Characteristics of coexisting attractors and ghost orbiting in an optomechanical microresonator.

We explore the nonlinear interactions of an optomechanical microresonator driven by two external optical signals. Optical whispering-gallery waves are coupled to acoustic surface waves of a fused silica medium in the equatorial plane of a generic microresonator. The system exhibits coexisting attractors whose behaviors include limit cycles, steady states, tori, quasi-chaos, and fully developed chaos with ghost orbits of a known attractor. Bifurcation diagrams demonstrate the existence of self-similarity, periodic windows, and coexisting attractors and show high-density lines within chaos that suggests a potential ghost orbit. In addition, the Lyapunov spectral components as a function of control parameter illuminate the dynamic nature of attractors and periodic windows with symmetric and asymmetric formations, their domains of existence, their bifurcations, and other nonlinear effects. We show that the power-shift method can access accurately and efficiently attractors in the optomechanical system as it does in other nonlinear systems. To test whether the ghost orbit is the link between two attractors interrupted by chaos, we examine the elements of the bifurcation diagrams as a function of control parameter. We also use detuning as a second control parameter to avoid the chaotic region and clarify that the two attractors are one.

Enhancement of Dissipative Sensing in a Microresonator Using Multimode Input.

Optical whispering-gallery microresonators have proven to be especially useful as chemical sensors. Most applications involve dispersive sensing, such as the frequency shift of resonator modes in response to a change in the ambient index of refraction. However, the response to dissipative interaction can be even more sensitive than the dispersive response. Dissipative sensing is most often conducted via a change in the mode linewidth owing to absorption in the analyte, but the change in the throughput dip depth of a mode can provide better sensitivity. Dispersive sensing can be enhanced when the input to the microresonator consists of multiple fiber or waveguide modes. Here, we show that multimode input can enhance dip-depth dissipative sensing by an even greater factor. We demonstrate that the multimode-input response relative to single-mode-input response using the same fiber or waveguide can be enhanced by a factor of more than one thousand, independent of the mode linewidth, or quality factor (Q), of the mode. We also show that multimode input makes the dip-depth response nearly one hundred times more sensitive than the linewidth-change response. These enhancement factors are predicted by making only two measurements of dip depth in the absence of an analyte: one with the two input modes in phase with each other, and one with them out of phase.

Cross-polarization coupling of whispering-gallery modes due to the spin-orbit interaction of light.

Light can couple between two orthogonally polarized whispering-gallery modes of a microresonator; the effect is easily observable when those modes are frequency degenerate, and can result in coupled-mode induced transparency (CMIT). Experimental observations of CMIT show that the cross-polarization coupling (CPC) strength is typically 10-8-10-7 per round trip. It is shown in this Letter that polarization rotation resulting from optical spin-orbit interaction through the experimentally realistic asymmetry of a microresonator about its equator can produce CPC with strengths in the same range as observed in experiments.

pH sensing using whispering gallery modes of a silica hollow bottle resonator.

The limitations of electrochemical pH sensors have stimulated the development of optical pH sensing methods. In the method reported here, swellable pH-sensitive polymer particles are deposited on the interior surface of a silica hollow bottle resonator. As the pH of the buffer solution in contact with the particles increases, the refractive index of the particles decreases. As a result, whispering gallery modes with internal evanescent components shift in frequency as a function of pH. This shift is monitored by the throughput of tunable diode laser light coupled into the whispering gallery modes using a tapered fiber. Plots of selected mode frequencies vs. pH yielded sigmoid shaped titration curves similar to those obtained using turbidity to monitor refractive index changes of the particles as a function of pH. The response time of 10-15 s and best resolution of 0.06 pH unit represent improvements over previous optical pH sensing methods.

Optical method for measuring thermal accommodation coefficients using a whispering-gallery microresonator.

A novel optical method has been developed for the measurement of thermal accommodation coefficients in the temperature-jump regime. The temperature dependence of the resonant frequency of a fused-silica microresonator's whispering-gallery mode is used to measure the rate at which the microresonator comes into thermal equilibrium with the ambient gas. The thermal relaxation time is related to the thermal conductivity of the gas under some simplifying assumptions and measuring this time as a function of gas pressure determines the thermal accommodation coefficient. Using a low-power tunable diode laser of wavelength around 1570 nm to probe a microsphere's whispering-gallery mode through tapered-fiber coupling, we have measured the accommodation coefficients of air, helium, and nitrogen on fused silica at room temperature. In addition, by applying thin-film coatings to the microsphere's surface, we have demonstrated that accommodation coefficients can be measured for various gases on a wide range of modified surfaces using this method.

Broadband optical absorbance spectroscopy using a whispering gallery mode microsphere resonator.

We demonstrate the ability to excite and monitor many whispering gallery modes (WGMs) of a microsphere resonator simultaneously in order to make broadband optical absorbance measurements. The 340 microm diameter microsphere is placed in a microfluidic channel. A hemispherical prism is used for coupling the WGMs into and out of the microsphere. The flat surface of the prism seals the microfluidic channel. The slight nonsphericity in the microsphere results in coupling to precessed modes whose emission is spatially separated from the reflected excitation light. The evanescent fields of the light trapped in WGMs interact with the surrounding environment. The change in transmission observed in the precessed modes is used to determine the absorbance of the surrounding environment. In contrast to our broadband optical absorbance measurements, previous WGM sensors have used only a single narrow mode to measure properties such as refractive index. With the microfluidic cell, we have measured the absorbance of solutions of dyes (lissamine green B, sunset yellow, orange G, and methylene blue), aromatic molecules (benzylamine and benzoic acid), and biological molecules (tryptophan, phenylalanine, tyrosine, and o-phospho-L-tyrosine) at visible and ultraviolet wavelengths. The microsphere surface was reacted with organosilane molecules to attach octadecyl groups, amino groups, and fluorogroups to the surface. Both electrostatic and hydrophobic interactions were observed between the analytes and the microsphere surface, as indicated by changes in the measured effective pathlength with different organosilanes. For a given analyte and coated microsphere, the pathlength measurement was repeatable within a few percent. Methylene blue dye had a very strong interaction with the surface and pathlengths of several centimeters were measured. Choosing an appropriate surface coating to interact with a specific analyte should result in the highest sensitivity detection.

Analysis of whispering-gallery microcavity-enhanced chemical absorption sensors.

A theoretical analysis of the operation of a chemical sensor based on cavity-enhanced optical absorption is given for a system in which the cavity is a dielectric whispering-gallery microresonator. Continuous-wave input is assumed, and the detection sensitivity is characterized in terms of an effective absorption path length. In the case of tunable single-frequency input, it is shown that monitoring analyte-induced changes in the throughput dip depth enables detection with relative sensitivity greater than that of frequency-shift and cavity-ringdown methods. In addition, for the case of broadband input and drop-port output, an analysis applicable to microcavity-enhanced absorbance spectroscopy experiments is given.

Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes.

Tunable diode laser absorption spectroscopy using microresonator whispering-gallery modes (WGMs) is demonstrated. WGMs are excited around the circumference of a cylindrical cavity 125 mum in diameter using an adiabatically tapered fiber. The microresonator is very conveniently tuned by stretching, enabling the locking of an individual WGM to the laser. As the laser is scanned in frequency over an atmospheric trace-gas absorption line, changes in the fiber throughput are recorded. The experimental results of cavity-enhanced detection using such a microresonator are centimeter effective absorption pathlengths in a volume of only a few hundred microns cubed. The measured effective absorption pathlengths are in good agreement with theory.