A theoretical model for sampled grating DBR laser integrated with SOA and MZ modulator

Lei Dong; Shengzhi Zhao; Shan Jiang; Shuihua Liu

doi:10.1364/OE.17.016756

1. Introduction

Recently, the InP-based monolithic integration technology is developing very fast and achieved some progress in commercialization [1]. Tunable laser integrated with a modulator is one of the most promising devices since it satisfies both requirements of high-capacity and high-speed for next generation network. What’s more, this technique can simplify system design, reduce package cost, and improve reliability [2]. A SGDBR laser integrated with amplifier and MZ modulator has been demonstrated that can be modulated at high data rate (≥ 10 Gbit/s) [3].

Computer-aided modeling tools can provide insight into the physical nature and predict its performance, thus help us correct the design before making it. Several models have been developed to analyze the laser-MZ modulator structures, such as rate-Eq. (4) and transfer matrix method (TMM) [5], but they are either limited in the small-signal behaviors, or unable to give the transient response. Compared with them, the time-domain traveling wave (TDTW) algorithm shows huge advantages in analyzing various diode lasers and passive devices, especially for the dynamical behaviors [6,7]. It has been applied to study a distributed feedback (DFB) laser integrated with MZ modulator [8]. However, it still has difficulties in dealing with the passive parts, such as Y-splitter and multimode interferometer (MMI), and should make some assumptions and simplifications. Moreover, it is unrealistic to apply it to the SGDBR laser integrated with MZ modulator since the size of this device is much larger and the structure is more complex.

An improvement in time-based method is proposed in Ref [9]. where the active and the passive parts of the device are performed in time- and frequency-domain separately, and then the latter would be transformed back into time domain via digital filter approach. This method enables us to choose the most suitable algorithms for different parts of the device. In this paper, the active region of the laser and the SOA section are modeled by the conventional TDTW, while the sampled grating sections and the MZ modulator are simulated by TMM and BPM, respectively. After obtaining both spectrums, they were transformed into time domain by reverse Fourier Transform, and coupled into the time-domain equations using convolution algorithm.

The main shortcoming by using time-domain representation is that it is more difficult to impose the spectral dependence of material gain than the frequency-domain method [7]. In our model, a so-called effective Bloch Equation (EBE) is incorporated [10,11]. The gain spectrum and the corresponding refractive index change of the multi-quantum wells (MQW) are firstly calculated by the microscopic theory, and then fitted by an analytical formula with some carrier-related parameters.

The paper is organized as follows: In section 2, the model for simulation and its implementation are discussed. The simulation results, including the spectrums of sampled grating and MZ modulator, static tuning map and large-signal modulation behaviors, are given in section 3. Finally, a brief conclusion is drawn in section 4.

2. Description of theoretical model

2.1 TDTW for active region of SGDBR and SOA section

TDTW method is suitable in dealing with the dynamic performance of device. The essence of this model is that the bidirectional optical fields move forward each time-step ∆t by a distance determined by the group velocity: ∆z = v_g∆t. The spectral information is naturally contained in the output field, thus all the complications in finding cavity modes can be avoided compared with the frequency-domain model [6].

Previous works only use the phenomenological rate equations for the gain and refractive index of the active material. This treatment is easy to grasp, however, fails to give accurate results when applying to widely tunable diode lasers and SOA since the nonuniform gain spectrum cannot be captured. The most serious model should incorporate the Semiconductor Bloch Equations (SBE) into the Maxwell equations with a self-consistent manner [10]. Unfortunately, due to the time scale of SBE is around 50-100 fs [12], the time steps should be small enough to avoid beyond the Nyquist limit. Therefore, it is not feasible because of the formidable computation involved.

In this work, the gain spectrum of the QWs is firstly calculated by k∙p theory [13] and Free-Carrier theory [12], and then it was fitted to the susceptibility χ with a Lorentzian function [11]

\begin{array}{l} χ (N, ω) \equiv \frac{2}{\sqrt{ε_{r}}} δ n (N, ω) - j \frac{1}{β} g (N, ω) \\ \begin{array}{c}  \end{array} = χ_{0} + \sum_{i = 1}^{T} \frac{A_{i} (N)}{ω + ω_{0} - ω_{p} (N) - δ_{i} (N) + j Γ_{i} (N)} \end{array}

where δn, g are carrier- and frequency-related refractive index change and material gain, respectively. 𝜒₀ is the susceptibility at a reference frequency, 𝛽 is the propagation constant, 𝜔₀ is the reference angular frequency, 𝜔_p is the material gain peak position, and δ_i, Γ_i, and A_i taken as the carrier-dependent fitting parameters.

Then the fitting results are substituted into the time-domain coupled-wave equations which can be written as [11]

(\frac{1}{v_{g}} \frac{\partial}{\partial t} \pm \frac{\partial}{\partial z}) E_{F / R} = [Γ g_{0} - α + j k_{0} Γ Δ n_{0}] E_{F / R} + \frac{j β}{2 ε_{0}} \sum_{i = 1}^{T} Δ p_{i}^{F / R} (z, t) + S

where E_F _/ _R are the forward and reverse optical fields, α is the internal losses, k ₀ is the wave number, and Γ is the optical confinement factor. S is the spontaneous noises and can be approximated by a complex Gaussian distributed random number generator that satisfies the correlation

〈 S (z, t) S_{_{}}^{*} (z', t') 〉 = γ K (\frac{B N^{2}}{L}) v_{g} δ (z - z') δ (t - t')

where L is the laser cavity length, 𝛾 is the spontaneous coupling factor, K is Petermann’s coefficient, B is bimolecular recombination coefficient and N is the carrier density.

∆p_i^F/R are the frequency-dependent polarization and satisfy the following relationships

\frac{\partial}{\partial t} Δ p_{i}^{F / R} = [j ω_{p} (z) + j δ_{i} (z) + Γ_{i} (z)] Δ p_{i}^{F / R} + j ε_{0} A_{i} (z) E_{F/R}

The rate equation for the carrier density N can be written as [11]

\begin{array}{l} \frac{d N}{d t} = η \frac{I}{e \cdot w d} - \frac{N}{τ} - B N^{2} - C N^{3} - \frac{g_{0}}{4 ℏ ω_{0} β} ({| E_{F} |}^{2} + {| E_{R} |}^{2}) \\ \begin{array}{c}  \end{array} + \frac{j}{4 ℏ ω_{0} ε_{0}} (Δ p_{1}^{F *} E_{F} - Δ p_{1}^{F} E_{F}^{*} + Δ p_{1}^{R *} E_{R} - Δ p_{1}^{R} E_{R}^{*}) \end{array}

where η is the injection efficiency, I is the injection current, and w and d is the waveguide width and thickness. The parameter τ stands for the electron lifetime, and C is Auger recombination coefficient.

2.2 TMM for front and rear sampled-grating regions

The front/rear sampled grating (F/RSG) regions are composed of periodic repetition of the sampling section. This periodic dielectric stacks can be very conveniently modeled by TMM and have been introduced in our previous work [14]. Only two matrices are needed for each sampling section: one for the corrugated waveguide and the other is for the planar Fabry-Perot section [15]. By cascading these transfer matrices as a building block, a general sampled grating model can be obtained. The carrier-dependent refractive index and the corresponding loss in these sections are attributed to the free-carrier plasma effect [16].

The carrier density related to the injection current is derived from the rate Eq. (6) but neglecting the last term of right-hand side by assuming that no appreciable photon buildup

\frac{d N}{d t} = η \frac{I}{e \cdot w d_{p}} - \frac{N}{τ_{p}} - B N^{2} - C_{p} N^{3}

where d_p, τ_p and C_p stand for waveguide thickness, electron lifetime and Auger recombination coefficient in the passive waveguide, respectively.

2.3 BPM for MZ modulator section

The MZ modulator can also be modeled by TMM [5]. However, due to the complex and aperiodic geometries of the modulator, different matrix units are required for each part. Furthermore, some important parameters in TMM, such as mode partition ratio of the Y splitter, were also extracted by BPM [5]. BPM, on the other hand, is conceptually straightforward and can be readily applied to complex structures without having to develop specialized versions of the method [17]. At present, this method is well established and much software is commercially available.

The spectral properties of MZ section in our model is simulated by OlympIOs software which is an integrated platform for design, simulation and mask layout in passive optics devices. The BPM module contains both 2D and 3D BPM propagators. A predominant feature of this software is that it can define variables, such as wavelength and refractive index. The “Vary BPM” would start a series of simulations while varying the value of a variable for each run [18]. This function would facilitate immensely to our work because the spectrum file of MZ section can be obtained conveniently only by setting several variables.

2.4 Model implementation

The model implementation is summarized as follows:

First, the band structures of the MQW are calculated by the k∙p theory based on Luttinger-Kohn’s model. The gain spectrum and the corresponding carrier-induced refractive index change are modeled by the free-carrier theory [11]. After then, all the fitting parameters in Eq. (1) are extracted with respect to different carrier density using the Levenberg-Marquardt algorithm [19]. Only one Lorentzain oscillator (T = 1) is used for approximation in this case [10].

Second, the spectrums of MZ modulator are calculated by OlympIOs software while setting wavelength and reverse bias voltage as variables. The calculation results would be saved into a file waiting to be called by the main program.

Third, the active region of the SGDBR laser and the SOA section are divided into many subsections, thus the corresponding time-step ∆t is determined as: ∆z = v_g∆t. In each time step, the optical field, the polarization, and the carrier density will update themselves according to Eq. (2), (4) and (5).

In order to transform the frequency-domain parameters of the passive parts to time representation, the finite impulse response (FIR) filter would be utilized. The reason for the preference of FIR over infinite impulse response (IIR) filter is that the former would be unconditionally stable and hence is easy to handle. It is said the FIR is less accurate compared with IIR, however, it can be improved by increasing the filter order. Furthermore, the FIR filter can also provide linear phase response which is very important for the phase-sensitive device [20]. Therefore, the coefficients of F/RSG and MZ modulator modeled in the frequency domain are converted to time domain by the reverse Discrete Fourier Transform (DFT) [9]

x (t) = \frac{1}{M} \sum_{k = 0}^{M - 1} X (f) e^{2 π j k f Δ t}

where X(f) stands for the transmission or reflection spectrum coefficients of the passive devices.

The output or optical reflection field at facet of the active region and SOA section can be determined by the time-domain transmission or reflection coefficients convoluted with input optical filed

Y = \sum_{k = 0}^{M} x^{k} (t) y^{n - k}

where x^k(t) stands for the transmission or reflection coefficient in time-domain extracted from (7) at the specific time k, while y is the input optical filed from facets.

3. Simulation results

The structure of device used in this simulation is referred from [4] which is shown in Fig. 1 . The total length of device is 3.4 mm, consisting of the 1.75 mm SGDBR laser, 0.4 mm SOA, and 1 mm MZ modulator. For typical spatial step is 1-5 μm [8], there would be thousands of subsections. Therefore, it is a rather challengeable work to apply full TDTW method to this device.

Fig. 1 Schematic configuration of a SGDBR integrated with SOA and MZ modulator with 2 × 2 MMI output coupler.

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The laser includes a 550 μm gain section, a 75 μm phase section, a 100 μm rear absorber, and two sampled grating mirrors [3]. The absorber is neglected in the model, due to its main function is to reduce the reflection from the back facet. The RSG contains twelve 61.5 μm sampling periods with 6 μm grating bursts and the FSG has five 68.5 μm sampling periods with 4 μm grating bursts. A 97-μm-long 1 × 2 MMI is cascaded behind SOA. The separation between the two branches is 20μm. The output coupler is a 2 × 2 MMI that is 170-μm-long and 10-μm-wide with two output waveguides curved at the facet for reducing reflections so that the AR coating requirements are minimized. The 250-μm-long branch is explored in our model. A π-phase shift region is introduced into the Upper Branch and is controlled by a forward-biased dc electrode since its effect in varying the refractive index is much stronger than the reverse one. For the flexibility of our model, other structure parameters for the passive sections can be easily substituted and do not affect the stability and self-consistent within the time-domain part. The related physical parameters used for simulation are listed in Table 1 .

Table 1. Simulation Parameters

View Table

The integration technique for the laser and passive functional units is accomplished by utilizing an offset quantum-well structure where the MQW active region is grown above a passive bulk waveguide and selectively etched from regions where gain is not required, leaving the non-absorbing waveguide [3]. A schematic of the epitaxial layer structure is shown in Fig. 2 . The gain spectrum and the refractive index change for the active and SOA sections obtained by the microscopic theory and the corresponding fitting results derived from Eq. (1) are shown in Fig. 3 .

Fig. 2 Active/passive offset-quantum well structure. This figure is referred from Ref [3].

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Fig. 3 (a) Gain and (b) refractive index change with respect to different carrier density for active and SOA sections. The solid lines are the results from the microscopic theory, while the dash lines are the fitting results.

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The static simulation results of SGDBR laser with SOA are given in Fig. 4 . The reflection spectrums of F/RSG calculated by TMM are illustrated in Fig. 4(a). The tuning map as a function of FSG current and the output spectrum from the SOA facet are depicted in Fig. 4 (b) and (c). The active, phase and SOA currents are maintained at 100, 0, and 100 mA, respectively. The maximum scanning currents for the FSG and RSG are 30 mA. The spectrum can be obtained by transforming the output complex field to the frequency domain via fast Fourier transform (FFT). The tuning range is around 45 nm covered from 1525.8 nm to 1570.6 nm, while the published result is around 40 nm [21]. The reason for this deviation may be due to the parasitic thermal effect is neglected in this model which has the reverse tendency on the variation of refractive index [16].

Fig. 4 (a) Reflection spectrum of the F/RSG without current injection. (b) Tuning characteristics of SGDBR laser, the maximum tuning current injected in the F/RSG are 30 mA. (c) Superimposed of tuning spectra of ten different wavelengths. (d) SOA gain as a function of SOA length.

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The gain characteristics as a function of current bias on the SOA with different lengths are shown in Fig. 4(d). The transparency currents are 9.9 mA, 13.2 mA and 15.2 mA for 400 μm, 600 μm and 800 μm long, and the corresponding gain values at 100 mA are 6.1 dB, 7.5 dB and 8.8 dB, respectively. These simulation results are quantitatively agreed with the experimental report [3].

The simulation for the MZ modulator is implemented in OlympIOs 2D-BPM propagators. Before simulation, the effective refractive indices of “background” and waveguide are calculated by the finite difference Mode Solver of the software [18]. The calculation results are 3.22 and 3.26, respectively. To improve the accuracy of the BPM at wide angles, the Padé order and the discretisation order are set as 2 [18]. The BPM simulation result is given in Fig. 5 . In the simulation program, the indices in 𝜋-phase region and both upper and lower branch are set as variables corresponding to the external excitation. The former is altered by the carrier injection which is as same as the F/RSG. While the change of refractive index in the MZ branch driven by the reverse bias can be attributed to electrooptic (EO) effect including Pockels effect (linear effect) and Kerr effect (quadratic effect). The formulations can be written as [22]

Δ n_{P o c k e l s} = \frac{1}{2} n^{3} r_{41} (V / d_{p}), Δ n_{K e r r} = \frac{1}{2} n^{3} R_{K e r r} {(V / d_{p})}^{2}

where n is the effective refractive index of the waveguide, V is the applied reverse bias, and d_p is the thickness of the passive waveguide. r₄₁ and R_Kerr are the Pockels and Kerr coefficients, respectively. For InGaAsP/InP materials, they are found to be [22]

r_{41} = 1.4 \times 10^{- 10} c m / V, R_{k e r r} = 1.5 \times 10^{- 10} \exp (- 8.85 Δ E) c m^{2} / V^{2}

where ∆E is the difference (in eV) between the photon energy of the guided light and the quaternary material fundamental gap energy.

Fig. 5 BPM simulation result of MZ modulator section using OlympIOs software.

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Figure 6 (a) illustrates the transmission curves for Lumped Electrode versus with the voltage applied in the upper and lower branches with the Push-Pull configuration while the center wavelength is set at 1.57 μm. The half wave voltage calculated by the model is around 6.8 V. In the push-pull configuration, the voltage applied to upper branch is modulated between 3.5 V and 0 V, and the voltage applied to lower branch is modulated between 3.5 V and 6.8 V. The characteristic spectrums of MZ modulator section versus with the wavelength is illustrated in Fig. 6 (b) under different bias. In the model, the number of voltage steps for both branches are chose as 36.

Fig. 6 (a) Transmission curves for MZ modulator at 1.57 μm. The solid line is for the lumped electrode, while the dash-dot line is for the push-pull configuration. (b) Characteristic spectrums of MZ modulator under different voltage in the upper branch for the push-pull configuration.

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The electrical signal is modeled using a Gaussian function, which is written as [8]

V (t) = V_{s t a r t} + (V_{s t o p} - V_{s t a r t}) (1 - \exp (- t^{2} / τ_{R C}^{2}))

where τ_RC is the time constant and assumed as 25 ps. The sequence of driven signal is assumed to be 0 1 0 1 1 0 0 1 0 at 10 Gbps and is shown in Fig. 7 (a) .

Fig. 7 Large-signal modulation response of the device. (a) Driven signal in the upper branch (solid line) and the lower branch (dash line) (b) output power (c) output spectrum from the upper end and (d) time resolved chirp performance from the upper end of the 2 × 2 MMI.

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The main limitation of the BPM algorithm is that it can only treat the forwardly propagating waves [18]. Therefore, the reflection spectrum of MZ modulator cannot be obtained. However, this problem can be solved by using bidirectional propagating technique [23]. Moreover, since the reflection from the facet is detrimental for the performance of modulation [4], many approaches have been applied to minimize it. Such as an absorber is integrated behind the RSG region, the MMI component lengths are optimized and tapered, the interfaces between active and passive sections are angled, the waveguide is weakly guided, and a broadband multilayer AR layer is employed at the output [3]. Therefore, it has good reasons for us to neglect the reflection in this case.

The output power from the upper end of the MZ modulator is illustrated in Fig. 7 (b). In the calculation, the spontaneous emission noise is switched off in order to obtain a clean modulation response. Since there is no reflections are considered in the model, the relaxation phenomenon cannot be observed in the output power when switching the signal from “0” to “1”. However, similar simulation results were also reported in the Ref [8]. with a 2 × 2 MMI output coupler, and it is attributed to the low reflection from the tilted output facet. Therefore, it is reasonable to utilize uni-directional BPM for this structure because it has good immunity to the optical feedback. The corresponding output spectrum and the time-resolved chirp response are shown in Fig. 7 (c) and (d). Since no reflection is assumed in our model, the chirped frequency spikes in Fig. 7 (d) can only be attributed to the nonlinearity of the EO effect and the magnitude are determined by the steep extent of the modulation signal [8].

4. Conclusion

A new and comprehensive model for a SGDBR laser integrated with SOA and MZ modulator is presented in this paper. Due to the big size of the device and the complexity of the passive units, it is very hard or even technologically impossible to apply traditional full time-domain model to it. In this model, the active region and SOA section are still simulated by traditional TDTW method combined with EBE. Thus the nature of nonuniform gain spectrum and refractive index change of active material can be captured in our time-domain model. The passive sections of the device, F/RSG and MZ modulator, are firstly treated by method in frequency representation, then both spectrums are transformed back into time-domain by digital filter approach and coupled with electric fields at the facets. The whole model is still operated in time-domain, so the dynamical characteristics of the device can be accurately and effectively simulated.

The performance of the device, including the tuning characteristics and the large-signal modulation, has been successfully simulated in our model. The main limitation of our presented model is that it fails to treat the bidirectional propagating waves in the MZ modulator section. Therefore, there is no relaxation phenomenon when switching the signal from “off” to “on” state, and the chirp response of the modulation may be also less accurate since only the nonlinear EO effect is considered. However, due to the feasibility of our model, this problem can be solved by introducing bidirectional propagating technique and does not impact the time-domain parts. These results confirmed that the model can be developed as a powerful simulation platform for the studying of the complex PICs.

Acknowledgements

This work was supported by National Basic Research Program of China (973 Program) under Grant No. 2010CB327603.

References and links

1. I. P. Kaminow, “Optical integrated circuits: a personal perspective,” J. Lightwave Technol. 26(9), 994–1004 (2008). [CrossRef]

2. Infinera white paper, “Photonic Integrated Circuits,” http://www.infinera.com.

3. J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach–Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003). [CrossRef]

4. P. Brosson and P. Delansay, “Modeling of the static and dynamic responses of an integrated laser Mach-Zehnder modulator and comparison with an integrated laser EA modulator,” J. Lightwave Technol. 16(12), 2407–2418 (1998). [CrossRef]

5. X. Li, W. P. Huang, D. M. Adams, C. Rolland, and T. Makino, “Modeling and design of a DFB laser integrated with a Mach–Zehnder modulator,” IEEE J. Quantum Electron. 34(10), 1807–1815 (1998). [CrossRef]

6. J. Carroll, J. Whiteaway, and D. Plumb, Distributed Feedback Semiconductor Lasers (The Institution of Electrical Engineers, London, 1998).

7. E. A. Avrutin, V. Nikolaev, and D. Gallagher, “Monolithic mode-locked semiconductor lasers,” NUSOD 185–215 (2004).

8. S. F. Yu and N. Q. Ngo, “Simple model for a distributed feedback laser integrated with a Mach-Zehnder modulator,” IEEE J. Quantum Electron. 38(8), 1062–1074 (2002). [CrossRef]

9. W. Li, W. Huang, and X. Li, “Digital Filter Approach for Simulation of a Complex Integrated Laser Diode Based on the Traveling-Wave Model,” IEEE J. Quantum Electron. 40(5), 473–480 (2004). [CrossRef]

10. C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33(9), 1543–1550 (1997). [CrossRef]

11. J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed]

12. W. W. Chow, and S. W. Koch, Semiconductor-laser fundamentals (Springer-Verlag, Berlin, 1999).

13. S. L. Chuang, “Efficient band-structure calculations of strained quantum wells,” Phys. Rev. B 43(12), 9649–9661 (1991). [CrossRef]

14. L. Dong, R. K. Zhang, D. L. Wang, S. Jiang, Y. L. Yu, S. Z. Zhao, and S. H. Liu, “Modeling wavelength switching of widely tunable sampled-grating DBR lasers using traveling-wave model with digital filter approach,” IEEE Photon. Technol. Lett. 20(20), 1721–1723 (2008). [CrossRef]

15. T. Makino, “Transfer-Matrix Formulation of Spontaneous Emission Noise of DFB Semiconductor Lasers,” J. Lightwave Technol. 9(1), 84–91 (1991). [CrossRef]

16. J. Buus, M. C. Amann, and D. J. Blumenthal, Tunable Laser Diodes and Related Optical Sources (John Wiley & Sons, Hoboken, New Jersey, 2005).

17. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000). [CrossRef]

18. OlympiOs manual, http://www.c2v.nl/.

19. D. Kincaid, and W. Cheney, Numerical analysis-mathematics of scientific computing (China Machine Press, Beijing, 2005).

20. S. K. Mitra, Digital Signal Processing-A Compute-Based Approach (Publishing House of Electronics Industry, Beijing, 2006).

21. E. J. Skogen, J. S. Barton, S. P. DenBaars, and L. A. Coldren, “Tunable sampled-grating DBR lasers using quantum-well intermixing,” IEEE Photon. Technol. Lett. 14(9), 1243–1245 (2002). [CrossRef]

22. J. F. Vinchant, J. A. Cavailles, M. Erman, P. Jarry, and M. Renaud, “InP/GaInAsP guided-wave phase modulators based on carrier-induced effects: theory and experiment,” J. Lightwave Technol. 10(1), 63–70 (1992). [CrossRef]

23. P. Kaczmarski and P. E. Lagasse, “Bidirectional beam propagation method,” Electron. Lett. 24(11), 675–676 (1988). [CrossRef]

Parameters	Symbol	Values
Waveguide loss	α	30 cm⁻¹
Confinement factor	Γ	0.26
Group refractive index	n_g	3.7
Carrier lifetime in active region	τ	1 × 10⁻⁹ s
Carrier lifetime in passive region	τ_P	10 × 10⁻⁹ s
Bimolecular recombination coefficient	B	10⁻¹⁰ cm⁻³s⁻¹
Auger coefficient in active region	C	2.5 × 10⁻²⁹ cm⁻⁶s⁻¹
Auger coefficient in passive region	C_p	7 × 10⁻²⁹ cm⁻⁶s⁻¹
Injection efficiency	η	0.8
Spontaneous coupling coefficient	𝛾	5 × 10⁻⁵
Pertermnn factor	K	1

A theoretical model for sampled grating DBR laser integrated with SOA and MZ modulator

Abstract

1. Introduction

2. Description of theoretical model

2.1 TDTW for active region of SGDBR and SOA section

2.2 TMM for front and rear sampled-grating regions

2.3 BPM for MZ modulator section

2.4 Model implementation

3. Simulation results

4. Conclusion

Acknowledgements

References and links

Cited By

Figures (7)

Tables (1)

Equations (11)

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