Mário R. G. Leiria, Inwoong Kim, Adolfo V. T. Cartaxo, IEEE, and Guifang Li, "Experimental Study of Pattern-Independent Phase Noise Accumulation in an All-Optical Clock Recovery Chain Based on Two-Section Gain-Coupled DFB Lasers", Journal of Lightwave Technology, Vol. 26, No. 12, pp. 1661-1670, June 15, 2008

• Abstract—The pattern-independent phase noise accumulation in a chain of all-optical clock recovery devices (CRDs) based on two-section gain-coupled distributed feedback (TS-DFB) laser operating in the coherent mode is studied experimentally and theoretically. A simple theoretical model, where the CRD output phase noise is equal to the sum of the phase noise introduced by the CRD and the CRD input phase noise filtered by the phase noise transfer function, has been proposed for the CRD equivalent phase noise model. The accumulation of pattern-independent phase noise is investigated experimentally and theoretically for different cut-off frequencies of the phase noise transfer function of the TS-DFB laser and two different optical signal to noise ratios. It is shown that, due to the phase noise added by the CRD, phase noise accumulates in the passband of the phase noise transfer function, with the phase noise transfer function well approximated by a first-order lowpass filter. Excellent qualitative agreement between the experimental results and the theoretical model is observed. Also, it is concluded that the phase noise accumulation model for CRD, where the recovered clock is locked to the optical power of the incoming clock signal, presented by other authors holds in a qualitative point of view for the TS-DFB laser operating in the coherent mode. Since the root-mean-square (rms) of the timing jitter is proportional to the square root of the integrated power spectral density of the phase noise, the results show that a smaller cut-off frequency of the phase noise transfer function does not lead to a smaller rms value of the pattern-independent timing jitter along the chain of all-optical CRDs based on TS-DFB laser. It is shown that the minimum rms of the pattern-independent timing jitter along the CRD chain results from a compromise between the cut-off frequency of the phase noise transfer function and the phase noise introduced by the TS-DFB laser.

• A dual mode multi-section gain-coupled distributed feedback laser with tunable mode spacing is subharmonically injection locked at 0.315 THz. The injected signal consists of an optical comb with harmonics 35 GHz apart and a bandwidth of approximately 1.9 THz. The optical comb is a result of strong four-wave mixing in a highly-nonlinear dispersion-shifted fiber. In order to observe locking of the multi-section laser, the output is optically downconverted to RF frequencies using the same optical comb. The locked multi-section DFB laser is a coherent and tunable optical source suitable for continuous-wave terahertz generation systems.

• The self-consistent mode-beating model is applied to a two-section partially gain-coupled distributed feedback (TS-GC DFB) laser with low coupling strengths. The model is based on introducing a fixed detuning parameter to the governing rate equations of the slowly-varying fields. The existence of quasi-symmetrical, a mix of quasi–symmetrical and asymmetrical, and asymmetrical mode beating depends on the coupling strength of the cavity. The quasi-symmetrical mode beating predicted here is similar in characteristics to the mode beating found in index-coupled self-pulsating lasers. It has a continuous and a wide tuning range. The asymmetrical mode beating is capable of producing self-pulsations over multiple self-pulsating regimes and higher self-pulsating frequencies than the quasi-symmetrical mode beating.

• The role of cavity conditions in the dynamics of two-section gain-coupled distributed feedback (DFB) lasers is investigated using a self-consistent model. Self-sustained pulsation (SSP) exists only for devices with strongly coupled DFB gratings. As the coupling strength increases, multiple SSP regimes are developed. The SSP frequency tuning range increases as cavity length decreases. The frequency and modulation index predicted by the model agree well with experimental results. The facet condition of each section is found to affect SSP differently because of the asymmetrical behavior of the modes responsible for SSP.

• It is shown that two-section gain-coupled DFB lasers with large section lengths and weak distributed feedback coupling exhibit a self-pulsation tuning range greater than reported previously. The phase noise of a sideband injection locked self pulsation is measured and the jitter introduced by the self-pulsing laser found to be negligible.

• We report the first analysis and experimental demonstration of tunable microwave/millimeter-wave signal generation in two-section gain-coupled distributed-feedback (DFB) lasers. Continuous tuning from 20 to 64 GHz was directly observed and characterized both in the electrical and optical domain. The mechanism of microwave generation in two-section gaincoupled DFB lasers is different from that of two-section index-coupled DFB lasers previously reported. As a result, gain coupling can lead to simultaneous large modulation indexes and high frequencies in two-section DFB lasers.

• We present a traveling-wave large-signal simulation of the spatiotemporal dynamics of two-section distributed feedback lasers, emphasizing the self-pulsation phenomenon. For index-coupled lasers, self-pulsation is a result of the interaction of two modes, each spatially confined primarily to one section. For partially gain-coupled lasers, self-pulsation is a result of the interaction of two modes, one that is spatially confined primarily to one section and another that belongs to both sections. The self-pulsation frequency-tuning range and the modulation index of partially gain-coupled lasers are found to be substantially larger than those of index-coupled lasers. Experimentally, self-pulsation with a frequency-tuning range from 20 to 60 GHz in two-section partially gain-coupled distributed-feedback lasers has been characterized in the electrical domain. The noise of self-pulsation was reduced experimentally by optical feedback.