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.     

Effect of a ring layer filled with various substances on the eigenfrequency and Q-factor of a cylindrical quasi-optical dielectric resonator

The influence of a ring layer filled with various substances on the eigenfrequency and Q-factor of a cylindrical quasi-optical dielectric (Teflon) resonator has been investigated. The spectral and energy characteristics of an axially homogeneous whispering gallery eigenmode of this resonator are analyzed for the first time as dependent on the radius and thickness of the ring layer. It is established that the eigenfrequency behaves differently when the ring layer is filled with liquids characterized by large and small losses.     

Three-photon absorption induced whispering gallery mode lasing in ZnO twin-rods microstructure

The ZnO twin-rods microstructure synthesized by hydrothermal method was employed as a whispering gallery mode lasing microcavity. The growth mechanism of the ZnO twin-rods single crystal was analyzed. Three-photon absorption induced whispering gallery mode lasing with low threshold was observed under the excitation of femtosecond pulses at 800 nm. The spectra from the individual branch and the connection part were investigated, and the whispering gallery mode lasing mechanism was discussed.     

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.     

Three-Nucleon Forces and Triplet Pairing in Neutron Matter

We report an experimental study of the electrical properties of liquid helium-4 in the temperature range 1.2–3 K. The experiment is carried out in the millimeter wave range using a whispering gallery mode dielectric resonator, and the complex permittivity of liquid helium is extracted from the data using the resonant perturbation method. The results for the temperature dependence of the dielectric constant are consistent with the previous studies. In addition, we find strong enhancement of the loss tangent around the superfluid transition temperature.     

High-Q whispering gallery traveling wave resonators for oscillator frequency stabilization

Usually a frequency-stabilized standing wave resonator-oscillator incorporating a resonator as a frequency discriminator requires a circulator to separate the injected and reflected wave, A ferrite circulator is a noisy device and can limit the phase noise or frequency stability. Moreover, we show that the noise in a circulator varies, and detailed low noise measurements are necessary to choose an appropriate quiet circulator. Thus, by realizing a configuration that does not require a circulator, an improvement in performance and reliability can be obtained. A solution to this problem is to design a high-Q whispering gallery traveling wave (WGTW) resonator. This device naturally separates the injected and reflected wave in the same way as a ring cavity at optical frequencies, without degrading the frequency discrimination. Q-factor measurements of a WGTW sapphire resonator are presented, along with a derivation of critical parameters to maximize the frequency discrimination. New measurements of noise in ferrite circulators and isolators have also been made, which is followed with a discussion on oscillator design.     

High Q-factor distributed bragg reflector resonators with reflectors of arbitrary thickness

The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses. This is achieved by designing a low-loss inner resonant region (usually free space) surrounded by an outer anti-resonant region made of distributed Bragg reflector layers. In this paper we develop a simple non-Maxwellian model and apply it to design three distinct cylindrical Bragg resonators based on the same set of single-crystal sapphire plates and rings by changing only the dimension of the cavity that supports the structure. To accomplish this, the simple model allows an arbitrary thickness for either the horizontal or the cylindrical dielectric reflectors by relaxing the condition that they must be lambda/4 thick. The model also allows for higher-order field variations in both the resonant and the anti-resonant regions. The resonators were constructed and experimental results were compared with the simple model and the rigorous method of lines analysis. For the fundamental mode, an unloaded Q-factor of 234,000 at 9.7 GHz was obtained. This is larger than that for a whispering gallery mode resonator. The resonator also exhibited a greatly reduced spurious mode density when compared to an overmoded whispering gallery mode resonator.     

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.     

Effect of a small cylindrical inhomogeneity on the eigenfrequency of a semicylindrical dielectric resonator featuring an axially homogeneous eigenmode

A semicylindrical dielectric resonator with a thin cylindrical inhomogeneity in the region of the field antinode of a whispering gallery eigenmode has been studied. Characteristic equations determining the complex eigenfrequencies of such resonators with axially homogeneous eigenmodes are obtained. It is shown that the presence of a dielectric or conducting inhomogeneity leads to a frequency shift and causes additional energy losses of the eigenmode.     

High-Q whispering modes in empty spherical cavity resonators

This work presents the study of high-order modes in spherical cavity resonators. In general there are resonant mode families, degenerate in frequency, that "whisper" around the spherical surface. We call these whispering spherical (WS) mode sets. Each set includes the well-known whispering gallery (WG) mode, which propagates like a ray around the azimuth. Also, we identify a new mode, which we label the whispering longitudinal (WL) mode. This mode propagates as a wave front along the longitudinal direction. The rest of the degenerate set propagates like a combination of the WG and WL modes. We show that transverse electric WS modes have high geometric factors, greater than 2000, which increase linearly with frequency. This is an order of magnitude greater than that of a TM/sub 010/ cylindrical resonator. Also, Q-factors as high as 65,000 at 13.3 GHz were measured at room temperature.     

The influence of finite end screens on the spectrum of oscillations in cylindrical quasioptical dielectric resonators

We have studied the influence of finite dimensions of the end screens on the spectrum of whispering gallery modes in a teflon cylindrical quasioptical resonator. The dependence of the resonance oscillation frequency on the radius of conducting end screens is determined for the first time. Variation of the screen radius leads to transformation of the axial index of HE modes.     

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.     

Excitation of ray oscillations in quasioptical dielectric cavities with whispering gallery modes

It is observed that ray oscillations may be excited together with whispering gallery modes in quasioptical dielectric cavities. It is shown that as the excitation conditions change, the fields of these oscillations gradually “split off” from the fields of the whispering gallery modes whose characteristics deteriorate. The angular spectrum of ray oscillations in dielectric cavities is determined. Pis’ma Zh. Tekh. Fiz. 23, 25–29 (August 12, 1997)     

Analysis of the rutile-ring method of frequency-temperature compensating a high-Q whispering gallery sapphire resonator

The rutile-ring method of dielectrically frequency-temperature compensating a high-Q whispering gallery (WG) sapphire resonator is presented. Two and three-dimensional finite element (FE) analysis has been implemented to design and analyze the performance of such resonators, with excellent agreement between theory and experiment. A high-Q factor of 30 million at 13 GHz, and compensation temperature of 56 K was obtained. It is shown the frequency-temperature compensation can occur either because the rutile adds a small perturbation to the sapphire resonator or because of a mode interaction with a resonant mode in the rutile. The characteristics of both of these methods are described, and it is shown that for high frequency stability, it is best to compensate perturbatively     

Detecting single viruses and nanoparticles using whispering gallery microlasers

There is a strong demand for portable systems that can detect and characterize individual pathogens and other nanoscale objects without the use of labels, for applications in human health, homeland security, environmental monitoring and diagnostics. However, most nanoscale objects of interest have low polarizabilities due to their small size and low refractive index contrast with the surrounding medium. This leads to weak light-matter interactions, and thus makes the label-free detection of single nanoparticles very difficult. Micro- and nano-photonic devices have emerged as highly sensitive platforms for such applications, because the combination of high quality factor Q and small mode volume V leads to significantly enhanced light-matter interactions. For example, whispering gallery mode microresonators have been used to detect and characterize single influenza virions and polystyrene nanoparticles with a radius of 30 nm (ref. 12) by measuring in the transmission spectrum either the resonance shift or mode splitting induced by the nanoscale objects. Increasing Q leads to a narrower resonance linewidth, which makes it possible to resolve smaller changes in the transmission spectrum, and thus leads to improved performance. Here, we report a whispering gallery mode microlaser-based real-time and label-free detection method that can detect individual 15-nm-radius polystyrene nanoparticles, 10-nm gold nanoparticles and influenza A virions in air, and 30 nm polystyrene nanoparticles in water. Our approach relies on measuring changes in the beat note that is produced when an ultra-narrow emission line from a whispering gallery mode microlaser is split into two modes by a nanoscale object, and these two modes then interfere. The ultimate detection limit is set by the laser linewidth, which can be made much narrower than the resonance linewidth of any passive resonator. This means that microlaser sensors have the potential to detect objects that are too small to be detected by passive resonator sensors.     

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.     

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.     

Plasmonic whispering gallery cavities as optical nanoantennas

We study the resonant modes of surface plasmon whispering gallery cavities based on a circular groove in a Au surface. We use spatially, angle-, and polarization-resolved cathodoluminescence spectroscopy to measure the resonant plasmonic local field distribution at deep-subwavelength resolution and determine the far-field radiation distribution for each plasmonic mode. We show mode-selective excitation of the plasmonic modes and resolve the modal angular radiation pattern. The results show that plasmonic whispering gallery resonators can be used as versatile antennas both in receiving and transmitting mode.     

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.