Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: Experiment and theory

We investigate experimentally and theoretically the dynamics of a semiconductor laser subject to filtered optical feedback. Depending on the feedback strength we find dynamical regimes with different dependence on the feedback phase. In particular, the influence of the feedback phase on cw emission and on frequency oscillations is characterized experimentally. We also measure the dependence of the filter mirror distance on the frequency oscillations. In general, good agreement between experiment and theory is found.

Figure 1

Setup of the FOF laser with a Fabry-Perot filter, piezotranslation stage, optical isolators (ISO), mirrors (M), and beamsplitter (BS). The detection for both the laser field and the feedback field consists of scanning Fabry-Perot interferometers, fast photodiodes, electrical spectrum analyzers, digital oscilloscopes, and slow photodiodes.

Figure 2

Overview of the different dynamical regimes I–VII that can be identified for different ranges of feedback strengths (shown here in units of threshold reduction).

Figure 3

Measured $2\pi$ cycle of the EFMs as a function of the detuning. Each panel shows the intensity of the feedback light as a function of increasing and decreasing pump current. The pump current was slowly modulated with a triangular ramp, which is shown in the top of each panel. Arrows indicate the motion of EFM plateaus with the change of the feedback phase. Between consecutive panels the feedback phase $C_p$ has changed by approximately $\pi ∕3$.

Figure 4

Computed $2\pi$ cycle of the EFMs as a function of the detuning for $\kappa =0.001$. Each panel shows the intensity of the feedback light $I_F$ as a function of the solitary laser frequency ${\Omega }_0$. Thick parts of the black EFM curve correspond to stable EFMs. Pairs of stable and unstable EFMs are born in saddle-node bifurcations. The gray curve is the curve of saddle-node bifurcations as parametrized by $C_p$. Arrows indicate the motion of EFM plateaus for increasing $C_p$. Between consecutive panels the feedback phase $C_p$ is changed by $\pi ∕3$.

Figure 5

Measured relaxation and frequency oscillations, namely optical spectrum (a1), RIN spectrum of the laser light (a2), and RIN spectrum of the feedback light (a3) of ROs; and optical spectrum (b1), RIN spectrum of the laser light (b2) and RIN spectrum of the feedback light (b3) of FOs.

Figure 6

Computed relaxation and frequency oscillations, namely optical spectrum (a1), RIN spectrum of the laser light (a2), RIN spectrum of the feedback light (a3), and time series (a4) of the laser (gray) and feedback light (black) of ROs; and optical spectrum (b1), RIN spectrum of the laser light (b2), RIN spectrum of the feedback light (b3), and time series (a4) of the laser (gray) and feedback light (black) of FOs. The horizontal gray line indicates the estimated noise level of $10\mathrm{dB}$. The light gray region in the RIN spectra is the experimentally accessible frequency range.

Figure 7

One cycle of the measured feedback phase dependence in regime I. Shown are optical spectra of the laser field; between consecutive panels the feedback phase has changed by approximately $\pi ∕3$.

Figure 8

Computed feedback phase dependence for $\kappa =0.009$. The black curve is the feedback intensity of EFMs as parametrized by $C_p$; modes (엯) and antimodes (×) for $C_p=0$ are also shown. The gray bubble (bounded by minimum and the maximum amplitudes) is a region of stable FOs.

Figure 9

Optical spectrum (a) and RIN spectrum (b) of the feedback light for quasiperiodic oscillations with RO and FO components.

Figure 10

Optical spectrum (a) and RIN spectrum (b) of the feedback light showing complicated dynamics in the low frequency part of the laser frequency.

Figure 11

Optical spectrum (a) and RIN spectrum (b) of the feedback light showing complicated dynamics in both the RO domain and the FO domain.

Figure 12

Measured dependence of the FO frequency on the distance between the filter mirrors; the vertical bars indicate the tuning range of the FO frequency when changing the feedback phase.

Figure 13

Computed dependence of the FO frequency on the distance between the filter mirrors. Shown is a (black) curve of FOs; the gray shaded region indicates the possible FO frequencies when $C_p$ is varied.