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High-Frequency Oscillations and Self-Mode Locking in Short External-Cavity Laser Diodes
Abstract
An effect of compound-cavity mode competition for a laser diode
with a short external cavity is investigated analytically and
numerically on the basis of a round-trip approximation for emitted
photons in the external cavity. Due to the noncoincidence of the
compound-cavity modes with possible frequencies of stationary lasing,
such competition may cause self-locking of two compound-cavity modes
with deep high-frequency oscillations of the laser output for a short
(typically ⩽5 mm) external cavity. Simple analytical expressions for
critical feedback parameters and the frequencies of self-oscillations
are given, as well as a generalized diagram of different dynamic regimes
of a short external-cavity laser, which shows these regimes of
high-frequency self-oscillations as well as coherence collapse
instability. The results may be considered a guideline for the design of
high-speed laser diodes with an integrated passive cavity. In
particular, such a device may be a very efficient pulse source in the
microwave (>20 GHz) region
... Mode beating (MB) requires two longitudinal modes which are simultaneously lasing. This corresponds to the configuration first investigated by Tager and Petermann [TP94]. The most important finding of their work was a stable coexistence of mode and antimode, provided sufficiently strong feedback and an appropriate feedback phase. ...
... Below the feedback strength required for MB only single-mode dynamics occurs. An analysis of the short cavity regime in [TP94] has shown that the single-mode scenario can give rise to self-sustained pulsations. These oscillations are similar as in multisection lasers comprising two detuned gratings [TWS + 00]. ...
... At a particular phase, mode and anti-mode arrive at comparable threshold densities (triangles). Here, both modes accommodate to each other at a common density and MB pulsations emerge in a Hopf bifurcation [TP94;WT02]. This scenario is reminiscent of the bifurcation bridges predicted for long delay times [ERGK00]. ...
In dieser Arbeit wird die Selbstorganisation in Halbleiterlasern mit ultrakurzer optischer Rueckkopplung untersucht. Es wurden eine Vielzahl neuer nichtlinearer dynamischer Szenarien experimentell praepariert und untersucht, wobei die Steuerung der relevanten Rueckkopplungsparameter ueber Injektionsstroeme erfolgt. Zwei verschiedene Typen von selbsterhaltenden Intensitaetspulsationen wurden abhaengig von der Phase und der Staerke der Rueckkopplung gefunden. Ein Pulsationstyp entsteht in einer Hopf-Bifurkation aus gedaempften Relaxationsoszillationen. Beim zweiten Pulsationstyp handelt es sich um Schwebungs-Oszillationen zweier verschiedener konkurrierender Moden der Gesamtkavitaet. Diese Ergebnisse repraesentieren experimentelle Beweise fuer theoretische Vorhersagen. Die Koexistenz von Schwebungsoszillationen und Relaxationsoszillationen fuehrt zum uebergang von regulaeren Pulsationen in chaotische Emission ueber eine quasiperiodische Route zum Chaos. Ein ploetzlicher Untergang des Chaos deutet auf ein Boundary-Crisis-Szenario hin. Die Existenz chaotischer Saettel, die transienten chaotischen Dynamiken nach einer Boundary Crisis zugrunde liegen und die Erregung von chaotischen Transienten ist eng verwandt mit konventioneller Erregbarkeit, wird experimentell verifiziert. Es wird der Einfluss externen Gaussschen Rauschens nahe von sub- und superkritischen Hopf-Bifurkationen untersucht. Rausch-induzierte Schwingungen tauchen als verrauschte Vorlaeufer in Form von lorentzfoermigen Spitzen im Powerspektrum auf. Der Kohaerenzfaktor, definiert durch das Produkt aus Hoehe der Spitze und Qualitaetsfaktor, zeigt fuer beide Typen von Hopf-Bifurkationen ein nichtmonotones Verhalten. Damit wird Kohaerenzresonanz experimentell demonstriert. Die Messungen zeigen neben diesen uebereinstimmungen auch qualitative Unterschiede zwischen den beiden Faellen. Die experimentellen Ergebnisse werden mittels eines allgemeinen Modells fuer rauschgetriebene Bewegungen in der Naehe von Bifurkationen untersucht.
... As a result, intense pulses of light are generated, with the periodicity of the fundamental external cavity frequency. With the presence of optical feedback, it is possible to sustain mode locking and take advantage of this phenomenon to generate time-periodic short pulses [86,119]. ...
... Pulsing states have been reported in a laser with COF since 1994 by Tager and Petermann [119]. This kind of self-pulsations in a laser with COF correspond to a bridge connecting two Hopf bifurcations associated with two frequency-detuned ECMs. ...
... This makes the observation of such ECM beating and Hopf bridge quite difficult. In addition, self-pulsing dynamics at the external cavity frequency resulting from this ECM beating are typically limited to so-called short external cavity in the COF case [119]. ...
This thesis is a theoretical and experimental study of the dynamics of an edge-emitting laser diode (850 nm) with phase-conjugate feedback. The experimental device is designed to see the dynamical range of the laser through the temporal and spectral properties while the feedback rate varies. Phase-conjugate feedback is performed through four-wave mixing in a photorefractive crystal. The propagation time of the laser beam in the external cavity is termed external time delay. Under the effect of the feedback, the system shows a wide dynamical range including chaos and self-pulsing states which characteristic properties are determined by the length of the external cavity. For the first time self-pulsing states at frequencies multiples of the fundamental frequency of the external cavity are evidenced. Simulations carried out based on the commonly-used Lang-Kobayashi laser rate equations provide theoretical confirmations to the experimental observations. The main topics tackled here are chaos crisis and bistability of pulsing solutions, self-pulsing regimes (through their stabilization and destabilization) and the transitions between them, characterization of extreme events of two kinds along with their statistical distribution and delay-induced deterministic coherence resonance of low frequency fluctuations. Beyond the fundamental interest of these results and the many comparisons that can be made with other laser systems, applications in the field of all-optical signal generation and control of chaos are direct consequences of this study.
... In this work, the stability limit was described as a relationship of k versus ω R for a fixed τ. Later, in 1994, Tager and Petermann [42] presented similar work to [41], in which the gain in the electric field amplitude equation was considered as nonlinear, but the gain in the electric field phase equation was still linear. Two new coupling equations were derived from the system determinant under the assumptions different to [41], that is, ...
... The two coupling equations are similar to those derived in [25], but they include the influence of compound cavity mode competition on the stability of an SL with short external cavities. The stability limit was then presented as a relationship of k versus τ and k versus the initial phase shift in the external cavity for a fixed J in [42]. In 1998, Masoller and Abraham [43] investigated the influence of k on the stability limit when the SL is biased well above the threshold. ...
... If taking the assumptions as described in [21], [24], [25], and [40]- [42] and ignoring the nonlinear gain, the system determinant D(s) in Eq. (11) becomes the same as the ones given in [21], [24], [25], [41], and [42]. Therefore Eq. (11) provides a more comprehensive description on the stability property of an SL with EOF system. ...
... Subjecting semiconductor laser to external optical feedback induces variety of changes in the laser output, ranging between linewidth narrowing to coherence collapse, and from stable CW operation or period-1 oscillations with low noise to chaotic dynamics with noisiest levels [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. An experimental study of the so-called 'regimes of feedback' and the associated characteristic dynamics of semiconductor lasers was undertaken by Tkach and Chaprylyvy [15]. ...
... As the length decreases, the laser exhibits chaos cycles with the increase of the feedback strength. In this case the route-to-chaos may include period-one oscillations, period doubling, or subharmonics oscillations depending on the period of the round-trip in the external cavity relative to the period of relaxation oscillation of the laser [9,12,18,19]. As the external cavity gets shorter, the number of chaos cycles decreases and the feedback range of the chaos cycle becomes narrower [20]. ...
Abstract We report on achieving tuned single mode operation of a multimode semiconductor laser by coupling it to a very-short external cavity with selective feedback. We show that the induced uniform feedback light from the very-short external cavity can induce single-mode oscillation over a broad range of optical feedback. Then by applying selective external to the optimum settings of the single-mode oscillation, we predict tuning of the single-mode output over a wavelength range of ~ 20 nm by detuning the peak wavelength of optical feedback from the central wavelength of the modal gain. The study is based on modeling of the dynamics of multimode semiconductor laser subject to selective optical feedback. The model takes into account mechanisms of both self- and cross-modal gain suppression, and the study is concerned with the very-short external cavity that corresponds to stable continuous-wave (CW) operation.
... It should be noted that the pulses discussed in this letter are different from those in [17][18][19][20][21] which are also generated using an SL with EOF. In this paper, pulses refer to emissions of light characterised by a fixed duration and repetition frequency. ...
... In this paper, pulses refer to emissions of light characterised by a fixed duration and repetition frequency. In contrast, in [17][18][19][20][21], the pulses are harmonic oscillations of a continuous light intensity which corresponds to period one oscillation of the SL with EOF [22]. These two types of pulses have their own advantages and applications in other contexts. ...
In this study, the authors propose a novel technique for generating ultrashort pulses using a semiconductor laser subject to strong optical feedback from short external cavities. The influence of three system parameters, viz. the external cavity length, the injection current and the feedback strength on the characteristics of the ultrashort pulses is numerically investigated. The results show that the pulse width decreases and the pulse peak increases with increase of any of these three parameters. The repetition frequency of the ultrashort pulses decreases with increase of the feedback strength but increases with increase of the injection current. Based on these results, ultrashort pulses with a pulse width of 3.6 ps and a repetition frequency of 2.3 GHz have been achieved when the injection current is four times the threshold current. The pulse width can be further decreased and the repetition frequency can be further increased by appropriately adjusting the external cavity length and feedback strength. The results presented in this study open up a new route for designing ultrashort pulse generators for incorporation in future photonic integrated optical circuits.
... For some time, it has been considered a challenge to make a semiconductor laser oscillate at frequencies higher than its relaxation oscillation frequency. In a laser with Conventional Optical Feedback (COF), oscillations at a frequency inversely proportional to the External Cavity (EC) length can be obtained [25,[111][112][113][114][115]. Effort has been made on obtaining ultrashort cavities, which was achieved thanks to Distributed Feedback (DFB) lasers where the external cavity is integrated with the laser device [116] and oscillations at high frequency have been unlocked [117]. ...
... This different behavior is due to the fact that in COF, there are no self-pulsating ECMs as with PCF. Rather, the ECMs are SS solutions and the oscillating solutions observed are either excitation of the relaxation oscillations or oscillations at the EC frequency [113]. ...
Nous étudions l’influence d’une rétroaction optique à conjugaison de phase dans une diode laser. Ce type de rétroaction a été peu étudié et nous montrons ici qu’il donne des résultats intéressants, permettant de débloquer du contenu à haute fréquence. Cela pourrait mener à de meilleures performances dans des systèmes de génération de nombres aléatoires utilisant du chaos optique.
... In shorter devices the relative magnitude of the two main driving frequencies, the relaxation oscillation frequency (fRO) and the external cavity frequency (f ext ), can span both the shortcavity and long-cavity condition for such systems. A system is classified as being either short-cavity, when f RO is much less than f ext , or long-cavity, when f RO is much larger than f ext [13,14]. Traditional delayed optical feedback systems typically have external cavities of more than a few centimeters and therefore fall into the long-cavity regime (LCR) with f ext generally much less than the high frequency relaxation oscillations (several GHz to tens of GHz) which are characteristic of semiconductor lasers. ...
... A study of a 3-section device with integrated phase and amplifier sections also observed self-pulsations whilst tuning both the optical feedback phase and strength [23]. No chaotic outputs were observed in these devices due to the requirement of very high feedback levels to push a short cavity system into coherence collapse [14]. In order to target the growing number of applications of chaotic outputs, integrated devices with additional passive waveguides were developed to achieve longer cavity lengths suitable for producing chaotic signals [9]. ...
A 4-section semiconductor laser with integrated optical feedback has been shown experimentally to be capable of operating in either the short- or long-cavity regime, by controlling the device relaxation oscillation frequency relative to the external cavity frequency. Systematic increase of the laser injection current, and the resulting increase in relaxation oscillation frequency, allowed the transition between the two regimes of operation to be observed. The system displayed a gradual transition from a dynamic dominated by regular pulse packages in the short-cavity regime to one dominated by broadband chaotic output when operating in the long-cavity regime. This suggests that the “short cavity” regular pulse packages continue to co-exist with the “long cavity” broadband chaotic dynamic in the system studied. It is the relative power associated with each of these dynamics that changes. This may occur more generally in similar systems.
... This is achieved by introducing external perturbation through the reflection and partial reinjection of emitted light back into the laser cavity. Its practicality and efficiency in providing such perturbations are widely acknowledged [28][29][30]. ...
A novel method for the generation of an optical frequency comb (OFC) is presented. The proposed approach uses a laser diode with optical feedback and operating at a specific nonlinear dynamic state named periodic window. In this case, the laser spectrum exhibits a feature with a series of discrete, equally spaced frequency components, and the repetition rate can be flexibly adjusted by varying the system parameters (e.g., external cavity length), which can provide many potential applications. As an application example, a dual-OFC system for distance measurement is presented. The results demonstrate the system’s ability to achieve target distance detection, underscoring its potential for real-world applications in this field.
... The recent focus of high-speed DMLs has turned to multisectional structures that utilize the photon-photon resonance (PPR) effect [14], [15]. The interaction between the lasing and a nearby second mode can happen at a much higher frequency, thereby having the potential to drastically extend the smallsignal intensity modulation response [16], [17], [18], [19]. However, the intensity modulation response rapidly decays at the CPR tail, leading to a significant indentation between the PPR and CPR frequencies, which cuts off the bandwidth below PPR. ...
Conventional push-pull modulated (PPM) distributed feedback (DFB) lasers exploit structures with symmetry, which wastes a significant amount of the optical power output from the rear facet. To improve the power efficiency, PPM DFB lasers with asymmetrically coated facets can be considered. However, the resulted imbalanced push-pull modulation causes a dip in device small-signal intensity modulation response near the carrier-photon resonance (CPR) frequency, which distorts the waveform and even cuts off the bandwidth. This work proposes an asymmetric section length design in conjunction with the asymmetric facet coating to offset the aforementioned effect on device intensity modulation response. With a delayed push-pull modulation (DPPM) scheme further incorporated, our simulation result shows that the PPM DFB laser with optimized asymmetric structure can enhance the power efficiency and maintain a smooth modulation bandwidth up to around 50 GHz.
... Oscillations at f EC can also be obtained in laser diodes from the beating between two external cavity modes [150]. For short delays (τ ≪ 1/ f RO ), the system can reach therefore high frequencies [151]. With longer delays, harmonics of 2n+1 2 f EC have been reported in nonlinear optical cavities [149,152] and have been also observed in systems with OF [153,154]. ...
This thesis studied the dynamics of a laser diode subjected to a phase conjugate feedback (PCF). I analyzed both numerically and experimentally the evolution of the laser power, with speeds of the order of a few tens of GHz. First, I studied the chaotic signal generated by such a system, both by simulations and by experiment. Three indicators were considered: the chaos bandwidth, i.e. the range of frequencies over which the energy of the signal is distributed, the spectral flatness, which verifies that the energy is not concentrated on a single frequency, and the permutation entropy, which studies whether patterns are repeated in the signal. I observed that the chaos generated by such a system was both broadband (bandwidth of about 30 GHz) and complex (permutation entropy up to 0.994). Such chaos was observed over a wide range of experimental parameters, including the feedback strength, the feedback delay, or the laser pump current. Then, I study the very fast periodic phenomena previously observed with the PCF, the external cavity modes (ECM). The ECMs are regular self-pulsations of the laser power, at a frequency equal to a multiple of the frequency associated with the feedback delay. We extend previous experimental studies by varying the feedback strength, the feedback delay and the laser pump current. In particular, we observe experimentally two results that had only been numerically predicted. First, the ECMs are bistable, i.e. under the same experimental parameters they can have different frequencies. Secondly, we show that the frequency of the ECMs does not change significantly if we change the delay without varying the other parameters of the experiment. Finally, we study numerically the generation of square waves with phase conjugate feedback. We observe that the resulting dynamics are similar to those obtained with non-phase conjugate optical feedback.
... In contrast to the approach of spatial mode profile engineering to reduce the linewidth 9 , the optical confinement factor is fixed for the Fano BIC laser, and the reduction of the linewidth therefore does not compromise the laser threshold (Supplementary Note A.2). External cavity lasers are a well-known and commercially important approach to reducing laser linewidth. However, such devices are macroscopic in nature, as well as suffering from multimode effects that require external filtering and careful alignment [4][5][6][7][8] . The Fano BIC laser does not have these trade-offs and, as we have shown, can be scaled into the microscopic regime. ...
It is an important challenge to reduce the power consumption and size of lasers, but progress has been impeded by quantum noise overwhelming the coherent radiation at reduced power levels. Thus, despite considerable progress in microscale and nanoscale lasers, such as photonic crystal lasers, metallic lasers and plasmonic lasers, the coherence length remains very limited. Here we show that a bound state in the continuum based on Fano interference can effectively quench quantum fluctuations. Although fragile in nature, this unusual state redistributes photons such that the effect of spontaneous emission is suppressed. Based on this concept, we experimentally demonstrate a microscopic laser with a linewidth that is more than 20 times smaller than existing microscopic lasers and show that further reduction by several orders of magnitude is feasible. These findings pave the way for numerous applications of microscopic lasers and point to new opportunities beyond photonics. Quantum noise is suppressed by a bound state in the continuum (BIC) approach, enabling a microlaser with narrow linewidth compared to other small lasers.
... Similar effects have also been observed for laser diodes with a three-dimensional (3D) gain medium [27][28][29][30][31][32] as well as quantum-dash lasers under optoelectronic feedback [33,34]. As the deterministic generation mechanism of the periodic states lies within the locking of the internal and external frequency components and therefore requires them to be close together, these oscillations are different from the high-frequency oscillations occurring for short optical feedback [35], pure frequency oscillations [31,36], or noise-driven low-frequency oscillations [37,38]. Moreover, the analysis of the locking effect suggested that a high damping and a strong amplitude-phase coupling are * hausen@campus.tu-berlin.de ...
The influence of optical feedback on semiconductor lasers has been a widely studied field of research due to fundamental interests as well as the optimization of optical data transmission and computing. Recent publications have shown that it is possible to induce a periodic pulselike output in quantum-dot and quantum-well laser diodes based on the locking of the external cavity modes and the relaxation oscillation frequency. We present an in-depth analysis of this effect. We choose submonolayer quantum dots as a gain system, as these provide a relatively strong amplitude-phase coupling, which has proven to be very beneficial for these locking effects to occur. By introducing an alternative theoretical model, we can correctly reproduce the essential features of the gain system and validate them by comparison to our experimental results. From this starting point we can further explore how the staircase behavior of the oscillation frequency with increasing pump current can be influenced by changing various laser parameters. The staircase behavior is induced by a reordering of the Hopf bifurcations giving birth to the regular pulselike oscillations.
... Different approaches have been used in order to explain the dynamics of semiconductor lasers (SLs) in presence of OF, such as the delayed difference equation [50]- [52] or the compound cavity model [53], Lang and Kobayashi (L- K) model [6]. Refined investigation is followed on how the stationary state of the laser with feedback undergoes changes, loses its stability, and with growing feedback gives rise to more complicated behaviour again pushing the laser back to its stable monomode state by introducing the current modulation. ...
The back-reflection of emitted laser beam (optical feedback, also know as selfmixing ) from various external interfaces are sufficient to cause instability, and prohibiting its use in various fields such as communication, spectroscopy, imaging to name a few. So it is desirable to study the laser dynamics and the conditions causing it to be stable in spite of strong optical feedback. With the aid of mathematical formulation, simulation and backed by experimental evidences, it is demonstrated that the frequency deviation of the laser emission due to current (intensity) modulation alters the dynamic state and boundary conditions of the system such that even under large optical feedback strength, the laser may attain stability and retain single modal state. The frequency deviation resulting from former is shown to modify the phase of the system in opposite direction to that induced by the later, showing that there exists an optimal modulation current which compensates the effect of optical feedback and may be used to retain the laser in single modal stationary state. The method thus provides a methodology to avoid optical feedback-induced instability in semiconductor lasers by using the proper amplitude of current (intensity) modulation.
... Similar effects have also been observed for laser diodes with a three-dimensional (3D) gain medium [27][28][29][30][31][32] as well as quantum-dash lasers under optoelectronic feedback [33,34]. As the deterministic generation mechanism of the periodic states lies within the locking of the internal and external frequency components and therefore requires them to be close together, these oscillations are different from the high-frequency oscillations occurring for short optical feedback [35], pure frequency oscillations [31,36], or noise-driven low-frequency oscillations [37,38]. Moreover, the analysis of the locking effect suggested that a high damping and a strong amplitude-phase coupling are * hausen@campus.tu-berlin.de ...
The influence of optical feedback on semiconductor lasers has been a widely studied field of research due to fundamental interests as well as the optimization of optical data transmission and computing. Recent publications have shown that it is possible to induce a periodic pulsed like output in quantum-dot and quantum-well laser diodes utilizing the locking of the external cavity modes and the relaxation oscillation frequency. We present an in-depth analysis of this effect. We choose submonolayer quantum dots as a gain system, as these provide a relatively strong amplitude-phase coupling, which has proven to be very beneficial for these locking effects to occur. Introducing a new theoretical model we can correctly reproduce the essential features of the gain system and validate them by comparison to our experimental results. From this starting point we can further explore how the staircase behavior of the oscillation frequency with increasing pump current can be influenced by changing various laser parameters. The staircase behavior is induced by a reordering of the Hopf bifurcations giving birth to the regular pulsed-like oscillations.
... Отметим также работу [11] о бифуркациях коразмерности три, приводящих к сложной динамике в окрестности отдельной моды. Другой тип решений, соответствующий режиму биений двух мод внешнего резонатора, описан аналитически в работе [12,13]. ...
We study a model of single-mode semiconductor laser with the optical feedback. This model bases on DDE (Lang–Kobayashi model). With the help of local analysis methods we built a continuous set of quasinormal forms in the neighbourhood of critical values. The ability of coexistence of a large number of steady oscillating states is discussed.
... Various approaches towards P1 stabilization in optical feedback schemes have been reported, where P1 stabilization was achieved by reducing microwave linewidth and suppressing residual noise peaks. For instance, approaches using short-cavity optical feedback were numerically and experimentally demonstrated [32][33][34][35][36]. In these approaches, the cavity round-trip time was set to be shorter than the laser relaxation oscillation time. ...
Period-one (P1) oscillations in a semiconductor laser under optical feedback from a narrowband fiber Bragg grating (FBG) are numerically investigated. FBG feedback enhances the stability of P1 oscillations compared to the conventional mirror feedback in the form of P1 microwave linewidth and phase noise reduction and residual noise peaks suppression. In the proposed scheme, the FBG has a narrow bandwidth smaller than the laser relaxation oscillation frequency. Then it effectively suppresses the coherence collapse of the laser by filtered feedback. Hence it can keep the laser in P1 operation even under relatively strong feedback. Besides, a uniform FBG has a comb-filtered reflectivity spectrum with a main lobe surrounded by several side lobes. Hence it can limit the external cavity modes by each lobe. As a result, FBG feedback can reduce microwave linewidth and phase noise by sustaining stronger feedback power and improve side-peak suppression ratio (SPSR) by filtering external cavity modes. The effects of stabilization are enhanced by properly increasing grating bandwidth. By fine-tuning the feedback delay time, the microwave linewidth can be reduced to a local minimum which reveals the optimal locking between P1 frequency and one of the external cavity modes. Increasing the feedback delay time, the local minimum linewidth can be further reduced. FBG feedback reduces the microwave linewidth by up to more than an order of magnitude and improves the SPSR by up to more than two orders of magnitude than mirror feedback using the same delay time.
... In such photonic microwave oscillators, tunability over ∼10 GHz has been demonstrated [19]- [24]. Lasers with integrated optical feedback have been shown numerically and experimentally to generate periodic pulsating dynamics in [25]- [29]. These devices are fabricated to include two separate integrated phase tuning and amplifier sections that must be powered separately. ...
The stabilization of a relatively simple microwave oscillator tunable across the full X-band based on a laser subjected to optical feedback is achieved. Specifically, a resonance effect based on locking the two inherent dynamic frequencies of the system, as well as optoelectronic feedback are utilized to achieve a sub-ps jitter and typical phase noise in the range of –107 dBc/Hz at 10 kHz offset from an oscillation frequency that can be tuned from 5.5 to 12.1 GHz. Further, the microwave signal is extracted from the laser-diode injection terminals and eliminates the need for multiple lasers, radio-frequency filters, and external RF sources. This architecture therefore realizes a compact and low-cost microwave photonic oscillator.
... They are typically observed for sufficiently long external cavities (typically > 1 cm) and with moderate feedback strength. For shorter external cavities (for which the external cavity length is such that f RO τ ext ≪ 1), feedback-induced high-frequency self-oscillations (in the range of tens of GHz) have been reported as a result of a self-locking mechanism of two compound-cavity modes which have almost equal cavity losses [89]. Another intriguing nonlinear dynamics different from the LFF and which has been observed in the short external cavity configuration is the so-called regular pulse package (RPP): the light intensity exhibits a fast regime of high-frequency pulses in the GHz range intensity which are modulated by a relatively low-frequency signal (of hundreds of MHz) [90,91,92]. ...
Le laser à cavité verticale émettant par la surface (VCSEL ou Vertical-Cavity Surface-Emitting Laser) comporte des avantages compétitifs par rapport aux lasers émettant par le côté. Le VCSEL présente souvent deux modes de polarisation linéaire orthogonaux avec des fréquences et des gains optiques presque identiques. Dès lors, de faibles perturbations telles que des modifications du courant d injection ou de la température peuvent induire des basculements de polarisation. Toutefois, en utilisant un schéma d injection optique d un faisceau laser externe, il est possible de contrôler ces instabilités de polarisation. Nous nous intéressons au contrôle du basculement de polarisation, à la bistabilité de polarisation ainsi qu à la compétition des modes transverses d un VCSEL soumis à injection optique de polarisation orthogonale. En variant les paramètres d injection¡(puissance injectée et désaccord en fréquence entre le laser maître et le VCSEL), nous montrons que le basculement de polarisation implique des dynamiques non linéaires telles le mélange d ondes, le cycle limite, la résonance subharmonique ainsi qu une route de doublement de période vers le chaos optique. L analyse des bifurcations sous-jacentes permet de dresser une cartographie des dynamiques de basculement de polarisation du VCSEL. orthogonaux affecte la qualité de la synchronisation du chaos. Ces résultats sont intéressants dans le cadre du développement de liaisons de communication sécurisée par chaos optique. Dans notre thèse, nous étudions également la synchronisation du chaos de VCSELs dans un schéma de couplage unidirectionnel. Nous montrons que la compétition des modes de polarisation linéaire
... The pulsing frequency is determined by the feedback strength and delay time. The mechanism underlying this periodic dynamics has been explained as being a phenomenon of beating between stable and unstable steady state solutions and is specific to lasers in the short cavity regime [13], [26], [30], [31]. In this example, the pulsing frequency is represented by a sharp peak in the corresponding radio-frequency (RF) spectrum in Fig. 2(b.2) at 9.5 GHz. ...
We report a comprehensive experimental investigation of the nonlinear dynamics yielded in five photonic integrated circuits, each consisting of a semiconductor laser with optical feedback from a short external cavity. The external cavity lengths are different for each laser and range from 1.3 to 10.3 mm, allowing for analyzing the dependence of the dynamical scenario on the feedback delay time.We draw two-dimensional bifurcation diagrams and study the relative predominance of the different dynamics exhibited in each laser when the feedback strength and the laser injection current are varied. We identify that, in the commonly-termed short cavity regime, small variations of the external cavity length can result in totally different dynamical distributions, suggesting the possibility to use the feedback delay time as a means to control laser behaviors.
... Such a structure is equivalently an external cavity laser, which is capable of supporting single mode, dual mode, periodic oscillation mode and chaotic mode [12], depending on the feedback strength and phase, which can be adjusted via the control of IP and IA. For dual-mode applications, the mode separation scales with the feedback coefficient and reciprocal of the cavity roundtrip time [13]. To get a high mode beating frequency from the dual modes, a shorter cavity is required. ...
As a compact multi-functional device, monolithic integrated multi-section semiconductor laser has a wide range of applications in optical communication systems and microwave photonics with its advantages in cost, size, power consumption and integration possibilities with other components. In this paper, we will review the design and characteristics of monolithically integrated dual mode semiconductor laser, with special emphasis on amplified feedback lasers (AFL). Then, their application in optical clock recovery and high frequency photonic microwave generation will be discussed
... They are typically observed for sufficiently long external cavities (typically > 1 cm) and with moderate feedback strength. For shorter external cavities (for which the external cavity length is such that f RO τ ext ≪ 1), feedback-induced high-frequency self-oscillations (in the range of tens of GHz) have been reported as a result of a self-locking mechanism of two compound-cavity modes which have almost equal cavity losses [89]. Another intriguing nonlinear dynamics different from the LFF and which has been observed in the short external cavity configuration is the so-called regular pulse package (RPP): the light intensity exhibits a fast regime of high-frequency pulses in the GHz range intensity which are modulated by a relatively low-frequency signal (of hundreds of MHz) [90,91,92]. ...
Vertical-cavity surface-emitting lasers (VCSELs) have competitive advantages with respect to conventional edge-emitting lasers such as the fabrication of dense two-dimensional VCSEL arrays for optical interconnects. VCSELs exhibit intriguing polarization properties which are critical in polarization-sensitive applications. Polarization switching (PS) between two VCSEL's preferential orthogonal linearly polarized (LP) modes may be induced by changing the bias current, temperature or, externally, through orthogonally polarized optical injection. Depending on optical injection parameters, i.e., the injected power and the frequency detuning, injection-locking of the VCSEL can be achieved.
We contribute to the study of polarization bistability, polarization switching (PS), injection-locking and transverse mode competition in a VCSEL subject to orthogonal continuous-wave optical injection. We experimentally show and theoretically demonstrate that PS and locking may involve rich nonlinear dynamics including wave mixing, limit cycle, subharmonic resonances or a period-doubling route to chaos. In particular, we analyze the interplay between PS and the underlying nonlinear dynamics, and unveil its bifurcation mechanisms. Our study brings a new insight into the physics of polarization dynamics in externally-driven VCSELs.
Chaos synchronization of coupled VCSELs is also investigated. A feedback-induced chaotic light from the master VCSEL is unidirectionally injected into the slave VCSEL. We show that the synchronization quality can be significantly enhanced when chaos involves both orthogonal LP modes. This result is interesting for chaos communication schemes based on VCSELs.
... За последние 30 лет как численно, так и экспериментально обнаружен целый ряд новых сложных режимов генерации лазерных систем, обусловленных воздействием отраженного излучения на резонатор. В их числе отметим такие явления как колебания Петермана-Тейгера [8,9], регулярные импульсные пакеты [10,11], низкочастотные флуктуации [2,7,12,13], когерентный коллапс [2-4, 7, 12]. Глубокое понимание механизмов их возникновения открывает новые способы для управления режимами генерации, а значит, и новые возможности в приложениях. ...
1,2]. В первую очередь, это связано с их непосредственным прикладным значением. Однако эта причина не единственная. Как отмечено в [1], лазер принадлежит к числу систем, которые не только способны демонстрировать сложное поведение, но и более многих других пригодны для исследования общих закономерностей нелинейной динамики. Действительно, в целом ряде случаев лазе-ры функционируют в существенно нелинейных режимах. В наибольшей степени это замечание касается так называемой полуклассической теории лазера, которая пред-лагает целую иерархию нелинейных уравнений, надежно обоснованных с позиций квантовой электродинамики и количественно подтвержденных экспериментами. Особый класс моделей лазерных систем представляют собой модели, учи-тывающие воздействие запаздывающей оптической обратной связи. Их сложность обусловлена тем, что этот класс задач описывается в терминах дифференциальных уравнений с запаздыванием, которые обладают бесконечным числом степеней свобо-ды. Кроме того, динамические системы с запаздыванием демонстрируют различные типы неустойчивостей, обусловленные воздействием задержки. Например, для по-лупроводниковых лазеров с оптической обратной связью наблюдаются различные пути перехода к хаосу: квазипериодический [3], через каскад бифуркаций удвоения периода [4], сценарий Икеды [5], перемежаемость и кризис аттракторов [6, 7]. За последние 30 лет как численно, так и экспериментально обнаружен целый ряд новых сложных режимов генерации лазерных систем, обусловленных воздей-ствием отраженного излучения на резонатор. В их числе отметим такие явления как 167 колебания Петермана–Тейгера [8, 9], регулярные импульсные пакеты [10, 11], низко-частотные флуктуации [2, 7, 12, 13], когерентный коллапс [2–4, 7, 12]. Глубокое пони-мание механизмов их возникновения открывает новые способы для управления ре-жимами генерации, а значит, и новые возможности в приложениях. В таких областях, как хранение данных или оптические и оптоволоконные коммуникации отражения и связанные с ними сложные сопутствующие эффекты неизбежны. Например, искаже-ния сигнала при передаче данных нередко обусловлены неминуемыми отражениями от торцов волноводов. Поэтому изучение влияния оптической запаздывающей обрат-ной связи на работу лазеров разных типов представляет собой важную прикладную задачу. В настоящей работе предпринимается попытка математически упростить ис-ходные динамические уравнения с целью исследования феномена когерентного кол-лапса с новых позиций. Суть этого феномена заключается в дестабилизации лазера, приводящей к резкому уширению (в сотни и тысячи раз) спектра излучения. Как от-мечается в [2,3,12], состояние когерентного коллапса достигается, когда ток накачки заметно превосходит первую пороговую величину и интенсивность отраженного из-лучения достигает некоторого критического значения.
... Considering the fact that shortening the external cavity may obtain a higher M-B oscillation frequency [24], [25], we designed a short cavity AFL recently. This type of AFL can be used to generate dual wavelength output with wide frequency separation, as well as a chaos output with broad bandwidth. ...
The dynamics of monolithically integrated amplified feedback lasers (AFL) is investigated through numerical simulation and experimental verification. The period-doubling route to chaos and high-frequency microwave generation are demonstrated through simulation. Then, we design and fabricate monolithically integrated AFLs. Mappings of dynamic states and oscillation frequency in the parameter space of phase section current $I_{rm P}$ and amplifier section current $I_{rm A}$ are depicted. For relative small $I_{rm A}$, the period doubling evolution to chaos is presented with the increase of $I_{rm P}$ . For the relative large $I_{rm A}$, a high-frequency mode-beating (M-B) pulsation can be observed under suitable value of $I_{rm P}$. The oscillation frequency of period-one is about 10 GHz and the frequency of M-B pulsation is over 40 GHz for the device with a total length of 780 μm.
... This is shown in figure 4.1, below. Other theoretical analysis of short external cavity diode lasers [65,247] predict similar behaviour with the addition of regions of high frequency oscillations for cavity lengths approaching the condition for suppression of coherence collapse. ...
... Former works have already proposed numerical studies and experimental observations of oscillation resonance due to carrier relaxation in semiconductor lasers 15,16 or due to optical feedback in coupled cavity. 17 This phenomena leads to an output self-pulsation allowing to generate an optical modulation enhanced by a resonance effect. In our laser, an important optical modulation at the characteristic relaxation frequency is observed both in the time domain using a real time oscilloscope with a wide bandwidth up to 4 GHz and simultaneously in the frequency domain using an electrical spectrum analyzer. ...
We propose in this communication an experimental study of the relaxation
oscillations behavior in mode-locked lasers. The semiconductor self-pulsating
laser diode is composed by two gain sections, without saturable absorber. It is
made of bulk structure and designed for optical telecommunication applications.
This specific device allows two different regimes of optical modulation: the
first one corresponds to the resonance of the relaxation oscillations and the
second one, to the mode-locking regime at FSR value. This singular behavior
leads us to characterize the self-pulsations which are coexisting in the laser
and to describe two regimes of output modulation: the first one appears thanks
to the resonance of the oscillation relaxation and the other one corresponds to
the FSR of the Fabry-Perot laser at 40 GHz.
Recent advances in monolithically integrated multi-section semiconductor lasers (MI-MSSLs) have propelled microwave photonic (MWP) technologies to new potentials with a compact, reliable, and green implementation. Much research has examined that MI-MSSLs can realize the same or even better MWP functions compared to discrete lasers by taking advantages of enhanced light–matter interactions. Here, we review these recent advances in this emerging field and discuss the corresponding photonic microwave applications. Three main kinds of MI-MSSL structures are demonstrated in general including passive feedback laser, active/amplified feedback laser, as well as monolithically integrated mutually injected semiconductor laser. The focus of this paper is on the MWP techniques based on the nonlinear dynamics of MI-MSSLs. The primary MWP applications considered in this paper cover from electro-optic conversion characteristics enhancement, photonic microwave generation, microwave photonic filter, to multi-wavelength laser array for wavelength division multiplexing radio-over-fiber (WDM-RoF) networks. Especially, the four special dynamic states of free-running oscillation, mode-beating self-pulsations (MB-SPs), period-one (P1) oscillation, and sideband injection locking are considered and demonstrated in detail for photonic microwave generation. We also take a look at the future prospects of the research directions and challenges in this area.
The chapter focuses on ultra-fast light sources for achieving small footprint and lower-power-consumption optical transceivers and covers various important light sources such as directly-modulated diode lasers with high optical-gain materials, low chirp externally-modulated diode lasers, and ultra-fast diode lasers with new structure and modulation scheme. The chapter starts with an in-depth theoretical treatment of key characteristics and dependences, illustrates typical realizations of ultra-fast diode lasers and integrated laser-modulators, and includes relevant operation and performance characteristics as well. In response to strong demand for datacom and access network applications selected variants of edge emitting transmitters are presented with particular emphasis on spectral and bandwidth efficiency.
We report on a bifurcation mechanism following which an external-cavity laser diode emits regular oscillating output power at a high frequency. This frequency does not vary with the external-cavity length and it can be adjusted by varying the feedback strength. We observe this phenomenon numerically by investigating the external-cavity modes generated by a semiconductor laser subject to a phase-conjugate optical feedback. Particularly, we explore the effects of both the feedback rate and the time delay induced by the feedback on the frequency of the external-cavity modes. Counterintuitively, we evidence that having a short cavity does not necessarily yield oscillations at higher frequencies. We show that the key parameter in order to generate high-frequency solutions is the feedback rate. This parameter fixes the frequency of the solutions obtained independently of the time delay. We finally relate our observations to Hopf bifurcation phenomena.
Common applications using optical chaos in a semiconductor laser include, among others, random number generation and chaos-encrypted communications. They rely on chaos of high dimension with a large bandwidth and a high entropy growth rate to achieve good results. Optical chaos from a semiconductor laser with conventional optical feedback (COF) is typically used as the primary source of chaos. Additional enhancing techniques are used to enlarge the chaos bandwidth. In this contribution, we show experimentally how using phase-conjugate feedback (PCF) can naturally produce a chaos of higher bandwidth than COF. PCF is an alternative to COF which consists of feeding the conjugate of the optical output back into the laser cavity, with a time-delay. Thanks to an oscilloscope with a fast sampling rate, and a large bandwidth, we were able to measure and observe the time-resolved frequency dynamics with a good precision. In the regime of low-frequency fluctuations (LFF), where dropouts of optical power occur randomly, we were able to compare the difference in dynamics before and after a dropout, for PCF and COF. In the range of attainable reflectivities, we measured a bandwidth increase of up to 27 % with PCF when compared to COF. Interestingly, we found that high-frequency dynamics are enabled before dropouts in PCF, where it was theoretically shown that the system jumps between destabilized self-pulsing states at harmonics of the external-cavity frequency, the so-called external-cavity modes (ECMs). This observation tends to confirm that ECMs in PCF are indeed fundamentally different than ECMs in COF, where they are simple steady-states. Finally, we believe that the enhancing techniques used with COF could also be used with PCF to obtain even wider chaotic bandwidths. These results could lead to studies about the dimension and the entropy growth rate of chaos from a laser diode with PCF.
Modulation bandwidth enhancement of an optically controlled single-mode semiconductor laser is achieved by introducing an external cavity into the laser. A calculation based on a rate equation model shows that the 3-dB bandwidth of the optically controlled external cavity laser (OC-ECL) can be substantially enhanced by controlling the feedback light intensity and phase properly. A broad 3-dB bandwidth of 59 GHz is experimentally confirmed by using the fabricated OC-ECL. The results suggest that a combination of cross-gain modulation and photon–photon resonance is suitable to enhance the modulation bandwidth of semiconductor lasers.
This work investigates DFB-Lasers with short integrated optical feedback and applications of these components for optical signal processing. For the first time DFB-Lasers with passive and active optical feedback are fabricated and experimentally analyzed.
The objective is to realize devices with stable selfpulsations with frequencies in the range of 40 GHz.
Stable, frequency-tunable selfpulsations (12 bis 45 GHz) can be adjusted in DFB-Lasers with short amplified feedback. Numerical models are applied to understand the self-stabilizing effect of the high frequency pulsations induced by the additional carrier density in the feedback.
The locking properties of the 40 GHz selfpulsation to an external optical signal are analyzed with the help of a linear locking theory known from electronical oscillators. The locked selfpulsation can be used for all-optical clock recovery. An experiment, where the all-optical clock recovery is used to drive a 160 Gb/s to 40 Gb/s demultiplexer, qualifies the developed device for system application.
This paper presents the results revealing the influence of the nonlinear gain on the stability limit of a semiconductor laser (SL) with external optical feedback (EOF). A new system determinant is derived from the original Lang and Kobayashi (L-K) equations. By making analysis on the locus of the roots of the system determinant, the stability limit of the system is obtained, from which a number of important and interesting phenomenon revealed by the nonlinear gain is uncovered. The correctness of results is verified by numerical simulations.
We report experimentally on the bifurcation cascade leading to the appearance of self-pulsation in a photonic integrated circuit in which a laser diode is subjected to delayed optical feedback. We study the evolution of the self-pulsing frequency with the increase of both the feedback strength and the injection current. Experimental observations show good qualitative accordance with numerical results carried out with the Lang-Kobayashi rate equation model. We explain the mechanism underlying the self-pulsations by a phenomenon of beating between successive pairs of external cavity modes and antimodes.
In dieser Arbeit werden zwei nichtlineare Phänomene untersucht, Multistabilität durch verzögerte Rückkopplung und Synchronisation von quasiperiodischen Oszillationen. Dies geschieht mit Hilfe von Halbleiterlasern und auf dem selben Chip wie der Laser integrierter ultrakurzer optischer Rückkopplung. Verzögerte Rückkopplung ist unter anderem die Ursache für das Phänomen der Faltung von Lasermoden, und damit für das Auftreten von mehreren möglichen Laserzuständen für die selben Parameter. Ein tristabiles Regime von Dauerstrichzuständen kann im Experiment für mehrere breite Parameterbereiche der Rückkopplung beobachtet werden. Sehr nahe der Laserschwelle wird einer der Laserzustände durch den stabilen ``aus''''-Zustand ersetzt. Theoretische Betrachtungen im Rahmen des paradigmatischen Lang-Kobayashi Models verzögerter Rückkopplung ermöglichen eine in sich konsistente Interpretation der experimentellen Ergebnisse. Neben der Beeinflussung des stationären Verhaltens eines Halbleiterlasers kann verzögerte Rückkopplung Instabilitäten in der Laseremission hervorrufen. Abhängig von Rückkoppelstärke und -phase werden zwei verschiedene Intensitätspulsationen des emittierten Lichtes beobachtet. Synchronisationsprozesse solcher Pulsationen wurden von mir in einem System von zwei verschiedenen gekoppelten Multisektionslasern untersucht. Periodische Selbstpulsationen von Laser 1 werden hierfür in Laser 2 injiziert, welcher sich in einem Regime quasiperiodischer Intentensitätspulsationen mit zwei fundamentalen Frequenzen befindet. Das Experiment zeigt eine neue Art von Übergang zu synchronem Verhalten, welche kürzlich mit Hilfe von gekoppelten generischen Phasen- und van der Pol Oszillatormodellen aufgedeckt wurde. Desweiteren konnten bislang unerforschte Prozesse des Kohärenzübertrags auch zu nichtsynchronisierten Oszillationen beobachtet werden.
One particularity of semiconductor lasers is their low tolerance to optical feedback, which can be of disadvantage for technological applications. For example, to use semiconductor lasers as transmitters in optical networks, expensive optical isolators are needed to avoid back reflections that can lead to temporal instabilities of the lasers (coherence collapse).
We report a direct, modulated bandwidth enhancement in a amplified feedback laser (AFL), both experimentally and numerically. By means of fabricated devices, an enhanced −3 dB bandwidth of 27 GHz with an in-band flatness of ±3 dB is experimentally confirmed at 13 °C. It is numerically confirmed that the modulated bandwidth of the AFL can be enhanced to two times its original bandwidth, with more controlled flexibility to realize a flat, small-signal response.
Extreme intensity pulses sharing statistical properties similar to rogue waves have been recently observed in a laser diode with phase-conjugate feedback [A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 38, 703 (2013)], but remain unexplained. We demonstrate here that a rate equation model of a laser diode that includes an instantaneous phase-conjugate feedback field reproduces qualitatively well the statistical features of these extreme events as identified in the experiment, i.e., the deviation of the intensity statistics to a Gaussian-shape statistics and the statistics of the time separating extreme events. The numerical simulations confirm the importance of the feedback strength in increasing the number of such extreme events and allow us to explain how extreme events emerge from a sequence of bifurcations on self-pulsating solutions, the so-called external cavity modes.
Thanks to the band-gap engineering of quantum confined semiconductor materials and the development of semiconductor-based saturable absorber mirrors, recent years have seen the development of compact and low-cost external-cavity laser diodes generating pulses at several tens of GHz. The physics of the bifurcation leading to selfpulsation leads however to an intrinsic limitation: the fundamental repetition rate is fixed to and limited by the externalcavity round-trip time. By contrast, we demonstrate here that an external-cavity diode laser may generate fundamental self-pulsating dynamics at harmonics of the external-cavity frequency, when a phase conjugate mirror replaces the conventional mirror. As is known from theory, a laser diode with phase conjugate external feedback supports a single stationary solution that bifurcates to self-pulsating dynamics of increasing frequency when increasing the amount of light reflected back to the laser diode. The self-pulsation frequency then increases in step of the external-cavity frequency as one increases the feedback strength. We provide here the first experimental evidence of such harmonic external-cavity fundamental self-pulsation. As a proof-of-concept, we generate experimentally a self-pulsating dynamics at twice and three times the fundamental external-cavity frequency using an edge-emitting laser with a self-pumped ring-cavity photorefractive phase conjugator. Numerical simulations also predict stable higher harmonics.
We study the system of delayed differential equations modeling the dynamics of semiconductor laser with optical feedback (Lang-Kobayashi model). In the case of instability of external cavity modes we derive the ensembles of quasi-normal forms which appear to be the parabolic (or degenerate parabolic) partial differential equations for slowly varied amplitude of the electric field. Coexistence of a large number of multi-frequency oscillatory regimes is discussed.
A tunable two-section amplified feedback laser, which employs an amplifier section as the integrated feedback cavity, is designed and fabricated for dual-mode operation with mode separation of 100 GHz. Detailed simulations and experimental characterizations on the performance of the laser are presented. Promising dual-mode emission with continuous tuning range over 16 GHz (87.41-103.64 GHz) is experimentally demonstrated.
In this paper, a novel lowpass filter using defected ground structure (DGS) with a stopband up to 40GHz is realized using Rogers RT5880 substrate ( thickness = 0.508 mm). The filter is combined with two parts, the top single microstrip and the bottom DGS. The simulated and measured results show the great stopband performance of this filter. The passband of this lowpass filter is from 10 MHz to 4.85 GHz, with the typical insertion loss of 0.6 dB and the minimum return loss of 30 dB, while the stopband starts from 5.2 GHz to 40 GHz and all S21 is below −23dB. Compared to other lowpass filter, this filter has an ultra-wide stopband in the same size (80mm * 10mm) and is realized only by DGS rather than modifying the top microstrip.
A monolithic semiconductor laser, which can generate high frequency mode-beating over 100GHz, is reported. This laser employs a semiconductor optical amplifier (SOA) as the integrated feedback cavity of a complex-coupled distributed feedback laser (DFB). Stable dual-mode emission, with low strength difference is demonstrated. Mode-beating frequency of this laser can be tuned from 87.41 to 103.64 GHz, when the currents injected into each laser section are adjusted. In all frequency range, the strength difference of two main modes is smaller than 10 dB and the strength of the other side mode is 20 dB lower than the two main modes.
We analyze the regime of strong perturbation in a laser diode subjected to delayed optical feedback (DOF) from an external reflector, and study the intermediate region between short and long cavities, using Lang and Kobayashi equations to follow the dynamic regimes of the DOF system. We find that well-known regimes of unperturbed oscillations, period one, multi-periodic, and chaos are dictated by interplay of coupling factor K, distance L, and phase $Phi ({rm mod}.2pi)$ of the external reflector, and linewidth enhancement factor $alpha$. We plot the boundaries of different regimes in the ${rm K}hbox{-}Phi$ plane for several values of L and $alpha$, and characterize them in the transition from very short cavity $({rm L}<0.01~{rm L}_{{rm fr}})$ with negligible high-level effects, to long cavity $({rm L}=0.5~{rm L}_{{rm fr}})$ where the ${rm K}hbox{-}Phi$ plane is almost completely filled with chaos. We show that chaos and periodicity regimes are only found at ${rm C}>1$, though for ${rm C}<1$ the DOF system is also subject to self-mixing perturbations. Self-mixing induced FM and AM of the optical signal are found in all regions of stable oscillations, and for ${rm C}>1$ frequency switching occurs at a certain $Phi$mula> for any K and L. Chaos develops at increased K and L in correspondence to loci of frequency switching.
We present a new method to generate short optical pulses with repetition
rates from 20 to beyond 100 GHz based on the injection technique. No
electrical modulation current is required. The light injection from one
continuous wave (CW) operated multi quantum well (MQW)-DFB-laser into
another generates stable sinusoidal laser pulses. Transmission of the
pulses over a dispersion shifted fibre (DSF) generates solitons with the
desired pulse width and a time bandwidth product of 0.315.
The radiation stability of an injection laser with an external cavity under both CW and continuous lasing conditions is investigated theoretically and experimentally.
Semiconductor lasers, also denoted as laser diodes, are a key element in an increasing number of optoelectronic systems. The performance of these systems strongly relies on the performance of their component laser diodes. As an example, Fig. 1.1 shows a simple optical fibre communication system in which the laser diode converts electrical signals into optical signals, which are transmitted by an optical fibre and finally received by a photodiode.
First Page of the Article
Results of a numerical analysis of the stability of external cavity lasers with short external cavities are presented. If the external cavity is shorter than about 5 mm (air equivalent), the laser remains stable for any feedback from that cavity without any coherence collapse. The results can be considered also as guidelines for the design of laser diodes with integrated passive cavities.< >
We have measured the effects of feedback on the spectra of 1.5-μm DFB lasers from feedback power ratios as low as -80 dB up to -8 dB. Five distinct regimes of effects are observed with well defined transitions between them. The dependence of these effects on the distance to the reflection is also investigated.
The effect of external optical feedback on resonant frequency, threshold gain, and spectral linewidth of distributed feedback (DFB) semiconductor lasers is theoretically analyzed. The analysis applies to any type of laser cavity formed by a corrugated waveguide limited by partially reflecting facets. It is shown that the sensitivity to optical feedback on a facet is closely related to the power emitted through this facet. Numerical results on wavelength selectivity and on sensitivity to optical feedback are given for conventional DFB lasers having an AR-coated facet and for quarter-wave-shifted (QWS) DFB lasers with AR-coatings on both facets. Both laser types are found to be more sensitive to optical feedback on their AR-coated facet than Fabry-Perot lasers for low kL . On the other hand, QWS-DFB lasers are found to be relatively insensitive to optical feedback for large kL .
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.
Line broadening up to 25 GHz in a single-mode semiconductor laser with relatively strong optical feedback is reported and theoretically analyzed. Measurements of the coherence function were performed using a Michelson interferometer and demonstrate that the coherence length decreases by a factor 1000 (to approximately 10 mm) due to optical feedback. A self-consistent theoretical description is given, which is based on the view that coherence collapse is maintained due to optical-feedback-delay effects, in which quantum fluctuations play no role of importance. A connection with recently suggested chaotic behavior is made. The theoretical results obtained are in good qualitative and reasonable quantitative agreement with measurements.
A detailed theoretical analysis of stability is presented for a semiconductor laser in an external cavity. The limits of stable operation are determined as a function of the external cavity parameters and the linewidth enhancement factor α. Instability is related to jumps of the laser frequency between external cavity modes (frequency bistability) or to feedback-induced intensity pulsations due to the carrier density dependence of the refractive index. The limit of bistability is derived from the steady-state solutions of the rate equations and the intensity pulsation limit is obtained from a small-signal analysis. This analysis also gives the location of zeros in the system determinant and the resulting FM noise spectrum. For practical applications we emphasize the determination of the stable tuning range for the phase in the external cavity and the classification of the possible types of instability for various feedback levels.
The effect of external optical feedback on the linewidth of a single-mode injection laser is considered theoretically. A set of three rate equations with Langevin noise sources is used to obtain the power spectrum. If the high-frequency structure in the power spectrum is ignored, the line shape is Lorentzian and exhibits broadening or narrowing depending on the external-cavity phase shift. Particular attention is paid to the line narrowing after including the effect of carrrier-induced index changes.
Theory and experiments on optical feedback effects in index-guided single-mode semiconductor lasers are presented. Evidence is found for the existence of a characteristic parameter C which indicates the relative strength of the optical feedback. Near the transition (C approximately equals 1. 0) from low to high feedback, the feedback-induced low-frequency intensity noise shows a maximum. At higher feedback hysteresis and instabilities are dominant, whereas the feedback-induced noise is low again.
Influences on the semiconductor laser properties of external optical feedback, i.e., return of a portion of the laser output from a reflector external to the laser cavity, have been examined. Experimental observations with a single mode laser is presented with analysis based on a compound cavity laser model, which has been found to explain essential features of the experimental results. In particular, it has been demonstrated that a laser with external feedback can be multistable and show hysteresis phenomena, analogous to those of non-linear Fabry-Perot resonator. It has also been shown that the dynamic properties of injection lasers are significantly affected by external feedback, depending on interference conditions between returned light and the field inside the laser diode.
An investigation was made of the nonlinear interaction between spectral modes in an injection laser with external resonator which had two resonant feedback channels. These channels were provided by diffraction gratings used as tunable selective elements. The emission occurred at two wavelengths and, in addition to the usual competition due to the interaction of the fields via the population inversion, there was an interaction which depended on the magnitude and sign of the spectral separation between the modes. When this separation was 1 nm or less the long-wavelength mode was emitted preferentially. The anomalous competition was attributed to the parametric interaction between the modes.
The results of a linear analysis of stationary generation
stability for short external cavity laser diodes in a wide range of
coupling coefficients, with the effect of external cavity mode beating
being taken into account, are presented. Besides the coherence-collapse
transition, high-frequency instability due to mode interaction is
revealed and investigated. The results of linear theory are confirmed by
computer simulations. They may be considered as guidelines for the
design of high-speed laser diodes with integrated passive cavities
The authors present a detailed theoretical and experimental
investigation of the nonlinear dynamics of a semiconductor laser with
optical feedback. The results show that the coherence collapsed state is
a chaotic attractor and that chaos is reached for increasing feedback
level through a quasi-periodic route interrupted by frequency locking.
Furthermore, the coexistence of two attractors, associated with the same
external cavity mode, but having different relaxation oscillation
frequencies, is demonstrated and explained
A simple analytic expression for the critical feedback level,
above which a semiconductor laser becomes unstable, is derived. This
tolerable feedback level increases with increasing damping of the
relaxation oscillations. Good agreement is found between the analytic
expression and numerical evaluations of the rate equations
The effect of external feedback on a single-mode semiconductor
laser is estimated by a numerical solution of the nonlinear rate
equations. The analysis yields an excellent description of published
experimental results. It is found that the lasing mode with the minimum
linewidth is most stable rather than the mode with minimum threshold
gain. The transition to the coherence-collapse regime is of particular
interest. It usually occurs for feedback fractions ≈10<sup>-4</sup>,
but it can be shifted to considerably larger feedback levels either by
increasing the emitted optical power or the laser length or by
decreasing the linewidth enhancement factor α
Chaos in semiconductor lasers with optical feedback: Theory and experiment
- J Mørk
- B Τromborg
- J Mark