Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network. A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given. The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed. An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities. Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.

Improved Loaded Quality Factor of Cavity Resonators with Cross lris Coupling

The performance of circular, rectangular and cross irises for the coupling of microwave power to rectangular waveguide cavity resonators is discussed. For the measurement of complex permittivity of materials using cavity perturbation techniques, rectangular cavities with high Q-factors are required. Compared to the conventional rectangular and circular irises, the cross Iris coupling structure provides very high loaded quality factor for all the resonant frequencies. The proposes cross iris coupling structure enhances the accuracy of complex permittivity measurements.

Analysis of mode quality factors and mode reflectivities for nanowire cavity by FDTD technique

The mode frequency and the quality factor of nanowire cavities are calculated from the intensity spectrum obtained by the finite-difference time-domain (FDTD) technique and the Pade approximation. In a free-standing nanowire cavity with dielectric constant epsilon = 6.0 and a length of 5 mu m, quality factors of 130, 159, and 151 are obtained for the HE11 modes with a wavelength around 375 nm, at cavity radius of 60, 75, and 90 nm, respectively. The corresponding quality factors reduce to 78, 94, and 86 for a nanowire cavity standing on a sapphire substrate with a refractive index of 1.8. The mode quality factors are also calculated for the TE01 and TM01 modes, and the mode reflectivities are calculated from the mode quality factors.

Broadband coaxial cavity resonator for complex permittivity measurements of liquids

A novel cavity perturbation technique using coaxial cavity resonators for the measurement of complex permittivity of liquids is presented. The method employs two types of resonators (Resonator I and Resonator II). Resonator I operates in the frequency range 600 MHz-7 GHz and resonator II operates in the frequency range 4 GHz-14 GHz. The introduction of the capillary tube filled with the sample liquid into the coaxial resonator causes shifts in the resonance frequency and loaded Q-factor of the resonator. The shifts in the resonance frequency and loaded Q-factor are used to determine the real and imaginary parts of the complex permittivity of the sample liquid, respectively. Using this technique, the dielectric parameters of water and nitrobenzene are measured. The results are compared with those obtained using other standard methods. The sources of errors are analyzed.

Multimode resonances in metallically confined square-resonator microlasers

Directional emission InP/AlGaInAs square-resonator microlasers with a side length of 20 mu m are fabricated by standard photolithography and inductively coupled-plasma etching technique. Multimode resonances with about seven distinct mode peaks in a free-spectral range are observed from 1460 to 1560 nm with the free-spectral range of 12.1 nm near the wavelength of 1510 nm, and the mode refractive index versus the photon energy E (eV) as 3.07152+0.18304E are obtained by fitting the laser spectra with an analytical mode wavelength formula derived by light ray method. In addition, mode field pattern is simulated for cold cavity by two dimensional finite-difference time-domain technique.

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

Dielectric properties of certain biological materials at microwave frequencies.

In the medical field, microwaves play a larger role for treatment than diagnosis. For the detection of diseases by microwave methods, it is essential to know the dielectric properties of biological materials. For the present study, a cavity perturbation technique was employed to determine the dielectric properties of these materials. Rectangular cavity resonators were used to measure the complex permittivity of human bile, bile stones, gastric juice and saliva. The measurements were carried out in the S and J bands. It is observed that normal and infected bile have different dielectric constant and loss tangent. Dielectric constant of infected bile and gastric juice varies from patient to patient. Detection and extraction of bile stone with possible method of treatment is also discussed.

Hybrid photonic crystal lasers

Energy efficient Wavelength Division Multiplexing (WDM) is the key to satisfying the future bandwidth requirements of datacentres. As the silicon photonics platform is regarded the only technology able to meet the required power and cost efficiency levels, the development of silicon photonics compatible narrow linewidth lasers is now crucial. We discuss the requirements for such laser systems and report the experimental demonstration of a compact uncooled external-cavity mW-class laser architecture with a tunable Si Photonic Crystal resonant reflector, suitable for direct Frequency Modulation.

Cavity-Enhanced Photoacoustic Detection Using Acoustic and Fiber-Optic Resonators

A wineglass has been used as an acoustic resonator to enhance the photoacoustic signal generated by laser excitation of absorbing dyes in solution. The amplitude of the acoustic signal was recorded using a fiber-optic transducer based on a Fabry-Pérot cavity attached to the rim of the wineglass. The optical and acoustic properties of the setup were characterized, and it was used to quantify the concentration of phosphomolybdenum blue and methyl red solutions. Detection limits of 1.2 ppm and 8 muM were obtained, respectively.

Loss Determination in Microsphere Resonators by Phase-Shift Cavity Ring-Down Measurements

The optical loss of whispering gallery modes of resonantly excited microresonator spheres is determined by optical lifetime measurements. The phase-shift cavity ring-down technique is used to extract ring-down times and optical loss from the difference in amplitude modulation phase between the light entering the microresonator and light scattered from the microresonator. In addition, the phase lag of the light exiting the waveguide, which was used to couple light into the resonator, was measured. The intensity and phase measurements were fully described by a model that assumed interference of the cavity modes with the light propagating in the waveguide.

Nonlinear optics and wavelength translation via cavity-optomechanics

The field of cavity-optomechanics explores the interaction of light with sound in an ever increasing array of devices. This interaction allows the mechanical system to be both sensed and controlled by the optical system, opening up a wide variety of experiments including the cooling of the mechanical resonator to its quantum mechanical ground state and the squeezing of the optical field upon interaction with the mechanical resonator, to name two.

In this work we explore two very different systems with different types of optomechanical coupling. The first system consists of two microdisk optical resonators stacked on top of each other and separated by a very small slot. The interaction of the disks causes their optical resonance frequencies to be extremely sensitive to the gap between the disks. By careful control of the gap between the disks, the optomechanical coupling can be made to be quadratic to first order which is uncommon in optomechanical systems. With this quadratic coupling the light field is now sensitive to the energy of the mechanical resonator and can directly control the potential energy trapping the mechanical motion. This ability to directly control the spring constant without modifying the energy of the mechanical system, unlike in linear optomechanical coupling, is explored.

Next, the bulk of this thesis deals with a high mechanical frequency optomechanical crystal which is used to coherently convert photons between different frequencies. This is accomplished via the engineered linear optomechanical coupling in these devices. Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed and, in terms of an equivalent photon number signal level, are found to correspond to an internal noise level of only 6 and 4 times 10x^-3 quanta, respectively.

We begin by developing the requisite theoretical background to describe the system. A significant amount of time is then spent describing the fabrication of these silicon nanobeams, with an emphasis on understanding the specifics and motivation. The experimental demonstration of wavelength conversion is then described and analyzed. It is determined that the method of getting photons into the cavity and collected from the cavity is a fundamental limiting factor in the overall efficiency. Finally, a new coupling scheme is designed, fabricated, and tested that provides a means of coupling greater than 90% of photons into and out of the cavity, addressing one of the largest obstacles with the initial wavelength conversion experiment.

Cavity Optomechanics at Millikelvin Temperatures

The field of cavity optomechanics, which concerns the coupling of a mechanical object's motion to the electromagnetic field of a high finesse cavity, allows for exquisitely sensitive measurements of mechanical motion, from large-scale gravitational wave detection to microscale accelerometers. Moreover, it provides a potential means to control and engineer the state of a macroscopic mechanical object at the quantum level, provided one can realize sufficiently strong interaction strengths relative to the ambient thermal noise. Recent experiments utilizing the optomechanical interaction to cool mechanical resonators to their motional quantum ground state allow for a variety of quantum engineering applications, including preparation of non-classical mechanical states and coherent optical to microwave conversion. Optomechanical crystals (OMCs), in which bandgaps for both optical and mechanical waves can be introduced through patterning of a material, provide one particularly attractive means for realizing strong interactions between high-frequency mechanical resonators and near-infrared light. Beyond the usual paradigm of cavity optomechanics involving isolated single mechanical elements, OMCs can also be fashioned into planar circuits for photons and phonons, and arrays of optomechanical elements can be interconnected via optical and acoustic waveguides. Such coupled OMC arrays have been proposed as a way to realize quantum optomechanical memories, nanomechanical circuits for continuous variable quantum information processing and phononic quantum networks, and as a platform for engineering and studying quantum many-body physics of optomechanical meta-materials.

However, while ground state occupancies (that is, average phonon occupancies less than one) have been achieved in OMC cavities utilizing laser cooling techniques, parasitic absorption and the concomitant degradation of the mechanical quality factor fundamentally limit this approach. On the other hand, the high mechanical frequency of these systems allows for the possibility of using a dilution refrigerator to simultaneously achieve low thermal occupancy and long mechanical coherence time by passively cooling the device to the millikelvin regime. This thesis describes efforts to realize the measurement of OMC cavities inside a dilution refrigerator, including the development of fridge-compatible optical coupling schemes and the characterization of the heating dynamics of the mechanical resonator at sub-kelvin temperatures.

We will begin by summarizing the theoretical framework used to describe cavity optomechanical systems, as well as a handful of the quantum applications envisioned for such devices. Then, we will present background on the design of the nanobeam OMC cavities used for this work, along with details of the design and characterization of tapered fiber couplers for optical coupling inside the fridge. Finally, we will present measurements of the devices at fridge base temperatures of T_f = 10 mK, using both heterodyne spectroscopy and time-resolved sideband photon counting, as well as detailed analysis of the prospects for future quantum applications based on the observed optically-induced heating.

Fiber-optic integration and efficient detection schemes for optomechanical resonators

With the advent of the laser in the year 1960, the field of optics experienced a renaissance from what was considered to be a dull, solved subject to an active area of development, with applications and discoveries which are yet to be exhausted 55 years later. Light is now nearly ubiquitous not only in cutting-edge research in physics, chemistry, and biology, but also in modern technology and infrastructure. One quality of light, that of the imparted radiation pressure force upon reflection from an object, has attracted intense interest from researchers seeking to precisely monitor and control the motional degrees of freedom of an object using light. These optomechanical interactions have inspired myriad proposals, ranging from quantum memories and transducers in quantum information networks to precision metrology of classical forces. Alongside advances in micro- and nano-fabrication, the burgeoning field of optomechanics has yielded a class of highly engineered systems designed to produce strong interactions between light and motion.

Optomechanical crystals are one such system in which the patterning of periodic holes in thin dielectric films traps both light and sound waves to a micro-scale volume. These devices feature strong radiation pressure coupling between high-quality optical cavity modes and internal nanomechanical resonances. Whether for applications in the quantum or classical domain, the utility of optomechanical crystals hinges on the degree to which light radiating from the device, having interacted with mechanical motion, can be collected and detected in an experimental apparatus consisting of conventional optical components such as lenses and optical fibers. While several efficient methods of optical coupling exist to meet this task, most are unsuitable for the cryogenic or vacuum integration required for many applications. The first portion of this dissertation will detail the development of robust and efficient methods of optically coupling optomechanical resonators to optical fibers, with an emphasis on fabrication processes and optical characterization.

I will then proceed to describe a few experiments enabled by the fiber couplers. The first studies the performance of an optomechanical resonator as a precise sensor for continuous position measurement. The sensitivity of the measurement, limited by the detection efficiency of intracavity photons, is compared to the standard quantum limit imposed by the quantum properties of the laser probe light. The added noise of the measurement is seen to fall within a factor of 3 of the standard quantum limit, representing an order of magnitude improvement over previous experiments utilizing optomechanical crystals, and matching the performance of similar measurements in the microwave domain.

The next experiment uses single photon counting to detect individual phonon emission and absorption events within the nanomechanical oscillator. The scattering of laser light from mechanical motion produces correlated photon-phonon pairs, and detection of the emitted photon corresponds to an effective phonon counting scheme. In the process of scattering, the coherence properties of the mechanical oscillation are mapped onto the reflected light. Intensity interferometry of the reflected light then allows measurement of the temporal coherence of the acoustic field. These correlations are measured for a range of experimental conditions, including the optomechanical amplification of the mechanics to a self-oscillation regime, and comparisons are drawn to a laser system for phonons. Finally, prospects for using phonon counting and intensity interferometry to produce non-classical mechanical states are detailed following recent proposals in literature.

Output beam quality of edge pumped planar waveguide lasers with confocal unstable resonators

Output beam quality of edge pumped planar waveguide lasers with confocal unstable resonators is investigated by diffraction methods, taking into account gain saturation, asymmetric pumping, and beam interaction. The influences of pumping uniformity, doping concentration, cavity length and effective Fresnel number are analyzed with respect to output beam quality and pumping efficiency. It is found that good beam quality and high efficiency can be obtained with asymmetric pumping and optimized negative branch confocal unstable resonators. (c) 2005 The Optical Society of Japan.