Open Access
Add to BibSonomy
Abstract
This article experimentally demonstrates that the relative intensity noise (RIN) of a mid-infrared quantum cascade laser is insensitive to the optical feedback for feedback ratios up to 31% (−5.1 dB). The RIN of the free-running laser is in the range of −150 dB/Hz to −160 dB/Hz, while the optical feedback induced RIN variation is less than ± 2.0 dB. In addition, the feedback-induced lasing frequency variation is less than 2.0 GHz. Rate equation analyses of the laser are in good agreement with the experimental observations.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum cascade lasers (QCLs) have been widely employed for the demonstration of gas sensing, using the fingerprint molecule absorption lines in the mid-infrared spectral range [1]. Although distributed feedback QCLs are suitable for most gas sensing applications, laser noise including the intensity noise and the phase noise can limit the laser’s application in high resolution and high sensitivity spectroscopy [2]. Optical feedback, which is usually unwanted to semiconductor lasers, can significantly alter the laser noise characteristics. Particularly, strong optical feedback beyond the critical feedback level drives semiconductor lasers into coherence collapse (also known as chaos), where both the intensity noise and the phase noise are substantially raised [3–5]. A lot of efforts have been devoted to the investigation of the critical feedback level of QCLs since 2010s. Theoretical analysis has demonstrated that QCLs were ultra-stable against optical feedback, owing to the short carrier lifetime and the near-zero linewidth broadening factor (LBF) [6–9]. On the other hand, experiments showed that a QCL was destabilized at an optical feedback ratio around 10% [10], while one QCL exhibited low-frequency fluctuation at a feedback ratio around 3.0%, when it was operated close to the lasing threshold [11].
The intensity noise of semiconductor lasers is usually characterized by the parameter relative intensity noise (RIN), which is defined as the ratio between the power spectral density of the intensity noise and the squared average optical power [12]. Interestingly, D. Weidmann et al. reported that the RIN of QCL is sensitive to optical feedback [13], whereas T. Inoue et al. observed that the optical feedback had negligible effect on the RIN [14]. On the other hand, accurate control of optical feedback with proper phase can reduce the RIN of QCL up to about 10 dB, when the laser is operated close to the lasing threshold [15]. It is worthwhile to mention that the optical injection technique has been successfully employed to reduce the RIN of QCLs by 10 dB as well [16,17]. In addition, Long-delay optical feedback is proved to significantly suppress the low-frequency phase noise of QCL and hence to narrow the spectral linewidth, which is helpful for both cavity-enhanced absorption spectroscopy and for cavity ring-down spectroscopy [18,19]. Optical feedback does not only affect the laser noise, but also changes the laser’s power, frequency and the voltage across the laser device. These effects have been explored as an interferometry to extract physical parameters including the LBF and the spectral linewidth [20,21], to develop new technique of gas sensing [22], and to produce spectral imaging in the THz domain [23]. Besides, the optical feedback was also used for beam shaping of high-power broad-area QCLs [24].
This work investigates optical feedback effects on the RIN of a mid-infrared QCL. It is experimentally found that the feedback induced lasing frequency variation is less than 0.06 /cm (1.8 GHz). In addition, the feedback induced RIN change is less than ± 1.6 dB, and hence the RIN of the QCL is rather insensitive to the optical feedback. Besides, we do not observe any chaotic oscillations up to a feedback ratio of 31%, suggesting that the QCL is highly tolerant to optical feedback. These experimental observations are well supported by theoretical investigations using a rate equation model. It is demonstrated that the feedback phase, the feedback delay, and the LBF have little impact on the RIN of QCLs.
2. Experiments and discussion
The QCL under study was grown on an InP substrate by solid-source molecular beam epitaxy based on a two-phonon resonance design [25,26]. The active region is formed by InGaAs/InAlAs quantum wells, and the total cascading stage number is 30. The QCL was fabricated into ridge waveguide with a ridge width of 8.5 µm and a cavity length of 2.0 mm. The front facet was cleaved with a reflectivity of 27%, while the rear facet was coated with high reflectivity of 95%. Figure 1 shows the experimental setup for the measurement of the optical feedback effect on the RIN of the QCL. The QCL is pumped by a low-noise current source (Newport, LDC-3736), and its operation temperature is maintained at 20°C by a thermo-electric cooler. The laser output is collimated through an aspherical lens with a focal length of 4.0 mm. The light beam is split into two paths using a beam splitter, and its reflectivity is polarization dependent (57% for the TM polarized light). The reflection path provides optical feedback using a gold mirror. The optical length from the QCL to the gold mirror is 25.0 cm, corresponding to an external mode spacing of 0.6 GHz. The feedback ratio is controlled by two polarizers. The polarizer P1 is aligned with the TM polarization of the QCL, while rotating polarizer P2 leads to continuously tunable feedback ratio. The feedback power is monitored by a power meter, and the feedback ratio is carefully calculated considering the loss of all the optical elements in the optical path. This setup can achieve a maximum feedback ratio of about 31%. The other path passes through another beam splitter for characterization. The optical spectrum of the QCL is recorded on a high-resolution (0.08 /cm) Fourier transform infrared spectrometer (FTIR, Bruker Vertex 80). The optical signal is converted to the electrical one by a wideband HgCdTe photodetector (PD, Vigo PVI-4TE-6) with a bandwidth of 450 MHz. The photocurrent is amplified by a high-speed preamplifier (AMP, Vigo FIP). The DC voltage is recorded on an oscilloscope, while the AC noise spectrum is measured by a broadband electrical spectrum analyzer (ESA).
Fig. 1. Experimental setup. BS1, BS2: Beam splitter, P1,2: Polarizer, FTIR: Fourier transform infrared spectrometer, PD: Photodiode, AMP: Preamplifier, and ESA: Electrical spectrum analyzer.
Figure 2(a) shows that the lasing threshold current of the free-running QCL is 286 mA (corresponding to a threshold current density of 1.68 kA/cm2), and the threshold voltage is 10.8 V. The QCL emits a single longitudinal mode around 2206 /cm (4.53 µm) for pump currents up to 410 mA, and the lasing wavenumber decreases with increasing pump current in Fig. 2(b) (see 300 mA and 400 mA). For pump currents above 420 mA, the QCL becomes dual modes with a separation of about 2.0/cm (see 420 mA and 440 mA in Fig. 2(b)). The mode of smaller wavenumber becomes stronger at a higher pump current. The generation of dual modes can be attributed to the spatial hole burning effect and/or the Risken-Nummedal-Graham-Haken instability [27,28].
Fig. 2. (a) L-I-V curve of the free-running QCL. (b) Optical spectra at several pump currents. The QCL becomes dual modes above 420 mA.
Figure 3(a) shows that the optical feedback reduces the lasing threshold from 286 mA without feedback down to 280 mA with a feedback ratio of 30.9%. On the other hand, the output power is enhanced by increasing the optical feedback strength. The fluctuation of the optical power is due to the variation of the feedback phase, which leads to either constructive or destructive interference between the internal cavity mode and the external cavity mode [29]. Figure 3(b) and Fig. 3(c) present the optical spectra for various feedback ratios at 340 mA and 380 mA, respectively. It is shown that the QCL remains single mode for all the measured feedback ratios from 1.93% up to 30.9%. Besides, all the optical spectra have no significant linewidth broadening, based on the limited resolution of the FTIR. It suggests that we did not observe the appearance of coherent collapse or chaotic oscillation, which can lead to substantial linewidth broadening [30]. The QCL exhibits the same behavior for other pump currents in the range of 300 to 410 mA. While the optical feedback always shifts the lasing peak to the blue side (arrow) at 340 mA in Fig. 3(b), the optical spectra at 380 mA in Fig. 3(c) are firstly shifted to the blue side and then to the red side (arrows). Through fitting the optical spectra using a Gaussian function, we can extract the wavenumber of the lasing peak. Figure 4 demonstrates that optical feedback shifts the peak wavenumber of the QCL. While the wavenumber at low pump currents (300 mA and 320 mA) only experiences a little variation, the wavenumber at high pump currents shifts toward the blue side. The maximum wavenumber shift reaches up to 0.054 /cm (1.62 GHz), which is achieved at 380 mA with a feedback ratio of 22.8%.
Fig. 3. Optical feedback effects on (a) the L-I curve, (b) the optical spectra at 340 mA, and (c) the optical spectra at 380 mA. The arrows indicate shift trend of the lasing peak.
The RIN of the QCL is measured by the ratio of the power spectral density of the laser intensity noise to the DC power of the photocurrent [31,32]. Figure 5(a) presents that the RIN spectrum generally declines with increasing pump current. The current noise of the power source has been demonstrated to dominate the RIN in the frequency range of 0-100 MHz [31]. Above 420 mA, the RIN within 0-100 MHz slightly increases, because the dual-mode lasing (see Fig. 2(b)) leads to higher mode partitioning noise [12]. The RIN in the range of 100-300 MHz is almost constant. Therefore, we average the RIN over 100-300 MHz as shown in Fig. 5(b). The averaged RIN of the free-running QCL decreases with the pump current as those observed in [13,14,32,33]. The single mode emission of the QCL reaches a minimum RIN down to −157 dB/Hz at 420 mA. Interestingly, the averaged RIN above 420 mA reduces substantially in the dual-mode lasing regime (right side of dashed line). This is out of expectation because multimode lasing usually leads to higher intensity noise than single-mode lasing due to the mode competition. The significant reduction of the RIN probably suggests the strong phase correlation between the two modes [34]. Similar behavior has been observed in a multimode QCL, where harmonic frequency combs are invoked by the third-order population pulsation nonlinearity [35]. The dual modes with such a strong phase correlation are very desirable for the generation of low-noise photonic microwaves, since the frequency difference is about 60 GHz [36]. In addition, it is also useful for multiple gas spectroscopy [37].
Fig. 5. (a) Measured RIN spectra of the free-running QCL. (b) RINs averaged over 100-300 MHz. The dashed line indicates the onset of dual-mode lasing.
When the QCL is subject to optical feedback, Fig. 6(a) shows that the RIN spectrum of the QCL pumped at 340 mA is slightly suppressed in the frequency range of 100-300 MHz. However, for the feedback ratio of 10.6%, the RIN in 0-100 MHz is obviously raised by optical feedback. This is because in-phase optical feedback enhances not only the power of the main lasing mode, but also the power of side modes. Consequently, the mode partitioning noise becomes higher, resulting in higher low-frequency RIN (see Fig. 5(a)). Figure 6(b) proves that the averaged RIN over 100-300 MHz at 340 mA is reduced by about 1.7 dB at a feedback ratio of 30.9%. However, the optical feedback does not reduce the RIN at all pump currents, depending on the feedback phase. In contrast, the averaged RINs at 320 mA and 410 mA in Fig. 6(b) are raised by optical feedback, whereas the maximum RIN increase is only 1.6 dB. In comparison, strong optical feedback can raise the RIN of common interband laser diodes by more than 20 dB, which is at least two orders of magnitude higher than that of the measured QCL [3,30]. The little variation of the RIN also confirms the absence of chaos, which can significantly raise the RIN level of semiconductor lasers [3,30]. Therefore, Fig. 6 demonstrates that the QCL is insensitive to the optical feedback, in strong contrast to common laser diodes.
Fig. 6. Optical feedback effects on (a) the RIN spectra at 340 mA, and (b) the difference of the average RIN over 100-300 MHz with respect to the free-running value.
3. Simulations and discussion
In order to confirm the experimental observations, we theoretically study the RIN characteristics using the rate equation approach, and discuss the effects of feedback phase and feedback delay. The rate equation is constructed based on the three-level band structure of QCLs [32,38,39]. The carrier dynamics of the upper lasing level (N3), the lower lasing level (N2), and the bottom level (N1) are respectively given by
The carrier noise and the spontaneous emission noise are characterized by the Langevin noise sources F3,2,1, FS, and Fϕ [12]. The correlation strengths of the noise sources have been reported in [39,42]. Technical noise sources are not taken into account in the rate equation model. The Langevin noise sources perturb the laser away from the steady-state solutions. Within the framework of small-signal analysis, the responses of the carriers (δN3, δN2), the photon (δS) and the phase (δϕ) in the frequency domain are derived as
The simulated RIN of the free-running QCL in Fig. 7 is almost constant in the low frequency range (<1.0 GHz), while decreases as the frequency increases. The simulated RIN levels are similar to those measured in Fig. 5. The optical feedback mainly changes the low-frequency RIN level for both ϕ0=0 (Fig. 7(a)) and ϕ0=π (Fig. 7(b)), while ripples appear at multiples of the external cavity frequency (2.0 GHz). It is remarked that the measurement in Fig. 6 failed to observe any ripples, because the fundamental external cavity frequency (600 MHz) is beyond the bandwidth of the photodetector (450 MHz). However, we do observe small ripples in experiment when we elongate the feedback length to make the external cavity frequency smaller (not shown in this work), which agrees well with the simulation observation. On the other hand, the excitation of ripples by optical feedback is not unique for QCLs, but common for any other semiconductor lasers [30]. Figure 7(c) demonstrates that the feedback can either reduce or raise the low-frequency RIN level, depending on the initial phase and the feedback ratio. As the feedback ratio increases, the minimum RIN occurs at a larger initial phase (dashed line), which is ϕ0= −0.2π at rext= −40 dB and becomes ϕ0 = 0.5π at rext= −10 dB. However, the maximum RIN reduction is only 3.0 dB for rext= −10 dB. On the other hand, the maximum RIN increase is 4.1 dB, which occurs at ϕ0 = 0.8π and rext= −26 dB. This simulated small RIN variation confirms the experimental results in Fig. 6.
Fig. 7. Simulated intrinsic RIN spectra with optical feedback for (a) ϕ0=0 and for (b) ϕ0=π. (c) Low-frequency RIN difference with respect to the free-running case. The pump current is 1.2×Ith, the feedback delay time is τext=0.5 ns, and the LBF is αH=0.5. The dashed line in (c) indicates the minimum RIN at a certain feedback ratio.
Figure 8(a) demonstrates that the feedback delay has little impact on the RIN variation, for a small LBF of αH=0.5 associated with an initial phase of ϕ0=0. However, for an initial phase of ϕ0=π in Fig. 8(b), the RIN becomes sensitive to the feedback delay for a feedback ratio above −20 dB, and a longer external cavity is desirable to reduce the RIN. For a large LBF of αH=2.0, the RIN becomes slightly sensitive to the feedback delay for ϕ0=0 in Fig. 8(c), in comparison with Fig. 8(a). In contrast, the RIN is strongly dependent on the feedback delay for ϕ0=π in Fig. 8(d). Nevertheless, the feedback induced RIN changes in all cases are less than 3.0 dB, either increase or decrease.
Fig. 8. Low-frequency RIN difference with optical feedback for (a) αH=0.5, ϕ0=0; (b) αH=0.5, ϕ0=π; (c) αH=2.0, ϕ0=0; and (d) αH=2.0, ϕ0=π. The pump current of the QCL is fixed at 1.2×Ith.
4. Conclusion
In summary, we demonstrate the mid-infrared QCL is insensitive to the optical feedback with feedback ratios up to 31% (−5.1 dB). The feedback induced frequency shift is less than 1.8 GHz, while the RIN variation is less than ± 2.0 dB. Employing a small-signal analysis of a set of rate equations, we theoretically prove that the feedback phase, the feedback delay, and the LBF have little influence on the RIN of QCLs, which agrees well with the experimental observations. The insensitivity of the RIN enables the usage of strong optical feedback to reduce the phase noise and the spectral linewidth of QCLs, which will be investigated in future work.
Funding
Shanghai Pujiang Program (17PJ1406500); National Natural Science Foundation of China (NSFC) (61804095).
References
1. A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, and R. Curl, “Application of quantum cascade lasers to trace gas analysis,” Appl. Phys. B 90(2), 165–176 (2008). [CrossRef]
2. A. Hugi, G. Villares, S. Blaser, H. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012). [CrossRef]
3. N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988). [CrossRef]
4. D. Lenstra, B. Verbeek, and A. D. Boef, “Coherence collapse in singlemode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985). [CrossRef]
5. J. Helms and K. Petermann, “A simple analytic expression for the stable operation range of laser diode with optical feedback,” IEEE J. Quantum Electron. 26(5), 833–836 (1990). [CrossRef]
6. F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, S. Borri, M. S. Vitiello, H. E. Beere, D. A. Ritchie, and G. Scamarcio, “Intrinsic stability of quantum cascade lasers against optical feedback,” Opt. Express 21(11), 13748–13757 (2013). [CrossRef]
7. L. L. Columbo and M. Brambilla, “Multimode regimes in quantum cascade lasers with optical feedback,” Opt. Express 22(9), 10105–10118 (2014). [CrossRef]
8. G. Friart, G. Van der Sande, G. Verschaffelt, and T. Erneux, “Analytical stability boundaries for quantum cascade lasers subject to optical feedback,” Phys. Rev. E 93(5), 052201 (2016). [CrossRef]
9. L. Weicker, D. Wolfersberger, and M. Sciamanna, “Stability analysis of a quantum cascade laser subject to phase-conjugate feedback,” Phys. Rev. E 98(1), 012214 (2018). [CrossRef]
10. L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µm distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105(13), 131112 (2014). [CrossRef]
11. L. Jumpertz, K. Schires, M. Carras, M. Sciamanna, and F. Grillot, “Chaotic light at mid-infrared wavelength,” Light: Sci. Appl. 5(6), e16088 (2016). [CrossRef]
12. L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits (John Wiley, 2012), Chap. 5.
13. D. Weidmann, K. Smith, and B. Ellison, “Experimental investigation of high-frequency noise and optical feedback effects using a 9.7 µm continuous-wave distributed-feedback quantum-cascade laser,” Appl. Opt. 46(6), 947–953 (2007). [CrossRef]
14. T. Inoue, S. Mori, K. Tsushima, and K. Kasahara, “Quantum cascade laser intensity noise under external feedback conditions estimated from self-mixing method,” Electron. Lett. 49(6), 407–409 (2013). [CrossRef]
15. C. Juretzka, M. Carras, F. Schad, L. Drzewietzki, S. Breuer, and W. Elsäßer, “9.5 dB relative intensity noise reduction in quantum cascade laser by detuned loading,” Electron. Lett. 49(24), 1548–1550 (2013). [CrossRef]
16. H. Simos, A. Bogris, D. Syvridis, and W. Elsäßer, “Intensity Noise Properties of Mid-Infrared Injection Locked Quantum Cascade Lasers: I. Modeling,” IEEE J. Quantum Electron. 50(2), 98–105 (2014). [CrossRef]
17. C. Juretzka, H. Simos, A. Bogris, D. Syvridis, W. Elsäßer, and M. Carras, “Intensity Noise Properties of Midinfrared Injection Locked Quantum Cascade Lasers: II. Experiments,” IEEE J. Quantum Electron. 51(1), 1–8 (2015). [CrossRef]
18. G. Maisons, P. G. Carbajo, M. Carras, and D. Romanini, “Optical-feedback cavity-enhanced absorption spectroscopy with a quantum cascade laser,” Opt. Lett. 35(21), 3607–3609 (2010). [CrossRef]
19. R. Terabayashi, V. Sonnenschein, H. Tomita, N. Hayashi, S. Kato, L. Jin, M. Yamanaka, N. Nishizawa, A. Sato, K. Nozawa, K. Hashizume, T. Oh-hara, and T. Iguchi, “Optical feedback in dfb quantum cascade laser for mid-infrared cavity ring-down spectroscopy,” Hyperfine Interact. 238(1), 10 (2017). [CrossRef]
20. J. Von Staden, T. Gensty, W. Elsäßer, G. Giuliani, and C. Mann, “Measurements of the α factor of a distributed-feedback quantum cascade laser by an optical feedback self-mixing technique,” Opt. Lett. 31(17), 2574–2576 (2006). [CrossRef]
21. M. C. Cardilli, M. Dabbicco, F. P. Mezzapesa, and G. Scamarcio, “Linewidth measurement of mid infrared quantum cascade laser by optical feedback interferometry,” Appl. Phys. Lett. 108(3), 031105 (2016). [CrossRef]
22. T. Hagelschuer, M. Wienold, H. Richter, L. Schrottke, H. T. Grahn, and H. W. Hubers, “Real-time gas sensing based on optical feedback in a terahertz quantum-cascade laser,” Opt. Express 25(24), 30203–30213 (2017). [CrossRef]
23. F. P. Mezzapesa, L. L. Columbo, M. Brambilla, M. Dabbicco, M. S. Vitiello, and G. Scamarcio, “Imaging of free carriers in semiconductors via optical feedback in terahertz quantum cascade lasers,” Appl. Phys. Lett. 104(4), 041112 (2014). [CrossRef]
24. S. Ferre, L. Jumpertz, M. Carras, R. Ferreira, and F. Grillot, “Beam shaping in high-power broad-area quantum cascade lasers using optical feedback,” Sci. Rep. 7(1), 44284 (2017). [CrossRef]
25. J. C. Zhang, F. Q. Liu, S. Tan, D. Y. Yao, L. J. Wang, L. Li, J. Q. Liu, and Z. G. Wang, “High-performance uncooled distributed-feedback quantum cascade laser without lateral regrowth,” Appl. Phys. Lett. 100(11), 112105 (2012). [CrossRef]
26. F.-Q. Liu, L. Li, L. Wang, J. Liu, W. Zhang, Q. Zhang, W. Liu, Q. Lu, and Z. Wang, “Solid source MBE growth of quantum cascade lasers,” Appl. Phys. A 97(3), 527–532 (2009). [CrossRef]
27. A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77(5), 053804 (2008). [CrossRef]
28. T. S. Mansuripur, C. Vernet, P. Chevalier, G. Aoust, B. Schwarz, F. Xie, C. Caneau, K. Lascola, C.-e. Zah, D. P. Caffey, T. Day, L. J. Missaggia, M. K. Connors, C. A. Wang, A. Belyanin, and F. Capasso, “Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator,” Phys. Rev. A 94(6), 063807 (2016). [CrossRef]
29. H. Kakiuchida and J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30(9), 2087–2097 (1994). [CrossRef]
30. J. Ohtsubo, Semiconductor Lasers Stability, Instability and Chaos, Springer Series in Optical Sciences (Springer, 2012).
31. Y. Deng, B.-B. Zhao, Y.-T. Gu, and C. Wang, “Relative intensity noise of a continuous-wave interband cascade laser at room temperature,” Opt. Lett. 44(6), 1375–1378 (2019). [CrossRef]
32. T. Gensty, W. Elsäßer, and C. Mann, “Intensity noise properties of quantum cascade lasers,” Opt. Express 13(6), 2032–2039 (2005). [CrossRef]
33. Y. Takagi, N. Kumazaki, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Relative intensity noise measurements of 5 µm quantum cascade laser and 1.55 µm semiconductor laser,” Electron. Lett. 44(14), 860–861 (2008). [CrossRef]
34. P. Bardella, L. Columbo, and M. Gioannini, “Self-generation of optical frequency comb in single section quantum dot Fabry-Perot lasers: a theoretical study,” Opt. Express 25(21), 26234–26252 (2017). [CrossRef]
35. D. Kazakov, M. Piccardo, Y. Wang, P. Chevalier, T. S. Mansuripur, F. Xie, C.-e. Zah, K. Lascola, A. Belyanin, and F. Capasso, “Self-starting harmonic frequency comb generation in a quantum cascade laser,” Nat. Photonics 11(12), 789–792 (2017). [CrossRef]
36. I. Sergachev, R. Maulini, T. Gresch, S. Blaser, A. Bismuto, A. Müller, Y. Bidaux, T. Südmeyer, and S. Schilt, “Frequency stability of a dual wavelength quantum cascade laser,” Opt. Express 25(10), 11027–11037 (2017). [CrossRef]
37. J. Jágerská, P. Jouy, A. Hugi, B. Tuzson, H. Looser, M. Mangold, M. Beck, L. Emmenegger, and J. Faist, “Dual-wavelength quantum cascade laser for trace gas spectroscopy,” Appl. Phys. Lett. 105(16), 161109 (2014). [CrossRef]
38. F. Rana and R. J. Ram, “Current noise and photon noise in quantum cascade lasers,” Phys. Rev. B 65(12), 125313 (2002). [CrossRef]
39. X.-G. Wang, F. Grillot, and C. Wang, “Rate equation modeling of the frequency noise and the intrinsic spectral linewidth in quantum cascade lasers,” Opt. Express 26(3), 2325–2334 (2018). [CrossRef]
40. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef]
41. C. Otto, B. Globisch, K. Lüdge, E. Schöll, and T. Erneux, “Complex dynamics of semiconductor quantum dot lasers subject to delayed optical feedback,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 22(10), 1250246 (2012). [CrossRef]
42. X.-G. Wang, B.-B. Zhao, F. Grillot, and C. Wang, “Frequency noise suppression of optical injection-locked quantum cascade lasers,” Opt. Express 26(12), 15167–15176 (2018). [CrossRef]
