Moderate Feedback Research Articles

Noncontact vibration sensors based on current modulated external cavity semiconductor lasers

An improvement in performance and design of noncontact vibration sensors based on external cavity semiconductor lasers is demonstrated. A technique for narrowing RF spectral peaks in external cavity lasers with moderate optical feedback by direct current modulation is explained. Current modulation frequencies suitable for use with developed position and vibration sensors are identified. Improvements in accuracy and resolution for the sensors are recorded and illustrated.

Synchronous Sisyphus effect in diode lasers subject to optical feedback

Diode lasers exposed to moderate optical feedback, when biased near threshold, exhibit low-frequency intensity fluctuations in the RF spectrum that materialize as dropout events in the intensity time series. We recorded high-quality intensity time traces and frequency spectra of these events that show a new phenomenon in which the dropout events synchronize and appear at regular time intervals. The fine structure of the individual dropouts is recorded with an ultrafast digitizer that reveals the presence of fast oscillations occurring in the picosecond range. Numerical work based on the single-mode single-delay Lang and Kobayashi rate equations shows a locked state consisting of sharp intensity pulses that are slowly modulated and locked to an extraordinarily regular pattern.

Wavelet analysis of low frequency fluctuations of a semiconductor laser

Wavelet transform analysis of experimentally measured intensity fluctuations distinguishes the transition from low frequency fluctuations at moderate feedback to stable operation at strong feedback. Comparison of these results with those of a wavelet analysis of lowpass filtered solutions of the Lang-Kobayashi equations for deterministic evolution of a single mode semiconductor laser with optical feedback finds substantial agreement in the part of the wavelet spectrum corresponding to slow dynamics. Substantial disagreement is found in the fast dynamics, which lessens when noise is added to the equations.

Phase-shifted laser feedback interferometry

We have introduced the techniques of phase-shifting interferometry into a laser feedback interference microscope based on a helium-neon laser. With moderate feedback, multiple reflections between the sample and the laser are shown to be negligible, and the interferometer responds sinusoidally with a well-characterized fringe modulation. One can obtain higher signal-to-noise ratios by determining the number of additional terms required for modeling the effect of multiple reflections on the phase and visibility measurements in the high-feedback regime. Changes in optical path length are determined with nanometer precision without phase averaging or lock-in detection.

Dynamics in a compound cavity semiconductor laser induced by small external-cavity-length change

For the short-range variations of the external cavity length, the dynamic behaviors of a semiconductor laser with optical feedback are investigated by the numerical simulations and experiments. Under the condition of a single-mode oscillation, the laser output power shows periodic undulation along the external cavity length whose period is equal to half of the optical wavelength. At weak to moderate external optical feedback, stable, periodic, quasi-periodic, and chaotic oscillations of the laser output power are observed within the periodic undulation. Experimental results of periodic and quasi-periodic oscillations obtained by the laser output power and the optical spectrum support the predictions from the numerical analysis based on the rate equations.

Stability and modulation properties of a semiconductor laser with weak optical feedback from a distant reflector

We analyse the stability of the steady-state solutions of the compound system formed by a single-longitudinal-mode semiconductor laser and an external reflector. Of the large number of these external cavity modes (ECMs) created in pairs of modes and antimodes by moderate feedback, the antimodes are always unstable, while the modes may be stable or unstable when created. The ECMs that have a large positive frequency shift with respect to the emission frequency of the solitary laser are unstable when created. In contrast, the ECMs that have a large, negative frequency shift are stable on creation and remain stable over a relatively large feedback range. For sufficiently large feedback an ECM that is created stable gives way to a time-dependent solution (limit cycle or torus) that is localized in phase space around the ECM; several time-dependent attractors may coexist. Approximating the dynamical equations, taking into account terms up to second order, we obtain relations for the amplitudes of the oscillations of the laser variables for these attractors. The external cavity length and the injection current are key parameters which determine these amplitudes. Our approximations are in good agreement with numerical simulations, and hold even far from the bifurcation points where these attractors originate.

Relative intensity noise for laser diodes with arbitrary amounts of optical feedback

A unified study of the noise characteristics of semiconductor lasers with optical feedback and short external cavity length is presented. A new set of nonlinear rate equations that can describe a laser diode with any amount of optical feedback is proposed. The relative intensity noise (RIN) is calculated by using a numerical solution of these equations. This paper concentrates mainly on the moderate and strong feedback regimes. The spectral phenomena observed during the transition from the weak feedback to the coherence collapse regime and then to the strong feedback regime are studied and explained. The effect of the variation of some of the laser diode parameters on the RIN characteristics is also investigated.

Fast Pulsing and Chaotic Itinerancy with a Drift in the Coherence Collapse of Semiconductor Lasers

We report the first experimental observation of irregular picosecond light pulses within the coherence collapse of a semiconductor laser subject to delayed moderate optical feedback. This pulsing behavior agrees with the recent explanation of low frequency fluctuations as chaotic itinerancy with a drift. Theory and experiments show very good agreement.

Lateral spatial effects of feedback in gain-guided and broad-area semiconductor lasers

Starting from Fresnel diffraction theory, we derive analytic expressions for the lateral spatial dependence of feedback fields for the cases of conventional and phase-conjugate optical feedback. By using numerical simulations we show that for narrow-stripe gain-guided lasers, both types of optical feedback from an external cavity can convert the twin-lobed far fields into a nearly single-lobed far field. We also find that conventional and phase-conjugate feedbacks in broad-area lasers induce a spatial modulation of the lateral field that increases the tendency for filamentation at moderate (-30 dB) feedback levels.

Sisyphus effect in semiconductor lasers with optical feedback

We identify the various physical mechanisms in low frequency fluctuations, which occur when a semiconductor laser is subject to moderate optical feedback while operating close to its solitary laser threshold. In attempting to reach the maximum gain mode, which often is stable, the system forms short mode-locked pulses. In between pulses mode-slipping can occur, generally in the direction of maximum gain. Inevitably, the trajectory passes too close to one of the many saddle points, which will take the system back to the solitary laser state.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamical and noise properties of laser diodes subject to strong optical feedback

Dynamical and noise properties of laser diodes subject to strong optical feedback have been investigated. Under strong optical feedback a conventional rate-equation approach is not valid, and thus an iterative traveling-wave model has been developed to describe this operating regime. Attention has been given to identifying the transition from stable strong-feedback operation to the coherence collapse regime obtained with moderate optical feedback.

Laser diode coupled to a single-delay external Kerr cavity

We investigate the steady state and the dynamic behavior of a laser diode coupled to an external single-delay, 2 ns, Kerr cavity throughout the typical five feedback levels. We show that over a large range of feedback levels, for various Kerr constants, the steady state power dependent spectrum consists of one frequency which is shifted about 0.03 GHz from the solitary laser frequency. This is manifested by suppressing mode hopping at moderate feedback levels corresponding to level II. Similarly, coherence collapse is suppressed and its onset is shifted to higher feedback levels.

Turn-on jitter in semiconductor lasers with moderate reflecting feedback

Numerical simulations are used to investigate the impact of moderate external feedback on the turn-on timing jitter inherent in directly modulated semiconductor lasers. Enhanced turn-on jitter is found to be due to the feedback-induced intensity noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear injection locking dynamics and the onset of coherence collapse in external cavity lasers

A theoretical analysis is presented of the experimentally observed collapse of coherence in semiconductor lasers exposed to moderate optical feedback. A main point in the analysis is, that coherence collapse in the delayed-feedback (DFB) system shows up as bistability in a much simpler model which corresponds to an injection locking system. Based on this, the authors derive a simple analytical expression, valid for DFB as well as Fabry-Perot lasers, for the critical feedback level at which coherence collapse sets in. Simulations of the nonlinear injection locking model reveal the presence of complicated nonlinear dynamics with period-doubling bifurcations and coexisting attractors even inside what is normally denoted the stable locking range.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Noise characteristics of PCM-modulated single-mode semiconductor laser diodes with distant optical feedback

The relative intensity noise (RIN) and the linewidth of a PCM-modulated single-mode laser diode with moderate optical feedback within the coherence collapse regime has been investigated. The results are used to characterise the performance of a directly modulated PCM-optical system with arbitrary optical feedback.

Bistability and low-frequency fluctuations in semiconductor lasers with optical feedback: a theoretical analysis

Near-threshold operation of a semiconductor laser exposed to moderate optical feedback may lead to low-frequency fluctuations. In the same region, a kink is observed in the light-current characteristic. Here it is demonstrated that these nonlinear phenomena are predicted by a noise driven multimode traveling-wave model. The dynamics of the low-frequency fluctuations are explained qualitatively in terms of bistability through an iterative description.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Instability of semiconductor lasers due to optical feedback from distant reflectors

We explain an istability occurring in continuously operating lasers due to moderate feedback from distant reflectors. This instability occurs despite the fact that the laser is stable with respect to small deviations from steady-state operation. It is the result of finite phase and carrier number changes caused by fluctuations in spontaneous emission. We predict several properties that agree with recent experimental observations: 1) the instability only occurs when the laser reaches a steady state that maximizes coherent feedback and laser light intensity; 2) the instability vanishes at strong feedback levels; and 3) at moderate feedback levels, the laser will be nearly stable at threshold, but unstable when operated well above threshold. The latter behavior results in a nonlinear "kinked" shape in the light versus current relation.

Heart rate change in Type A and Type B males as a function of response cost and task difficulty.

ABSTRACTTonic changes in heart rate (HR) and somatic motor activity were monitored in 70 Type A and 70 Type B males to determine if these groups differ in psychologically‐mediated HR reactivity to a specific appetitive situation. A and B types were defined by extreme scores on the Jenkins Activity Survey. Subjects performed a continuous button‐pushing task during a practice trial and 4 trials involving high (loss of money), low (loss of points), or no response cost (RC) for performance failure, and high, moderate, low, or no levels of failure feedback on performance. Greater HR increases from practice were predicted for high RC vs. low RC, and for Type As vs. Type Bs. Additionally, in the high RC condition, HR was expected to diminish across trials more in those receiving high and low failure feedback compared with those receiving moderate failure feedback. Results confirmed the first two expectations. Furthermore, the HR difference between Type As and Type Bs was magnified under high RC conditions. The last expectation was not confirmed, but further analyses suggested that failure feedback influenced Type Bs but not Type As. Greater intrinsic appetitive motivation of Type As may account for their greater HR increase in response to opportunities for active avoidance, as well as for reward.

Arterial pressure regulation: Overriding dominance of the kidneys in long-term regulation and in hypertension

The body is endowed with many different arterial pressure regulating mechanisms, some of which operate rapidly, some slowly; some of which operate at low pressure ranges, some at normal pressure ranges, and some at high pressure ranges; some of which have weak feedback gains, some of which have moderate feedback gains, and one of which has infinite gain when sufficient time is allowed for its control functions to reach the state of equilibrium. The infinite gain pressure control system is based on the effect of arterial pressure on renal output of water and salt. If the arterial pressure becomes too high, the output becomes greater than the net intake of water and salt, and the body becomes progressively dehydrated until this dehydration causes the pressure to return all the way to normal. It is this “all the way” response that is the cause of the infinite gain. Because of the infinite gain of this control mechanism, it is the one that determines the long range level of arterial pressure. Many factors can affect the operation of the renal-body fluid mechanism for arterial pressure regulation. These include nervous effects acting on the kidney, hormonal factors acting on the kidneys, pathology of the kidney, and so forth. However, the principle of infinite gain in this system requires that, in some way, all long-term arterial pressure regulation must involve the balance between intake and output of water and salt and almost invariably involves the kidneys.

A study of the constant-temperature hot-wire anemometer

The conventional ‘bridge-feedback amplifier’ constant-temperature hot-wire anemometer is analysed to determine its static and dynamic response. The effects of moderate feedback amplifier gain, bridge imbalance, stray bridge reactance, amplifier offset voltage, lack of common mode rejection, amplifier frequency response and departure from constant transconducture are included. The root loci of the system are mapped out and the consequences of the analysis are discussed from the viewpoint of both the operator and the designer.