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1015 20 25 field (section) number Fig. 2: Calculated normalized space optical field (normalized relative power) for the proposed TSDFB without self-pulsation, including forward field (from left to right, the leftest point has smallest field), reverse field (from left to right, the leftest point has largest field), and sum field.The self-pulsation situation generates periodic waveform, and it is intuitional that the internal optical field patterns should be changed and unstable compared with fig.2. The internal optical field patterns should be dynamic for each periodic waveform; that is, it is difficult for the optical field patterns in space to be almost over-lapped. A TS-DFB may be processed with anti-reflective (AR) coating on both facets; otherwise, the reflective effect from natural facets should be considered. Fig.3 (a}-(c) show the first case, i.e. with AR-coating; and Fig.4 (a)"{c) show the first case, i.e. with natural facets. Fig.3 (a) shows the calculated optical spectrum for TS-DFB mode-beating mechanism under self-pulsation for long time example, the typical field patterns for the DFB with A/4 phase shift has been simulated by the Finite-Difference method [3]. Optical Field Analysis and Numerical CalculationFinite-Difference method also works well for laser with many modes, with spectral mixing, or with noise. In a clock source, the excitation is due to random 'spontaneous noise'. Hence, the outputs are never precisely the same for run-to-run, or iterations. In other words, the result traces of iteration-to-iteration could be calculated, and the accumulative field pattern of all iterations could be visualized. The Finite-Difference method could be also applied to analyze the multi-section DFB; we focus on the proposed TS-DFB with two same long sections in order to avoid some complex effect caused by unequal ratio.It is interesting to view the difference between optical field under non-self-pulsation and optical field under self-pulsation. For the former, the output is stable. Hence, it is intuitional to image that the optical field should be more stable. That is, for different calculation iterations, the optical field patterns in space should be "almost over-lapped", as shown in fig.2. nonllalized relative power shift laver 8ratmilayer~J • • •I~~~~ã ctive layer Fig. I: Schema of the two sections DFB.The structure of TS-DFB is similar to a conventional index-coupled DFB laser, so it has the advantages of easy fabrication, low threshold current, large operating temperature range, high reliability, and low cost. The section with a shift layer has a larger effective index and thus a larger Bragg wavelength. While the self-pulsation takes place, the output waveform is periodic. Several viewpoints of such the phenomenon have been proposed and measured, for example, injection currents, self-pulsation frequency, and self-pulsation region [2].However, it is more difficult to measure the internal variation inside the device, especial for the internal optical field analysis in space distribution and in time doma...

We propose a numerical model to estimate the self-sustained pulsation frequency (SSP frequency) for a two-section distributed feedback laser (TS-DFB). A modulation transfer function is derived from the rate equations for carriers and photons. The SSP frequency can be obtained from the singularity condition of the transfer function. A useful but simple systematic design procedure is proposed for investigating the effects of various structural parameters on the SSP condition. The device parameters varied in the analysis include carrier density, section length ratio, grating coupling coefficient, and the refractive index change caused by adding a shift-layer. The device structure used for the SSP experiments and analysis is a TS-DFB laser with a shift-layer. This type of lasers can have stable lasing mode with large side-mode suppression ratio such that the inherent mode instability in a conventional index-guide DFB laser can be eliminated in this structure. This can simplify the operation of the SSP laser. The analysis model can also be applied to other laser structures. The results of numerical analysis match well with the experimental data.

We propose a numerical model, including modulation transform function and self-sustained pulsation condition, to estimate the self-sustained pulsation frequency, matched to the measured pulsation frequency, which considers the structure factors in a two-section distributed feedback laser with a thin shift-layer.

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