Beat Regime Research Articles

Gyroscopically coupled in-plane and transverse vibrations of an annular free-clamped microplate

In this work, we construct and study a model of coupled plane-transverse oscillations of a circular thin plate with a concentric hole under the action of Coriolis and centrifugal inertia forces caused by the rotation of the system along an axis located in the plane of the plate. Equations of vibrations in partial derivatives are obtained using the variational principle of Hamilton - Ostrogradsky. Assuming the smallness of the angular velocity of rotation with respect to the frequency of the working skew-symmetric flexural form of the plate oscillations, an approximate analytical solution is found for both the radial and circumferential, and transverse components of the displacement field in the free oscillation mode. Using the Galerkin projection method, the problem was reduced to a system of two second-order linear differential equations for modal coordinates of mutually orthogonal basic skew-symmetric modes of the plate vibrations. It is found that the regime of initially excited harmonic oscillations in the presence of rotation is transformed into the regime of amplitude-modulated beats. Analytical expressions are found both for the frequency of the slow beat envelope and for the relative depth of their amplitude modulation. The fundamental possibility of determining the modulus of the projection of the angular velocity vector onto the plane of the plate from the measured value of the envelope frequency is shown. The problem of choosing the optimal geometric shape of the resonator from the point of view of maximizing the sensitivity of the system to changes in the value of the angular velocity of rotation is studied. The question of determining the direction of the projection of the angular velocity vector onto the plane of the plate from the measured depth of the amplitude modulation of the beat regime is considered.

Lock-in range in a semiconductor ring laser gyroscope.

A locking range in a semiconductor ring laser (SRL) is theoretically analyzed. The simplified model accounting for the specific features of a SRL uses the carrier diffusion and the linewidth enhancement factor. For stabilization of the steady-state bidirectional lasing, we introduce in this model an active feedback loop that creates the intracavity losses proportional to the intensity difference between the counterpropagating waves. Frequency locking of the counterpropagating waves in the region of stability of steady-state bidirectional lasing is considered. Specific features inherent in the locking range in a SRL are discussed. When backscattering coupling is strong, the frequency locking of the counterpropagating waves does not switch to a beat regime at any rotation rate. In the case of weak backscattering coupling, analytical expressions for the locking range are derived. It is shown that an active feedback loop has a strong impact on a locking range. In a He-Ne laser, the locking range is determined by dissipative backscattering, and there is no locking with conservative scattering. Unlike a He-Ne laser, conservative backscattering in a SRL has a strong impact on the locking range.

Interaction of counterpropagating waves in a Nd :YVO4 ring laser

We have experimentally studied the stationary regime of bidirectional lasing and self-modulation regimes in a Nd :YVO4 solid-state ring laser (SSRL) in the presence of phase nonreciprocity of the ring cavity. It is found that the emission spectrum in the regime of frequency matching of counterpropagating waves is much narrower than in a Nd :YAG SSRL. When the phase nonreciprocity increases in the matching regime, one of the counterpropagating waves is suppressed, and this regime does not switch to the beat regime.

Biasing the beat regime of a solid-state ring laser: from a magnetometer to a multioscillator rotation sensor

In this paper, we discuss the possible applications of a solid-state ring laser comprising a feedback loop for stabilizing the bidirectional regime and a magneto-optic element for frequency-shifting the counterpropagating modes. In a first simple two-mode configuration, this device is shown to be sensitive to small changes in the rotation rate and external magnetic field. In a second more sophisticated version, the magnetic sensitivity can be significantly reduced thanks to multioscillator operation. The results of our proof-of-principle four-mode experiment are discussed, and some improvements are suggested toward a high-performance solid-state ring laser gyroscope without lock-in.

Nuclearγresonance time-domain interferometry: Quantum beat and radiative coupling regimes compared in revealing quasielastic scattering

Nuclear $\ensuremath{\gamma}$ resonance time-domain interferometry (TDI) is a method where the interference pattern is built in time during the delayed scattering of synchrotron radiation by a system composed of two nuclear resonant targets and a nonresonant sample placed in between. The radiation transmitted through the upstream target is scattered by the sample at a finite angle and is transmitted through the downstream target. Atomic motions in the sample perturbing the delayed radiation can be revealed directly in the time interference pattern. The unique sharpness of nuclear resonant scattering allows one to investigate atomic motions proceeding for times in the range of nanoseconds to microseconds. The radiative coupling (RC) regime of TDI where the radiation from the upstream nuclear target is in resonance with the downstream target was investigated experimentally and compared with the quantum beat (QB) regime where the resonances in the targets are well separated. Clear evolutions of the interference patterns were observed with glycerol as a sample in both regimes, manifesting the increase of quasielastic scattering both with increasing temperature and with momentum transfer. However, the increase of quasielastic scattering is revealed in quite different ways: in the QB regime through pronounced changes of the quantum beat modulation of a fixed interference pattern, in the RC regime via strong changes of the interference pattern itself, mainly of its dynamical beat structure. It was possible to find relaxation parameters by which the two sets of completely different time evolutions for the QB and RC regimes were consistently fitted. Such a treatment will in the future considerably enlarge the dynamic range of the method and increase the reliability of the data analysis.

Ultrafast time-resolved quantum beats in the polarization state of coherent emission from quantum wells

Dual-channel spectral interferometry is used to measure the ellipticity, the orientation of the polarization ellipse, and the sense of rotation of the four-wave-mixing signal from a GaAs-AlGaAs multiple quantum well. Each parameter is observed to oscillate dramatically at the heavy-hole-light-hole quantum beat frequency. During each beat period (in the strong quantum beat regime), the ellipticity oscillates twice between linear and almost-circular polarization, the orientation of the polarization ellipse rotates through a complete 180 degrees , and the sense of rotation changes from left- to right-circular polarization.

Frequency characteristics of a mode-locked solid-state ring laser with self-pumping waves

An efficient method for suppressing the competition between counterpropagating waves and stabilizing the beats was developed for a rotating solid-state ring laser with a homogeneously broadened gain profile of the active medium. Use was made of self-pumping waves created under the conditions of steady-state mode locking using a diffraction acoustooptic feedback loop. Experimental and theoretical investigations were made of the influence of such self-pumping waves, of the laser parameters, and of the nonreciprocal acoustooptic effects on the amplitude-frequency characteristics of a YAG:Nd3+ ring laser. Considerable distortions of the frequency characteristics of this laser observed under transient mode locking conditions were due to the appearance of frequency modulation of ultrashort pulses. Weakening of the coupling between the counterpropagating waves, optimization of the parameters of the acoustooptic feedback loop, and detuning of the modulation frequency from the intermode value established a stable beat regime characterized by slight distortions of the frequency characteristics even near the interval of locking of the counterpropagating wave frequencies.

Stabilization of the beat regime and alternating-sign optical nonreciprocity in the case of time-dependent self-diffraction of self-pumping waves in the active medium of a ring solid state laser

A new method is proposed for controlling the amplitude-frequency characteristics of a rotating ring solid-state laser with a homogeneously broadened gain profile of the active medium operating under mode-locked conditions. This method involves the use of ultrashort self-pumping pulses generated by a time-dependent diffraction acoustooptic feedback loop and characterized by a Doppler-modulated optical frequency. It was found experimentally that time-dependent self-diffraction of the main and self-pumping ultrashort pulses by interference population-inversion gratings induced in the active medium gives rise to a new nonreciprocal optical effect (self-induced alternating-sign difference between the frequencies of the counterpropagating waves) and stabilizes the beat regime in such a ring laser.

Solid-state ring laser with self-pumping waves operating under active mode-locking conditions

Theoretical and experimental investigations were made of the amplitude and frequency characteristics of a rotating solid-state (YAG:Nd3+) ring laser with self-pumping waves. The self-pumping wave method produced effectively the competition between opposite waves and made it possible to achieve a stable beat regime in this laser. The use of self-pumping waves in a solid-state laser under active mode-locking conditions was found to have a number of advantages over free running. Various methods for generation of self-pumping waves under active mode-locking conditions were proposed and tested experimentally: this demonstrated ways of improving considerably the amplitude and frequency characteristics of the rotating solid-state laser.

Use of self-pumping waves for weakening the competition between opposite waves in a ring laser

A new method is suggested for weakening the competition between opposite waves by reflection of self-pumping waves from additional population inversion gratings induced by them in the active medium. A theoretical study is made of the characteristics of a solid-state ring laser when self-pumping waves are used in the beat regime.

Use of a feedback loop for the stabilization of a beat regime in a solid-state ring laser

Theoretical and experimental investigations were made of the influence of a magnetooptic feedback loop creating a difference between the losses for opposite waves, proportional to the difference between their intensities, on the amplitude and frequency characteristics of a rotating solidstate ring laser with a homogeneously broadened luminescence line of the active substance. Analytic solutions were obtained for the description of possible lasing regimes and a study was made of their stability for arbitrary values of the difference between the frequencies of the opposite waves. It was found that a feedback loop with a large transfer coefficient was capable of ensuring stable and simultaneous lasing under several regimes. It was established experimentally that optimization of the parameters of the loop in a rotating YAG:Nd3+ ring laser resulted in stabilization of the beat regime and expanded significantly the range of existence of this regime. The inertia of the feedback loop observed on increase of its transfer coefficient resulted in an instability of bidirectional lasing, giving rise to antiphase oscillations of the intensities of the opposite waves. A study was made of the transient processes which occurred as a result of abrupt changes in the signal in the feedback loop. The results of theoretical investigations were in good agreement with the experiments.

Magnetooptic effects in a YAG:Nd3+ring laser with a nonplanar resonator

An experimental investigation was made of the influence of the Faraday and Zeeman effects on the operation of a YAG:Nd3+ ring laser with a nonplanar resonator. The opposite waves were decoupled by a polarization-frequency method and an unusual lasing regime was observed: in this regime one of the waves had the circular polarization and the opposite one was linearly polarized. The magnetooptic effects could be used to establish different transverse structures of the opposite-wave fields. Magnetooptic modulation was used to switch the direction of emission from the laser avoiding transient processes at a relaxation frequency. A magnetooptic feedback based on the difference between the intensities of the opposite waves resulted in a considerable reduction in the concurrent attenuation and established a beat regime in a wide range of the frequency splitting between the opposite waves. Variation of the feedback parameters of the laser resulted in a strong hysteresis and produced bistable states.

Influence of a difference between the resonatorQfactors on the interaction of opposite waves in solid-state ring lasers

A theoretical analysis is made of the characteristics of a solid-state ring laser with a small difference between the resonator Q factors for the opposite waves. It is found that in a certain range of frequency biases ..cap omega.., a difference between the Q factors results in equalization of the opposite wave intensities and in the appearance of a beat regime. The amplitude and frequency characteristics are found to be asymmetric functions of ..cap omega... In the asymptotic range of large Vertical Bar ..cap omega.. Vertical Bar the same wave is found to be suppressed for ..cap omega..>0 and ..cap omega..<0.

Existence and stability of the beat regime with resonator frequency in a ring laser

Existence and stability of the beat regime with resonator frequency in a ring laser

Minimum lock-in region in a dynamic beat regime of a ring laser

Increased accuracy in the measurement of small angular displacements of a ring laser is achieved by modulating the bias (the difference frequency between waves proportional to rotation rate) sinusoidally, or by applying a square-wave bias (switching) [i, 2]. An approximate solution of the simplified phase equation describing the frequency characteristics of a ring laser under these conditions was found in [I, 2]. According to these results, the minimum lock-in region in such a dynamic beat regime is zero. A more accurate phase equa~ tion than that considered in [i, 2] is analyzed by the method of averages in this paper, and it is established that for a sinusoidal bias variation the minimum lock-in region differs from zero.