Comparison of Talbot and 1-to- N-way phase-locked array resonators

Phased-array resonators provide an important basis for achieving high output powers from arrays of low-power elements. We have recently proposed a novel form of 1-to-N-way phased-array resonator based on the beam splitting and regeneration characteristics of rectangular sectioned multimode waveguides. We compare its performance with that of the widely used, yet problematic, Talbot resonator. Our design is found to have significant advantages over the Talbot resonator in terms of improved modal stability, unique photon-mixing characteristics, and near- and far-field outputs of quasi-Gaussian form.     

Theory of 1-N-way phase-locked resonators with perturbations in the array elements.

The recently proposed 1-N-way resonator based on beam splitting and beam combining effects in rectangular cross-sectional multimode waveguides offers a valuable way in which N low-power laser elements can be combined in a coherent fashion. We develop a theory of such resonators in the presence of perturbations in the N-element array. We demonstrate that despite the presence of perturbations there is only one possible mode of the resonator. The theory is used to provide an understanding of the effects of a number of possible perturbations that could arise as a result of manufacturing processes and operational effects. The results give scaling laws for the design tolerances on array element mirror tilt, array element optical path length control, and the effects of array element malfunction and their need for gain balance.     

Planar two-dimensional Bragg resonators with corrugated surfaces: Theory and experiment

The electrodynamic properties of a planar two-dimensional Bragg resonator with two-dimensional distributed feedback were studied. A high selectivity of the resonator with respect to the longitudinal and the transverse mode indices is demonstrated, the mode spectrum being significantly dependent on the surface relief pattern of the resonator plates. The theoretical results are confirmed by measurements under “cold” conditions.     

Theory and design of piezoelectric resonators immune to acceleration: present state of the art

A typical low noise oscillator uses a crystal resonator as the frequency-determining element. An understanding of the fundamental nature of acceleration sensitivity in crystal oscillators resides primarily in understanding the behavior of the crystal resonator. The driving factor behind the acceleration-induced frequency shift is shown to be deformation of the resonator. The deformation drives two effects: an essentially linear change in the frequency-determining dimensions of the resonator and an essentially nonlinear effect of changing the velocity of the propagating wave. In this paper, the fundamental nature of acceleration sensitivity is reviewed and clarified, and attendant design guidance is developed for piezoelectric resonators. The basic properties of acceleration sensitivity and general design guidance are developed through the simple examples of “bulk acoustic wave (BAW) in a box” and “surface transverse wave (STW) in a box.” These examples serve to clarify a number of concepts, including the role of mode shape and the basic difference between the BAW and STW cases. The design equations clarify the functional dependencies of the acceleration sensitivities on the full range of crystal resonator design and fabrication parameters     

Power-scalable system of phase-locked single-mode diode lasers

The direct use of diode lasers for high-power applications in material processing is limited to applications with relatively low beam quality and power density requirements. To achieve high beam quality one must use single-mode diode lasers, however with the drawback of relatively low optical output powers from these components. To realize a high-power system while conserving the high beam quality of the individual emitters requires coherent coupling of the emitters. Such a power-scalable system consisting of 19 slave lasers that are injection locked by one master laser has been built and investigated, with low-power diode lasers used for system demonstration. The optical power of the 19 injection-locked lasers is coupled into polarization-maintaining single-mode fibers and geometrically superimposed by a lens array and a focusing lens. The phase of each emitter is controlled by a simple electronic phase-control loop. The coherence of each slave laser is stabilized by computer control of the laser current and guarantees a stable degree of coherence of the whole system of 0.7. An enhancement factor of 13.2 in peak power density compared with that which was achievable with the incoherent superposition of the diode lasers was observed.     

Design of a phase-locked multimode SAW oscillator

A 60-100 MHz multimode SAW (surface acoustic wave) oscillator with comb spacing Deltaf=10 MHz used a low-loss SPUDT (single-phase unidirectional transducer) comb filter in conjunction with two varactor-based control elements and two feedback loops, for mode selection and stability enhancement over long dwell times. The end aim is to reduce close-in phase noise over that of the unlocked oscillator, corresponding to improved intermediate-term time-domain stability. Frequency deviation was less than 20 Hz over two hours in each of the five comb modes.     

Computer-aided measurement of Q-factor with application toquasi-optical open resonators

A technique for automated measurement of Q based on the observation of resonator response at a set of points near resonance is presented. The resonance curve, suitably corrected for noise and the presence of unwanted modes, is transformed into a linear graph. On the basis of this transformation, an analysis of error in the measurement of Q is carried out. An example of measurement on an open resonator at 97 GHz, with an accuracy of about 1% in the evaluation of Q is included     

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     

Microphonic sensitivity of surface-acoustic-wave resonators

The shift in resonant frequency due to acceleration has been measured for surface-acoustic-wave resonators (SAWRs). SAWR devices were subjected to vibration from 5 Hz to 10 kHz with peak accelerations ranging from 10(-2) to 10(3) g. The vibration was applied both normal to and in the plane of propagating surface wave yielding microphonic sensitivities on the order of 1 ppb/g. To confirm the results of the direct measurement method, an oscillator loop was closed around the vibrated SAWR and the magnitudes of the FM sidebands were measured to indicate the resulting frequency shift. Several bulk crystal resonators were also measured and it was found that the microphonic sensitivities were generally comparable in magnitude to those of the SAWRs but spanned much wider ranges.     

Modeling of waveguide-coupled SAW resonators

Coupling of modes in space (COMS) is applied to the analysis of waveguide coupled surface acoustic wave (SAW) resonators. Standard one-dimensional COMS equations are extended to model distributed coupling between adjacent SAW reflector arrays. Computed frequency responses are presented for two-pole and four-pole waveguide coupled resonators     

Microwave characteristics of Sm(Co1/2Ti1/2)O3 dielectric resonators

The microwave dielectric properties of Sm(Co_1/2Ti_1/2)O₃ ceramics have been investigated. Sm(Co_1/2Ti_1/2)O₃ ceramics were prepared by conventional solid-state route. The dielectric constant values (ε_r) saturated at 23.5–25.5. The Q×f values of 21,500–76,000 (at 10 GHz) can be obtained when the sintering temperatures are in the range of 1300–1420 °C. The temperature coefficient of resonant frequency τ_f was a function of sintering temperature. The ε_r value of 25.5, Q×f value of 76,000 (at 10 GHz) and τ_f value of −16.3 ppm/°C were obtained for Sm(Co_1/2Ti_1/2)O₃ ceramics sintered at 1360 °C for 4 h. For applications of high selective microwave ceramic resonator, filter and antenna, Sm(Co_1/2Ti_1/2)O₃ is proposed as a suitable material candidate.     

Acceleration sensitivity of surface wave resonators

In light of the substantial performance advantages of STW over SAW in various areas, theoretical and experimental studies of the acceleration sensitivities of STW and SAW resonators have been undertaken. The purpose of the studios has been to understand the fundamental nature of STW and SAW acceleration sensitivities, and to determine whether the performance advantages of STW seen in other areas extend to the case of acceleration sensitivity. The basic approach utilizes the perturbation theory developed by Tiersten to calculate the acceleration sensitivities of both STW and SAW resonators. The acceleration-induced bias is conveniently written in terms of acceleration-induced deformation gradients and factored elastic stiffness expressions. This representation clarifies important concepts regarding the frequency shift and the involved elastic constants, and provides the designer with insight into the basic nature of the problem. The dependencies of the normal acceleration sensitivities on substrate and mode shape parameters and the fundamental nature of plate flexure are discussed at length. The calculations compare favorably to recent experimental results     

Linear frequency tuning of SAW resonators

Frequency tuning in SAW (surface acoustic wave) resonator-stabilized oscillators is normally accomplished via utilization of a voltage-controlled phase shifter. The design of abrupt junction varactor diode-inductor networks which employ impedance transformation techniques to obtain linear frequency tuning of two-port SAW resonators is reported. The approach is similar to that previously developed for linear tuning of bulk wave, quartz crystal resonators. This technique uses varactor diode parallel inductance to provide a linear reactance versus voltage network, which is effectively connected in series with the resonator motional impedance in order to tune the effective resonator center frequency. Typical tuning ranges are significantly larger than those achievable using the phase shifter approach, and are on the order of 400 ppm for the 320-MHz resonator used.     

Scattering analysis of two-port SAW resonators

Linear equations derived from the scattering matrix approach to the two-port resonator were solved, and analytical expressions for the normalized SAW amplitudes were obtained. Asynchronous and synchronous resonators were analyzed numerically. It was shown that the output of the two-port resonator is a sum of two signals. In the case of the asynchronous resonator, these signals are in phase at a resonance frequency; for the synchronous resonator, they are in phase quadrature, which causes the higher insertion loss of the synchronous resonator