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We demonstrate a method for generation of beams of light with large angular momenta. The method utilizes whispering gallery mode resonators that transform a plane electromagnetic wave into high order Bessel beams. Interference pattern among the beams as well as shadow pictures induced by the beams are observed and studied.
A whispering gallery mode (WGM) resonator device and method capable of filtering sidebands of optical modulators are provided. The method includes providing an optical resonator adapted to support whispering gallery modes and forming a first field and a second field from a first location and a second location, respectively, at the circumference of the optical resonator and being separated by an arc angle, .alpha.. The method includes adjusting relative phase between the first field and the second field in accordance to a differential phase, .beta., and combining the first and the second fields into an output. Particular selection of the arc angle, .alpha., and the differential phase, .beta., can determine the function of the output.
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The optical properties associated with small particles, which include aerosols, hydrosols and solid microspheres have an impact on several areas of science and engineering. Since the advent of high-speed computers and lasers, the interaction of light with matter in the form of small particles with a discontinuous optical boundary relative to the surroundings has been much better understood. Various nonlinear optical effects have been observed involving interaction of a laser beam with both solid microspheres and liquid microdroplets. These include observation of second and third harmonic generation, four wave mixing, optical visibility, two photon absorption, observation of stimulated emission and lasing, and Stimulated Raman Scattering. Many of these effects are observed with laser intensities which are orders of magnitude less than that required by threshold condition for interactions in macroscopic bulk medium. The primary reason for this is twofold. The front surface of the microsphere acts as a thick lens to enhance the internal intensity of the input laser radiation, and the spherical shape of the droplet acts as an optical cavity to provide feedback at specific wavelengths corresponding to the whispering gallery modes or the morphology dependent resonances (MDR's). The most interesting and significant recent finding in this field is undoubtedly the existence of resonance peaks in linear and nonlinear optical spectra. Such resonance peaks are only dependent on the particle morphology, which means the size, shape and refractive index of the particle. Because of the simultaneous presence of these resonances, they have been referred to by many names, including structural resonances, whispering modes or whispering gallery modes, creeping waves, circumferential waves, surfaces modes, and virtual modes. All of these names refer to the same phenomena, i.e. morphology dependent resonances (MDR's) which has already been described and predicted precisely by electromagnetic theory and Loentz-Mie theory since 1908. MDR's can become important when the particle size (radius a) approaches and exceeds the wavelength of the electromagnetic wave (lambda) and the refractive index of the particle is greater than that of the surrounding medium. Such resonances are easiest to observe from a single particle with high symmetry, such as a sphere, spheroid, or cylinder. MDR's correspond to solutions of the characteristic equations of the electromagnetic fields in the presence of a sphere.
A diamond turning process has made possible a significant advance in the art of whispering-gallery-mode (WGM) optical resonators. By use of this process, it is possible to fashion crystalline materials into WGM resonators that have ultrahigh resonance quality factors (high Q values), are compact (ranging in size from millimeters down to tens of microns), and support single electromagnetic modes. This development combines and extends the developments reported in "Few- Mode Whispering-Gallery-Mode Resonators" (NPO-41256), NASA Tech Briefs, Vol. 30, No. 1 (January 2006), page 16a and "Fabrication of Submillimeter Axisymmetric Optical Components" (NPO-42056), NASA Tech Briefs, Vol. 31, No. 5 (May 2007), page 10a. To recapitulate from the first cited prior article: A WGM resonator of this special type consists of a rod, made of a suitable transparent material, from which protrudes a thin circumferential belt of the same material. The belt is integral with the rest of the rod and acts as a circumferential waveguide. If the depth and width of the belt are made appropriately small, then the belt acts as though it were the core of a single-mode optical fiber: the belt and the rod material adjacent to it support a single, circumferentially propagating mode or family of modes. To recapitulate from the second cited prior article: A major step in the fabrication of a WGM resonator of this special type is diamond turning or computer numerically controlled machining of a rod of a suitable transparent crystalline material on an ultrahigh-precision lathe. During the rotation of a spindle in which the rod is mounted, a diamond tool is used to cut the rod. A computer program is used to control stepping motors that move the diamond tool, thereby controlling the shape cut by the tool. Because the shape can be controlled via software, it is possible to choose a shape designed to optimize a resonator spectrum, including, if desired, to limit the resonator to supporting a single mode. After diamond turning, a resonator can be polished to increase its Q. By virtue of its largely automated, computer-controlled nature, the process is suitable for mass production of nominally identical single-mode WGM resonators. In a demonstration of the capabilities afforded by this development, a number of WGM resonators of various designs were fabricated side by side on the surface of a single CaF2 rod (see figure).
We propose a scheme of a resonant cw microwave-optical parametric oscillator based on high-Q whispering gallery modes excited in a nonlinear dielectric cavity. Such an oscillator has an extremely low threshold and stable operation, and may be used in spectroscopy and metrology.
We report the first demonstration of a UV laser using a high-Q whispering gallery mode (WGM) resonator of Ce+: LiCaAlF6. We show that WGM resonators from LiCaAlF6 can achieve a Q of 2.6 x 10(sup 7) at UV. We demonstrated a UV laser at 290 nm with a pulsed pump laser at 266 nm. The experiments showed the low pump threshold intensity of 7.5 x 10(sup 9) W/m(sup 2) and slope efficiency of 25%. We have also observed lasing delay dynamics. These results are consistent with our modeling and theoretical estimates, and pave the way for a low threshold cw UV laser using WGM resonator cavity.
Progress has been made toward solving some practical problems in the implementation of terahertz-to-optical frequency converters utilizing whispering-gallery-mode (WGM) resonators. Such frequency converters are expected to be essential parts of non-cryogenic terahertz- radiation receivers that are, variously, under development or contemplated for a variety of applications in airborne and spaceborne instrumentation for astronomical and military uses. In most respects, the basic principles of terahertz-to-optical frequency conversion in WGM resonators are the same as those of microwave (sub-terahertz)-to-optical frequency conversion in WGM resonators, various aspects of which were discussed in the three preceeding articles. To recapitulate: In a receiver following this approach, a preamplified incoming microwave signal (in the present case, a terahertz signal) is up-converted to an optical signal by a technique that exploits the nonlinearity of the electromagnetic response of a whispering-gallery-mode (WGM) resonator made of LiNbO3 or another suitable electro-optical material. Upconversion takes place by three-wave mixing in the resonator. To ensure the required interaction among the optical and terahertz signals, the WGM resonator must be designed and fabricated to function as an electro-optical modulator while simultaneously exhibiting (1) resonance at the required microwave and optical operating frequencies and (2) phase matching among the microwave and optical signals circulating in the resonator. Downstream of the WGM resonator, the up-converted signal is processed photonically by use of a tunable optical filter or local oscillator and is then detected. The practical problems addressed in the present development effort are the following: Satisfaction of the optical and terahertz resonance-frequency requirement is a straightforward matter, inasmuch as the optical and terahertz spectra can be measured. However, satisfaction of the phase-matching requirement is more difficult. The approach followed in the present development is to perform computer simulations of the microwave and optical signals circulating in the resonator to test for phase matching. To enable excitation of the terahertz WGM resonator mode, it is also necessary to ensure phase matching between that mode and the incoming terahertz radiation. In the present development, the incoming signal is coupled into the WGM resonator via a tapered waveguide in the form of a fused silica rod. The phase-matching requirement is satisfied at one point along the taper; the rod is positioned with this point in proximity to the WGM resonator. To maximize the conversion efficiency, it is necessary to maximize the spatial overlap among the terahertz and optical modes in the WGM resonator. In the absence of a special design effort to address this issue, there would be little such overlap because, as a consequence of a large difference between wavelengths, the optical and terahertz modes would be concentrated at different depths from the rim of a WGM resonator. In the present development, overlap is ensured by constructing the WGM resonator as a ring (see figure) so thin that the optical and terahertz modes are effectively forced to overlap.
Optical sidebands have been generated with relative frequency tens to hundreds of GHz by using optical sidebands that are generated in a cascade process in high-quality optical resonators with Kerr nonlinearity, such as whispering gallery mode (WGM) resonators. For this purpose, the WGM resonator needs to be optically pumped at two frequencies matching its resonances. These two optical components can be one or several free spectral ranges (FSRs), equal to approximately 12 GHz, in this example, apart from each other, and can be easily derived from a monochromatic pump with an ordinary EOM (electro-optic modulation) operating at half the FSR frequency. With sufficient nonlinearity, an optical cascade process will convert the two pump frequencies into a comb-like structure extending many FSRs around the carrier frequency. This has a demonstratively efficient frequency conversion of this type with only a few milliwatt optical pump power. The concept of using Kerr nonlinearity in a resonator for non-degenerate wave mixing has been discussed before, but it was a common belief that this was a weak process requiring very high peak powers to be observable. It was not thought possible for this approach to compete with electro-optical modulators in CW applications, especially those at lower optical powers. By using the high-Q WGM resonators, the effective Kerr nonlinearity can be made so high that, using even weak seeding bands available from a conventional EOM, one can effectively multiply the optical sidebands, extending them into an otherwise inaccessible frequency range.
Suitably configured whispering-gallery-mode (WGM) optical resonators have been proposed as delay lines for trains of short light pulses. Until now, it has been common practice to implement an optical delay line as a coiled long optical fiber, which is bulky and tends to be noisy. An alternative has been to implement an optical delay line as a coupled-resonator optical waveguide (a chain of coupled optical resonators), which is compact but limits the width of the pulse spectrum to the width of an optical resonance and thereby places a lower limit on the duration of a pulse. In contrast, a delay line according to the proposal could be implemented as a single WGM resonator, and the pulses delayed by the resonator could be so short that their spectral widths could greatly exceed the spectral width of any single resonance. The proposal emerged from theoretical and experimental studies of the propagation of a pulse train in a WGM resonator. An important element of the theoretical study was recognition that the traditional definition of group velocity in effect, the velocity of a single pulse comprising a packet of waves propagating in a medium, the responsivity of which is a monotonous function of frequency does not necessarily apply in the case of a WGM resonator or other medium having a spectrum consisting of discrete resonance peaks at different frequencies. A new definition of group velocity, applicable to a train of pulses propagating in such a medium, was introduced and found to lead to the discovery of previously unknown features of propagation. Notably, it was found that in a micro - sphere optical resonator that supports a suitable combination of WGM modes, the group velocity for a train of light pulses could be positive, zero, or negative. A positive group velocity could be so small that the delay could be much longer than the ring-down time of the resonator; a delay of such great length is impossible for a single pulse interacting with either a linearly responding lossless resonator or a coupled- resonator optical waveguide.
Microwave-to-optical frequency converters based on whispering-gallery-mode (WGM) resonators have been proposed as mixers for the input ends of microwave receivers in which, downstream of the input ends, signals would be processed photonically. A frequency converter as proposed (see figure) would exploit the nonlinearity of the electromagnetic response of a WGM resonator made of LiNbO3 or another suitable ferroelectric material. Up-conversion would take place by three-wave mixing in the resonator. The WGM resonator would be de - signed and fabricated to obtain (1) resonance at both the microwave and the optical operating frequencies and (2) phase matching among the input and output microwave and optical signals as described in the immediately preceding article. Because the resonator would be all dielectric there would be no metal electrodes signal losses would be very low and, consequently, the resonance quality factors (Q values) of the microwave and optical fields would be very large. The long lifetimes associated with the large Q values would enable attainment of high efficiency of nonlinear interaction with low saturation power. It is anticipated that efficiency would be especially well enhanced by the combination of optical and microwave resonances in operation at input signal frequencies between 90 and 300 GHz.
We predict the propagation of slow and fast light in two co-resonant coupled optical resonators. In coupled resonators, slow light can propagate without attenuation by a cancellation of absorption as a result of mode splitting and destructive interference, whereas transparent fast light propagation can be achieved by the assistance of gain and splitting of the intracavity resonances, which consequently change the dispersion from normal to anomalous. The effective steady-state response of coupled- resonators is derived using the temporal coupled-mode formalism, and the absorptive and dispersive responses are described. Specifically, the occurrence of slow light via coupled-resonator-induced transparency and gain-assisted fast light are discussed. Keywords: whispering gallery modes, optical resonators, slow light, fast light, superluminal pulse propagation, coupled optical resonators.
Optical oscillators that exploit resonantly enhanced four-wave mixing in nonlinear whispering-gallery-mode (WGM) resonators are under investigation for potential utility as low-power, ultra-miniature sources of stable, spectrally pure microwave signals. There are numerous potential uses for such oscillators in radar systems, communication systems, and scientific instrumentation. The resonator in an oscillator of this type is made of a crystalline material that exhibits cubic Kerr nonlinearity, which supports the four-photon parametric process also known as four-wave mixing. The oscillator can be characterized as all-optical in the sense that the entire process of generation of the microwave signal takes place within the WGM resonator. The resonantly enhanced four-wave mixing yields coherent, phase-modulated optical signals at frequencies governed by the resonator structure. The frequency of the phase-modulation signal, which is in the microwave range, equals the difference between the frequencies of the optical signals; hence, this frequency is also governed by the resonator structure. Hence, further, the microwave signal is stable and can be used as a reference signal. The figure schematically depicts the apparatus used in a proof-of-principle experiment. Linearly polarized pump light was generated by an yttrium aluminum garnet laser at a wavelength of 1.32 microns. By use of a 90:10 fiber-optic splitter and optical fibers, some of the laser light was sent into a delay line and some was transmitted to one face of glass coupling prism, that, in turn, coupled the laser light into a crystalline CaF2 WGM disk resonator that had a resonance quality factor (Q) of 6x10(exp 9). The output light of the resonator was collected via another face of the coupling prism and a single-mode optical fiber, which transmitted the light to a 50:50 fiber-optic splitter. One output of this splitter was sent to a slow photodiode to obtain a DC signal for locking the laser to a particular resonator mode. The other output of this splitter was combined with the delayed laser signal in another 50:50 fiber-optic splitter used as a combiner. The output.of the combiner was fed to a fast photodiode that demodulated light and generated microwave signal. In this optical configuration, the resonator was incorporated into one arm of a Mach-Zehnder interferometer, which was necessary for the following reasons: It was found that when the output of the resonator was sent directly to a fast photodiode, the output of the photodiode did not include a measurable microwave signal. However, when the resonator was placed in an arm of the interferometer and the delay in the other arm was set at the correct value, the microwave signal appeared. Such behavior is distinctly characteristic of phase-modulated light. The phase-modulation signal had a frequency of about 8 GHz, corresponding to the free spectral range of the resonator. The spectral width of this microwave signal was less than 200 Hz. The threshold pump power for generating the microwave signal was about 1 mW. It would be possible to reduce the threshold power by several orders of magnitude if resonators could be made from crystalline materials in dimensions comparable to those of micro-resonators heretofore made from fused silica.
We theoretically study a parallel configuration of two interacting whispering gallery mode optical resonators and show a narrow-band modal structure as a basis for a widely tunable delay line. For the optimum coupling configuration the system can possess an unusually narrow spectral feature with a much narrower bandwidth than the loaded bandwidth of each individual resonator.
Bimaterial thermal compensators have been proposed as inexpensive means of preventing (to first order) or reducing temperature-related changes in the resonance frequencies of whispering-gallery-mode (WGM) optical resonators. A bimaterial compensator would apply, to a WGM resonator, a pressure that would slightly change the shape of the resonator and thereby change its resonance frequencies. Through suitable choice of the compensator dimensions and materials, it should be possible to make the temperature dependence of the pressure-induced frequency shift equal in magnitude and opposite in sign to the temperature dependence of the frequency shift of the uncompensated resonator so that, to first order, a change in temperature would cause zero net change in frequency.
Phase matching of diverse electromagnetic modes (specifically, coexisting optical and microwave modes) in a whispering-gallery-mode (WGM) resonator has been predicted theoretically and verified experimentally. Such phase matching is necessary for storage of microwave/terahertz and optical electromagnetic energy in the same resonator, as needed for exploitation of nonlinear optical phenomena. WGM resonators are used in research on nonlinear optical phenomena at low optical intensities and as a basis for design and fabrication of novel optical devices. Examples of nonlinear optical phenomena recently demonstrated in WGM resonators include low-threshold Raman lasing, optomechanical oscillations, frequency doubling, and hyperparametric oscillations. The present findings regarding phase matching were made in research on low-threshold, strongly nondegenerate parametric oscillations in lithium niobate WGM resonators. The principle of operation of such an oscillator is rooted in two previously observed phenomena: (1) stimulated Raman scattering by polaritons in lithium niobate and (2) phase matching of nonlinear optical processes via geometrical confinement of light. The oscillator is partly similar to terahertz oscillators based on lithium niobate crystals, the key difference being that a novel geometrical configuration of this oscillator supports oscillation in the regime. The high resonance quality factors (Q values) typical of WGM resonators make it possible to achieve oscillation at a threshold signal level much lower than that in a non-WGM-resonator lithium niobate crystal.
This paper discusses the demonstrated accuracy and utility of a 2-D finite element methodology for whispering gallery mode sapphire resonators.
A technological revolution is occurring in the field of fiber lasers. Over the past two years, the level of power has increased from approx. 100 watts to nearly 1 kilowatt. We are developing a novel fiber laser system, which is a satellite-based LIDAR transmitter of multi-lines. The system is made of a hollow fiber filled with micro-spheres doped with lasing materials. Each sphere has its inherent optical cavity, which makes the system a cavity free and in the same time, emits multi-laser lines for simultaneous multi-task operations. The system is also rugged, compact, lightweight, and durable. Our earlier studies on micro-spheres doped with different laser dyes demonstrated the emission of extremely fine laser lines of less than 3 A line-width, which are of interest for spectroscopic applications, sensing, imaging, and optical communications. Individual dye-doped micro-spheres demonstrated a lasing resonance peaks phenomenon in their fluorescence spectra of linear and nonlinear features that do not exist in the bulk dye solutions. Each individual micro-sphere acts as a laser system with inherent cavity, where the fluorescence line suffers multiple internal reflections within the micro-sphere and gains enough energy to become a laser line. Such resonance peaks are dependent on the sphere's morphology, size, shape, and its refractive index. These resonance peaks are named structural resonance, whispering modes or whispering gallery modes, creeping waves, circumferential waves, surfaces modes, and virtual modes. All of these names refer to the same phenomenon of morphology dependent resonance (MDR), which has already been described and predicted precisely by electromagnetic theory and Lorentz-Mie theory since 1908. The resonance peaks become more obvious when the particle size approaches and exceeds the wavelength of the laser used and the relative index of the particle is greater than that of the surrounding medium. Additional information is included in the original extended abstract.