Hongrok Chang

Whispering-gallery mode splitting in coupled microresonators

Using iterative methods we demonstrate that, for a structure consisting of N-coupled microspheres or ring resonators, the morphology-dependent resonances split into N higher-Q modes, in direct analogy with other types of oscillators. Moreover, for odd numbers of identical lossless coupled rings, the circulating intensity in the innermost ring increases exponentially with N when there is strong coupling to even-numbered rings and weak coupling to odd-numbered rings.

Coherence Phenomena in Coupled Optical Resonators

Abstract We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrödinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.

Slow and fast light in coupled microresonators

We predict the propagation of slow and fast light in two co-resonant coupled optical resonators. In coupled resonators, slow light can propagate without attenuation by a cancellation of absorption as a result of mode splitting and destructive interference, whereas transparent fast light propagation can be achieved by the assistance of gain and splitting of the intracavity resonances, which consequently change the dispersion from normal to anomalous. The effective steady-state response of coupled-resonators is derived using the temporal coupled-mode formalism, and the absorptive and dispersive responses are described. Specifically, the occurrence of slow light via coupled-resonator-induced transparency and gain-assisted fast light are discussed.

Dispersion enhancement in atom-cavity and coupled cavity systems

We present an entirely linear all-optical method of dispersion enhancement using coupled cavities that leads to a substantial increase in system transmission in comparison with atom-cavity systems. This is achieved by tuning the system to an anomalous dispersion condition by under-coupling at least one of the cavities to the other. The intracavity anomalous dispersion is then associated with a dip in reflection (and in turn with a peak in transmission) rather than with an absorption resonance as in the case of the atomic vapor. We find that in contrast with the atom-cavity system where mode reshaping always contributes to the mode pushing, in coupled cavity systems reshaping of the mode profile can either contribute to or oppose the mode pushing, and even reverse it under appropriate conditions leading to a reduced scale factor in transmission. We demonstrate a method for further optimizing the transmission of both atom-cavity and coupled-cavity systems, but show that this leads to a more rectangular mode profile and a reduction in the scale factor bandwidth. We also derive the cavity scale factor in reflection for both atom-cavity and coupled cavity systems and show that in reflection the reshaping of the mode profile can either contribute to or oppose the mode pushing, but cannot reverse it.

Tuning the Sensitivity of an Optical Cavity with Slow and Fast Light

We have measured mode pushing by the dispersion of a rubidium vapor in a Fabry-Perot cavity and have shown that the scale factor and sensitivity of a passive cavity can be strongly enhanced by the presence of such an anomalous dispersion medium. The enhancement is the result of the atom-cavity coupling, which provides a positive feedback to the cavity response. The cavity sensitivity can also be controlled and tuned through a pole by a second, optical pumping, beam applied transverse to the cavity. Alternatively, the sensitivity can be controlled by the introduction of a second counter-propagating input beam that interferes with the first beam, coherently increasing the cavity absorptance. We show that the pole in the sensitivity occurs when the sum of the effective group index and an additional cavity delay factor that accounts for mode reshaping goes to zero, and is an example of an exceptional point, commonly associated with coupled non- Hermitian Hamiltonian systems. Additionally we show that a normal dispersion feature can decrease the cavity scale factor and can be generated through velocity selective optical pumping.

High-precision, accurate optical frequency reference using a Fabry–Perót diode laser

We show that the optical output of a temperature and current-tuned Fabry-Perót diode laser system, with no external optical feedback and in which the frequency is locked to Doppler-free hyperfine resonances of the 87Rb D2 line, can achieve high frequency stability and accuracy. Experimental results are presented for the spectral linewidth, frequency stability, and frequency accuracy of the source. Although our optical source is limited by a short-term spectral linewidth greater than 2 MHz, beat signal measurements from two such sources demonstrate a frequency stability of 1.1 kHz, or minimum Allan deviation of 4×10-12, at an integration time τ=15 s and with a frequency accuracy of 60 kHz at τ=300 s. We demonstrate the use of the optical source for the precision measurement of hyperfine level frequency spacings in the 5P3∕2 excited state of 87Rb and provide an accurate frequency scale for optical spectroscopy.

Fast-light enhancement by polarization mode coupling in a single optical cavity

We present an entirely linear all-optical method of dispersion enhancement that relies on mode coupling between the orthogonal polarization modes of a single optical cavity, eliminating the necessity of using an atomic medium to produce the required anomalous dispersion, which decreases the dependence of the scale factor on temperature and increases signal-to-noise by reducing absorption and nonlinear effects. The use of a single cavity results in common mode rejection of the noise and drift that would be present in a system of two coupled cavities. We show that the scale-factor-to-mode-width ratio is increased above unity for this system and demonstrate tuning of the scale factor by (i) directly varying the mode coupling via rotation of an intracavity half wave plate, and (ii) coherent control of the cavity reflectance which is achieved simply by varying the incident polarization superposition. These tuning methods allow us to achieve unprecedented enhancements in the scale factor and in the scale-factor-to-mode-width ratio by closely approaching the critical anomalous dispersion condition.

Dispersive elements for enhanced-laser gyroscopy and cavity stabilization

We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and enhanced gyroscopic sensitivity. We find an enhancement in the sensitivity of a laser gyroscope to rotation for normal dispersion, while anomalous dispersion can be used to self-stabilize an optical cavity. Our results indicate that atomic media, even coherent superpositions in multilevel atoms, are of limited use for these applications, because the amplitude and phase filters work against one another, i.e., decreasing the modulation frequency increases its amplitude and vice-versa. On the other hand, for optical resonators the dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together. We find that for over-coupled resonators, the absorption and normal dispersion on-resonance increase the contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the gyroscopic response. Under-coupled resonators can be used to stabilize the frequency of a laser cavity, but result in a concomitant increase in amplitude fluctuations. As a more ideal solution we propose the use of a variety of coupled-resonator-induced transparency that is accompanied by anomalous dispersion.

Induced transparency and absorption in coupled microresonators

We review the conditions for the occurrence of coherence phenomena in passive coupled optical microresonators. We derive the effective steady-state response and determine conditions for induced transparency and absorption in these systems.

Enhancement of Optical Nonlinearities Via Whispering Gallery Mode Splitting

An iterative method is applied to the analysis of N-coupled ring resonators. Splitting of the modes into N higher-Q modes occurs when the round-trip phase shifts in each ring are equal, in agreement with results for planar resonators and whispering gallery modes (WGMs) in coupled microparticles. This mode-splitting is, therefore, a universal phenomenon for resonant structures, and can lead to reduced thresholds for nonlinear optical effects.