We present an experimental and theoretical study of optical feedback in a semiconductor laser for the case of an extremely short external cavity (EC) configuration. When the length of the EC is changed both the output power and the voltage drop onto the laser are modulated with a period of half of the solitary laser wavelength. We also perform modulation experiments in which the EC length is modulated with amplitude corresponding to the half of the solitary laser wavelength and with different signal shapes. In this way we prove that by using optical feedback we are able to detect very small features. Such detection is of general interest from an application point of view, e.g. for optical data readouts, resulting in a reduced number of optical components. Optical feedback also affects the frequency of the laser light and results in a longitudinal mode hopping. With increasing the EC length we observe mode hops between neighboring solitary laser modes followed by large jumps at the EC frequency splitting. These large EC mode hops can be exploited for broad band frequency tuning of the emitted light. We also study the dependence of the amplitude and the period of the EC mode hops on the EC length. We reveal the existence of a cut-off EC length of a few micrometers for which the amplitude of the EC mode hops reaches a maximum and then strongly decreases. We give a theoretical explanation of our experimental findings based on Fabry-Perot resonant condition for coupled cavities.
We study the influence of delayed optical feedback from a short external cavity on the emission dynamics of semiconductor lasers using the Lang and Kobayashi rate equation model. We present the bifurcation scenario leading to regular pulse packages (RPP) and give examples of bistability between RPP and time-periodic or
steady state solutions. We investigate the change of the shape of the envelope of RPP in the transition to LFF. We analyze regions of feedback parameters for which RPP occurs. Detailed mapping shows that with increasing the delay time the windows of RPP broaden, merge and finally shrink when approaching the relaxation oscillation
(RO) period. In such a way the largest region of RPP occurs for delays around half of the RO period of the solitary laser. Moreover, the period of RPP also possesses a minimum as a function of the delay time corresponding to approximately the half of the RO period. For smaller delays the RPP period shows an oscillatory behavior
with the delay which we identify as being due to the destabilization of the RPP in the vicinity of newly born external cavity modes. Furthermore, we reveal continuous increase of the period of the RPP with the feedback rate. Finally, we study the scaling of the frequency of the pulse package envelope with the injection current. Our results contribute to better understanding of the origin and the peculiarities of the RPP dynamics.
Semiconductor lasers can be used simultaneously as optical sources
and optical sensors, as they are extremely sensitive to a small
amount of coherent optical feedback. We present a survey on experimental results on optical feedback in semiconductor lasers
and on different approaches to describe its effect on the laser
properties. We show that for long and moderate long external
cavities (hundreds of meters down to centimeters) the Lang-Kobayashi delay model, multiple delays and multimode delay rate equation models are in very good agreement with experiments on edge emitting lasers (EELs) and vertical-cavity surface-emitting lasers (VCSELs). We present examples of frequency and polarization mode hopping, periodic and quasiperiodic behavior, different routes to chaos, regular pulse packages, high frequency pulsations and stochastic and coherence resonance, that all have been experimentally and numerically demonstrated. Suitable models for studying laser diodes subject to optical feedback from extremely short external cavity, or ESEC (of the order of the wavelength) are the composite cavity and the multimode butt coupling models that either consider the field
amplitudes after multiple reflections in the external cavity (EC)
as stationary or treat the whole compound cavity at once. Numerical and experimental studies showed that optical feedback in ESEC leads to detectable change of the laser output power or the voltage drop over the laser for a small change of either the phase or the optical feedback strength. As an example, we discuss experimental and numerical results on spectral and polarization properties of VCSELs subject of insensitive optical feedback from ESEC. The wavelength and the current of polarization switching between the two linearly polarized fundamental modes of the VCSEL are periodically modulated with the external cavity length. High contrast polarization switching is thus possible for quarter-wavelength change of external cavity length. In the case of EEL we experimentally demonstrate that with changing the length of the EC the emitted power, the wavelength and the laser voltage are periodically modulated. We explain the longitudinal mode-hopping between the neighboring composite cavity modes followed by large jumps at the external cavity frequency splitting as a result of the spectral modulation of the effective losses of the composite cavity system.
We have recently unveiled a new dynamics in Vertical-Cavity Surface-Emitting Lasers (VCSELs), induced by a time-delayed optical feedback [M. Sciamanna et al., Opt. Lett. 28, 1543-1545 (2003)]. The optical feedback is responsible for multiple polarization switchings as we increase the injection current. If the current is fixed close to a switching point, the VCSEL exhibits a bistable regime: the laser randomly hops between the two VCSEL linearly polarized (LP) modes, this mode hopping being driven by the laser spontaneous emission noise. Each hop is accompanied by delayed feedback induced instabilities such as rapid anticorrelated oscillations in the intensities of the two LP modes at the frequency of the external cavity (EC). These rapid delay-periodic oscillations therefore complement the slow polarization bistable mode-hopping. Here we summarize our previous theoretical and experimental conclusions and we report on further statistical studies of this optical feedback induced polarization mode-hopping in VCSELs. Interestingly, we show that the addition of an optimal amount of noise on the VCSEL injection current may give rise to coherence resonance. When the noise intensity is optimal, the delay-periodic oscillations in the VCSEL mode-hopping regime exhibit a maximal regularity, i.e. the VCSEL exhibits a sequence of regular pulses at the EC frequency. This almost periodic signal is generated by the interaction between the time-delay and the noise driven mode-hopping dynamics, without the need for an external periodic signal. Our results contribute to recent investigations of coherence resonance in non excitable systems and give evidence of coherence resonance in a realistic, optical bistable system with time-delay, that is, a mode-hopping VCSEL subject to optical feedback.
Vertical-cavity surface-emitting lasers have shown similar sensitivity to optical feedback as conventional edge-emitting
lasers, but new interesting phenomena can be observed due to the coexistence of two linearly polarized (LP) fundamental modes. We report on new dynamic effects in VCSELs induced by polarization insensitive optical feedback from a distant mirror, namely the appearance of low frequency random hops between the two LP modes in a nominally stable LP solitary laser. This behavior resembles that of the mode hopping in a solitary VCSEL close to its polarization switching point. However, a careful observation shows that superimposed on the low frequency polarization mode-hopping, fast oscillatory behavior at a frequency close to the external-cavity frequency appears. A complementary study of the polarization
resolved optical spectra reveals jumps between several peaks identified as external cavity modes. We analyze the dynamics using a two-mode rate equation model with delay and noise. We numerically observe polarization mode-hopping in good qualitative agreement with our experimental findings. In particular, the low-frequency hops are complemented with fast oscillations at a frequency close to the external-cavity one and the calculated optical spectra reveal the presence of a limited number of ECMs in each LP-comb. This indicates that the dynamics is created by the interplay of noise, bistability
and optical feedback. We will further discuss the effect of noise on delayed bistable laser systems in the context of new dynamical concepts, like coherence resonance and stochastic resonance.