Theory of Self‐pulsing in Photonic Crystal Fano Lasers

Abstract

Laser self‐pulsing was a phenomenon exclusive to macroscopic lasers until recently, where self‐starting laser pulsation in a microscopic photonic crystal Fano laser was reported. In this paper a theoretical model is developed to describe the Fano laser, including descriptions of the highly‐dispersive Fano mirror, the laser frequency and the threshold gain. The model is based upon a combination of conventional laser rate equations and coupled‐mode theory. The dynamical model is used to demonstrate how the laser has two regimes of operation, continuous‐wave output and self‐pulsing, and these regimes are characterised using phase diagrams, establishing the regime of self‐pulsing numerically. Furthermore, the physics behind the self‐pulsing mechanism are explained in detail and it is demonstrated how cavity absorption makes the Fano mirror function as a saturable absorber, leading to Q‐switched pulse generation. A stability analysis is used to demonstrate how the dominant mechanism of instability is relaxation oscillations becoming un‐damped. Finally the effect of varying key self‐pulsing parameters is investigated by characterisation of the change in self‐pulsing regions.

Two-dimensional phase-space picture of the photonic crystal Fano laser

“…The spectral width of the resonance is determined by the quality factor of the nanocavity enabling the realization of a narrow-band mirror. The dynamic operation of the laser is modeled using a combination of coupled-mode theory and conventional laser rate equations [11]. The model has been used to demonstrate that there are two regimes of operation, the continuous-wave Figure 1.…”

“…regime and a self-pulsing regime [11]. Particularly, it has been shown that as the real part of any of the eigenvalues of the underlying stability matrix, evaluated at the steady-state, becomes positive, the relaxation oscillation becomes undamped resulting in the laser becoming unstable and self-pulsing behaviour setting in [11,12].…”

“…regime and a self-pulsing regime [11]. Particularly, it has been shown that as the real part of any of the eigenvalues of the underlying stability matrix, evaluated at the steady-state, becomes positive, the relaxation oscillation becomes undamped resulting in the laser becoming unstable and self-pulsing behaviour setting in [11,12]. However, it does not fully explain the origin of instability in the whole parameter space of the laser as there exists a region in which the laser can become unstable even when all the steady-state eigenvalues are negative [11].…”

Suppression of Coherence Collapse in Semiconductor Fano Lasers

“…This realises a type of bound-mode-in-continuum [18], which functions as a cavity mode. This configuration was experimentally realised in a photonic crystal platform [15], showing remarkable properties including pinned single-mode lasing and the first case of self-pulsing in a microscopic laser [15,19], and it has also been suggested that the frequency modulation bandwidth of this laser may be orders of magnitude larger than conventional lasers [20]. The photonic crystal platform itself has also provided numerous promising microscopic lasers for the photonic integrated circuits of the future [21][22][23].…”

“…This model has proven to work well for both Fabry-Perot and distributed feedback lasers, as well as VCSELs [5], but in order to describe the Fano laser a generalisation is necessary. The generalisation consists of coupling the Lang-Kobayashi model to a dynamical equation for the field stored in the nanocavity [14,19], in order to temporally resolve the Fano interference. This approach is also of interest for studying other coupled systems with complicated external feedback arrangements due to the general nature of the formulation.…”