Locking bandwidth of actively mode-locked semiconductor lasers using fiber-grating external cavities

Classical coupled oscillators model of the rational harmonic mode locked laser

“…However, because of the large optical dimension of the mode locked laser system, practically, sometimes it is very difficult to implement due to the requirements of large computer memory and computation time, though some efforts have been made to get over these technical difficulties. 12,13 Besides, the numerical method does not provide so much physics insight as the analytical approaches.…”

Digital filter approach for Simulation of a complex integrated laser diode based on the traveling-wave model

“…For the FabryPérot laser case, we only need to set the coupling coefficient equal to zero, and replace by and assume that the reference wavelength is the gain peak wavelength. The finite difference scheme of the above equations is standard, which can be found in our previous work [9] or some recent works [10], [11], but the optical field at the end of the laser cavity should be calculated using the new scheme described in the following section, i.e., the end field will interact with the reflection digital filter extracted from the whole passive component.…”

“…1, the output optical field at a specific time can be expressed by the input optical field at this specific time and earlier at the interface of the active and passive parts as (10) where is the digital filter coefficients, which can be determined from the response function, i.e., the transmission coefficient of the passive components in the frequency domain (11) From (11), we find that could be obtained easily by a reverse fast Fourier transform (FFT) transformation of the transmission coefficient function in the frequency domain. Similarly, the reflected field from the passive part to the active part at a specific time can also be expressed by the input fields at this specific time and earlier as (12) where is the digital filter coefficients, which can be determined from the reflectivity coefficient of the passive part in the frequency domain (13) From (11) and (13), we can see that the extracted filters for the passive components are a set of time sequence complex numbers:…”

“…More importantly, we can readily incorporate the spectral properties of the passive sections, which can be obtained from measurements or other analytical/numerical models such as the beam propagation method (BPM). Our method is different from [11]. It is similar to the approach of [7], but we will present a general recipe suitable for all complicated integrated devices.…”

“…However, to extend the application of the traveling-wave model to the case of complicated photonics circuit which consists of both active and sophisticated passive parts is not straightforward. Zhai et al have used the novel scattering matrix method in combination with transmission line model of laser to investigate the mode-locking laser with fiber Bragg grating [11]. It is also reported that, in the pioneer VPI products, it is allowed for the digital filters based on transfer-matrix analysis of Bragg gratings to be combined with the time-domain model of laser diodes [8].…”