Open Access
Add to BibSonomyAbstract
Silicon photonics packaging without optical isolator is of significant importance to realize low fabrication cost and small device size. In this report, impact of external feedback on DFB laser performance is investigated both theoretically and experimentally. Dynamic transfer matrix method and rate equation model are coupled to describe the dynamic interaction between optical field and carriers in a DFB structure under the feedback by external reflection. The calculation model exhibits laser spectrum splits and output intensity fluctuates with increase of the degree of external feedback, in good agreement with experimental results. The theoretical analysis is performed under various feedback parameters, and the optimum packaging condition for DFB laser chip in silicon photonics is guided.
© 2014 Optical Society of America
1. Introduction
Standing on the verge of exa-scale computing era, the performance limitation of CMOS transistors has been perennially driving optical interconnect for further technical sophistication; low cost, low power consumption, as well as high bandwidth density [1–3]. Organic Optical MCM is promising for next-generation computers [4]. Meanwhile, silicon photonics is an attractive technology owing to its advantages of highly dense on-chip integration, long-distance transmission by single mode optical propagation, high bandwidth per single thread of fiber with WDM, and potential compatibility with wafer scale CMOS process for low cost [5–11]. However, in order to achieve low cost and high density, packaging technology of silicon photonics still requires significant improvement. In particular, laser chip packaging is one of the most critical issues to be solved.
As silicon is passive semiconductor of indirect transition type, in general III-V active materials are used to supply light sources to silicon photonics chip. One potent method is to directly bond III-V layer onto Si waveguide where DFB structure is preliminarily patterned [12, 13]. Another method is to mount a commercial or tailored laser array chip onto a silicon chip [14, 15]. This method profits in utilizing a matured laser chip which can provide high-power and low-threshold laser emission, but instead requires highly efficient optical coupling with a silicon waveguide. In both of the above methods, negative impact of external feedback on laser performance is a critical issue.
When a semiconductor laser operates under the existence of external reflection at, for instance, end facets of a waveguide, such an external reflection facet configures an external cavity and corresponding external optical modes [16]. Due to the unexpected multi-mode laser operation, optical spectrum splits into several spikes, and output power intensity fluctuates unstably. That signal fluctuation increases RIN (Relative Intensity Noise), and significantly degrades signal quality (eye diagram) in particular at high-speed operation at 25 Gbps or more. Generally optical isolators are utilized in telecom and data-com in order to block the reflected light from entering back into a laser, however, in silicon photonics packaging, use of isolator should be evaded due to its unacceptably high cost and large device size. Some reports exhibit that employing partial-gain structure [17] or laterally-loss coupled structure [18] can improve the feedback tolerance of a DFB laser, but they sacrifice the laser output power. Apart from using isolator or improving DFB laser structure, laser chip packaging method may well be optimized for releasing external feedback impact.
In this report, we investigate the feedback impact on DFB laser performance by both experiments and calculation. The calculation model is constructed by coupling dynamic transfer matrix method and rate equation model. It is shown that the model represents time dependent laser performance under external feedback in good agreement with experimental results. The feedback impact is explored with varying external feedback condition, and the optimized packaging condition to minimize the feedback is guided.
2. Modeling of DFB laser with external feedback
In order to model the time development spectral dynamics of a DFB laser under external feedback, we employ dynamic transfer matrix method coupled with rate equation [19, 20].
2.1 Dynamic transfer matrix method
In this method, as described in [19, 20], the conventional transfer matrix method which deals with only static state [16] is expanded to a dynamic algorithm in which temporal evolution of optical field of each wavelength component is sequentially calculated. A DFB structure is divided into a cascade of sections each of which has the same length dz. Each section has information of carrier density N and a transfer matrix M. All the physical parameters are assumed to be constant in each section (see Fig. 1). The basic concept of this method is to calculate the variation of forward and backward travelling wave amplitude at each matrix in each time step. Now we consider the situation that forward and backward wave with amplitudes of Ef and Eb at positions k and k + 1 respectively are entering a section expressed by a matrix M. After passing a single time step Δt, Ef and Eb appear at opposite sides: k + 1 and k each, described as
Expanding the matrix M to its elements, Eq. (1) reads Depending on the section’s type, homogeneous index or step index from n1 to n2, matrix M is defined as In Eq. (3), β gives wave number expressed as β = λ / 2π + i g / 2. Here, λ is the wavelength of interest and g stands for laser gain, which is determined by carrier density N as will be described later.
Fig. 1 Conceptual diagram of dynamic transfer matrix method. DFB structure is divided into a cascade of sections, in which all the physical parameters are assumed to be constant.
Equations (2a) and (2b) are applied to all the wavelength components in the spectral range of interest. The calculation is performed through the whole wavelength components and sections, and then iterated over the time development.
2.2 Rate equation
In order to take into account the dynamic interaction between photons and carriers, a rate equation is coupled to the above model. Carrier density N at each section is calculated by
Here, J is the injection current density to active region, q is the unit charge of an electron, Br is the recombination factor of gain, d is the waveguide thickness, vg is the group velocity of the light, and S is the photon density given by S = {|Ef (k)|2 + |Ef (k + 1)|2 + |Eb(k)|2 + |Eb(k + 1)|2}/2vg.. After N is calculated by Eq. (4), the laser gain g at the section is obtained bywhere Ntr is the transparency carrier density, ε is the gain compression factor, and dg/dN is the differential gain.2.3 External feedback
For introducing the external feedback effect, we set a mirror with reflectivity of rext at the location Lext away from the edge of the DFB structure (see Fig. 1). The external cavity consists of W number of external sections (meaning, Lext = dz × W). For saving computation time, the external cavity is supposed to have a single matrix given by MW. In order to take into account the feedback impact of not only phase shift but also photons’ round trip time delay, traveling wave at dt × W sec ago is used for Ef (t, k) at the external cavity to perform Eq. (1).
3. Experimental and simulation results
In order to investigate the feedback effect on DFB laser performance, we carry out experiments and calculations with varying feedback level.
3.1 Experiments
To investigate the feedback impact on DFB laser performance, an optical feedback circuit is constructed following the setup explained in [17]. Figure 2 gives a schematic diagram of the setup. A commercial DFB laser chip is used for the experiments. Output light from the laser is coupled to a lensed fiber, and 1% of the light is divided by a directional coupler to be monitored by a power meter and a spectrum analyzer, and the other 99% is guided to a circulator, which turns the light back to the laser as external feedback. A variable optical attenuator is inserted in the round trip feedback path to vary the feedback level. In this setup, the round trip external cavity length is kept about 1 m. The DFB laser is DC biased at 100 mA, emitting 20 mW output power at 1493 nm wavelength. We measure the laser emission spectrum and RIN of the optical output as a function of the feedback level ranging from −34 dB to −15 dB.
Fig. 2 Schematic diagram of the experimental setup for investigation of external feedback impact on DFB laser performance.
Figure 3 exhibits emission spectra obtained at different feedback levels. When the feedback level is around −34 dB, the emission spectrum shows a single lasing peak (see Fig. 3(a)), but with feedback level around −27 dB, some side modes appear around the center of the spectrum (see Fig. 3(b)). Under the existence of higher feedback level around −22 dB, the side modes exhibit more enhanced oscillation (see Fig. 3(c)). Accompanied with the multi-resonant peaks, RIN is confirmed to increase as a function of feedback level (see Fig. 4).
Fig. 3 Experimentally obtained emission spectra of the DFB laser under the feedback level of (a) −34 dB, (b) −27 dB, and (c) −22 dB.
Increase of external feedback induces spectral splitting when the feedback exceeds some threshold [21–23]. The experimentally observed side modes correspond to the reported splitting. In this feedback regime, mode hopping between side modes can also take place, resulting in the increase of RIN. In Fig. 4, RIN stays constant through the feedback range from −35 to −30 dB, but start increasing at around −30 dB. This threshold value corresponds to the one reported in [17].
3.2 Calculation results
Calculations are performed under the similar condition as the above experiments. The DFB structure is designed to include a λ/4 phase shifter at the central area, where wavelength components around 1500 nm are moderately confined. κL is set to be 2. The whole sections of the DFB are equally excited by total current injection of 100 mA. The external cavity length Lext is set to be 1 m, same as the experiments. Parameters used in the calculations are listed in Table 1.
Table 1. Calculation parameters
The emission spectrum exhibits a single sharp lasing peak under the feedback level of −30 dB (Fig. 5(a)), but several external modes start oscillating with feedback level of −25dB (Fig. 5(b)). The further feedback enhances the external mode oscillation and leads to multi-mode oscillation state (Fig. 5(c)). The spectral splitting confirmed in the simulation is consistent with the experimental results and previous reports [21–23] as argued in the previous section (3.1).
Fig. 5 Calculated emission spectra of DFB laser under the feedback level of (a) −30 dB, (b) −25 dB, and (c) −20 dB.
4. Feedback tolerance of a DFB laser
External feedback impact in silicon photonics packaging is investigated by calculation. When a DFB laser chip is mounted onto a silicon chip, external reflection occurs dominantly at the edges of the silicon waveguide (or, in many cases it is terminated by spot-size converters). Additional reflections can also occur at junctions between silicon waveguide and silicon photonics components such as a modulator. First the dynamic response of laser modes is analyzed in detail under external feedback, and then feedback range within which DFB laser can maintain stable single-mode operation is scrutinized.
4.1 Dynamic response of the optical modes
The whole sections of the DFB laser matrix are excited by total carrier injection rate of 100 mA as same as the experiments, but now the external cavity length is set to be 6 mm, which is the possible length of external cavity formed in a silicon photonics package.
The calculated emission spectra and their temporal development are shown in Fig. 6 under different feedback levels. Under the low feedback level −30 dB, the DFB mode oscillates with temporal noise due the interference with the reflected light, being accompanied with external modes which also have temporal noise (see Figs. 6(a) and 6(b)). Under the higher feedback level −20 dB, Q-factors of the external modes increase and thereby their lasing thresholds get closer to the DFB main mode’s one. That gives rise to nonlinear interaction via laser gain between external and the main modes, which is so-called mode competition, takes place. The interaction leads to rapid energy exchange between the modes (see in the dashed box in Fig. 6(d)), being similar to mode hopping, and also causes unstable response in slower temporal range as well. Compared with the case of 1 m cavity length in the previous section, temporal noise becomes moderate because of larger external mode spacing and then weak modal interaction. Nevertheless, it is confirmed as mentioned above that additional external feedback increases temporal noise, which increases RIN as same as 1 m case observed by experiments.
Fig. 6 Dynamic transition of emission spectra under feedback levels of −30 dB (a) and −20 dB (b). Time development of each optical modes arrowed as A, B, and C in (a,c) are plotted in (b, d) respectively.
4.2 Feedback tolerance for different external cavity condition
It is notable that temporal instability of the laser modes are mainly caused by the interaction between neighboring modes, and therefore it would be possible to achieve more stable operation by reducing the modal interaction. Such an interaction is generally induced by modes’ overlap in terms of space and frequency. Here we consider the way to decrease the overlap in frequency domain. The simplest way is to make wider wavelength spacing between the modes by means of shortening the external cavity length. Shortening the external cavity would not only reduce the temporal noise, but also achieve single mode operation in case that external modes are well separated away from the DFB main mode which oscillates at the gain peak.
Calculations are conducted with varying external cavity length Lext (mm) and feedback level R (dB). Lext is given as the length in the air, corresponding to Lext /neff (mm) in a silicon waveguide (neff is effective index). The bias condition is same as the ones explained in the previous section (4.1). The calculated temporal developments of emission spectra are shown in Fig. 7. It is shown on the spectra that shortening the external cavity pushes external side modes far from the DFB main mode. Since the farer side modes profit lower laser gain, their oscillations are well suppressed and single mode operation is realized, provided that the feedback level is low (see Figs. 7(a)–7(h)). Meanwhile, under the higher feedback levels, external modes obtain higher Q-factors, and their oscillations become comparable with or even excess the main mode, and the laser operation becomes multi-mode regime (see Figs. 7(i)–7(p)). With regard to temporal noise, unstable fluctuations are confirmed on longer Lext, but the temporal intensity becomes stable when Lext is less than 7.5 mm in spite of the fact that the operation regime is still multi-mode. Even if stronger feedback is given, the stability is not affected in short Lext. These stable oscillations attribute to spectral separation by shortening external cavity.
Fig. 7 Calculated dynamic spectral transition as a function of external cavity length Lext and feedback level R. Lext in air and in a silicon waveguide are shown in black and blue letters respectively.
The above results indicate that shortening external cavity makes the threshold feedback level for multi-mode oscillation higher. As was confirmed, when Lext is 2.8 mm in the air (1 mm in a silicon waveguide), single mode operation is marginally achieved even at R = −25 dB. Furthermore, temporally stable oscillation free from noise is also realized when Lext is less than 7.5 mm in the air (2.5 mm in a silicon waveguide) regardless of feedback levels.
Behaviour of RIN at different cavity lengths will depend on external feedback level. In case that feedback level is high, lasing thresholds of side modes and main mode are close. In that case, when mode spacing between main and side modes are short due to long external cavity length, temporal fluctuations of feedback itself and external conditions like temperature will make side modes oscillate and mode hopping may occur, resulting in increase of RIN. Even if side modes do not oscillate, their spontaneous emission constitutes RIN, but do not increase with carrier injection because the gain is clumped at main mode’s threshold. When mode spacing is broad due to short external cavity length, side modes are difficult to oscillate because they locate at far from centre of the gain spectrum. Spontaneous emission will not constitute RIN because gain is small, but carrier injection will increase gain because the gain clump is weak at gain spectrum edges. On the other hand, in case that feedback level is small, lasing thresholds of side modes are larger than main mode’s one. In that case, mode hopping is difficult to occur, and the rate of spontaneous emission contributing to side modes is so small that the effect is negligible.
Finally, concerning the external feedback light from the reflection facet at the back of a waveguide, it should be addressed that in silicon photonics technology today, large propagation loss of a silicon waveguide attenuates the external feedback light enough to make its impact negligible. In the near future, low-loss waveguides would make the feedback impact more considerable, and solutions such as shortening external cavity would become requisite.
5. Conclusion
In this report, we investigated the external feedback impact on DFB laser performance in silicon photonics packaging by both experiments and calculation. The calculation method was constructed by coupling dynamic transfer matrix method and rate equation model, and confirmed to work fine in good agreement with experiments. The feedback impact was explored with varying external feedback condition: external cavity length and feedback level. It was confirmed that shortening external cavity reduces feedback impact. DFB laser maintains single mode operation free from temporal noise when the external cavity has less than ~2.5 mm in the air (~1 mm in a silicon waveguide), even under considerable feedback level −25 dB.
Acknowledgment
We acknowledge Dr. Yi-Hao Chen for assisting the experimental work and discussing the results.
References and links
1. P. Pepeljugoski, J. Kash, F. Doany, D. Kuchta, L. Schares, C. Schow, M. Taubenblatt, B. J. Offrein, and A. Benner, “Towards exaflop servers and supercomputers: The roadmap for lower power and higher density optical interconnects,” in Proceedings of 36th European Conference and Exhibition on Optical Communication (Torino, 2010). [CrossRef]
2. M. Taubenblatt, “Optical interconnects for high-performance computing,” J. Lightwave Technol. 30(4), 448–457 (2012). [CrossRef]
3. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express 20(S2), A293–A308 (2012). [CrossRef] [PubMed]
4. M. Tokunari, H-H Hsu, K. Toriyama, H. Noma, and S. Nakagawa, “High-bandwidth density and low-power optical MCM using waveguide-integrated organic substrate,” (to be published in J. Lightwave Technol.)
5. Y. Vlasov, “Silicon CMOS-integrated nano-photonics for computer and data communications beyond 100G,” IEEE Commun. Mag. 50, S67–S72 (2012).
6. S. Assefa, S. Shank, W. Green, M. Khater, E. Kiewra, C. Reinholm, S. Kamlapurkar, A. Rylyakov, C. Schow, F. Horst, P. Huapu, T. Topuria, P. Rice, D. M. Gill, J. Rosenberg, T. Barwicz, Y. Min, J. Proesel, J. Hofrichter, B. J. Offrein, G. Xiaoxiong, W. Haensch, J. Ellis-Monaghan, and Y. Vlasov, “A 90 nm CMOS integrated nano-photonics technology for 25Gbps WDM optical communications applications,” IEDM (IEEE International Electron Devices Meeting), postdeadline session 33.8 (2012).
7. Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013). [CrossRef]
8. W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106–17113 (2007). [CrossRef] [PubMed]
9. S. Matsuo, K. Takeda, T. Sato, M. Notomi, A. Shinya, K. Nozaki, H. Taniyama, K. Hasebe, and T. Kakitsuka, “Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser,” Opt. Express 20(4), 3773–3780 (2012). [CrossRef] [PubMed]
10. C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55-μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012). [CrossRef]
11. T. Baba, “Nanostructured silicon photonics devices fabricated by CMOS-compatible process,” Proceedings of Photonics Global Conference (Singapore, 2012). [CrossRef]
12. S. Keyvaninia, G. Roelkens, D. Van Thourhout, C. Jany, M. Lamponi, A. Le Liepvre, F. Lelarge, D. Make, G.-H. Duan, D. Bordel, and J.-M. Fedeli, “Demonstration of a heterogeneously integrated III-V/SOI single wavelength tunable laser,” Opt. Express 21(3), 3784–3792 (2013). [CrossRef] [PubMed]
13. H. Park, A. Fang, S. Kodama, and J. Bowers, “Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells,” Opt. Express 13(23), 9460–9464 (2005). [CrossRef] [PubMed]
14. N. Fujioka, T. Chu, and M. Ishizaka, “Compact and low power consumption hybrid integrated wavelength tunable laser,” J. Lightwave Technol. 28(21), 3115–3120 (2010).
15. T. Shimizu, N. Hatori, M. Okano, M. Ishizaka, Y. Urino, T. Yamamoto, M. Mori, T. Nakamura, and Y. Arakawa, “High density hybrid integrated light source with a laser diode array on a silicon optical waveguide platform for inter-chip optical interconnection,” in Proceedings of IEEE International Conference on Group IV Photonics (London, 2011), pp.181–183. [CrossRef]
16. L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits (Wiley, 2012).
17. M. Gotoda, T. Nishimura, K. Matsumoto, T. Aoyagi, and K. Yoshiara, “Highly external optical feedback-tolerant 1.49-μm single-mode lasers with partially corrugated gratings,” IEEE J. Sel. Top. Quantum Electron. 15(3), 612–617 (2009). [CrossRef]
18. H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. J. Malloy, and L. F. Lester, “High external feedback resistance of laterally loss-coupled distributed feedback quantum dot semiconductor lasers,” IEEE Photonics Technol. Lett. 15(11), 1504–1506 (2003). [CrossRef]
19. M. G. Davis and R. F. O’Dowd, “A transfer matrix method based large-signal dynamic model for multielectrode DFB lasers,” IEEE J. Quantum Electron. 30(11), 2458–2466 (1994). [CrossRef]
20. O. Lavrova and D. Blumenthal, “Detailed transfer matrix method-based dynamic model for multisection widely tunable GCSR lasers,” J. Lightwave Technol. 18(9), 1274–1283 (2000).
21. 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]
22. J. Helms, C. Kurtzke, and K. Petermann, “External feedback requirements for coherent optical communication systems,” J. Lightwave Technol. 10(8), 1137–1141 (1992). [CrossRef]
23. K. Petermann, “External optical feedback phenomena in semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 1(2), 480–489 (1995). [CrossRef]
