Resonance shifts of transverse-electric whispering gallery modes in a spheroidal resonator

A variational method was applied to find the wave function of a transverse-electric whispering gallery mode (WGM) in a spheroidal resonator of a uniform refractive index (RI). It was found that the electric field is tangential to the resonator surface as in the sphere, up to the linear order of the ellipticity. Using the wave function, the resonance shift due to adsorption of a thin, uniform dielectric layer onto the surface and the shift by a uniform RI change in the surroundings were evaluated in the perturbation theory. The shift by the RI change is not affected by the ellipticity, but the shift by the layer adsorption now depends on the meridional order. However, the correction is not large unless the ellipticity is large and the meridional order is away from the one for the equatorial mode of WGM.     

Effect of the ellipticity of a dielectric resonator on the induced whispering gallery modes

The influence of ellipticity of a dielectric resonator on the whispering gallery (WG) oscillation modes induced by a lumped radiation source was studied. Dependence of the spectral characteristics of resonators and the spatial distributions of oscillation fields on the WG mode propagation direction is experimentally determined.     

An ultralow noise microwave oscillator based on a high-Q liquidnitrogen cooled sapphire resonator

Two liquid nitrogen-cooled sapphire loaded cavities (SLC's) operating at about 80 K have been successfully constructed, Both cavities were designed to operate on the whispering gallery (WG) E_{12, 1, δ} mode at a resonant frequency of 8.95 GHz. The first SLC was used as the frequency-determining element in a loop oscillator, while the second was used as a frequency discriminator to measure oscillator phase noise. The single sideband phase noise of a free running loop oscillator incorporating the first SLC was measured as -133 dBc/Hz at an offset frequency of 1 kHz, and was limited by the SLC Q-factor and the amplifier flicker phase noise. By using specially designed feedback electronics the oscillator phase noise was reduced to -156 dBc/Hz and -162 dBc/Hz at 1 and 10 kHz offset, respectively. This measurement was shown to be limited by the electronic flicker noise imposed by the phase detector in the feedback electronics, To our knowledge the phase noise and resonator Q-factor of 6×10⁷ represent the best results ever measured at liquid nitrogen temperatures or above     

Ultrasensitive thermal sensors based on whispering gallery modes in a polymer core optical ring resonator

This study proposes a thermal sensor based on whispering gallery modes (WGMs) in a polymer core optical ring resonator (PCORR). The thermal sensitivity and detection limit (i.e., the temperature resolution) for WGMs of various orders and polarizations are theoretically studied as a function of the ring wall thickness. The results show that the temperature detection limits can be as low as 4×10(-5) and 6×10(-6) K for laser linewidths of 2 and 0.3 MHz, respectively. The ultrahigh temperature resolution makes the PCORR a very promising platform for temperature measurement. The analysis also shows that the WGM of a lower order has better thermal sensing performance and a thinner optimal thickness of the ring resonator.     

Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique

The anisotropic loss tangent has been determined in monocrystalline sapphire for components parallel and perpendicular to the crystal axis, using the whispering gallery (WG) mode method. The Q-factors of quasi-TE and quasi-TM modes were measured precisely in four cylindrical sapphire resonators at room temperature, from which was determined a maximum attainable Q-factor of (2.1 +/- 0.2) x 10(5) at 9 GHz in a quasi-TM mode. Sapphire dielectric material from three different manufacturers was compared over the 270-345 K temperature range and the 5-16 GHz frequency range.     

Rigorous analysis of whispering gallery mode frequency conversion because of time variation of refractive index in a spherical resonator

We investigate theoretically the switching effects for the whispering gallery modes in a spherical dielectric resonator when its material is subject to abrupt time change in permittivity. A rigorous analytical approach is used to study the transformation process. Details of both the transient response and the steady-state regime are described.     

Frequency-temperature compensation in Ti(3+) and Ti(4+ ) doped sapphire whispering gallery mode resonators

A new method of compensating the frequency-temperature dependence of high-and monolithic sapphire dielectric resonators near liquid nitrogen temperature is presented. This is achieved by doping monocrystalline sapphire with Ti(3+) ions. This technique offers significant advantages over other methods.     

Sensitivity and optimization of a high-Q sapphire dielectric motion-sensing transducer

A high-Q sapphire dielectric motion sensing transducer that operates at microwave frequencies has been developed. The device uses cylindrical whispering gallery modes of quality factor greater than 10 (5) at room temperature and greater than 10(8) at 4 K. The tuning coefficient of the transducer resonance frequency with respect to displacement was measured to be of the order of a few MHz/mum. An electromagnetic model that predicts the resonant frequency and tuning coefficient has been developed and was verified by experiment. We implemented the model to determine what aspect ratio and what dielectric mode is necessary to maximize the sensitivity. We found that the optimum mode type was a TM whispering gallery mode with azimuthal mode number of about 7 for a resonator of 3 cm in diameter. Also, we determined that the tuning coefficients were maximized by choosing an aspect ratio that has a large diameter with respect to the height. By implementing a microwave pump oscillator of SSB phase noise -125 dBc/Hz at 1 kHz; offset, we have measured a sensitivity of order 10 (-16) m/ radicalHz. We show that this can be improved with existing technology to 10(-18) m/ radicalHz, and that in the near future this may be further improved to 10(-19) m/ radicalHz.     

Discontinuous spectral element method modeling of optical coupling by whispering gallery modes between microcylinders

We introduce a high-order time-domain discontinuous spectral element method for the study of the optical coupling by evanescent whispering gallery modes between two microcylinders, the building blocks of coupled resonator optical waveguide devices. By using the discontinuous spectral element method with a Dubiner orthogonal polynomial basis on triangles and a Legendre nodal orthogonal basis on quadrilaterals, we conduct a systematic study of the optical coupling by whispering gallery modes between two microcylinders and demonstrate the successful coupling between the microcylinders and also the dependence of such a coupling on the separation and the size variation of the microcylinders.     

Determination of binding kinetics using whispering gallery mode microcavities

Silica optical microcavity sensors show great promise in the kinetic evaluation of binding pairs, fundamental in understanding biomolecular interactions. Here, we develop and demonstrate a novel platform, based on bioconjugated silica microsphere resonators, to study the binding kinetics of the biotin-streptavidin system. We characterize the optical performance, verify the covalent attachment of biotin to the surface, and perform streptavidin detection experiments. We perform preliminary kinetic analysis of the detection data which shows the potential of whispering gallery mode resonators in the determination of the dissociation constant of the binding pair, which is in good agreement with previously published values.     

Observation of whispering gallery modes in lasers with cut disk cavities

Whispering gallery modes (WGMs) have been observed in lasers with cut disk (half-and quarterdisk) cavities operating at room temperature in the 2.0–2.4 μm wavelength range. The possibility of WGM generation in a disk-sector cavity is theoretically studied. It is established that the intermode distance in a full-and half-disk cavity is the same, while that in the quarter-disk cavity is doubled. A new method for the radiation extraction from WGM lasers is proposed.     

Ultrasensitive chemical sensors based on whispering gallery modes in a microsphere coated with zeolite

We propose a highly sensitive chemical sensor by functionally coating a zeolite film on the external surface of an optical microsphere. Using the perturbation theory, a model is developed to calculate sensor sensitivity and analyze the impact of the zeolite film thickness. The quality factor and detection limit are also investigated by using an approximate model. Simulations show that a zeolite coating can effectively increase sensitivity. The results provide physical insights for the design and optimization of various parameters for desired sensor performance.     

Whispering gallery modes induced in a partly shielded hemispherical dielectric resonator

Whispering gallery modes induced in a partly shielded hemispherical dielectric resonator by lumped radiation sources were experimentally studied for the symmetric and asymmetric arrangement of the hemisphere relative to the cylindrical metal shield. The oscillation mode characteristics are presented for the shielded hemispherical resonator and an analogous open dielectric resonator. The proposed resonator is a promising device for the creation of highly stable solid-state millimetric wave oscillators.     

Q-factor measurement of quasi-optical dielectric resonators under conditions of the whispering gallery mode degeneration removal

An approach that allows one to determine the unloaded quality factor of a quasi-optical dielectric resonator (QDR) under conditions of the resonance line splitting corresponding to twofold degenerative whispering gallery (WG) mode has been proposed. The resonator is represented by an equivalent network as two oscillatory circuits with a certain coupling between them. The approach allows one to determine the Q-factor of a single oscillatory circuit using three measured parameters, namely: 1) ratio between specific amplitudes of the resonator amplitude-frequency response (or its second derivative); 2) resonant frequency; and 3) frequency splitting of the response (or its respective second derivative). The proposed technique is illustrated by the measurements in the millimeter-wave range for sapphire quasi-optical resonators with conducting and high-T/sub c/ superconducting (HTS) film endplates.     

1/f frequency noise of 2-GHZ high-Q thin-film sapphire resonators

We present experimental results on intrinsic 1/f frequency modulation (FM) noise in high-overtone thin-film sapphire resonators that operate at 2 GHz. The resonators exhibit several high-Q resonant modes approximately 100 kHz apart, which repeat every 13 MHz. A loaded Q of approximately 20000 was estimated from the phase response. The results show that the FM noise of the resonators varied between S_y (10 Hz)=-202 dB relative (rel) to 1/Hz and -210 dB rel to 1/Hz. The equivalent phase modulation (PM) noise of an oscillator using these resonators (assuming a noiseless amplifier) would range from L(10 Hz)=-39 to -47 dBc/Hz     

Controlled photon transfer between two individual nanoemitters via shared high-Q modes of a microsphere resonator

We realize controlled cavity-mediated photon transfer between two single nanoparticles over a distance of several tens of micrometers. First, we show how a single nanoscopic emitter attached to a near-field probe can be coupled to high-Q whispering-gallery modes of a silica microsphere at will. Then we demonstrate transfer of energy between this and a second nanoparticle deposited on the sphere surface. We estimate the photon transfer efficiency to be about 6 orders of magnitude higher than that via free-space propagation at comparable separations.     

Visual observation of frequency tuning in whispering gallery mode diode laser at room temperature

Technical Physics Letters - We report on the direct observation of an increase in the wavelength of output radiation during the pumping current pulse in a whispering gallery mode (WGM)...     

Characterization technique of optical whispering gallery mode resonators in the microwave frequency domain for optoelectronic oscillators

Optical Q factor measurements are performed on a whispering gallery mode (WGM) disk resonator using a microwave frequency domain approach instead of using an optical domain approach. An absence of hysteretic behavior and a better linearity are obtained when performing linewidth measurements by using a microwave modulation for scanning the resonances instead of the piezoelectric-based frequency tuning capability of the laser. The WGM resonator is then used to stabilize a microwave optoelectronic oscillator. The microwave output of this system generates a 12.48 GHz signal with -94 dBc/Hz phase noise at 10 kHz offset.     

Thermostable refractive index sensors based on whispering gallery modes in a microsphere coated with poly(methyl methacrylate)

This study proposes a thermostable refractive index (RI) sensor consisting of a silica microsphere coated with a poly(methyl methacrylate) (PMMA) layer. The first-order and second-order whispering gallery modes (WGMs) of both TE and TM polarizations are considered theoretically. The layer thickness is carefully optimized to eliminate the thermal drift and enhance the RI sensitivity and detection limit. In various WGMs, at the thermostable thickness of the PMMA layer, the first-order TM mode corresponds to the highest sensitivity and the smallest detection limit. The theoretical predictions provide guidelines for the design and fabrication of thermostable RI sensors.