Abstract
Quantum dot (QD) laser devices can be successfully used in optical communications due to their unique properties caused by the carrier localization in three dimensions. In particular, quantum dot‐in‐a‐well (QDWELL) lasers are characterized by an extremely low threshold current density and the high modulation frequency. However, their operation rate is limited by the strongly nonlinear electron and hole scattering rates in and out of QD. We investigated theoretically the nonlinear optical phenomena in QDWELL lasers and amplifiers under the optical injection. We have shown that the synchronization of the carrier dynamics in QD and quantum well (QW) caused by the optical injection improves the QDWELL laser performance and, in particular, enhances the relaxation oscillation (RO) frequency. As a result, the QDWELL laser performance in the analogous optical link (AOL) is significantly improving. The optical injection also improves the performance of the QDWELL‐based semiconductor optical amplifiers (SOA).
Keywords
- quantum dot (QD)
- quantum well (QW)
- laser
- semiconductor optical amplifier (SOA)
- optical communications
1. Introduction
Advanced high‐capacity communication systems are necessary for different applications, such as medical diagnosis, traffic safety, Internet, data services, etc. [1]. These new applications generate a giant data traffic which requires the time sensitive analysis and data processing at high‐performance computing infrastructures (HPC) and the data storage, transport, and exchange in datacenters (DC) [1]. Recently, all‐optical architecture of DC has been proposed. It is based on the switching of all data in the optical domain [1]. This approach requires the development of new photonic devices [1]. One of the most efficient technologies for the realization of such devices is Silicon Photonics. Silicon Photonics can resolve the so‐called bandwidth bottleneck by the integration of photonic integrated circuits (PIC) and electronic integrated circuits [1]. The active components such as lasers are made of the III‐V compositions. There are two techniques of the III‐V laser integration with PIC: (i) the III‐V laser die can be butt‐coupled to the silicon photonic chip using active alignment and (ii) III‐V materials are wafer bonded to the silicon photonic chip in order to fabricate lasers lithographically aligned to the silicon waveguide circuit [1].
A generic optical communication system consists of an optical transmitter, optical communication channel, and an optical receiver [2]. A block diagram of such a system is shown in Figure 1 [2].
The information highways providing these services are based on optical fibers [1]. Typically, silica optical fibers are used as the communication channel due to their low losses of about 0.2 dB/km [2]. In such a case, the losses are 20 dB after the propagation distance of 100 km, and the optical power decrease by 100 times defines the amplifier spacing in the long‐haul lightwave systems [2, 3]. In long‐haul networks extended over thousands of kilometers fiber losses are compensated by using a chain of amplifiers boosting the signal power periodically to its original value [1, 2]. Erbium‐doped fiber amplifiers (EDFA) are widely used in optical communication systems due to their compatibility with transmission fibers, energy efficiency, and low cost [1, 2]. Raman amplifier operation is based on the stimulated Raman scattering (SRS) in silica fibers [2]. The advantages of the Raman amplifiers are the using of the fiber itself as an active medium and the large bandwidth [2]. However, the Raman amplifiers require a comparatively large pumping power [2].
The optical communication system performance is limited by the fiber dispersion leading to the optical pulse broadening with propagation through the channel [2, 3]. As a result, the original signal recovery with the high enough accuracy may be impossible [2]. The dispersion influence is strongly manifested in multimode fibers (MMFs) where different fiber modes propagate with different velocities. For this reason, optical communication systems are mainly based on single‐mode fibers (SMFs) [2]. In such a case, the intermodal dispersion vanishes because the pulse energy is carried by a single mode [2]. The main types of the SMF dispersion are as follows: (i) group velocity dispersion (GVD) is caused by group velocity
Optical transmitter converts the electrical signal into the optical signal and launches it into the optical fiber [2]. An optical transmitter consists of an optical source, a modulator, and a channel coupler [2]. An optical source is usually a semiconductor laser or light‐emitting diode (LED) compatible with the optical communication channel [2]. In LED, population inversion is not realized, and the light is generated through spontaneous emission caused by the radiative recombination of electron‐hole pairs in the active layer [2]. In semiconductor lasers, the stimulated emission of light is the dominating operation mechanism [2, 4]. For this reason, the LED radiation is rather weak as compared to the semiconductor laser light. The typical values of the launched power are less than 100 μW (−10 dBm) for LED and about 1 mW (10 dBm) for semiconductor lasers [2]. The optical signal is generated by the direct or external modulation of the optical carrier wave radiated by a semiconductor laser [2]. Generally, time, quadrature, polarization, and frequency are widely used in optical networking technologies for complex quadrature modulation formats, polarization multiplexing, digital pulse shaping, and coherent detection [1]. Recently, space as a physical dimension for modulation and multiplexing in communication systems attracted interest for fiber capacity scaling [1]. Space‐division multiplexing (SDM) uses multiplicity of space channels, or spatial parallelism, in order to increase capacity of the optical communication system [1]. For instance, fiber bundles 10 × 10 Gb/s or 4 × 25 Gb/s can be used for the implementation of 100 Gb/s commercial client interfaces [1].
In the case of the direct modulation, the semiconductor laser is biased near the threshold and driven by the electrical sinusoidal signal for analog modulation or electrical signal bit stream for digital modulation [2]. In the case of the external modulation, two types of the external modulators are mainly used: the Mach‐Zehnder modulator (MZM) and the electro absorption modulator (EAM) [2, 4]. The channel coupler is a microlens focusing the optical signal onto the optical fiber entrance plane [2]. The bit rate of optical transmitters is limited by electronic components [2].
An optical receiver converts the optical signal into the electrical domain and recovers the transmitted data [2, 4]. The structure of the optical receiver depends on the modulation format. Consider first the on‐off keying (OOK) modulation, where an electrical binary stream modulates the optical carrier intensity inside an optical transmitter [2, 4]. In such a case, the directly modulated optical signal after the propagation through the optical fiber is converted in the receiver directly into the original digital signal in the electrical domain [2]. The main component of the receiver is a semiconductor photodetector (PD) converting light into electrical signal through the photoelectric effect [2]. Such a communication system is intensity modulation with direct detection (IM/DD) system [2]. PD should possess high sensitivity, fast response, low noise, low cost, and high reliability [2]. Generally, the transmission quality is characterized by the received signal‐to‐noise ratio (SNR) given by
Unlike the IM/DD system, the performance of the system with a coherent detection technique is limited by the shot‐noise alone [2, 4, 5]. Another important advantage of the coherent detection is the possibility of the detection of signals with advanced modulated formats such as frequency‐shift keying (FSK), binary phase‐shift keying (PSK), quadrature PSK, and 16‐quadrature amplitude modulation (QAM) allowing bit rates of 50, 100, and 200 Gb/s [1, 2, 4]. In the case of the coherent detection, the input optical signal with the optical carrier frequency
Optical signal processing in optical communication systems is based on the linear and nonlinear optical techniques used for the manipulation and processing of digital, analogue, and quantum information [1]. Ultrafast optical nonlinearities provide an operation rate advantage as compared to the electronic techniques for switching, regeneration, wavelength conversion, performance monitoring, and analog digital conversion (ADC) [1]. In particular, semiconductor optical amplifiers (SOAs) can be used in such applications due to their high operation rate and strong nonlinearity [1–3].
The brief review of the optical communication systems clearly shows that a semiconductor laser is a key component of both the transmitter and receiver. Evidently, for the highly efficient applications in optical communication systems, semiconductor laser performance should be characterized by low‐threshold current, high‐speed direct modulation, ultrashort optical pulse generation, narrow spectral linewidth, broad modulation bandwidth, comparatively high optical output power, low relative intensity noise (RIN), low cost, and low electrical power consumption [2, 6]. The objective of this chapter is the investigation of the optical injection influence on the performance of the novel semiconductor laser based on quantum dots (QD) in a quantum well (QW) structure. The number of publications concerning semiconductor lasers in general and QD lasers in particular is enormous and hardly observable. For this reason, in Section 2, we briefly discuss the structure, operation principle, and basic characteristics of a semiconductor laser widely used in optical communication systems. In Section 3, the fundamentals of a QD in QW (QDWELL) laser and SOA are discussed. The original theoretical results related to the dynamics and performance of the optically injected QDWELL lasers and SOA are presented in Section 4. The conclusions are presented in Section 5.
2. Structure and operation principle of a semiconductor laser
Semiconductor laser is an electrically pumped p‐i‐n diode [6]. In the forward‐biased diode, electrons in the conduction band and holes in the valence band are injected into the active layer placed between the p‐type and n‐type cladding layers [2, 6]. The structure of an edge‐emitting semiconductor laser is shown schematically in Figure 2 [2].
The cladding layers are made of the semiconductor material with the bandgap
The
AlxGa1‐xAs/GaAs/AlxGa1‐xAs heterostructure is shown in Figure 3 [6]. The concentration of donors
where
where
where
where
There exist single‐mode semiconductor lasers emitting light mainly in a single longitudinal mode such as distributed feedback (DFB) lasers, coupled‐cavity lasers, tunable lasers, and vertical‐cavity surface‐emitting lasers (VCSEL) [2]. The detailed analysis of structure and operation principles of these lasers can be found in Ref. [2] and references therein. Here, we only briefly discuss the peculiarities of these lasers following Ref. [2]. DFB laser has a built‐in periodic grating with the period
In a coupled‐cavity semiconductor laser, single‐mode operation is realized by coupling the laser cavity to an external cavity. The in‐phase feedback occurs only for the laser modes with a wavelength which almost coincides with a certain longitudinal mode of the external cavity [2]. The effective reflectivity of the laser facet close to the external cavity depends on the wavelength, and the losses of certain modes sharply decrease. The longitudinal mode which simultaneously has the highest gain and the lowest cavity loss becomes the dominant mode [2].
A tunable semiconductor laser typically consists of three sections: the active section, the phase‐control section, and the Bragg section [2]. Each one of these sections is biased independently by injecting different currents in a following way: the current injected into the Bragg section changes the Bragg wavelength
VCSEL emits light in a direction perpendicular to the active layer plane and operates in a single longitudinal mode regime due to the small cavity length of about 1 μm in a wide range of wavelengths of about 650–1600 nm [2]. The emitted light has a form of a circular beam which can be inserted into SMF with high efficiency [2].
The dynamics of the single‐mode semiconductor laser is described by the following rate equations for the number of electrons
where
The direct modulation of the laser emission can be realized if the injection current includes a time‐dependent component. In the case of a sinusoidal modulation, the modulation frequency
where
Consider now QW semiconductor lasers based on a heterostructure shown in Figure 3. If the thickness of the active layer
where
Similar expression can be written for the hole DOS. It is seen from Eq. (10) that carrier DOS in QW does not depend on the energy. The static and dynamic properties of the QW semiconductor laser can be described by the rate equations for the carrier density in QW
where
3. Structure and theoretical model of a quantum dot‐in‐a‐well (QDWELL) laser and SOA
QD is a nanostructure where the electron and hole motion is confined in three dimensions reducing the degrees of freedom to zero [7, 9]. The III‐V QDs are grown epitaxially on a semiconductor substrate [9]. The spontaneous formation of 3D islands during strained layer epitaxial growth is known as the Stranski‐Krastanov process [9]. A continuous film of a QW thickness beneath the QD is called the wetting layer (WL) [9, 10]. In QD, carriers occupy a finite number of energy levels defined by the solution of the Schrödinger equation for a 3D potential separating the inside of QD from the outside [7]. Typically, the spherical and pyramidal QD models are used [7]. The pyramidal model is more realistic since the QD grown by means of the Stranski‐Krastanov technology have approximately pyramidal form [9]. In such a case, the Schrödinger equation for QD can be solved numerically [7, 9]. Carrier DOS in QD is a
The turn‐on dynamics, the small signal and large signal responses of a QDWELL laser have been studied theoretically and experimentally in the fundamental works of Lüdge, Schöll and co‐workers [10, 13–18].
It has been shown that the complicated carrier dynamics in a QDWELL laser is determined by the nonradiative carrier‐carrier scattering processes between the QD and the QW [17]. The corresponding scattering rates
The nonlinearity of the scattering rates
The modulation characteristics of semiconductor lasers can be improved by the optical injection locking (OIL) [19]. OIL of semiconductor lasers provides a single‐mode regime and near‐single‐sideband modulation, strongly enhances the RO frequency and bandwidth, reduces nonlinearity, reduces RIN, reduces chirp, and increases link gain [19]. The directly modulated OIL transmission‐style system combining the master laser and the slave QDWELL laser in the transmission style is shown in Figure 5 [19].
In the transmission‐style system, the injected light from the master laser enters one slave QDWELL laser facet and output is taken from the other facet [19]. The direct modulation signal is applied to the QDWELL slave laser. An isolator prevents light coupling back to the master laser. A polarization controller (PC) is used to match the overlap of master and QDWELL slave laser polarizations. The master laser light coherently combines with the QDWELL slave laser light changing its internal field [19]. The slave laser radiation wavelength tends to the master laser radiation wavelength until the both wavelengths become equal locking the master laser light frequency and phase [19].
The dynamics of the optically injected QDWELL laser has been studied theoretically by using the Lüdge‐Schöll (LS) rate equations for the photon density per unit area
Here,
Under certain conditions, QDWELL laser can operate as a SOA for high‐speed applications [9]. Generally, SOA is the LED amplifying the input optical signal. SOAs are divided into two groups depending on their structure: (i) traveling wave amplifiers (TWA) and (ii) FP cavity amplifiers [9]. The block diagram of the TWA QDWELL SOA is shown in Figure 6.
SOA attracted a wide interest for applications in optical communication systems due to their small size, high gain, strong nonlinearity, and the possibility of on‐chip optoelectronic integration [2, 9]. QD SOAs are particularly promising candidates for the amplification of ultrafast pulses in the relatively broad spectral range due to their ultrafast carrier dynamics and inhomogeneous spectral broadening [9]. The SOA dynamics is described by the carrier rate equations, equation for the time‐dependent SOA gain and the equations for the slowly varying envelopes (SVE) of the optical pulses [2, 9].
The system of rate equations (14)–(16) should be modified for the case of a TWA QDWELL SOA. Eq. (17) for the electron and hole densities in the QW
where
Here,
where
where
QD SOA can be used for the ultrafast and distortion‐free amplification at pulse repetition rates of 20, 40, and 80 GHz with pulse durations of 710, 1.9, and 2.2 ps, respectively [9]. It should be noted that the amplification without patterning effect in QD SOA can be achieved at much lower pump current densities than in QW SOA [22].
4. Optical synchronization of a QDWELL laser dynamics and its influence on QDWELL laser and SOA performance
We investigated theoretically the optical synchronization of the carrier dynamics in the optically injected QDWELL laser and SOA and its influence on the QDWELL laser and SOA performance [23–27]. We solved numerically the LS equations (14)–(17) for the optically injected QDWELL laser [24–26] and Eqs. (17)–(22) for the QDWELL SOA [23, 27] using the typical values of QDWELL parameters and explicit expressions for the carrier scattering rates
It has been shown that the sufficiently strong optical injection leads to the synchronization of the electron and hole dynamics in QD [24]. In the transient turn‐on regime, the bias current and the optical output pulses are strongly synchronized in the case of a comparatively high optical injection power of several milliwatts and the moderate bias current density
The large‐signal response of the QDWELL laser is important for digital communication systems. In the case without the optical injection, the QDWELL laser large‐signal dynamics is determined by the QW carrier densities
where
The directly modulated QDWELL laser can be introduced into an analogous optical link (AOL) in the framework of ultra wideband (UWB) radio‐over‐fiber (UROOF) technology [26, 29, 30]. The UWB high‐speed AOL shown in Figure 7 consists of electrical/optical (E/O) converter, a standard SMF (SSMF) optical fiber, and optical/electrical (O/E) converter [30]. We solved numerically Eqs. (14)–(19) for the AOL based on the optically injected QDWELL laser and standard SMF (SSMF) [26]. We considered the small UWB signal with the modulation frequency of 60 GHz, the zero detuning
The calculated constellation of the output 4‐QAM modulation signal under the strong optical injection of about 1 mW is shown in Figure 8.
The constellation shown in Figure 8 is practically identical with the constellation of the input signal unlike the case without the optical injection [26]. The AOL error vector magnitude (EVM) dependence on the distance for the optical injection power of 10−3 and 1 mW is presented in Figure 9.
It is shown in Figure 9 that in the case of the strong optical injection, the AOL EVM decreases significantly due to the enhancement of the QDWELL laser modulation frequency [26].
The spectrum of the detected UWB signal for the modulation frequency of 60 GHz, zero detuning between the master and the slave lasers, high optical injection power of 1 mW, and the propagation distance of 50 km is shown in Figure 10 [26].
Consider now the influence of the optical pumping on the QDWELL SOA performance [23, 27]. We investigated the copropagating pumping and signal optical waves characterized by the optical power
Figure 11 shows that the pattern effect in the eye diagram vanishes up to the repetition frequency of 140 Gb/s. The output signal optical power and chirp time dependence are shown in Figure 12. It is shown in Figure 12 that due to the carrier dynamics synchronization provides the XGM process without the pattern effect, and the chirp reduces to about 5GHz and becomes symmetric [23, 27].
The strong optical pumping wave of several milliwatts during the XGM process may enhance the QDWELL SOA bandwidth up to 100 nm for a central wavelength of 1350 nm [27]. We investigated the ER dependence on the XGM detuning for the signal wave wavelength
ER reduces with the increase of the CW pumping wave power
5. Conclusions
QW and QD semiconductor lasers and SOA are promising candidates for applications in modern optical communication systems due to their comparatively low threshold current, high operation rate, high modulation bandwidth, low chirp, patterning‐free operation, and stability with respect to temperature variations. These QW and QD advantages are mainly caused by the one‐dimensional (1D) carrier localization in QW and three‐dimensional carrier localization in QD. QDWELL lasers are based on the number of QW layers with the embedded QD. In such a case, 2D electron and hole gas also exists in a QW carrier reservoir, i.e., WL. QDWELL lasers are characterized by the lowest possible threshold current and fast QD carrier dynamics due to the 3D localization of electrons and holes in QD. However, the carrier dynamics in QW and QD is desynchronized due to the strong nonlinear carrier scattering rates for the electron and hole transitions in and out of QD. As a result, the modulation frequency of QDWELL lasers is limited by a comparatively low RO frequency of about 7 GHz. The modulation frequency can be enhanced by an increase of the injection current. But the increase of the injection current leads to the QDWELL laser heating and significant performance deterioration. The modulation frequency and operation rate of semiconductor lasers and SOA can be improved by OIL using the master laser for the optical injection of the slave laser. We solved numerically the system of LS rate equations for QDWELL laser including the optical injection, the explicit expressions for the nonlinear carrier scattering rates, and the inhomogeneous spectral broadening specific for QD. The simulation results show that the carrier dynamics in QW and QD is synchronized by the sufficiently strong optical injection power
TWA QDWELL LED with an input optical signal operates as a QDWELL SOA. QDWELL SOA is described by the modified system of rate equations including the equations for the pumping and signal wave photon densities. In such a case, the sufficiently strong pumping wave simultaneously plays a role of the optical injection and synchronizes the carrier dynamics in QW and QD. The nonlinear optical processes of XGM and XPM occur in a QDWELL SOA. QDWELL SOA performance is improved, the fast gain recovery takes place, the gain bandwidth is enhanced, ER and chirp decreases.
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