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IEEE Photonics Technology Letters

Optical Mode Splitting in Ring-Shaped Hollow Bragg Cavity

Jiangfeng Xu

Published Oct 23, 2014• 1 citation
Publisher

Abstract

We investigate the optical modes of hollow ring resonator with omnidirectional reflector cladding by numerical method. We demonstrate that each TM0mlmode (or TE0mlmode) can split into two modes whose wavelengths are very close. The doublet effect is caused by the symmetry breaking at circular cross section when a straight waveguide is curled into a ring shape. The ring-shaped hollow Bragg cavity provides a platform to research the interaction of Rydberg atoms and light mode.

DOI
10.1109/lpt.2014.2363881

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•Aug 29, 2019•0 citations
We investigate the optical modes of hollow ring resonator with omnidirectional reflector cladding by numerical method. We demonstrate that each TM0mlmode (or TE0mlmode) can split into two modes whose wavelengths are very close. The doublet effect is caused by the symmetry breaking at circular cross section when a straight waveguide is curled into a ring shape. The ring-shaped hollow Bragg cavity provides a platform to research the interaction of Rydberg atoms and light mode.
Strong collective interaction of atoms with an optical cavity causes normal mode splitting of the cavity's resonances, whose width is given by the collective coupling strength. At low optical density of the atomic cloud the intensity distribution of light in the cavity is ruled by the cavity's mode function, which is solely determined by its geometry. In this regime the dynamics of the coupled atom-cavity system is conveniently described by the open Dicke model, which we apply to calculating normal mode splitting generated by periodically ordered clouds in linear and ring cavities. We also show how to use normal mode splitting as witness for Wannier-Bloch oscillations in the tight-binding limit. At high optical density the atomic distribution contributes to shaping the mode function. This regime escapes the open Dicke model, but can be treated by a transfer matrix model provided the saturation parameter is low. Applying this latter model to an atomic cloud periodically ordered into a one-dimensional lattice, we observe the formation of photonic bands gaps competing with the normal mode splitting. We discuss the limitations of both models and point out possible pathways to generalized theories.
The strong collective interaction of atoms with an optical cavity causes normal mode splitting of the cavity's resonances, whose width is given by the collective coupling strength. At low optical density of the atomic cloud, the intensity distribution of light in the cavity is ruled by the cavity's mode function, which is determined solely by its geometry. In this regime the dynamics of the coupled atom-cavity system is conveniently described by the open Dicke model, which we apply to calculating normal mode splitting generated by periodically ordered clouds in linear and ring cavities. We also show how to use normal mode splitting as a witness for Wannier-Bloch oscillations in the tight-binding limit. At high optical density the atomic distribution contributes to shaping the mode function. This regime escapes the open Dicke model, but can be treated by a transfer matrix model provided the saturation parameter is low. Applying this latter model to an atomic cloud periodically ordered into a one-dimensional lattice, we observe the formation of photonic bands gaps competing with the normal mode splitting. We discuss the limitations of both models and point out possible pathways to generalized theories.
A novel class of circular resonators, based on a radial defect surrounded by Bragg reflectors, is studied in detail. Simple rules for the design and analysis of such structures are derived using a transfer matrix formalism. Unlike conventional ring resonators, annular Bragg resonators (ABR) are not limited by the total internal reflection condition and can exhibit both large free spectral ranges and low bend losses. The Bragg reflection mechanism enables the confinement of light within a defect consisting of a low refractive index medium (such as air). Strong atom-photon interaction can be achieved in such a structure, making it a promising candidate for sensing and cavity quantum electrodynamics applications. For sensing applications, we show that the ABR structure can possess significantly higher sensitivity when compared to a conventional ring resonator sensor. Lasing action and low threshold levels are demonstrated in ABR lasers at telecommunication wavelengths under pulsed optical pumping at room temperatures. The impact of the intensity and dimensions of the pump spot on the emitted spectrum is studied in detail.
A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.
Spontaneous symmetry breaking can occur in the powers of two optical modes coupled into a ring resonator, described by a pair of coupled Lorentzian equations, and featuring tunable self- and cross-phase modulation terms. Investigated is a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self- and cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalized description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.
The focus of this thesis is to investigate and fabricate a platform that can facilitate the enhancement of light-matter interactions. By tightly confining the photons and atoms to the same region of space, the probability of interaction is drastically increased as compared to free space interactions. Specifically, we focus on forming an optical cavity (or resonator) incorporated into a hollow-core photonic crystal fiber (HCPCF) using two distinct types of reflective mirrors along the axis of the fiber while still permitting atoms to be loaded into the region of high field confinement. \n \nOne means of pursuing this goal that we explored was to propose and numerically simulate two methods for implementing Bragg gratings in a HCPCF. These two methods leave the hollow-core unobstructed and are both based on controlled selective injection of photosensitive polymers into the photonic-crystal region of the hollow-core fiber, followed by interference photolithography. We report the results of numerical simulations for the hollow core fiber with Bragg gratings formed by the two methods. We find that a reflectivity of > 99.99% should be achievable from such fiber-integrated mirrors. Such a device could support high cooperativity and strong coupling regimes to be achieved. \n \nWe also demonstrate a fiber-integrated Fabry-Pérot cavity formed by attaching a pair of dielectric metasurfaces to the ends of a hollow-core photonic-crystal fiber segment. The metasurfaces consist of perforated membranes designed as photonic-crystal slabs that act as planar mirrors but can potentially allow injection of gases through their holes into the hollow core of the fiber. We have so far observed cavities with finesse of 11 and Q-factors of ~ 4.5 × 10^5, but much higher values should be achievable with improved fabrication procedures. We expect this device to enable the advancement of new fiber lasers, enhanced gas spectroscopy, and studies of fundamental light-matter interactions and nonlinear optics. These mirrors can be designed to be polarization dichroic — transparent for one polarization and reflective for another. This unique property can be exploited to allow for all signals to be directed along the high optical depth axis of the cavity and may provide a excellent platform for applications such as optical switching. \n \nFinally, we develop a novel protocol for a single photon all-optical transistor and how it may be implemented in the above mentioned fiber cavity systems. This unique scheme utilizes a far off-resonant vacuum cavity mode to stimulate a Raman absorption process of a source photon which may be switched off by the insertion of a single gate photon into the cavity mode. Relatively high switching contrasts and ratios for the source photon transmission can be obtained in our system.