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Abstract
We demonstrate a high linear polarization, narrow linewidth hybrid laser composed of a semiconductor gain chip and a high birefringence waveguide Bragg grating (WBG). The laser operates in the C-band, and a maximum output power of 8.07 mW is obtained in the fiber waveguide. With careful temperature tuning, the hybrid laser can operate in a single longitudinal mode state from above the threshold current to 410 mA. The side mode suppression ratio (SMSR) reaches a value of 50.2 dB, and the polarization extinction ratio exceeds 39.6 dB. We numerically analyze the linewidth suppression for the Bragg grating based on adiabatic chirp theory. The hybrid laser shows a narrow linewidth of 4.15 kHz and a low relative intensity noise (RIN) of <-155 dBc/Hz, providing a high-performance light source for coherent light communication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Narrow-linewidth lasers have attracted considerable interest for a wide range of applications, such as digital coherent communications, wavelength-division-multiplexing (WDM) systems and high-resolution spectroscopy, due to their advantages of high coherence and low noise [1–3]. In the above systems, the spectral linewidth of the lasers is an essential issue because it determines the system performance and stability. Especially in the coherent communication region, the system is sensitive to the polarization and relative intensity noise (RIN), which are the crucial limitations on the receiver sensitivity and the bit error rate (BER) for the whole system [4,5]. Linear polarization, narrow linewidth light source is stable due to its polarization and spectrum purity, and the RIN caused by the competition between two orthogonal polarization modes will be lower. For example, a high-order multilevel modulation system (64 QAM or more) requires pump light source with kHz level linewidth output if the BER needs to be lower than 10−4 [6]. Furthermore, the polarization control of these laser sources is also a critical issue [7]. Another example is in quadrature phase shift keying (QPSK) modulation, a 90° optical hybrid is a key component to provide phase diversity of optical coherent receiver, for which linear polarization light source is an essential element in this format to obtain the perfect optical hybrid [8].
Among recent narrow linewidth lasers, the most attractive design is based on the use of a fiber or planar waveguide with a narrow bandwidth Bragg grating as the external cavity filter of a semiconductor gain chip (GC). A grating-based external cavity can greatly increase the effective cavity length of the laser and suppress the linewidth with an injection lock effect. A linewidth of several kHz or even sub kHz has been obtained through a semiconductor gain chip (GC) or laser diode and fiber Bragg grating reflector [9–11], and a GC with a low loss Si3N4 waveguide Bragg grating (WBG) can achieve a linewidth of 320 Hz [12].
However, almost no high linear polarization semiconductor lasers with a linewidth of several kHz have been demonstrated, while high linear lasers also have a wide range of applications in the field of optical communication. The linear polarization output performance can be evaluated from the polarization extinction ratio (PER), and many narrow linewidth semiconductor lasers have not demonstrated their PER characteristics [13–15]. Usually, a high linear polarization semiconductor laser is realized by using a polarizer after a light source, but this complicates the laser system and leads to high cost. Ryun Kyung Kim et al. achieved a directly linear semiconductor laser with a 45°-tilted grating in a planar waveguide; its PER was above 30 dB, but the linewidth performance was not demonstrated [16].
Our goal is to develop a high linear-polarized laser with a linewidth of several kHz. If narrowband WBG has a polarization mode selection function, it can be used to realize both narrow linewidth and linear polarization output coupling with a GC. The polarization function of a WBG can be evaluated by its birefringence, and high a birefringence WBG can be used to realize better linear polarization. A waveguide fabricated on a silica-on-silicon (SoS) platform has a quite high birefringence due to the thermal expansion mismatch between the core and substrate, typically in the range of 10−4∼10−3 [17]. This is an ideal platform to fabricate a linear polarization WBG. On the other hand, asymmetry in the waveguide core leads to geometrical birefringence, and etching the surface grating on the waveguide core can further enhance the birefringence of a WBG [18].
In this paper, we choose a high birefringence WBG as an external frequency filter. The total birefringence of the WBG is improved by using the characteristics of the SoS platform and surface grating. Compared to a tilted grating, the structure of our WBG is much simpler and easier to fabricate. The WBG is butt-coupled with a III/V gain chip, and a high linear polarization, narrow linewidth semiconductor laser is fabricated. Then, the measurement system is built to test the performance of our laser. The narrowest linewidth of the laser is 4.15 kHz, the output power is 8.07 mW, the side-mode suppression ratio (SMSR) is 50.2 dB, and the laser polarization extinction ratio (PER) is over 39.6 dB, which is the highest PER value in edge emitting semiconductor laser (EESL) configuration to our knowledge.
2. Structure and performance of the hybrid laser
2.1 Hybrid laser structure
A schematic of the hybrid laser is shown in Fig. 1(a). The hybrid laser contains a 1 mm homemade C-band GC and a 5 mm high birefringence WBG, while the length of grating region of the WBG is 4 mm. The GC includes a high reflectivity (HR) back facet and an anti-reflection (AR) coating on the front facet. Both terminals of the WBG are composed of facets angled at 8° with the AR coating on them, which can reduce the F-P cavity effect caused by the reflection of the WBG terminals. The active and passive parts are relatively long so as to form a long equivalent resonant cavity, increasing the lifetime of the photonics and narrowing the linewidth. A longer GC means a larger active region, which is potential to realize higher output power, directly influencing the intrinsic linewidth as the well-known modified Schawlow-Townes linewidth.
Fig. 1. (a) Schematic diagram of the hybrid laser. (b) Schematic diagram of high birefringence WBG for narrow linewidth linear polarization (ASE is for amplified spontaneous emission).
For the GC-WBG configuration of the hybrid laser, WBG works as an optical filter, which provides an external effective cavity length and negative feedback to realize a narrow linewidth. Furthermore, the TE and TM modes selected by our high birefringence WBG are separated through the birefringence effect. Hence, the SoS platform with high stress birefringence is used as the WBG material; etching the surface grating will further enhance the total birefringence of WBG; such a structure is much easier to fabricate compared to a tilted grating. As for our gain chip with compressive strained quantum well, TM mode of the gain chip is further suppressed and the center of the TM-ASE spectrum locates at the shorter wavelength side compared to the TE-ASE as the Fig. 1(b) shown [19]. The birefringence-free WBG TE and TM peaks overlap but the TM mode of the high birefringence WBG separates on the longer wavelength side; If the same GC is coupled with the two different WBGs, the mode splitting of high birefringence grating will cause TM mode to be located at the position with lower gain, enlarging the gain difference of the two eigenmodes compared to the birefringence free WBG. Owing to this gain difference, the TM mode will be further suppressed after a series of nonlinear processes. Therefore, the PER of the output light will be enhanced with our high birefringence WBG using an external cavity filter.
The structure of the high birefringence WBG is shown in Fig. 1(a), which is fabricated on SoS platform using displacement talbot lithography. Thus structure is composed of a three-layer rectangular waveguide with a surface etched grating on the top of core layer. The top and bottom cladding layers are both 15 μm thick silica, the core layer is 3.5 μm thick Ge-doped silica, and the width of the core is 3.5 μm. The index difference between the core and cladding layers is 2.5%. The Bragg wavelength of approximately 1550 nm gives a grating period $\Lambda $ of 528.4 nm with a core layer index of 1.465. Further specific preparation processes and parameters are described in our previous work [18].
The spectrum for the circular polarization of the grating of the WBG is shown in Fig. 2. The Bragg resonances of the TE mode and TM mode occur at 1551.56 nm and 1553.29 nm, respectively, with the mode wavelength separation $\mathrm{\Delta }\mathrm{\lambda }_B^{TM - TE}$ reaching 1.73 nm. The birefringence value is calculated by $\mathrm{\Delta }{n_{eff}} = \mathrm{\Delta }\mathrm{\lambda }_B^{TM - TE}/2\mathrm{\Lambda }$, the calculated birefringence value is 1.650×10−3. The 3 dB bandwidth of the TE and TM modes are 0.41 nm and 0.45 nm respectively. The WBG structure achieves good birefringence results.
A lens group is used between the output terminals of the WBG and polarization-maintaining fiber (PM fiber). The PM fiber is used to improve the stability of the output laser polarization state to obtain better PER performance. There is an isolator contained in the lens group to reduce unnecessary external feedback. All the above components are used to adjust the position of the device to find the best coupling point by monitoring the power output with the GC fixed onto the substrate by welding, WBG fixed onto the copper substrate by UV glue, the metallized optical fiber and lens group fixed by brackets, and the bracket welded onto the substrate. A thermoelectric cooler (TEC) is mounted onto the back of the GC to control the temperature.
2.2 Power-current-voltage characteristic of the hybrid laser
Figure 3 shows the power-current-voltage (PIV) curve and the jet color map plot for the optical spectra versus current of the hybrid laser. The bias current was controlled by a low-noise current source (ILX Lightwave, LDT-3620B), the temperature was controlled by a high-precision thermoelectric temperature controller (ILX Lightwave, LDT-5910C), and all the optical spectra obtained for the laser were measured by a high-resolution optical spectrum analyzer (OSA, AQ6370D,, Yokogawa). The highest power reached 8.07 mW at 400 mA, the output power is relatively low probably because the mode mismatch between WBG and GC. Figures 3(a) and (c) show the characteristics under constant room temperature (25 ℃) from 0 mA to 410 mA. The hybrid laser is not stable at constant temperature, there are many kinks in the P-I curve where mode hopping occurs, the output power fluctuates greatly and the laser operating state switches from a single longitudinal mode (SLM) to a multi-longitudinal mode (MLM).
Fig. 3. PIV curves for the hybrid laser (a) and jet color map plot for the optical spectra versus current (b) at constant temperature. The corresponding PIV (c) and optical spectra (d) with temperature tuning.
The change in the spectra and PIV curve shown in Figs. 3(a) and (c) indicate the typical characteristics of an external grating-based laser. The GC is heating due to the increase in bias current, and this process is accompanied by a change in the GC index, which changes the phase in the laser cavity. During the change of the phase, the laser operates in the SLM at the beginning of the bias current range and then transitions to the MLM condition when the laser cavity cannot support SLM operation. The MLM state broadens the spectrum, and the output power decreases considerably until the cavity phase increases to the work point where the devices snap back to the SLM state. After a range of MLM states, the phase increases to the point where the laser snaps back to the SLM state [11].
However, the hybrid laser operates in the SLM state in a fairly short current range (approximately 10 mA of current), and it easily jumps to the MLM state. Aiming to achieve a narrower linewidth, a longer GC and WBG were used, which leads to a small mode spacing for the equivalent cavity. In the MLM state, the dense cavity modes corresponding to the equivalent cavity are shown in Fig. 3(c), leading to a small phase tuning (current change) range in a specific longitudinal mode [15]. This also indicates that the mode competition is kindly acute, and there are more than two strong adjacent longitudinal modes with a small intensity difference in the MLM state, especially under a high bias current. This indicates a small gain difference between these longitudinal modes. The gain saturation mechanism further reduces this difference at high current, which results in stronger longitudinal modes.
For the sake of further intuitively clarifying the spectrum change from the SLM state to the MLM state, the laser spectra at 25 ℃ from 140 mA to 160 mA are shown in Fig. 4 (a period from MLM-SLM-MLM). The laser spectra also show acute mode competition in Fig. 4 (a)∼(f). When the phase snaps back from the MLM state to the SLM state as the current increases, the adjacent side modes become weaker because the lasing mode is gradually aligned with the optimal position of the grating. The side-mode suppression ratio (SMSR) at optimal (148 mA) is 41.4 dB, but the side modes become stronger with the current deviation from the optimal position. Finally, the laser jumps into the MLM state.
To make the hybrid laser operate in the SLM state above the whole threshold current, the operation temperature is carefully adjusted over the threshold current. According to the P-I curve in Fig. 3(b), there are fewer kinks and mode hopping occurs with temperature tuning. Actually, the lasing mode has an optimal operating point at each current, and temperature tuning can be used to control the cavity phase to align the lasing mode with the optimal grating peak. The gain saturation effect at high current makes the gain difference between the adjacent modes. The competition between the two longitudinal modes is so acute that both modes have the potential to be lasing modes, so the two lasing modes alternately appear at high bias currents (from 300 mA to 410 mA), as shown in Fig. 3(d). The red curve in Fig. 3(b) shows the tuning temperature versus current and shows periodic characteristics, corresponding to cavity phase changes. The temperature control of the TEC works for both the GC and WBG, and the wavelength temperature coefficient is 18 pm/℃.
Figure 5 shows the laser spectra from 140 mA to 160 mA with temperature tuning. The laser operates in excellent single longitudinal mode at all bias currents when the lasing mode is aligned. The maximum SMSR reaches 50.2 dB at 148 mA, a nearly 10 dB increase compared to constant temperature.
2.3 Polarization extinction ratio characteristic of the hybrid laser
The PER under the maximum output power (${P_{\max }}$=8.07 mW) was measured by a self-built polarization extinction ratio test system. By carefully rotating the linear polarization controller (Thorlabs, FBR-LPNIR) for a cycle and monitoring changes in the photonic diode (PD), a polar diagram for the normalized output power versus rotation angle was obtained, as shown in Fig. 6. The measured minimum power ${P_{\min }}$ is 0.88 μW, which gives a PER value exceeds 39.6 dB (PER=$10{\log _{10}}({P_{\max }}/{P_{\min }})$), the laser shows excellent TE mode linear polarization and the TM mode is highly suppressed. To our knowledge, it is the highest PER value in EESL configuration. This means our design gives a good result.
3. Laser linewidth and relative intensity noise
3.1 Adiabatic chirp factor numerical simulation
We used the theory of adiabatic chirp reduction to analyze the linewidth of our hybrid laser [20,21]. In our proposed scheme, the output of the GC is coupled to a narrow bandwidth Bragg reflector, and the Lorentzian linewidth will be suppressed. The configuration is simplified as an equivalent two mirror Fabry-Perot (FP) cavity laser. The back facet of the GC is the back HR mirror ${r_1}$ and is assumed to be 1 [22], and the output facet reflectivity is replaced by the complex-valued effective reflectivity ${r_{eff}}$
Based on Eqs. (1), (6) and (7), we calculate ${r_{eff}}$ and the chirp factor F as a function of the 1.6 nm (200 GHz) wavelength detuning range, and the calculated result is shown in Fig. 7. For a narrowband Bragg grating, 1.6 nm is several times larger than the bandwidth of the grating; thus, there are Bragg main resonance peaks and many side-lobe peaks in this range, as shown in Fig. 7(a). F in the energy gap of the Bragg grating is very low because the reflectivity is highest, which leads to the strongest optical refinement (small value of $A$) and minimum optical loss/transmission (small value of $B$). Around the energy gap, F is significantly enhanced [26]. Only the wavelengths around the Bragg resonance center are considered because it is difficult to lase at the other positions. Figure 7 (b) shows the simulation results at the 0.08 nm wavelength detuning range corresponding to the long wavelength side. The largest F value occurs at the long wavelength side, which deviates from the wavelength center, and the maximum linewidth reduction is approximately 2000, predicted to be $\mathrm{\Delta }\mathrm{\nu }$∼2 kHz for a 9 dBm (8 mW) output. Therefore, our WBG is designed for high reflectivity, and the lasing wavelength occurs at the longer side of the peak and away from the band gap of the grating, as shown by optical spectrum, that is, the region where F is greatly enhanced, so the linewidth can be suppressed significantly.
Fig. 7. (a) Calculated A, B and F values in the 1.6 nm wavelength detuning range. (b) The corresponding A, B, F values in the 0.08 nm wavelength detuning range
The linewidth of the laser can be calculated from its frequency noise power spectral density (FN-PSD) ${S_{\delta \nu }}(f )$ [27]. With the β-separation line defined as ${S_{\delta \nu }}(f )= 8\ln (2 )f/{\pi ^2}$, f is the Fourier frequency, and the FN-PSD is geometrically divided into two areas. For the slow frequency modulation ${S_{\delta \nu }}(f )> 8\ln (2 )f/{\pi ^2}$, this area significantly contributes to the linewidth of the laser [28]. In the fast modulation area, that is, ${S_{\delta \nu }}(f )< 8\ln (2 )f/{\pi ^2}$, f fluctuates too fast to influence the linewidth $\Delta \nu$ and only contributes to the wings of the line shape; thus, $\Delta \nu$ can be easily obtained by using the following formula:
M is the area between the FN-PSD curve and β-separation line. The dynamic noise of our hybrid laser is measured based on the phase reconstruction principle: the laser output is injected into a 120-degree phase difference interferometer, and the differential phase information is measured [29]. Then, the FN-PSD of the hybrid laser within a specific time is obtained by demodulating the measured phase information.Figure 8 shows the measured FN-PSD of the hybrid laser, and the gray line shows the β-separation line, these peaks on white noise platform are caused by the measurement system. These peaks are located in the fast frequency modulation area, they have little effect on the linewidth value and only affect the wings of the line shape as discussed above. The device is operated under a current of 400 mA at 25 ℃. The white noise platform is 753.6 Hz2/Hz@1MHz and the corresponding Lorentzian linewidth is 2.38 kHz. The calculated minimum integral linewidth of the laser (green points in Fig. 8(a)) is 4.15 kHz. It is larger than the Lorentzian linewidth because the actual laser line shape contains the Gaussian components. Therefore, the linewidth is greatly suppressed, but it is difficult to align the actual lasing wavelength to the point of maximum F, so the actual linewidth of the laser is slightly higher than the calculated linewidth. Figure 8 (b) shows the calculated Allan deviation for the frequency, which mainly evaluates the frequency stability. The Allan deviation of the frequency reaches 4.41×10−11, meaning that the frequency stability of hybrid laser is excellent owing to the negative feedback effect of the WBG, as discussed in adiabatic chirp theory.
Fig. 8. (a) The narrowest linewidth measured and calculated by the β isolation line algorithm. (b) Allan deviation of the laser frequency.
3.2 Relative intensity noise
To evaluate the RIN performance of our hybrid laser, a photonic diode, RF amplifier and electric spectrum analyzer are used to measure and analyze the laser frequency signal [30]. Figure 9 shows the measured RIN spectra at different temperatures and bias currents. All the data in this figure are measured multiple times and averaged to reduce the error. The bias currents are 240 mA, 280 mA, 320 mA, 360 mA and 400 mA, and the laser operates in the SLM state under all of the above currents. As shown in Fig. 9, the RIN decreases as the bias current increases, and the lowest RIN at 400 mA is <-155 dBc/Hz when the frequency is above 10 kHz and all the measured RIN values are lower than -149 dBc/Hz. There are several interaction peaks when the frequency is below 10 kHz, which are mainly contributed by the lasing mode and non-lasing mode reflected by the grating [12,13]. These peaks could be suppressed by grating apodization, and the mode interaction will be alleviated when the mode competition is suppressed.
4. Conclusion
We have demonstrated a high linear polarization, narrow linewidth hybrid semiconductor laser. The PER of the hybrid laser exceeds 39.6 dB based on a high birefringence WBG on a SoS platform, which operates with high linear polarization, which is much higher than the other EESLs. At the same time, the hybrid laser shows a good linewidth performance: the narrowest linewidth obtained is 4.15 kHz, and the minimum RIN is under -155 dBc/Hz. Based on adiabatic chirp theory, the mechanism for the narrowing of linewidth with the WBG is analyzed, and the adiabatic chirp reduction factor is found to sharply increase when the work point deviates from the band gap of the grating. The lasing wavelength of the high reflection grating easily appears in this region and could in theory be used to realize a narrower linewidth. The highest output power obtained is 8.07 mW, and the output power can be further improved by reducing the mode mismatch between the GC and WBG (for example, a spot-size converter on the front of the WBG). Furthermore, the structure of our hybrid laser can be optimized. The WBG is more suitable to work as the high reflection terminal with a appropriate reflection facet coated GC, which will mitigate adjacent mode competition and increase the output power. On the other hand, a GC with a shorter cavity length can also reduce the mode competition and linewidth.
Funding
National Natural Science Foundation of China (61874119, 61727822, 11774343, 51672264); Science and Technology Development Project of Jilin Province (20200401006GX); Finance Science and Technology Project of Hainan Province (ZDYF2020217).
Disclosures
The authors disclosure no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. S. Iadanza, A. P. Bakoz, P. K. J. Singaravelu, D. Panettieri, S. A. Schulz, G. C. R. Devarapu, S. Guerber, C. Baudot, F. Boeuf, S. Hegarty, and L. O’Faolain, “Thermally stable hybrid cavity laser based on silicon nitride gratings,” Appl. Opt. 57(22), E218–E223 (2018). [CrossRef]
2. Y. Wu, Y. Shi, Y. Zhao, L. Li, P. Wu, P. Dai, T. Fang, and X. Chen, “On-chip optical narrowband reflector based on anti-symmetric Bragg grating,” Opt. Express 27(26), 38541–38552 (2019). [CrossRef]
3. A. J. Zilkie, P. Seddighian, B. J. Bijlani, W. Qian, D. C. Lee, S. Fathololoumi, J. Fong, R. Shafiiha, D. Feng, B. J. Luff, X. Zheng, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Power-efficient III-V/silicon external cavity DBR lasers,” Opt. Express 20(21), 23456–23462 (2012). [CrossRef]
4. M. Faugeron, M. Tran, F. Lelarge, M. Chtioui, Y. Robert, E. Vinet, A. Enard, J. Jacquet, and F. V. Dijk, “High-power, low RIN 1.55-μm directly modulated DFB lasers for analog signal transmission,” IEEE Photonics Technol. Lett. 24(2), 116–118 (2012). [CrossRef]
5. Y. Zhang, Y. Zhang, Q. Zhao, C. Li, C. Yang, Z. Feng, H. Deng, E. Zhou, X. Xu, K. K. Y. Wong, Z. Yang, and S. Xu, “Ultra-narrow linewidth full C-band tunable single-frequency linear-polarization fiber laser,” Opt. Express 24(23), 26209–26214 (2016). [CrossRef]
6. M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in Proceeding of Optical Fiber Communication Conference (Optical Society of America, 2008), paper OtuM2.
7. G. P. Agrawal, Fiber-optic communication systems4th edition (John Wiley & Sons, 2012).
8. S. H. Chang, H. S. Chung, and K. Kim, “Impact of Quadrature Imbalance in Optical Coherent QPSK Receiver,” IEEE Photonics Technol. Lett. 21(11), 709–711 (2009). [CrossRef]
9. H. Ishii, N. Fujiwara, K. Watanabe, S. Kanazawa, M. Itoh, H. Takenouchi, Y. Miyamoto, K. Kasai, and M. Nakazawa, “Narrow linewidth tunable DFB laser array integrated with optical feedback planar lightwave circuit (PLC),” IEEE J. Select. Topics Quantum Electron. 23(6), 1–7 (2017). [CrossRef]
10. Y. Li, Y. Zhang, H. Chen, S. Yang, and M. Chen, “Tunable self-injected Fabry–Perot laser diode coupled to an external high-Q Si3N4 /SiO2 Microring Resonator,” J. Lightwave Technol. 36(16), 3269–3274 (2018). [CrossRef]
11. P. A. Morton and M. J. Morton, “High-power, ultra-low noise hybrid lasers for microwave photonics and optical sensing,” J. Lightwave Technol. 36(21), 5048–5057 (2018). [CrossRef]
12. D. Huang, M. A. Tran, J. Guo, J. Peters, T. Komljenovic, A. Malik, P. A. Morton, and J. E. Bowers, “High-power sub-kHz linewidth lasers fully integrated on silicon,” Optica 6(6), 745–752 (2019). [CrossRef]
13. P. Primiani, S. Boust, J. M. Fedeli, F. Duport, and F. V. Dijk, “Silicon nitride Bragg grating with joule thermal tuning for external cavity lasers,” IEEE Photonics Technol. Lett. 31(12), 983–986 (2019). [CrossRef]
14. Z. Wang, K. Van Gasse, V. Moskalenko, S. Latkowski, E. Bente, B. Kuyken, and G. Roelkens, “A III-V-on-Si ultra-dense comb laser,” Light: Sci. Appl. 6(5), e16260 (2017). [CrossRef]
15. A. P. Bakoz, A. A. Liles, A. A. Gonzalez-Fernandez, T. Habruseva, C. Hu, E. A. Viktorov, S. P. Hegarty, and L. O’Faolain, “Wavelength stability in a hybrid photonic crystal laser through controlled nonlinear absorptive heating in the reflector,” Light Sci Appl 7(1), 39 (2018). [CrossRef]
16. K. Ryun Kyung, L. Jong Hoon, S. Jeong Hwan, and L. Kyung Shik, “Highly linear-polarized external cavity lasers hybrid integrated on planar lightwave circuit platform,” IEEE Photonics Technol. Lett. 18(4), 580–582 (2006). [CrossRef]
17. M. T. Posner, T. Hiemstra, P. L. Mennea, R. H. S. Bannerman, U. B. Hoff, A. Eckstein, W. Steven Kolthammer, I. A. Walmsley, D. H. Smith, J. C. Gates, and P. G. R. Smith, “High-birefringence direct UV-written waveguides for use as heralded single-photon sources at telecommunication wavelengths,” Opt. Express 26(19), 24678–24686 (2018). [CrossRef]
18. X. Luo, C. Chen, L. Qin, X. Zhang, Y. Chen, B. Wang, L. Liang, P. Jia, Y. Ning, and L. Wang, “High-birefringence waveguide Bragg gratings fabricated in a silica-on-silicon platform with displacement Talbot lithography,” Opt. Mater. Express 10(10), 2406–2414 (2020). [CrossRef]
19. S. L. Chuang, Physics of Photonics Devices2nd Edition (Wiley, 2009).
20. S. D. Saliba, M. Junker, L. D. Turner, and R. E. Scholten, “Mode stability of external cavity diode lasers,” Appl. Opt. 48(35), 6692–6700 (2009). [CrossRef]
21. Y. Suematsu, S. Arai, and K. Kishino, “Dynamic single-mode semiconductor lasers with a distributed reflector,” J. Lightwave Technol. 1(1), 161–176 (1983). [CrossRef]
22. Tin Komljenovic, John Bowers, and E., “Monolithically integrated high-Q rings for narrow linewidth widely tunable Lasers,” IEEE J. Quantum Electron. 51(11), 1–10 (2015). [CrossRef]
23. G. P. Agrawal and C. H. Henry, “Modulation performance of a semiconductor laser coupled to an external high-Q resonator,” IEEE J. Quantum Electron. 24(2), 134–142 (1988). [CrossRef]
24. H. K. Hisham, G. A. Mahdiraji, A. F. Abas, M. A. Mahdi, and F. R. M. Adikan, “Linewidth optimization in fiber grating Fabry–Perot laser,” Opt. Eng 53(2), 02617 (2014). [CrossRef]
25. A. Konosuke, Y. Nobuhide, and Y. Hiroshi, “Strategy of optical negative feedback for narrow linewidth semiconductor lasers,” Opt. Express 26(16), 21159–21169 (2018). [CrossRef]
26. R. Kazarinov and C. Henry, “The relation of line narrowing and chirp reduction resulting from the coupling of a semiconductor laser to passive resonator,” IEEE J. Quantum Electron. 23(9), 1401–1409 (1987). [CrossRef]
27. L. Tombez, S. Schilt, J. D. Francesco, T. Fuehrer, B. Rein, T. Walther, G. D. Domenico, D. Hofstetter, and P. Thomann, “Linewidth of a quantum cascade laser assessed from its frequency noise spectrum and impact of the current driver,” Appl. Phys. B 109(3), 407–414 (2012). [CrossRef]
28. H. Dinesan, E. Fasci, A. D’Addio, A. Castrillo, and L. Gianfrani, “Characterization of the frequency stability of an optical frequency standard at 1.39 µm based upon noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” Opt. Express 23(2), 1757–1766 (2015). [CrossRef]
29. X. Zhang, F. Yang, Z. Feng, F. Wei, H. Cai, and R. Qu, “Narrow-linewidth swept laser phase reconstruction and noise measurement technology and its applications,” Opt. Express 26(25), 32958–32970 (2018). [CrossRef]
30. V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” Proc. SPIE 7913, 79131G (2011). [CrossRef]
