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Analysis of the optical feedback dynamics in InAs/GaAs quantum dot lasers directly grown on silicon

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Abstract

This work reports on a systematic investigation of the influence of optical feedback in InAs/GaAs quantum dot lasers epitaxially grown on silicon. The boundaries associated to the onset of the critical feedback level corresponding to the first Hopf bifurcation are extracted at different bias conditions with respect to the onset of the first excited state transition. Overall, results show that quantum dot lasers directly grown onto silicon are much more resistant to optical feedback than quantum well lasers, mostly resulting from a small linewidth enhancement factor of high-quality quantum dot material. However, results also unveil that the onset of the critical feedback level strongly depends on the excited-to-ground-state ratio, hence a figure of merit showing that a small ratio of the excited-to-ground-state lasing thresholds is not beneficial for maintaining a high degree of stability. This work brings further insights in the understanding of quantum dot laser physics and is useful for designing feedback resistant lasers for isolator-free transmission in metro, access, and data center optical networks, as well as for integrated photonics.

© 2018 Optical Society of America

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Figures (10)

Fig. 1.
Fig. 1. Cross-sectional schematic of an InAs QD laser epitaxially grown on (001) GaP/Si.
Fig. 2.
Fig. 2. Light-current characteristics of laser #4. The red markers correspond to the optical spectra depicted in Fig. 3.
Fig. 3.
Fig. 3. Optical spectra measured for QD laser #4: (I) above the GS threshold, (II) near-above the ES threshold, and (III) well-above the ES threshold. The bias conditions correspond to the red markers reported in Fig. 2.
Fig. 4.
Fig. 4. Spectral dependence of the α H -factor measured by ASE in QD lasers #2 and #3.
Fig. 5.
Fig. 5. Experimental setup used for investigating optical feedback. QD, QD laser diode; BKR, backreflector; SWT, optical switch; OSA, optical spectrum analyzer; ESA, electrical spectrum analyzer; PM, powermeter.
Fig. 6.
Fig. 6. Critical feedback level r crit as a function of the effective α H -factor for τ SRH = 0.1 , 0.5, 1, and 5 ns, according to Eq. (6).
Fig. 7.
Fig. 7. (a) Optical and (b) RF spectra for QD laser #2 operating in the free-running r ext = 0 (black) condition and under r ext = 20 % optical feedback at 2 × I th .
Fig. 8.
Fig. 8. (a) Optical and (b) RF spectra for QD laser #3 operating in the free-running (black) condition and under r ext = 20 % optical feedback at 2 × I th .
Fig. 9.
Fig. 9. Optical (first column) and RF (second column) spectra mappings of QD laser #3 measured at (a),(b)  2 × , (c),(d)  2.85 × , and (e),(f)  3.75 × I th GS bias. The green lines mark the critical feedback levels.
Fig. 10.
Fig. 10. Critical feedback level r crit for QD lasers #1, #2, #3, and #4 (with different ratio I th ES / I th GS ) plotted as a function of the ratio of the bias current to the ES lasing threshold I / I th ES .

Tables (1)

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Table 1. Parameters of the InAs/GaAs QD Lasers: Ridge Width, Threshold Currents, ES-to-GS Lasing Threshold Ratio, Peak Wavelengths, and GS–ES Energy Separation

Equations (7)

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d E d t = [ j ( ω ω 0 ) j L ( L ) W / N W / ω Δ N d z ] E ( t ) 2 C k τ in r ext E ( t τ ) ,
C k = j τ in 2 ( 1 r k 2 ) W / r k W / ω ,
W = 2 j β r r ( r l r r e 2 j β L 1 ) ,
d N d t = I e N τ c N τ SRH G | E | 2 ,
τ c 1 = τ c 1 + τ SRH 1 .
r crit = τ in 2 ( A f RO 2 + 1 / τ c ) 2 16 C l 2 ( 1 + α H 2 α H 4 ) ,
C l = 1 r l 2 2 r l .
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