Parameters Controlling Optical Feedback of Quantum-Dot Semiconductor Lasers

A simple model to describe the dynamics of a single mode semiconductor laser subject to a coherent optical feedback is proposed in 1980 by Lang and Kobayashi (LK). Feedback loop depends on external mirror and creates a passive external cavity, which is explicitly taken into account via the complex delayed electric field variable ( )   E t fed back into the laser. The round trip time is the main feature of the LK model of the laser beam. The LK model has open the door to a very complex dynamics since the system phase space has infinite dimensions and sustain a chaotic regime [1]. Optical feedback consist of two subjects, coherent and incoherent feedback, depending on whether the coherence time of the laser light is larger or smaller than the delay time (τ) respectively [2]. There are five distinct regimes that are defined by the level of the feedback power ratio, this is discusses in section 2. The great importance for dynamics of semiconductor lasers with optical feedback is due to the potential applications of such lasers for secure communications by means of chaotic synchronization. External perturbations such as injected signal, feedback, or pump current modulation are required to achieve a chaotic output. From a practical point of view, optical feedback provided by a back reflecting mirror is one of the simplest ways to achieve chaotic oscillations from a semiconductor laser, even weak optical feedback leads to complex dynamics. In particular, it can sustain a chaotic regime of low-frequency fluctuations with sudden irregular intensity dropouts followed by a gradual intensity recovery [6].


Introduction
A simple model to describe the dynamics of a single mode semiconductor laser subject to a coherent optical feedback is proposed in 1980 by Lang and Kobayashi (LK). Feedback loop depends on external mirror and creates a passive external cavity, which is explicitly taken into account via the complex delayed electric field variable ()   Et fed back into the laser. The round trip time is the main feature of the LK model of the laser beam. The LK model has open the door to a very complex dynamics since the system phase space has infinite dimensions and sustain a chaotic regime [1]. Optical feedback consist of two subjects, coherent and incoherent feedback, depending on whether the coherence time of the laser light is larger or smaller than the delay time (τ) respectively [2]. There are five distinct regimes that are defined by the level of the feedback power ratio, this is discusses in section 2. The great importance for dynamics of semiconductor lasers with optical feedback is due to the potential applications of such lasers for secure communications by means of chaotic synchronization. External perturbations such as injected signal, feedback, or pump current modulation are required to achieve a chaotic output. From a practical point of view, optical feedback provided by a back reflecting mirror is one of the simplest ways to achieve chaotic oscillations from a semiconductor laser, even weak optical feedback leads to complex dynamics. In particular, it can sustain a chaotic regime of low-frequency fluctuations with sudden irregular intensity dropouts followed by a gradual intensity recovery [6].
To improve semiconductor laser performance, a nanoscale active region, in the form of twodimensional quantum wells (one degree of freedom), one-dimensional quantum wires (two degrees of freedom), or zero-dimensional quantum dots (three degrees of freedom) are used [3]. Since quantum dot (QD) semiconductor materials have discrete energy subbands, one could expect symmetric emission lines, then the subject of great current interest is a sensitivity of QD semiconductor lasers to optical feedback [4]. QD lasers acquired more importance after significant progress in nanostructure growth by self-assembling technique. The first demonstration of a QD laser with low threshold current density was reported in 1994 [5]. A QD laser emits at wavelengths determined by the energy levels of the dots, rather than the bandgap energy. Thus, they offer the possibility of improved device performance and increased flexibility to adjust the wavelength. They have the maximum material and differential gain, at least 2-3 orders higher than QW lasers [6]. A QD laser is a semiconductor laser that uses QDs as the active laser medium in its light emitting region. Due to the tight confinement of charge carriers in QDs, they exhibit an electronic structure similar to atoms. Lasers fabricated from such an active media exhibit higher device performance compared to traditional semiconductor lasers based on bulk or quantum well active medium. Improvements in performance can appear in wide modulation bandwidth, while both lasing threshold, relative intensity noise, linewidth enhancement factor and temperature sensitivity are reduced. QD semiconductor lasers displays an interesting hybrid of atomic laser and standard quantum well semiconductor laser properties. Optical feedback containing very commonly in a wide variety of fields including biology, ecology and physics. In biology they occur in regulation and stabilization processes, e.g. blood cellproduction, neural control and respiratory physiology and control of physiological systems (heart rate, blood pressure, motor activity) [7,8].
This chapter covers a review and a study of optical feedback in QD lasers. Section 2 reviews the characteristics of optical feedback regimes, while in section 3, the new rate equations for laser dynamics to describe the active region and Parameters used in the calculations. Section 4 includes a study of time delay effect on optical feedback at threshold current, phase and time delay.

Diode lasers with optical feedback
Optical feedback depends on several parameters and effects on the operating characteristics of a diode laser. One of these effects is the re-injection of a fraction of light into the laser diode after a time (τ) later delayed optical feedback. The optical feedback regimes consists of five distinct regimes defined by the level of the feedback power ratio. These regimes are depend on the internal parameters of the solitary diode laser, such as the linewidth enhancement factor, the diode dimensions and the facet coatings. They are: Regime I corresponds to low feedback level were broadening or narrowing of the optical linewidth is observed depending on the feedback phase, the importance of this regime lies not in the manipulation of linewidths achievable, as greater control can be achieved in higher regimes. In regime II, two modes are observed do not simultaneously exist. As the feedback is increased towards regime III the mode hopping frequency and the mode splitting frequency increases. The transition to this regime from regime I is characterized by an observed line broadening. This regime overlaps regime I. The properties of regime III are single-mode operation and stability arises. The minimum linewidth mode has the best phase stability for this reason regime is inappropriate for most applications. This regime occupies only a very small value of feedback power ratios. Regime IV, which is observed for higher feedback levels, is associated with the coherence collapse this regime is useless for coherent communications. However, applications such as imaging or secure data transmission require highly incoherent sources. In regime V, a stable emission with a narrow linewidth at high feedback levels. This regime is characterized by very narrow-linewidth stable singlemode low intensity noise operation. The coherence of the laser is regained. It operates as a long cavity laser with a short active region. Experimentally it is usually required to antireflection coat the diode laser front facet in order to reach this regime. Due to the strong feedback in this regime the system is also much less sensitive to additional reflections. The system operating in this regime is often referred to as an external cavity diode laser (ECDL) [12].

The rate equations for laser dynamics
In the QD laser, we considers a separate system for electrons and holes in the QD ground state (GS) and exited state (ES) which typically applies for the self-organized QDs in the InN/In 0.8 Al 0.12 N/In 0.25 Al 0.75 N material system. The model used here is plotted in Fig. 1  , respectively. It is assumed that the stimulated emission can take place only due to recombination between the electrons and holes in the ES and GS. Then the rate equation system becomes: www.intechopen.com ( ( is the QD density. 12 , cc JJ are the current densities of electrons and holes, respectively. Equations (1)(2)(3)(4)(5)(6)(7)(8) are solved numerically to describe the dynamics of the carrier densities in wetting layer for electrons and holes and the occupation probability in ground and exited states for electrons and holes. The same curve is obtained for all the three delay times. The symmetric rise of both densities results from taking the same parameters (at most) for both carriers, although the hole density somewhat higher than electron WL. The relaxation oscillations appears in the behavior of ES occupation while it is completely removed in the WL carrier behavior. This can be reasoned to the faster relaxation time from WL to ES and longer escape time to WL. Fig. 6 shows the three-dimensional (3D) plot of the ES photon density and GS occupation probability vs. time. It shows that the feedback oscillations of ES field raises when the GS occupation probability goes to unity.

Coherent and non-coherent optical feedback
The coherence and non-coherence are depends on the phase between incident and reflected waves by external cavity.   www.intechopen.com and backward waves. When    electric field is completely damped. This results from the destructive interference between the laser and the delay fields. To discuss this case let us study ES occupation probability at these phases. This is shown in Fig. 8. A point one must refer to here is the time spent before feedback oscillations appears. When the fields are constructively interfere ( 0   ) the oscillations are appear earlier (~ after 5ns) then electron occupation is reduced. When / 2    , the interference have small effect where the oscillations appear at time (>1ns) and the reduction in electron occupation is small. In Fig. 9 a 3D plot of ES photon density vs. occupation probability of electrons and holes in ES. Although the occupation probability of electrons in ES goes to unity, the interference results in zero field at π-phase. This is also stressed by Fig. 9. Fig. 10 shows the 3D plot of ES photon density vs. occupation probability of (a): electrons and (b) holes in ES. Fig. 11 shows ES photon density vs. case the laser turns off, but due to current injection the carrier density increases until the gain is achieved again then, the laser turns on and undergoes relaxation oscillations. The memory of similar earlier events is retained [15] within the external cavity and reinjected into the laser cavity. Finally an equilibrium state is achieved. Depending on this, one can also relates the longer turn-on delay time with increasing  shown in Fig. 7 to the carrier depletion occurs with increasing incoherence.

Conclusions
The feedback in quantum dot lasers is discussed. The rate equations model using the delay differential equations is stated and solved numerically to elucidate the behavior of different states in the quantum dot laser. excited states in quantum dot is shown to have an important effect on the feedback. Effect of decoherence is studied and is shown to delays the laser field due to carrier depletion. www.intechopen.com