Passive Mode-locking of Discrete Mode Lasers

Spectral Filtering for Sinusoidal and Pulsed Intensity Output

Our approach to mode selection is particularly suited to designing laser cavities for mode-locking. This is because modes can be selected and their losses adjusted so that not only the repetition rate but also the pulse shape and duration can in principle  be specified independent of the gain medium dispersion and the cavity length.

An example was shown on our introductory page, where by selecting four modes, we can engineer a minimal mode-locked state with sinusoidal modulation of the intensity ouput at the mode-locking frequency. The intensity output of this device is similar to that of the dual-mode laser with THz primary mode spacing. For mode spacings of order 300 GHz or less, an additional pair of modes allows one to overcome wavelength bistability by enabling mode-locking of the device [IEEE T-MTT 58, 3083 (2010)]

Fig. 1 shows an example where six primary modes were selected at the first harmonic of the cavity. Here we obtained 2 ps pulses at 100 GHz repetition rate. More than six modes are locked in this example on account of power transfer by four-wave mixing [Opt. Lett. 35, 2200 (2010)]. We are particularly interested in building frequency domain models which can explain the phase space structure that we observe with these devices. This will enable us to understand the bifurcation structure that governs the appearance of Q-switching and mode-locking dynamics.

 

6mspc2 100GHz data

 

 

Fig.1: Mode-locked device with pulsed intensity ouput. (a) Feature density function and modal threshold gain (inset). Lower panel: Cavity schematic. (b) Mode-locked spectrum and auto-correlation showing pulsed output with 2 ps pulse duration at 100 GHz repetition rate.

Photonic Integration of Frequency Comb Sources

Mode-locked devices fabricated to our designs have improved noise performance and are closer to the Fourier transform limit compared to their Fabry-Perot equivalents [Optics Express 19, 13989 (2011).] For example, the sinusoidal sources can have a mode-beating linewidth as low as 1 MHz. This improvement may be a fundamental aspect related to the spectral filtering of cavity modes that we perform. We have also shown in our recent work that photonic integration of these devices will be possible where one or both of the external mirrors is replaced by a short Bragg grating section. By using a high resolution technique such a electron beam lithography to implement the grating profile and integrated bounding mirror, as many as sixteen primary modes may be selected. In this limit we can also address the frequency disperion of the lasing modes directly through the grating profile.

An example of dispersion compensation is shown in Fig. 2, where we have been able to limit the grating induced dispersion by accounting for scattering terms beyond first order in the grating index step. Ultimately, we would like to optimise the modal  thresholds and dispersion through the grating profile taking the nonlinear coupling of primary modes into account [Opt. Lett. 36, 2985 (2011)]. Modern self-assembled materials currently provide sufficient bandwidth to reach <500 fs pulses in simple Fabry-Perot devices. Much shorter pulses will be possible if we compensate for material dispersion directly through the grating profile. 

harmonic mode locking calculation

 Fig. 2: Calculation of the modal threshold gain and dispersion in a device designed to support a comb of sixteen primary modes. We imagine the device to include an integrated bounding mirror formed by a short Bragg grating section. With moderately coupled grating strengths as here, the grating induced dispersion dominates the material induced dispersion. The dispersion can be limited by including corrections that account for second order scattering effects.  



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