Lock-in Threshold Research Articles

Prediction of the Lock-in Threshold and Nonlinear Distortions of the Scale Factor of a Laser Gyroscope at the Stage of Assembly of a Ring Resonator

Prediction of the Lock-in Threshold and Nonlinear Distortions of the Scale Factor of a Laser Gyroscope at the Stage of Assembly of a Ring Resonator

Gyroscopic operation on the 3s2→2p10 543.3 nm transition of neon in a 2.56 m2 ring cavity.

We report the development and initial operation of a 6.4 meter perimeter laser gyroscope employing the 543.3nm, 3s2→2p10 transition of neon. Employing fused silica based supermirrors yielding a cavity Q of 3.9×1011 and an inferred lock in threshold below 1μHz, the gyroscope unlocked on the bias provided by Earth rotation alone with a measured Sagnac frequency of approximately 133Hz, which is 16% larger than that of the 632.8nm transition.

Limits imposed by nonlinear coupling on rotation sensitivity of a semiconductor ring laser gyroscope.

The sensitivity of a monolithically integrated semiconductor ring laser gyro is severely limited by the high value of the lock-in threshold. In this work, we calculate the lock-in threshold using perturbation theory and coupled mode theory analysis. It is shown that gyro sensitivity is limited to an input rotation rate of 108 deg / h due to nonlinear coupling between the countertraveling modes. This coupling arises due to the backreflection of modes from moving index gratings, induced by rotation. Lock-in threshold is directly proportional to the strength of nonlinear coupling and spatial overlap of the modes' energy densities with periodic index perturbations.

Method of lock-in threshold measurement in manufacture and operation of ring lasers

The paper focuses on a method of measuring the lock-in threshold in ring laser based on digital processing of RLG quadrature signals. Requirements on mechanical rotation providing acceptable measurement error are established. The method requires no precision rotating unit, excludes the human factor, is insensitive to equipment characteristics and easy to implement.

Detection efficiency enhancement of single-photon detector at 1.55-μm by using of single photons lock-in and optimal threshold

The detection efficiency considerations are often the true determining factor as to whether a sensitive measurement is feasible. We demonstrate a robust method of single photons lock-in to enhance the detection efficiency of InGaAs single-photon avalanche diodes at 1.55-μm wavelength and suppressing background noise. With the optimal threshold for discrimination, the detection efficiency is achieved to 1.87 times bigger than that of the conventional photon counting method.

Research and discussion on the lock-in threshold variation of ring laser gyro

The lock-in threshold can be obtained by reducing the rotation rate. The lock-in threshold obtained using this method is inconsistent with the angle random walk derived from Allan variance. A dynamic burn-in grating model is proposed. The burn-in effect happens in the mirror not only in the standing wave state, but also in the traveling wave state, and it responds dynamically to beat frequency, which is different from previous research results. It can be derived that the lock-in threshold increases with the decrease of rotation rate for this model, and many puzzling phenomena of the ring laser gyro can be explained.

Cooperative Quantum Phase Mixing Effect or Why the Continuous (He-Ne)-Laser Operates Without Inversion

Cooperative phase mixing effect (CPME) in the system of N-two-level atoms coupled to one and two resonance modes is described. Caused by irrationality of cooperative energy eigenvalues the CPME leads to quasi-periodic dynamics giving rise to superposition of states with both positive and negative inversions, so that the averaged inversion should be close to zero. To check inversionless operation of the continuous (He-Ne)-laser the nonperturbative theory of beatings in a rotating ring laser (RGL) has been suggested. The derived formula for beating frequency displays two states: with split frequencies of opposite modes and the lock-in regime. Comparison of this formula with the observed lock-in threshold rotation velocity has given the estimation (N_/V)~ (10-5-10-11) cm-3 as dependent on geometry and operation conditions.

Vortex pinning and lock-in effect in a layered superconductor with large in-plane anisotropy.

We use ac susceptibility to study the vortex pinning force anisotropy and the magnetic lock-in effect in the organic superconductor (TMTSF${)}_{2}$${\mathrm{ClO}}_{4}$, which is believed to have an in-plane anisotropy of ${\ensuremath{\gamma}}_{\mathit{b}\mathit{a}}$\ensuremath{\sim}10 and a maximum out-of-plane anisotropy ${\ensuremath{\gamma}}_{\mathit{c}\mathit{a}}$\ensuremath{\sim}100. Our measurements show only weak effects of the in-plane anisotropy. The pinning force for Josephson vortices (parallel to the conducting planes) is nearly independent of their orientation, except for a small but narrow peak (full width at half maximum \ensuremath{\simeq}6\ifmmode^\circ\else\textdegree\fi{}) when the vortices are parallel to the TMTSF stacks (a axis). The pinning force initially decreases as the vortices unlock from the layers, contrary to the behavior previously observed in the organic superconductor (BEDT-TTF${)}_{2}$Cu(SCN${)}_{2}$. The lock-in threshold field is only weakly dependent on the initial angle of the Josephson vortices in the ab plane.

Analysis of a ring-laser gyroscope with intracavity phase-conjugate coupling

A ring-laser gyroscope with the opposite modes coupled by an intracavity phase-conjugate interaction is examined analytically and numerically. It is shown that the coupling mitigates cross-saturation-induced mode extinction, allowing a homogeneously broadened medium to be used as the gain for a laser gyroscope. It is also shown that the coupling can induce a bias beat frequency that can potentially be used as an all-optical dither. The phase conjugation is shown to affect the lock-in threshold only indirectly. The results are compared with pertinent experiments from the literature.

Resonant diffraction mechanism, nonreciprocity, and lock-in in the ring-laser gyroscope.

Diffraction is shown to play a dramatic role in the frequency characteristics of ring-laser gyroscopes. It is proved theoretically and experimentally that a small misalignment of the cavity leads to a nonreciprocity of the resonant diffraction mechanism. The resonant diffraction losses of the two counterpropagating modes being then different, the asymmetries of their output-power versus cavity-frequency profiles are different. This leads to the existence of a frequency bias between the two modes. Diffraction is also shown to play a fundamental role in the lock-in mechanism. It is indeed experimentally demonstrated that the asymmetric evolution of the lock-in threshold with the laser frequency is governed by resonant diffraction mechanisms.

Nonreciprocal measurements in femtosecond ring lasers

Sensitive gyroscopic response has been demonstrated with a passively mode-locked ring dye laser. Rapid change in the phase of scattering has been identified as an important mechanism responsible for the extremely low lock-in threshold of this laser gyro. Coupling between counterpropagating pulses has been confirmed to take place only in the overlapping region of the pulses. Intracavity measurements of the electro-optical effect are demonstrated with fields as small as 20 mV/cm.

An argon ion ring laser as a gyroscope

As a prototype gyroscope for a precision measurement of the Earth's rotation ΩE, we set up an argon ion ring laser with an area of 1.4 m2. Different cavity geometries were tested in order to achieve a cancellation of the effect of the plasma flow. In a set-up with two laser tubes of the same type facing towards opposite directions, a stability of the beat frequency of 2–3 ΩE was measured. In a configuration with a double transition of the laser beam through the tube, the lock-in threshold was too high for the Earth's rotation to be measured, however, no effect of the plasma flow was observed.

The effects of icing on the dynamic response of thick aerofoils

SummaryVibration of a flexible wing strut of 30% thickness/chord ratio occurred during icing trials of a commuter aircraft. This was caused by the formation of ice on the leading-edge of the strut producing a ‘double-horned’ ice shape. The two horns formed one above the other, having very sharp leading-edges with radii less than 0·6% of the strut chord of 0·23 m.Wind tunnel testing demonstrated that, over a limited range of incidence angle, the flow around the flexible strut was dominated by a long separation bubble that periodically ‘burst’ and re-attached. This occurred at a reduced frequency of nominally 0·06, based upon the chord of the profile and the free stream velocity. The periodic flow was also spatially highly coherent, producing relatively large unsteady forces compared with the buffet forces generated by incoherent turbulent separated flows.A high-speed film was made using smoke visualisation of the flow around a 40% rigid scale model of the strut. This was used to correlate the unsteady pressure field, measured at 18 points around the profile, with the dynamic behaviour of the separation bubble.The periodicity was found to be inherent in the flows over both the flexible and rigid struts for a limited range of incidence, occurring even when structural response was restrained to a level below that at which lock-in occurred between the flow and the response motion. The peak value of the unsteady pressure was measured on the top surface of the upper ice horn. The root mean square value of 18% of the free stream dynamic pressure was measured, with response restrained to below the lock-in threshold.

A laser gyro with optimized resonator geometry

Experiments on laser gyros with adjustable beam path geometry yield a strong dependency between the lock-in threshold and the distribution of the backscatter sources. Based on a simple vector formalism, a theory is presented which describes the lock-in threshold as a function of the beam path geometry. In accordance with the experimental results, the theory is a helpful tool to minimize the lock-in threshold by an optimization of the resonator geometry. The theory also offers an explanation of the fact that the quality of laser gyros often differs, even between gyros of the same production series, under the same operating conditions and with mirrors of comparable quality.

Dependence of Lock-in Threshold and Winking Pattern on the Phase-Interaction of Scattering Waves in the Ring Laser

Relationships different from previously reported information about the direction of a ring-laser's rotation and winking pattern were observed. Also, the phase difference was observed between the periodic change of the winking intensity and the lock-in threshold when two mirrors are moved while interlocked with a constant optical path length. These phenomena could be satisfactorily explained by introducing the resultant change in the amplitude and the phase of the composite scattered waves from the displacement of the mirrors in self-consistent equations. it was shown that the inequality of the back-scattering rate among the three mirrors and the anisotropy of that to the oppositely directed traveling waves affected the above-mentioned phenomena in an important way.

Positive scale factor correction in the laser gyro

Unlike what was expected, a measurement of the scale factor in the laser gyro as a function of rotation showed it to increase with decreasing rate. At low rates the scale factor peaked and then rapidly dropped to zero at the lock-in threshold. The height of the maximum was found to increase and the width to decrease with operation of the laser closer to lasing threshold. The height varied between 0.003 and 0.3 percent of the nominal scale factor and the half-width varied between 5 and 45 deg/s. A theoretical description of the results was obtained in the asymptotic limit of rates high compared to the lock-in threshold. The shape of the scale factor curve was found to be Lorentzian with a width proportional to the excess gain. The sign of the scale factor correction was found to be due to the phasing of the backscattering, which is the source of the lock-in. This phasing was found to be consistent with the observed 180-deg phasing between the ac components of each beam when the laser is unlocked.

Phase modulation of a ring-laser gyro - Part I: Theory

The theory of a multimode ring-laser gyro with intracavity phase modulation is developed, starting from the wave equation for a rotating reference frame. The approach is to extract physical information without actually solving the equations. Considering each of the oppositely directed traveling waves (ODTW) separately, the behavior is similar to that of an ordinary two-mirror phase-modulated laser. However, when the waves are heterodyned to measure a beat frequency, small mode-pulling effects become important, and, if the ODTW are treated unequally by the system, a frequency error or offset results. Sources of offset include time variation of the modulator length, reactance of the gain medium, and detuning of the modulator frequency from axial mode spacing. When back reflections are included in the theory, the results reduce to the single-mode ring-laser case, with the coupling coefficient dependent upon overlap between the ODTW at the reflector. It is predicted that at low rotation rates the ODTW frequencies will still become locked together, except in a very special case where the lock-in threshold vanishes. Significance of the nature of the reflecting elements is discussed. Comments are made on the predicted merits of phase modulation as an improvement in the low-rotation-rate measuring capabilities of the device.

Loss Lock-In in the Ring Laser

In the ring laser, frequency synchronization between the oppositely directed traveling waves is usually attributed to mutual coupling by the mechanism of the backscattering of energy from each of the beams into the direction of the other. A new type of coupling is introduced where the standing wave state is shown to have less losses than the traveling wave state for rotations rates less than some critical lock-in threshold. The coupling mechanism is spacially varying losses over the cavity length. The minimum loss condition is also shown to determine the location of the nodes of the standing waves. In certain cases, lock-in thresholds due to nonuniform losses are shown to have the potential of being a few orders-of-magnitude greater than thresholds attributed to backscattering.