Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser

We have demonstrated and characterized the generation of ultra broadband microwave frequency combs with an optical pulse-injected semiconductor laser. Through optical pulse injection, the microwave frequency combs generated in the slave laser (SL) have bandwidths greater than 20 GHz within a ±5 dB amplitude variation, which is almost 3-fold of the 7 GHz relaxation oscillation frequency of the laser used. The line spacing of the comb is tunable from 990 MHz to 2.6 GHz, determined by the repetition frequency of the injection optical pulses produced by the master laser (ML) with optoelectronic feedback. At an offset frequency of 200 kHz, a single sideband (SSB) phase noise of−60 dBc/kHz (−90 dBc/Hz estimated) in the 1st harmonic is measured while a noise suppression relative to the injected regular pulsing state of the ML of more than 25 dB in the 17th harmonic is achieved. A pulsewidth of 29 ps and a rms timing jitter of 18.7 ps are obtained in the time domain for the microwave frequency comb generated. Further stabilization is realized by modulating the ML at the fundamental frequency of the injected regular pulsing state. The feasibility of utilizing the generated microwave frequency comb in frequency conversion and signal broadcasting is also explored. The conversion gain of each channel increases linearly as the signal power increases with a ratio of about 0.81 dB/dBm. © 2009 Optical Society of America OCIS codes: (140.5960) Semiconductor lasers, (190.3100) Instabilities and chaos, (350.4010) Microwaves, (140.3520) Injection-locked. References and links 1. T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (1997). 2. A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148-1151 (1999). 3. S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37, 329-336 (2001). 4. S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic application of nonlinear semiconductor laser dynamics,” Opt. and Quantum Electron. 40, 83-95 (2008). 5. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. Alan Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature. 438, 343-346 (2005). (C) 2009 OSA 12 October 2009 / Vol. 17, No. 21 / OPTICS EXPRESS 18596 #115692 $15.00 USD Received 13 Aug 2009; revised 25 Sep 2009; accepted 29 Sep 2009; published 30 Sep 2009 6. T. Yoshino, M. Nara, S. Mnatzakanian, B. S. Lee, and T. C. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 892-897 (1987). 7. S. K. Hwang, H. F. Chen, and C. T. Lin, “All-optical frequency conversion using nonlinear dynamics of semiconductor lasers,” Opt. Lett. 34, 812-814 (2009). 8. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. of Sel. Top. Quantum Electron. 10, 991-997 (2004). 9. F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40, 815-820 (2004). 10. W. W. Chow and S. Wieczorek, “Using chaos for remote sensing of laser radiation,” Opt. Express. 17, 7491-7504 (2009). 11. S. C. Chan, G. Q. Xia, and J. M. Liu, “Optical generation of a precise microwave frequency comb by harmonic frequency locking,” Opt. Lett. 32, 1917-1949 (2007). 12. C. B. Huang, S. G. Park, D. E. Leaird, and A. M. Weiner, “Nonlinear broadened phase-modulated continuouswave laser frequency combs characterized using DPSK decoding,” Opt. Express 16, 2520-2527 (2008). 13. S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett. 11, 551-553 (1999). 14. S. Ozharar, F. Quinlan, I. Ozdur, S. Gee, and P. J. Delfyett, “Ultraflat optical comb generation by phase-only modulation of continuous-wave light,” IEEE Photon. Technol. Lett. 20, 36-38 (2008). 15. H. Y. Ryu, H. S. Moon, and H. S. Suh, “Optical frequency comb generator based on actively mode-locked fiber ring laser using an acousto-optic modulator with injection-seeding,” Opt. Express 15, 11396-11401 (2007). 16. F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically mode-locked semiconductor-based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A: Pure Appl. Opt. 11, 103001-103023 (2009). 17. F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor lasers under repetitive optical pulse injection,” IEEE J. of Sel. Top. Quantum Electron. 15, 604-611 (2009). 18. Y. S. Juan and F. Y. Lin, “Microwave-frequency-comb generation utilizing a semiconductor laser subject to optical pulse injection from an optoelectronic feedback laser,” Opt. Lett. 34, 1636-1638 (2009). 19. For example, Picosecond Pulse Labs model 7112 comb generator. 20. T. B. Simpson, J. M. Liu, and A. Gavrielides, “Bandwidth enhancement and broadband noise reduction in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 1, 95-96 (1995). 21. N. Schunk and K. Petermann, “Noise analysis of injection-locked semiconductor injection lasers,” IEEE J. Quantum Electron. 22, 642-650 (1986). 22. From http://www.eu.anritsu.com/files/11410-00344.pdf 23. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Optoelectronic oscillator using a LiNbO3 phase modulator for selfoscillating frequency comb generation,” Opt. Lett. 31, 811-813 (2006).


Introduction
Nonlinear dynamics of semiconductor lasers under optical injection [1], optical feedback [2], and optoelectronic feedback [3] have been extensively studied in recent years.Various dynamical states have been investigated where many unique applications utilizing them have been proposed and demonstrated [4], such as secured communications [5], feedback interferometer [6], all-optical frequency conversion [7], laser chaos-based lidar [8], radar [9], and sensors [10].Lately, microwave frequency combs generated with the harmonic frequency-locked states in a negative optoelectronic feedback (NOEF) laser have been proposed [11].However, the microwave frequency combs generated have bandwidths of only a few GHz limited by the electronic bandwidth of the feedback loop.Moreover, large amplitude variation and severe nonharmonic spurs from the residual of the delay frequency also restrict their potential applications.
While optical techniques such as modulating CW light with external modulators [12,13,14] or mode-locking a laser [15,16] can generate optical frequency combs with large bandwidths and wide line spacings, spectral dispersion controls are required to faithfully convert the optical frequency combs into the microwave frequency combs with a small amplitude variation among the comb lines.To generate frequency combs with GHz line spacings, expensive high-frequency synthesizers and modulators for the external modulation and demanding stabilization for the mode-locked technique are needed.Moreover, the line spacings of the optical frequency combs generated by the mode-locked laser have limited tuning ranges (typically below 100 MHz) due to the fixed length of laser cavity.
Recently, nonlinear dynamics of semiconductor lasers under repetitive optical pulse injection have been investigated numerically [17], where frequency-locked states with different locking ratios have been observed.Generation of microwave frequency combs utilizing the frequencylocked states in an optical pulse-injected semiconductor laser has been proposed and experimentally demonstrated [18].By optically injecting a regular pulsing output from a master laser (ML) subject to optoelectronic feedback into a slave laser (SL), ultra broadband microwave frequency combs with low nonharmonic spurs and wide tuning range can be obtained.In this paper, we study the characteristics of the microwave frequency combs generated in an optical pulse-injected semiconductor laser in detail.The spectral linewidths and the single sideband (SSB) phase noise of each comb line are investigated to analyze their spectral purities and stabilities.The corresponding pulsewidths and timing jitters of the injected and output pulses from the ML and the SL are measured.The differences between a pulse-injected and a sinusoidally modulated light-injected semiconductor lasers are compared.Moreover, the potential applications of frequency conversion and signal broadcasting using the microwave frequency comb generated are also explored.Figure 1 shows the experimental setup of the microwave frequency comb generation system, in which a SL is subjected to optical pulse injection from a ML with optoelectronic feedback.The ML and SL used are two commercial 1.3 µm single-mode distributed (DFB) semiconductor lasers.Both lasers emit optical power of about 8.5 mW and have relaxation oscillation frequencies of 7 GHz deduced from their noise spectra when biased at J = 30 mA.The out-put of the ML is fed back to itself optoelectronically through a 10 GHz photodetector (Albis PDCS65T) to generate the regular pulsing states, a series of equal-amplitude pulses in time, from the nonlinear dynamics of the semiconductor laser [3].By adjusting the delay time and the feedback strength with the movable mirror and the variable attenuator, the repetition frequency f rep of the regular pulsing state can be tuned in a range between 990 MHz to 2.6 GHz mainly limited by the 3 GHz electric amplifier (JCA JCA003-201) used in our experiment.The optical pulses produced from the regular pulsing state are then injected into the SL optically through a free space circulator formed by the half-wave plates, the polarizing beam splitter, and the Faraday rotator.By adjusting the normalized injection strength ξ i (the ratio of the output fields of the SL to the ML) and the detuning frequency Ω (the difference in optical frequencies between the ML and the SL), the SL can be driven into various dynamical states.The output signals of the ML and the SL are detected by photodetectors (Discovery Semiconductors DSC30S) and amplifiers (MITEQ AFS6-00102000-30-10P-6) with 20 GHz bandwidths and recorded with a 26.5 GHz power spectrum analyzer (Agilent E4407B) and a 28 GHz sampling oscilloscope (Agilent 86100c with module 86106B).To modulate the laser current, a synthesized signal generator (Anritsu MG3690B) with a 3-dB linewidth below 1 Hz is used.Figures 2(a) and (b) show the power spectrum and the corresponding pulse train of the regular pulsing state of the ML under optoelectronic feedback with f rep = 1.15 GHz, where f rep can be easily tuned by varying the feedback delay time.While high-order harmonics are pre-sented in the spectrum of the regular pulsing state as shown in Fig. 2(a), only the fundamental frequency has a relatively larger magnitude.The magnitudes of the high-order components are significantly suppressed by the electronic bandwidth of the optoelectronic feedback loop.Under such condition, pulsewidths of 370 ps are measured for the regular pulsing state in the time domain as shown in Fig. 2(b).Note that, although utilizing electronic components with larger bandwidths may possibly overcome the bandwidth limitation effect and seems able to generate regular pulsing states with higher-order harmonics having larger amplitudes (preferred for microwave frequency combs), however, the generated regular pulsing state will pulse at a higher frequency instead due to the increase of the electronic bandwidth so that the higher-order harmonics will still be suppressed and inevitably fall beyond the already increased bandwidth owing to the increase of the line spacing.By injecting the generated optical pulses into the SL, various dynamical states can be obtained with different injection strengths and detuning frequencies [17].

Results and discussions
Figures 2(c) and (d) show the power spectrum and the corresponding pulse train of the microwave frequency comb generated with a line spacing of 1.15 GHz having the injection parameters set at J = 30 mA, ξ i = 0.31, and Ω = 8.2 GHz.Without any external modulation, the line spacing can be tuned by simply adjusting the delay length.As can be seen in Fig. 2(c), while the SL has a relaxation oscillation frequency of 7 GHz only, the microwave frequency comb generated has a bandwidth greater than 20 GHz within a ±5 dB amplitude variation benefited by the bandwidth enhancement effect through optical injection.Although having some ringings, the pulses emitted from the SL are clearly shortened and a pulsewidth of 29 ps is measured as shown in Fig. 2(d).Note that, while stronger injection can further enhanced the bandwidths, careful balancing between the injection parameters is necessary for the SL to maintain in the phase-locked state so that microwave frequency comb with small variation in the spectral envelope and low noise floor can be generated.With different injection parameters, microwave frequency combs with different bandwidths and spectral envelopes are observed.While microwave frequency combs with even smaller amplitude variations in narrower bandwidths are also obtainable (for instance, ±3 dB amplitude variation in 14 GHz bandwidth [18]), compared with the benchmark set by the commercial circuit-based comb generators that typically have ±20 dB in a 20 GHz range [19] and the microwave frequency combs generated by the harmonic frequency locking states from the NOEF system that have ±14 dB in a 3 GHz range, the microwave frequency comb demonstrated in this paper already shows a significant improvement in terms of even energy distribution among the comb lines.Moreover, while the microwave frequency combs generated from the NOEF system suffer from severe nonharmonic spurs as high as 14 dB above the background [11], little nonharmonic spurs (less than 3 dB from the background) is found in Fig. 2(c).The bandwidths of the microwave frequency combs generated in this study are also much broader than those generated with the NOEF system since the laser (i.e. the SL in this case) is only subjected to the optical pulse injection and is not limited by the electronic bandwidth of the feedback loop.
The higher-order harmonics in the spectrum of the injection pulse seen in Fig. 2(a), although with small magnitudes, are found very important in the microwave frequency comb generation process.To show the role of these higher-order harmonic components, the ML is directly current modulated at 1.15 GHz (same as the f rep ) without applying the optoelectronic feedback.Figures 3(a) and (b) show the power spectra of the ML and the SL, respectively.With only current modulation, no higher-order harmonic is seen in Fig. 3(a) for the ML.The modulated light is injected into the SL under exactly the same condition as in the pulse injection case and, without having the higher-order harmonics as the seeds, the SL generates only few higher-order harmonics with very small magnitudes as shown in Fig. 3(b).Without the higher-order harmonics, the energy can no longer be successfully redistributed among the preexisted frequency compo-= > Fig. 3. Power spectra of (a) the ML and (b) the SL when the ML is current modulated at 1.15 GHz without the optoelectronic feedback.nents (the seeds) through the nonlinear dynamics of frequency mixing and many higher-order harmonics are missing from the spectrum in the range of interest.However, although having current modulation on the ML alone cannot produce the desired microwave frequency combs as discussed, together with the optoelectronic feedback it can reduce the spectral linewidths and suppress the phase noise of the microwave frequency combs generated in the pulse injection configuration.
Figure 4 shows the power spectrum and the corresponding pulse train of the regular pulsing state of the ML and the microwave frequency comb of the SL under the same conditions as those used in Fig. 2 but with the ML current modulated at the 1 st harmonic frequency of 1.15 GHz.The pulsewidths of the ML and the SL measured from Figs. 4(b) and (d) are shortened to 312 and 24 ps, respectively.Moreover, the root-mean-square (rms) timing jitters for the ML and the SL are also reduced from 24.3 and 18.7 ps (without modulation) to 7.1 and 5.7 ps (with modulation), respectively.While the power spectra shown in Figs.4(a) and (c) seem similar to those shown in Figs.2(a) and (c), the linewidths and phase noise of each frequency components are significantly reduced when inspected with a finer resolution.To analyze the spectral purity of the generated microwave frequency comb, the microwave spectral linewidth and the single-sideband (SSB) phase noise of the ML and the SL are investigated using the power spectral analyzer.Figures 5(a) and (b) show the power spectra of the 1 st harmonics of the regular pulsing state of the ML and the generated microwave frequency comb of the SL shown in Figs.2(a) and (c), respectively, with a resolution bandwidth of 100 Hz.A 3-dB spectral linewidth of only 900 Hz is measured the 1 harmonic of the regular pulsing state as shown in Fig. 5(a), which is greatly stabilized due the phase in the opto-electronic feedback loop.The same frequency component of the microwave frequency comb in the SL is further reduced to about 500 Hz through optical injection [20,21] as shown in Fig. 5(b).Compared to the periodic oscillation states seen in a semiconductor laser subject to constant optical injection which have linewidths typically in the range of several MHz, both the regular pulsing state of the ML and the generated microwave frequency comb of the SL demonstrate excellent spectral purity.As mentioned earlier, direct current modulation on the ML at the fundamental frequency of the regular pulsing state can be applied when further stabilization is needed.Figures 5(c) and (d) show the power spectra of the ML and the SL with the same conditions as in Figs.5(a) and (b) respectively, except that the ML is current modulated at the fundamental frequency f rep = 1.15 GHz.As can be seen, the linewidths in both spectra are reduced to below 1 Hz (limited by the resolution of the spectral analyzer used), which are dictated by the linewidth of the electrical signal used in the modulation.Figures 6(a) and (b) show the SSB phase noise of the 1 st and the 17 th harmonics of the regular pulsing state of the ML (dotted curves) and the microwave frequency comb in the SL (solid curves) with (black) and without (red) the modulation, respectively, with a resolution bandwidth of 1 kHz.For the 1 st harmonics of the microwave frequency comb generated as shown in Fig. 6(a), a SSB phase noise of −60 dBc/kHz (−90 dBc/Hz estimated) is achieved at offset frequencies of 25 and 200 kHz with and without the modulation, respectively.Compared to the modulation signal that has a SSB phase noise of about -95 dBc/Hz at an offset frequency of 25 kHz [22], the obtained SSB phase noise is slightly higher due to the excess noise from the electrical components.For the 17 th harmonic shown in Fig. 6(b), a SSB phase noise suppression of more than 25 dB at an offset frequency of 200 kHz is achieved for the microwave frequency comb generated in the SL compared with the injected regular pulsing state from the ML.Another 15 dB of suppression is realized when the ML is applied with the modulation.Note that, while the SSB phase noise in both the ML and the SL output increase and accumulate as the orders of the harmonics increase as expected, noise suppression through optical injection and current modulation is observed in all of the comb lines that we have measured.Even without modulation, the spectral purity of the microwave frequency comb generated (SSB phase noise of about −90 dBc/Hz offset at 200 kHz) is comparable to the harmonic frequency-locked states of the NOEF laser (SSB phase noise of about −83 dBc/Hz offset at 200 kHz) [11] and the optical frequency comb generated with the optoelectronic oscillator using phase modulator (SSB phase noise of about −95 dBc/Hz offset at 200 kHz) [23].The microwave frequency combs generated with the pulse-injected semiconductor laser can be utilized in frequency conversion and signal broadcasting when an external microwave signal is modulated over one of the comb line.Figure 7(a) shows the power spectrum of the microwave frequency comb (green) with exactly 1.0 GHz line spacing generated with J = 28.3mA, ξ i = 0.31, and Ω = 11.7 GHz and the spectrum after applying an sinusoidal signal at the 6 th harmonic (black), respectively.The sinusoidal signal is from the same synthesized signal generator previously used to current modulate the master laser.As can be seen, through frequency mixing and energy redistribution, the applied signal is converted to all 20 microwave channels formed by the microwave frequency comb from 1 to 20 GHz.By measuring the ratio of the spectral peaks with and without the signal for each channel, the conversion gain of each channel for different signal power is obtained and shown in Fig. 7(b).As can be seen, the conversion gain of each channel increases linearly as the signal power increases.For both the down-conversion (2 nd and 5 th harmonics) and the up-conversion (7 th and 20 th harmonics) cases, the conversion gain increases with a ratio of about 0.81 dB/dBm.The ratio of the conversion gain between the converted channel to the self-modulation (6 th harmonics) is about 0.57.Note that, when the signal power is below −12 dBm, the conversion is too weak to be observed.When the signal power exceeds 20 dBm, the applied signal strongly influences the nonlinear dynamics of the SL and the laser tends to be driven into unstable states.Therefore, while adjusting for the desired conversion gain, the power of the applied signal has to be kept within the range so that the laser can be maintained in the microwave frequency comb state.

Conclusions
In conclusion, we have demonstrated and characterized the generation of ultra broadband microwave frequency combs with an optical pulse-injected semiconductor laser.Through optical pulse injection, the microwave frequency combs generated in the SL have bandwidths greater than 20 GHz within a ±5 dB amplitude variation.The line spacings of the combs can be tuned from 2.6 GHz, determined by the repetition frequency of the optical pulses generated by the ML with optoelectronic feedback.Compared microwave frequency combs generated by the semiconductor laser making use of harmonic frequencystates, the microwave combs demonstrated have little nonharmonic spurs and wider bandwidths.At an offset frequency of 200 kHz, SSB phase noise of −60 dBc/kHz (−90 dBc/Hz estimated) in the 1 st harmonic is measured while a noise suppression, relative to the injected regular pulsing state of the ML, of more than 25 dB in the 17 th harmonic is achieved.A pulsewidth of 29 ps and a rms timing jitter of 18.7 ps are obtained in the time domain for the microwave frequency comb generated.Further stabilization is realized by modulating the ML at the fundamental frequency of the injected regular pulsing state.Moreover, we also explore the feasibility of utilizing the generated microwave frequency comb in frequency conversion and signal broadcasting.The conversion gain of each channel increases linearly as the signal power increases with a ratio of about 0.81 dB/dBm.

Fig. 2 .
Fig. 2. (a) Power spectrum and (b) corresponding pulse train of the regular pulsing state in the ML subject to optoelectronic feedback and (c) power spectrum and (d) corresponded pulse train of the microwave frequency comb generated in the SL with J = 30 mA, ξ i = 0.31, and Ω = 8.2 GHz.

Fig. 4 .
Fig. 4. (a) Power spectrum and (b) corresponding pulse train of the regular pulsing state in the ML subject to optoelectronic feedback and (c) power spectrum and (d) corresponding pulse train of the microwave frequency comb generated in the SL with J = 30 mA, ξ i = 0.31, and Ω = 8.2 GHz.The ML is current modulated at the 1 st harmonic frequency of 1.15 GHz.

Fig. 5 .
Fig. 5. Power spectra of the 1 st harmonics of the regular pulsing state of the ML (a) without and (c) with the modulation and the generated microwave frequency comb in the SL (b) without and (d) with the modulation.The arrows mark the 3-dB spectral linewidths.

Fig. 6 .
Fig. 6. (Color online) SSB phase noise of (a) the 1 st and (b) the 17 th harmonics of the regular pulsing state of the ML (dotted curves) and the microwave frequency comb of the SL (solid curves) with (black) and without (red) the modulation.

Fig. 7 .
Fig. 7. (Color online) (a) Power spectrum of the microwave frequency comb (green) with exactly 1.0 GHz line spacing generated with J = 28.3mA, ξ i = 0.31, and Ω = 11.7 GHz and the spectrum after introducing a sinusoidal signal at the 6 th harmonic (black).(b) Conversion gain of each channel for different signal power.The solid lines are the linear fittings.