Self-injected semiconductor distributed feedback lasers for frequency chirp stabilization

Khalil Kechaou; Frédéric Grillot; Jean-Guy Provost; Bruno Thedrez; Didier Erasme

doi:10.1364/OE.20.026062

Optics Express
Vol. 20,
Issue 23,
pp. 26062-26074
(2012)
•https://doi.org/10.1364/OE.20.026062

Self-injected semiconductor distributed feedback lasers for frequency chirp stabilization

Khalil Kechaou, Frédéric Grillot, Jean-Guy Provost, Bruno Thedrez, and Didier Erasme

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Khalil Kechaou, Frédéric Grillot, Jean-Guy Provost, Bruno Thedrez, and Didier Erasme, "Self-injected semiconductor distributed feedback lasers for frequency chirp stabilization," Opt. Express 20, 26062-26074 (2012)

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Abstract

It is well known that semiconductor distributed feedback lasers (DFB) are key devices for optical communications. However direct modulation applications are limited by the frequency chirp induced by current modulation. We demonstrate that a proper external control laser operation leads to chirp-to-power ratio (CPR) stabilization over a wide range of modulation frequencies as compared to the free-running case. Under experimentally selected optical feedback conditions, the CPR decreases significantly in the adiabatic regime from about 650 MHz/mW in the solitary case down to 65 MHz/mW. Experimental results are also confirmed by numerical investigations based on the transfer matrix method. Simulations point out the possible optimization of the CPR in the adiabatic regime by considering a judicious cavity design in conjunction with a proper external control. These results demonstrate important routes for improving the transmission performance in optical telecommunication systems.

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Fig. 1 Schematic of the optical feedback loop

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Fig. 2 Amplitude (blue) and phase (red) of the CPR as a function of the modulation frequency for the solitary QW DFB laser.

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Fig. 3 Amplitude (blue) and phase (red) of the CPR as a function of the modulation frequency for various optical feedback Γ (a) Γ = 1.4 × 10⁻⁶, (b) Γ = 1.5 × 10⁻⁵, (c) Γ = 1.6 × 10⁻⁴, and (d) Γ = 5.5 × 10⁻³.

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Fig. 4 CPR in the adiabatic regime measured at 500 MHz as a function of the optical feedback strength for the QW DFB laser.

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Fig. 5 Measured 2β/m ratio as a function of the modulation frequency for the solitary case (red plot) and for an optical feedback of about Γ = 1.5 × 10⁻⁵ optical feedback (blue plot).

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Fig. 6 Calculated CPR in the adiabatic regime as a function of the output power for various feedback conditions (

0 % < R_{A R, e q} = {| r_{A R, e q} |}^{2} = γ < 4 %

) and for κL = 0.8, ϕ_HR≈0.9π

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Fig. 7 (a) Zoom from Fig. 6 showing the calculated CPR in the adiabatic regime as a function of the output power for various feedback conditions (κL = 0.8); (b) Calculated CPR in the adiabatic regime as a function of the effective front facet reflectivity (κL = 0.8, P₀ = 3.36 mW).

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Fig. 8 Calculated CPR in the adiabatic regime as a function of the output power for various feedback conditions for κL = 0.5 and L = 350 μm. Front facet reflectivity is 0.1% (green), 0.5% (black), 1% (red) and 2% (blue) respectively.

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Tables (1)

Table 1 Simulation parameters of AR/HR-DFB laser

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Equations (19)

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\frac{2 β}{m} = α_{H} \sqrt{1 + {(\frac{ω_{c}}{ω_{}})}^{2}}

f_{c} = \frac{1}{2 π} v_{g} \frac{\partial g}{\partial P} P

\frac{\partial g}{\partial P} = \frac{ε g}{1 + ε P}

\frac{d E}{d t} = [j ω + \frac{1}{2} (1 + j α_{H}) (G - 1 / τ_{p})] E (t) + K E (t - τ)

K = \frac{2 C_{A R} γ}{τ_{i}}

r_{A R, e q} = {\tilde{r}}_{A R} e^{- j φ_{A R}} + (1 - {| {\tilde{r}}_{A R} |}^{2}) \sqrt{γ} e^{- j ω τ} = {\tilde{r}}_{A R, e q} e^{j φ_{A R, e q}}

r_{H R, e q} = {\tilde{r}}_{H R} e^{- j φ_{H R}}

\frac{d N}{d t} = \frac{I (t)}{e} - \frac{N (t)}{τ_{e}} - G P (t)

\begin{array}{l} \bar{M_{P e r i o d}} = [\begin{matrix} \frac{n_{1} + n_{2}}{2 n_{1}} & \frac{n_{1} - n_{2}}{2 n_{1}} \\ \frac{n_{1} - n_{2}}{2 n_{1}} & \frac{n_{1} + n_{2}}{2 n_{1}} \end{matrix}] \times [\begin{matrix} e^{k_{2} l} & 0 \\ 0 & e^{- k_{2} l} \end{matrix}] \times \\ [\begin{matrix} \frac{n_{1} + n_{2}}{2 n_{2}} & \frac{n_{2} - n_{1}}{2 n_{2}} \\ \frac{n_{2} - n_{1}}{2 n_{2}} & \frac{n_{1} + n_{2}}{2 n_{2}} \end{matrix}] \times [\begin{matrix} e^{k_{1} l} & 0 \\ 0 & e^{- k_{1} l} \end{matrix}] \end{array}

\bar{M} = \bar{r_{H R}} \times \bar{φ_{H R}} \times \prod_{i = 1}^{i = N} {(\bar{M_{P e r i o d}})}^{m_{i}} \times \bar{φ_{A R, e q}} \times \bar{r_{A R, e q}}

\bar{r_{H R, e q}} = \frac{1}{\sqrt{1 - {\tilde{r}}_{H R}_{}^{2}}} [\begin{matrix} 1 & - {\tilde{r}}_{H R} \\ - {\tilde{r}}_{H R} & 1 \end{matrix}]

\bar{r_{A R, e q}} = \frac{1}{\sqrt{1 - {\tilde{r}}_{A R, e a}^{2}}} [\begin{matrix} 1 & {\tilde{r}}_{A R, e q} \\ {\tilde{r}}_{A R, e q} & 1 \end{matrix}]

\bar{φ_{H R}} = [\begin{matrix} e^{- j φ_{H R}} & 0 \\ 0 & e^{- j φ_{H R}} \end{matrix}]

\bar{φ_{A R, e q}} = [\begin{matrix} e^{j φ_{A R, e q}} & 0 \\ 0 & e^{j φ_{A R, e q}} \end{matrix}]

g (N, P) = \frac{g_{0} \cdot l n (\frac{e d_{q w} B_{r a d} N^{2}}{J_{0}})}{1 + ε P}

{\bar{M}}_{11} (α_{D F B}, λ) = 0

n (z) = n^{t h} + Γ_{c} \frac{d n}{d N} (N (z) - N_{t h})

r_{A R, e q} = \sqrt{γ} e^{- j ω τ} = {\tilde{r}}_{A R, e q} e^{j φ_{A R, e q}}

k = \frac{η_{i}}{e} \frac{α_{H}}{4 π} \frac{Γ_{c} ε}{V}

Parameters	Symbol	Value	Unit
Lasing wavelength	λ	1550	nm
Active layer’s length	L	350	μm
Quantum Well’s number	N_QW	6
Quantum Well’s thickness	d_qw	0.008	μm
Active layer’s width	w	1.3	μm
Effective index	n_eff	3.2
Group index	n_g	3.8
Bragg grating period	Λ	2.42 10⁻⁷	m
Confinement factor	Г_c	0.139
Gain compression coefficient	ε	3 10⁻¹⁷	cm³
Internal loss	α_int	19	cm⁻¹
Refractive index’s slope	∂n/∂N	−2.2 10⁻²⁰	cm³
Empirical gain coefficient	g₀	800	cm⁻¹
Transparency current density	J₀	50	A/cm²
Non-radiative recombinaison coefficient	A_nrad	0	s⁻¹
Radiative recombinaison coefficient	B_rad	8 10⁻¹¹	cm³/s
Auger recombinaison coefficient	C_aug	2 10⁻²⁹	cm⁶/s
Spontaneous emission factor	β_sp	10⁻⁴
Linewidth enhancement factor	α_H	3

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