Coupling of light from a microresonator TE mode to a coresonant TM mode will have a different strength than that of coupling from the TM mode to the TE mode. This coupling nonreciprocity, deriving from the optical spin-orbit interaction, is modeled numerically and confirmed experimentally by observing coupled-mode induced transparency and AutlerTownes splitting. By measuring the throughput spectrum in both polarizations when the input directly excites modes of only one polarization, the coupling strengths in both directions can be determined simultaneously by fitting to the numerical model. Some examples and implications are discussed here.
Coresonant, but orthogonally polarized, whispering gallery modes can couple to each other via the optical spin-orbit interaction. This cross-polarization coupling (CPC) can result in coupled-mode-induced transparency, attenuation, or Autler-Townes splitting. By fitting observed throughput spectra to a numerical model, the CPC strength can be determined and found to agree with the theory. The throughput response to input amplitude modulation provides an independent method of measuring the CPC strength. Observation and fitting of throughput spectra of both polarizations confirms that CPC is nonreciprocal. Induced transparency and attenuation can be observed even without CPC, by utilizing mode superposition. All these effects will be reviewed.
Theoretical calculation of the cross-polarization coupling between whispering-gallery modes in a microresonator shows that this coupling is, in general, asymmetric. The spin-orbit induced coupling of light from a TE mode to a coresonant TM mode will have a different strength than that of the coupling from the TM mode to the TE mode. This coupling asymmetry is confirmed in coupled-mode induced transparency experiments. By monitoring the throughput spectrum in both polarizations when the input directly excites only modes of one polarization, the coupling strengths in both directions are determined simultaneously by fitting to a model. Some examples and implications are discussed here.
Induced transparency in a microresonator can result from cross-polarization coupling of two coresonant orthogonally polarized whispering-gallery modes of very different Q. The coupling creates supermodes that are superpositions of the two modes. Mode superpositions that result from simultaneous excitation of two orthogonally polarized modes can also show induced transparency, even in the absence of cross-polarization coupling. Induced transparency is accompanied by pulse delay, and it is also possible to observe induced attenuation with pulse advancement or delay. These effects are proposed theoretically, modeled numerically, and confirmed experimentally; a summary is presented here
Optical whispering-gallery mode (WGM) microresonators have been widely used as chemical sensors. In practice, most WGM sensing is based on either mode frequency shift (dispersive) or mode linewidth change (dissipative). However, WGM sensors based on the fractional change in throughput dip depth (dissipative) can offer better sensitivity under certain conditions. Recently it was demonstrated that for WGM dip-depth sensors multimode input can further improve the sensitivity as compared to single-mode input. This enhancement in sensitivity is achieved by using an asymmetric tapered fiber to couple light in and out of the microresonator. In this report, we develop a model which predicts the waist radius of the fabricated asymmetric tapered fiber. The radius predicted by the model is verified by measuring the beat length for the two fiber modes that are excited and couple into a WGM.
Induced transparency and attenuation are observed in fiber-coupled microresonators due to coupling between coresonant whispering-gallery modes of orthogonal polarizations. Theoretical analysis has shown that this cross-polarization coupling is asymmetric (or nonreciprocal); the coupling from TE to TM generally has a different strength than TM to TE coupling, and the strengths depend on the mode numbers. In an experiment where one polarization is input and the outputs of both polarizations are simultaneously detected by matched detectors, the two coupling strengths are determined by fitting the experimental output spectra to a model. Comparison to theory may then lead to identification of the two modes involved, even when the microresonator dimensions are large compared to the wavelength. Some theoretical results that give similar coupling strengths to those observed in the experiment are presented to give an estimate of typical mode numbers involved.
Optical microresonators, in particular whispering-gallery microresonators, have proven to be especially useful as chemical sensors. In most applications, the sensing modality has been dispersive; an example is the frequency shift of resonator modes in response to a change in the ambient index of refraction. However, it has been shown that the response to dissipative interaction can be even more sensitive than the dispersive response. Dissipative sensing is most often carried out via a change in the mode linewidth owing to absorption in the analyte, but it has been demonstrated that the change in the throughput dip depth of a mode can provide better sensitivity than linewidth change. 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 dissipative sensing by an even greater factor. Having multimode input does not affect the linewidth response, but the enhancement factor for the dip-depth response can be quite large. We demonstrate that the multimode-input response relative to single-mode-input response using the same fiber or waveguide can be enhanced by more than three orders of magnitude. Furthermore, this enhancement is independent of the mode linewidth, or quality factor Q of the mode. The enhancement factor can be predicted by making only two measurements of dip depth in the absence of analyte: one with the two input modes in phase with each other, and one with them out of phase.
Optical whispering-gallery mode (WGM) microresonators have proven their ability to enhance light-matter interaction and hence are widely used for sensing. In contrast to the traditional approach of using symmetric adiabatic tapers to couple light into the resonators, we use an asymmetric non-adiabatically tapered fiber to couple light from two fiber modes into a microresonator. Previously it was shown that dissipative sensing of an absorbing analyte can be more sensitive than dispersive sensing, and that dissipative sensing based on dip depth change can be more sensitive than dissipative sensing based on linewidth change. In this report, we demonstrate an enhancement in sensitivity by three orders of magnitude for dissipative sensing based on dip depth change. The enhancement factor is independent of the quality factor Q of the WGM and is determined solely by the values of the throughput power in the absence of analyte when the two fiber modes are in and out of phase at the point where they couple into the WGM.
Adiabatically tapered fibers are often used to excite whispering gallery modes (WGMs) of microresonators used as chemical sensors. Recently it was demonstrated that using a non-adiabatic tapered fiber can enhance refractive index sensing. The incoming light is distributed between fundamental and higher-order fiber modes, whereas only the fundamental mode is detected because the uptaper is adiabatic. The interference effect between these fiber modes when exciting a WGM leads to the sensitivity enhancement. We have shown theoretically that even greater enhancement is possible for absorption sensing. For a given WGM, the predicted enhancement can be calculated by measuring the throughput power when the two fiber modes are in and out of phase at the input. Enhancement can be confirmed by sending the light in the reverse direction through the asymmetrically tapered fiber so that only one fiber mode is incident on the microresonator. Using a carefully designed asymmetrically tapered fiber, we have demonstrated this enhancement in experiments using a hollow bottle resonator (HBR) with an internal analyte. Absorption in the analyte causes a change in the WGM throughput fractional dip depth; these changes were studied with varying analyte concentration for forward and reverse propagation to evaluate the absorption sensitivity. For both liquid and gaseous analytes, our measured sensitivity enhancements are not inconsistent with the predicted enhancements of at least a factor of 100.
The cross polarization coupling (CPC) between orthogonally polarized modes in a single whispering-gallery microresonator can lead to electromagnetically induced transparency (EIT) like effects. Depending on the CPC strength, coupled mode induced transparency (CMIT), coupled mode induced attenuation (CMIA), or Autler-Townes splitting (ATS) can be observed. Previously, the values of CPC strength were found by fitting the experimental throughput spectra to a steady-state model. However, our dynamical analysis suggests an independent way of estimating the CPC strength by sinusoidal modulation at the input. From experimentally determined parameters, we first find one estimate of the CPC strength by model fitting as before. From the modulation frequency that gives the minimum throughput amplitude on resonance, we find another estimate of the CPC strength. Our preliminary experimental results show that the two values agree quite well, which means we have an independent way of finding the CPC strength.
Light can couple between TE and TM whispering-gallery modes (WGMs) of a microresonator; the effect is easily observable when those modes are frequency-degenerate, and can result in coupled-mode induced transparency (CMIT). Fitting experimental observations of CMIT with a numerical model in which the cross-polarization coupling strength is a free parameter shows that the coupling strength is typically 10-8 – 10-7 per round trip. It is shown here that polarization rotation of this magnitude can result from optical spin-orbit interaction through the asymmetry of a WGM. Using the eikonal approximation to describe a WGM, along with asymmetry of the microresonator about its equator, the maximum possible polarization rotation per round trip can be calculated. Then accounting for spatial overlap and phase mismatch of the coresonant WGMs, using coupled-mode theory, gives coupling strengths in agreement with experiment.
Whispering-gallery microresonators are well suited for use as sensors. For example, fluid analytes can be sensed through their effect on the refractive index or by their optical absorption. The former results in a frequency shift of a whispering-gallery mode (WGM); the latter changes the WGM’s intensity profile, and can be even more sensitive than the former. WGMs are typically excited by coupling of light from a tapered fiber. It has recently been demonstrated that using a non-adiabatic tapered fiber can produce a Fano resonance whose asymmetric shape can enhance the sensitivity of refractive-index sensing. The non-adiabatic taper allows the incoming light to be distributed between two fiber modes that interfere when exciting a single WGM, thereby producing the asymmetric resonance. However, just as absorption sensing can be more sensitive than index sensing, its enhancement by using a non-adiabatic taper can be greater as well. This enhancement is demonstrated theoretically here, and experiments for confirmation are underway.
Slow light, i.e., the delay of an incident resonant pulse, can be observed in the throughput of an optical whisperinggallery microresonator. It can be produced by a single overcoupled whispering-gallery mode (WGM), or, more usefully, through induced transparency effects that are observed in the case of two coresonant WGMs with very different quality factors. There are several different methods for achieving induced transparency, two of which will be considered here. In addition, under the right conditions, light in a WGM can excite acoustic WGMs by forward Brillouin scattering. This nonlinear process due to electrostriction has a threshold, above which energy is transferred from the first optical WGM to the acoustic WGM and to a lower-frequency optical WGM. When one of the optical WGMs taking part in this optomechanical process is also involved in the production of slow light, the pulse delay can be affected. Analytical expressions for pulse delay in the three cases mentioned above are examined in terms of the WGM intracavity powers and it is shown that when the higher-frequency optical WGM is responsible for slow light, the pulse delay is reduced when the optomechanical process occurs. This conclusion is verified by a numerical model.
Induced transparency and absorption effects can be observed in the throughput of an optical microresonator that has two coresonant modes with very different quality factors. There are several different methods for achieving these effects, which enable slow light and fast light, i.e., the delay or advancement of an incident resonant pulse. For example, mode coupling can be employed. This coupling can take place between modes of the same polarization or modes of orthogonal polarization. Another method is based on superposition, when two orthogonally polarized modes are driven simultaneously by linearly polarized input light and throughput of the same polarization as the input is detected. In general, induced transparency is accompanied by pulse delay, whereas induced absorption can be accompanied by pulse advancement or delay. A number of different methods for producing induced transparency or absorption are compared here. Several properties are considered for comparison. One involves the widths of the induced transparency or absorption window and of the corresponding spectral region of steep dispersion. Achievable pulse delays or advancements, along with pulse distortion and delay-bandwidth (or advancement-bandwidth) products, are also compared. Different methods allow for different amounts of control over various system parameters, and these are compared as well. The differences among the several methods are evaluated in consideration of suitability for employment in various applications.
Induced transparency and absorption effects are observed in the throughput of a hollow bottle microresonator using
either mode coupling or superposition of two coresonant orthogonally polarized whispering gallery modes of very
different quality factors (Q). The first method is based on intracavity cross polarization coupling when either the TE
mode or the TM mode is driven, resulting in coupled mode induced transparency (CMIT) and coupled mode induced
absorption (CMIA). The second method is based on superposition of the throughputs when the two modes are
simultaneously driven by input light linearly polarized at an angle of 45° with respect to the TE-TM basis of the
resonator, and throughput of the same polarization is detected. In this way, superposition can be created even in the
absence of cross polarization coupling. The observations using the second method are referred to as coresonant
polarization induced transparency and absorption (CPIT, CPIA). Coresonance between the TE and TM modes can be
obtained by strain tuning. The above behaviors are analogous to electromagnetically induced transparency and
absorption (EIT, EIA), and enable slow light and fast light, i.e., the delay or advancement of an incident resonant pulse.
Experimental results representative of several different types of behavior are presented here. Induced transparency is
seen to be accompanied by pulse delay, whereas induced absorption can be accompanied by pulse advancement or delay.
The results are analyzed and explained by simple analytical modeling and by comparison to the output of a more detailed
numerical model describing these effects.
The throughput of a single fiber-coupled whispering-gallery microresonator, such as a fused-silica microsphere, can exhibit induced transparency or absorption, leading to pulse delay or advancement, through the interaction of two coresonant orthogonally polarized whispering-gallery modes having very different quality factors (Q). There are two ways by which these behaviors may be realized. The first method, coupled-mode induced transparency and absorption (CMIT, CMIA), relies on intracavity cross-polarization coupling when only one mode is driven. The second method, coresonant polarization induced transparency and absorption (CPIT, CPIA), uses a simple superposition of orthogonal throughputs (in the absence of intracavity cross-polarization mode coupling) when the two modes are simultaneously driven. In both cases, the throughput behavior is observed on the same polarization component as that of the linearly polarized input. The pulse delay or advancement can be enhanced by taking advantage of the multimode capability of the tapered-fiber coupler, an advantage that is not available to free-space-beam-driven ring resonators. Some predictions of a numerical model for this enhancement, which assumes experimentally realistic conditions, are presented here.
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.
The throughput of a single fiber-coupled whispering-gallery microresonator, such as a fused-silica microsphere, can
exhibit behavior analogous to electromagnetically induced transparency and absorption (EIT, EIA). These effects enable
slow and fast light, respectively, in the form of pulse delay or advancement. Two different methods can be used to
realize this behavior; in both methods, the key feature is the use of two coresonant orthogonally polarized whisperinggallery
modes of very different quality factor (Q). The first method relies on intracavity cross-polarization coupling
when only one mode is driven, and the second method uses a simple superposition of orthogonal throughputs (in the
absence of intracavity cross-polarization mode coupling) when the two modes are simultaneously driven. We refer to
the behavior observed using the first method as coupled-mode induced transparency and absorption (CMIT, CMIA), and
the behavior of the second method as coresonant polarization induced transparency and absorption (CPIT, CPIA). In
both cases, polarization-sensitive detection of the throughput is used, and the EIT/EIA analog features are observed on
the same polarization component as that of the linearly polarized input. Some predictions of a numerical model of these
processes are presented here. In addition to a discussion of these predictions, which assume conditions accessible to
experiment, some experimental results are briefly described.
We use a tunable diode laser operating near 1570 nm to investigate various effects of the heat transfer from fused-silica
microspheres, with and without thin-film coatings, to the surrounding gas in a vacuum chamber. The resonance
frequencies of microsphere whispering-gallery modes (WGMs), excited by a tapered-fiber coupler, shift with changing
temperature (about -1.6 GHz/K at 1570 nm). This shift, primarily due to the temperature dependence of the refractive
index of fused silica, enables the measurements whose results are reported here: determination of the thermal
accommodation coefficient of air on different surfaces, and measurement of the optical absorption coefficients of surface
water layers and of a thin film coating. Our method for determining thermal accommodation coefficients involves
deducing the thermal conductivity of the air as a function of pressure by measuring the relaxation rate of an externally
heated microsphere to room temperature. Then, in a separate experiment, by observing thermal optical bistability of the
WGM resonances caused by absorption of the probe laser, the contribution of water or film absorption to the total loss is
found.
We describe the synthesis of gold nanorods (NRs) nucleated by HgTe nanoparticles (NPs) of average size 3 nm in diameter. Growth of ~200 nm by ~50 nm NRs on various surfaces is achieved by using an intermediary polyelectrolyte layer. A poly(dimethyldiallylammonium) chloride (PDDA) monolayer on the surface attracts the thioglycolic acid (TGA) capped HgTe NPs and assists in one-dimensional gold growth. Rod morphology is observed for approximately one third of the resulting features. Confirmation of Au deposition is obtained with x-ray photoelectron spectroscopy and optical absorption measurements that show an increase in the Au plasmon band with time spent in gold growth solution. Au NRs were grown directly on the surface of high quality factor (Q) optical resonators (microspheres and microcylinders). Although the coating procedure reduces the Q of the resonators, whispering gallery modes are sustained. This seeding technique, amenable to many different surfaces, may result in semiconductor-metal nanocomposites with novel electronic and optical properties.
Chemical absorption is investigated using the evanescent fraction of a whispering-gallery mode (WGM). An effective absorption path length of about 50 cm is obtained in methane sensing and about 100 cm in a liquid dye solution.
A prototype evanescent-wave sensor using resonant whispering-gallery modes of a fused-silica microsphere has been developed and is being applied to the detection of trace amounts of carbon dioxide, carbon monoxide, ammonia, and acetylene in the 1530 - 1580 nm wavelength region. Its sensitivity is comparable to that of typical multipass-cell systems, but our sensor is much more compact because of resonant cavity enhancement. It represents a significant improvement over current total-internal-reflection or fiber evanescent-wave sensors, owing to the longer effective absorption path length (tens of meters in a sphere less than a millimeter in diameter). The present sensitivity is about a hundred parts per million, equivalent to the level detected by a household carbon monoxide sensor. This sensitivity is for direct absorption measurements; wavelength-modulation spectroscopy is being implemented and should provide two or three orders of magnitude improvement. By extending the same techniques, using fluorozirconate- glass microspheres and stronger transitions in the mid- infrared, the sensitivity is expected to improve to about a part per billion.
We report advances in compression tuning of fused-silica microsphere whispering-gallery resonances and a practical use of the improved compression tuner. The advances include extending the tuning range and enhancing the tuner’s response speed; these lead to the new application of using the tuner to lock to a laser, keeping a single whispering-gallery mode on resonance as the laser frequency is scanned. The resonance frequency of the mode to be locked is weakly modulated by axial compression of the microsphere, and phase-sensitive detection of the fiber-coupled optical throughput is used for locking. Using a laser wavelength of either 1570 nm or 830 nm, we demonstrate a locked tracking range exceeding 30 GHz for a microsphere of 120 GHz free spectral range. The improved tuner design that makes this application possible allows coarse tuning over 1 THz and piezoelectric tuning over 80 GHz. Compression modulation rates of up to 13 kHz have also been achieved with this tuner, producing a tuning speed of at least 16 GHz/ms.
The high Q of a microsphere whispering-gallery mode allows for sensitive resonant detection of atoms or molecules. The species being detected absorbs energy from the mode's evanescent field. It can be identified by knowing the resonant wavelength of the driving laser, and its concentration can be determined from the absorption signal on the light in reflection or transmission. High sensitivity results from the long effective absorption path length provided by the whispering-gallery mode's large Q. There are many possible implementations of and applications for such a sensor; several of each are described herein. In particular, for atmospheric trace-gas sensing, the microsphere has the potential to rival the performance of the multipass cell, but in a much more compact and rugged system. Our construction of a prototype system for detection of carbon monoxide, carbon dioxide, and ammonia is described.
The optical whispering-gallery modes of dielectric microspheres can have extremely sharp resonances, with quality factors as large as Q = 1010. Using evanescent coupling for input and output, an effective ring resonator is produced, with a large intracavity field enhancement. It has been suggested that optical nonlinearities might be enhanced using these modes. Our effort to do so is described herein. The nonlinear medium is a composite, in which semiconductor nanoparticles are the active component and constitute a small volume fraction. This can be achieved by fabricating microspheres from semiconductor-doped glasses or by coating fused-silica spheres. Because the field distribution of a whispering-gallery mode is strongly localized near the sphere's surface and includes an evanescent tail external to the sphere, thin-film coating is a practical option, and this technique offers several advantages. The properties of whispering-gallery modes and optical coupling are discussed, the processes of fabrication and coating are described, and the operational characteristics and potential applications of nonlinear optical behavior in microspheres are considered.
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