent population return in coupled optical waveguides

Nida Naim, Li Deng, Jun Qian, Yueping Niu, Shangqing Gong

Published Mar 4, 2022• 2 citations
Publisher

Abstract

An optical analog to coherent population return (CPR) is carried out in two evanescently coupled waveguides. Thepropagation constants of the two waveguides are different and the coupling between them is slowly varied for the adiabatic condition.The analog to the CPR corresponds to complete light return. Furthermore, we simulate two extensions of the CPR. One is that thecoupling is unchanged after it reaches its maximum, while the another one is that the coupling is replaced by a sudden decrease fromthe maximum to zero (half-CPR). We can both observe nearly 50:50 beam splitting in the two extensions. However, the half-CPRperforms better, which implies its application for achromatic beam splitters. Finally, we note that the waveguide structure proposedhere for beam splitters is simpler than those based on the stimulated Raman adiabatic passage and the rapid adiabatic passage.

DOI
10.1080/09500340.2022.2045372

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An optical analog to coherent population return (CPR) is carried out in two evanescently coupled waveguides. Thepropagation constants of the two waveguides are different and the coupling between them is slowly varied for the adiabatic condition.The analog to the CPR corresponds to complete light return. Furthermore, we simulate two extensions of the CPR. One is that thecoupling is unchanged after it reaches its maximum, while the another one is that the coupling is replaced by a sudden decrease fromthe maximum to zero (half-CPR). We can both observe nearly 50:50 beam splitting in the two extensions. However, the half-CPRperforms better, which implies its application for achromatic beam splitters. Finally, we note that the waveguide structure proposedhere for beam splitters is simpler than those based on the stimulated Raman adiabatic passage and the rapid adiabatic passage.
In this paper, we investigate the optical analog to coherent population return (CPR) in coupled nonlinear waveguides. The nonlinearity sometimes plays a negative role in classical simulations of quantum adiabatic passages in waveguides. Nevertheless, it is interesting to note that the nonlinearity here helps simulating the adiabatic CPR technique. The CPR can still occur when the detuning (difference of the propagation constants) between the two nonlinear waveguides is moderate, which is a typical requirement of the technique. Moreover, the adiabatic process can appear when the detuning is small or zero. This is done by simply adjusting the incident light power, which is easy and of high accuracy compared with modulating the propagation constants. Therefore, the requirements towards the propagation constants of the waveguides are further relaxed in the nonlinear case. Finally, we point out that the CPR in nonlinear waveguides can be extended to design achromatic beam splitters.
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.
In this paper, optical simulation of double rapid adiabatic passage (RAP) is investigated in three evanescently coupled waveguides with longitudinally varying detunings of the propagation constants. Unlike the time-dependent detuning which is kept linearly increased or decreased when the RAP is applied in two-state atomic systems, here all possible situations of the corresponding space-dependent detunings with or without sign flips are considered. At the maximum of the couplings in the waveguide structure, the detunings tend to become zero and the sign flips are supposed to occur. Theoretical analysis shows that different light evolutions such as light splitting, complete light transfer, or complete light return can be realized adiabatically, depending on the choices of the detunings. Moreover, two of the above three phenomena can be observed simultaneously in the waveguide structure under some circumstances. The theoretical analysis is confirmed by numerical calculations. Due to the robustness of the double RAP, the technique can be applied to design optical devices such as achromatic beam splitters or beam couplers.
Classical wave optical analogs of coherent population transfer via a continuum, recently demonstrated for laser-driven atoms and molecules in the atomic physics context, are theoretically proposed for light waves propagating in waveguide-based photonic structures. In particular, it is shown that exploitation of the optical analogs of two-photon Rabi oscillations and stimulated Raman adiabatic passage via continuous states enables efficient transfer of light waves between two channel optical waveguides side coupled to a slab waveguide.
A variable achromatic optical beam splitter with one input and NNN output waveguide channels is introduced. The physical mechanism of this multiple beam splitter is adiabatic passage of light between neighboring optical waveguides in a fashion reminiscent of the technique of stimulated Raman adiabatic passage in quantum physics. The input and output waveguides are coupled via a mediator waveguide and the ratios of the light intensities in the output channels are controlled by the couplings of the respective waveguides to the mediator waveguide. Due to its adiabatic nature the beam splitting efficiency is robust to variations in the experimental parameters.