External Cavity Roundtrip Research Articles

Self-Pulsations in Terahertz Quantum Cascade Lasers under Strong Optical Feedback: The Effect of Multiple Reflections in the External Cavity.

We have recently reported the self-pulsation phenomenon under strong optical feedback in terahertz (THz) quantum cascade lasers (QCLs). One important issue, however, we left open: the effect of multiple round trips in the external cavity on the laser response to feedback. Our current analysis also casts additional light on the phenomenon of self-pulsations. Using only one external cavity round trip (ECRT) in the model has been the common approach following the seminal paper by Lang-Kobayashi in 1980. However, the conditions under which the Lang-Kobayashi model, in its original single-ECRT formulation, is applicable has been rarely explored. In this work, we investigate the self-pulsation phenomenon under multiple ECRTs. We found that the self-pulsation waveform changes when considering more than one ECRT. This we attribute to the combined effect of the extended external cavity length and the frequency modulation of the pulsation frequency by the optical feedback. Our findings add to the understanding of the optical feedback dynamics under multiple ECRTs and provide a pathway for selecting the appropriate numerical model to study the optical feedback dynamics in THz QCLs and semiconductor lasers in general.

Passive Mode-Locking and Tilted Waves in Broad-Area Vertical-Cavity Surface-Emitting Lasers

We show experimentally and theoretically that an electrically biased 200-μm multitransverse mode vertical-cavity surface-emitting laser can be passively mode-locked using optical feedback from a distant resonant saturable absorber mirror. This is achieved when one cavity is placed at the Fourier plane of the other. Such nonconventional optical feedback leads to the formation of two tilted plane waves traveling in the external cavity with opposite transverse components and alternating in time at every round-trip. Each of these plane waves gives birth to a train of mode-locked pulses separated by twice the external cavity round-trip, while the two trains are time shifted by a round-trip. A large portion of the transverse section of the device contributes to mode-locked emission leading to pulses of approximately 1-W peak power and 10-ps width. We discuss how inhomogeneities in the transverse section of the saturable absorber select the emitted tilted waves, thus leading to tunable emission over 4 nm.

Optimization of Timing Jitter Reduction by Optical Feedback for a Passively Mode-Locked Laser

We investigate the effect of optical self-feedback on the timing jitter of a passively mode-locked (ML) laser and compare the von Linde method with two pure time domain methods for calculating the timing jitter of such a system. We find that all three methods yield the same dependence of the timing jitter on the external cavity roundtrip time (delay time). Of these methods, the so-called long term jitter method is significantly less computationally expensive. We therefore use this method to investigate the influence of the delay time, feedback strength, and amplitude-phase coupling on the timing jitter. Our results show that, with vanishing amplitude-phase coupling, greater timing jitter reduction can be achieved with long delay times and larger feedback strengths, when feedback is near resonance. Off resonance, the timing jitter is increased. Non-vanishing amplitude-phase coupling can lead to destabilized pulse stream, even at the feedback main resonances.

Nonlinear dynamics and synchronization of an array of single mode laser diodes in external cavity subject to current modulation

We study the dynamics of an array of single mode laser diodes subject to filtered feedback provided by an external reflection grating. Our numerical simulations show that by modulating the injection current the array can be phase synchronized leading to high power coherent emission. The output peak power density can be varied by tuning the modulation frequency and can be resonantly enhanced once the frequency matches the inverse of external cavity round trip time and mode-locking behavior is realized. Both non-resonant and resonant injection current modulation results in an excellent degree of phase synchronization and coherence at certain modulation amplitudes and frequencies that is manifested by coherent enhancement of far-field optical intensity.

In-depth analysis of injection-seeded long external cavity InGaN/GaN surface-emitting laser

Optically pumped InGaN/GaN quantum well (QW) vertical-external-cavity surface-emitting laser operating at 420 nm wavelength with external cavity length of up to 50 mm has been realized. Use of injection seeding enables us to reach lasing operation even for pump pulse duration just slightly exceeding the external cavity roundtrip time. The carrier lifetime in the QWs was measured to be 2.5 ns, and lasing emission was obtained under pump pulses shorter (400 ps) or longer (10 ns) than the carrier lifetime in QWs. We studied experimentally the dependence of the lasing threshold on the length of external cavity and provided a model to explain this dependence. Further detailed measurements of the near field and far field patterns, optical spectrum, spontaneous emission factor, and delay time to emission of the lasing pulse confirm lasing at the external cavity mode.

Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser

Random bit generators (RBGs) are important in many aspects of statistical physics and crucial in Monte-Carlo simulations, stochastic modeling and quantum cryptography. The quality of a RBG is measured by the unpredictability of the bit string it produces and the speed at which the truly random bits can be generated. Deterministic algorithms generate pseudo-random numbers at high data rates as they are only limited by electronic hardware speed, but their unpredictability is limited by the very nature of their deterministic origin. It is widely accepted that the core of any true RBG must be an intrinsically non-deterministic physical process, e.g. measuring thermal noise from a resistor. Owing to low signal levels, such systems are highly susceptible to bias, introduced by amplification, and to small nonrandom external perturbations resulting in a limited generation rate, typically less than 100M bit/s. We present a physical random bit generator, based on a chaotic semiconductor laser, having delayed optical feedback, which operates reliably at rates up to 300Gbit/s. The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.

Simple and complex square waves in an edge-emitting diode laser with polarization-rotated optical feedback

Numerical and experimental results are presented for an edge-emitting diode laser with delayed optical feedback, where the polarization state of the feedback is rotated such that the natural laser mode is coupled into the orthogonal, unsupported mode. We examine the bifurcation structure and dynamics that give rise to a class of periodic, polarization-modulated solutions, the simplest of which is a square wave solution with a period related to but longer than twice the external cavity roundtrip time. Such solutions typically emerge when the feedback is strong and the differential losses in the normally unsupported polarization mode are small. We also observe more complex waveforms that maintain the same periodicity.

Randomness analysis of external cavity semiconductor laser as entropy source

In this paper, we employ chaotic light as an entropy source, generated by semiconductor lasers with optical feedback induced by external cavity, to generate 500 Mbit/s random number sequence and then study specifically the influence of external cavity length on randomness. The results indicate that the generated random sequence has an weak periodicity caused by the external cavity feedback under a single-channel chaotic source, and can only pass two or three tests of the National Institure of Standards and Technology(NIST) when the external-cavity round trip delay time is an integral multiple of the sampling time. On the other hand, the weak periodicity can be eliminated by using two different chaotic sources when their external cavity lengths are unproportional to each other, and the obtained random sequence can pass all tests of the NIST after XOR processing.

Combination of two basic types of synchronization in a coupled semiconductor laser system

Combination of two basic types of synchronization, anticipatory synchronization and lagged synchronization, is investigated numerically between two coupled semiconductor lasers. It is found that lagged synchronization produced by a backward coupling with a suitable delay can combine with the originally hidden anticipatory synchronization and produce a type of synchronization overcoming the original lagged synchronization produced by a forward coupling. We study the combination synchronization phenomenon when the delay of the backward coupling is different from that of the original anticipatory synchronization. Our results suggest that the synchronization combination phenomenon might allow an interpretation of an experimental observation by Sivaprakasam et al. [Phys. Rev. Lett. 87, 154101 (2001)] that the anticipating time is irrespective of the external-cavity round trip time, which to date remains to be understood.

Experimental Demonstration of Anticipating Synchronization in Chaotic Semiconductor Lasers with Optical Feedback

We report the first experimental observation of anticipating chaotic synchronization in an optical system using two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of an optical feedback in an external-cavity configuration. It is found that the anticipation time does not depend on the external-cavity round trip time of the transmitter.

Modelocking of interferometric Y-lasers in an external cavity

The first report on active modelocking of interferometric Y-lasers in an external cavity are reported. Pulse widths between 20 and 30 ps for 1.3- mu m and 1.55- mu m devices were achieved by modulation of the injection current synchronously to the external cavity roundtrip frequency. A time-bandwidth-product of 0.97 was determined for 1.55- mu m devices.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reflection noise in index-guided InGaAsP lasers

We report a detailed study of the excess noise induced in index-guided InGaAsP laser structures by reflection feedback. The phenomena of high-frequency noise (1-5 GHz), low-frequency noise (< 100 MHz), and intensity fluctuations are shown to have a common physical origin in the unusual instability of the coupled laser-external cavity system. After a randomly occurring light intensity drop, the light output recovers in 10-15 steps, each corresponding to an external cavity roundtrip (high-frequency noise); the total recovery time corresponds to the low-frequency noise. The instability, and the subsequent noise, can be suppressed under conditions of very strong feedback such as obtained for lasers with anti-reflection-coated facets. The reflection noise characteristics are shown to be largely independent of the laser structure and structure modifications such as distributed feedback.

Theory of noise in semiconductor lasers in the presence of optical feedback

We derive analytical expressions for the power spectral densities of intensity and frequency noise of single mode semiconductor lasers in the presence of an optical feedback. By explicitly taking into account the spontaneous emission processes into the laser mode, we obtain a behavior which, at high frequencies significantly differs from the usual one, and is in good agreement with recent experimental results. In particular, we are able to show in which way the intensity and frequency noise, besides being influenced by the external cavity length, are affected by the presence of the well known resonant peaks in the noise spectra of the solitary laser and how a substantial lowering and flattening in the noise spectra can be obtained with external cavity round trip times shorter than the inverse of the peak resonant frequency. We also present experimental results in good agreement with the theoretical ones.

Modulation detuning characteristics of actively mode-locked diode lasers

Existing frequency domain models for the active mode locking of diode lasers are appropriate for antireflection- (AR-) coated devices. This paper presents the first frequency domain model for non-AR-coated devices. The use of uncoated devices permits the independent measurement of all of the important laser parameters required for the model, so that no adjustable parameters are needed. An additional novel feature of this model is that the effect of gain saturation on the exact shape of the gain waveform is allowed for in a completely self-consistent fashion. Experimental studies were carried out on uncoated undegraded commerical laser diodes. Threshold reductions of 25-30 percent were achieved for external cavity operation. The mode-locking studies reported in this paper were carried out above the external threshold current, with a sinusoidal modulation near 1 GHz at a modulation index of 4 percent. The results of these studies showed good agreement with the predictions of the model presented here, in contrast with the predictions of the existing models. Specifically, the modulation frequency corresponding to the shortest most intense mode-locked pulses was found to occur at a fraction of 1 percent below the frequency matched to the external cavity roundtrip time. As well, the predicted effects of gain saturation were observed in the detailed structure of the mode-locked pulses, and in their detuning characteristics.

Interaction of a bistable injection laser with an external optical cavity

Experimental results on interactions of a bistable laser with an external optical cavity are presented. Switching of a bistable injection laser can be done by varying the amount of optical feedback. The optical switching is accompanied by a switching of the voltage across the absorber section. This can be utilized in digital optical disk readout. A bistable laser with an antireflection coating on one facet is more suitable for this task. No pulsations can be observed in a bistable laser with optical feedback if the absorber section is biased with a constant current source; but when it is biased with a voltage source, pulsation occurs at the external cavity round trip frequency. This indicates that even though the intrinsic absorption of the semiconductor material does not saturate easier than the gain, the presence of such absorptions in GaAs lasers can still produce pulsations when the electrical aspect is taken into account.