Experimental Evidence of Coherence Resonance in a Time-Delayed Bistable System

We report on the experimental observation of coherence resonance in a bistable system with delay. Our system consists of a vertical-cavity surface-emitting laser subject to time-delayed optical feedback simultaneously from a long and from an extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hopping regime and of the signal to noise ratio in the power spectrum.

Figure 1

Experimental setup. SMOF, single-mode optical fiber; PC, polarization controller; L, lens; P, polarizer; BS, beam splitter; D, photodiode; PD, high speed photodiode.

Figure 2

(a) Polarization-switching current when increasing (solid black curve) and decreasing (gray curve) the injection current versus $L_1$. The black dashed line represents the threshold current. (b) Experimentally obtained polarization-resolved power versus current curve at $L_1=9.5\mu \mathrm{m}$. Gray (black) line represents the low (high) frequency LP mode, while solid (dashed) lines represent the two LP modes for slowly increasing (decreasing) the injection current ($0.1\mathrm{mA}/\mathrm{s}$).

Figure 3

(a) Time trace of polarization mode hopping (power emitted in the high frequency LP mode when $\Gamma =8.5$) influenced by time-delayed optical feedback ($\tau \simeq 27\mathrm{ns}$) with an enlargement in (b). (c) RTD of ${\tau }_1$, ${\tau }_2$, and ${\tau }_{\mathrm{JRT}}$.

Figure 4

Joint residence time distribution for external noise set to (a) $-145$, (b) $-120$, and (c) $-105\mathrm{dBm}/\mathrm{Hz}$. (d) Zoom of the peak at 27 ns for different noise intensities.

Figure 5

Area of the first peak of the JRTD shown in Fig. 4 as a function of the input noise. The background has been subtracted before calculating the area and $\Gamma =45$.

Figure 6

(a) Electrical spectrum of the polarization-resolved output power at different noise intensities from $-105$ to $-145\mathrm{dBm}/\mathrm{Hz}$. (b) Signal to noise ratio of the first peak in the electrical spectrum (at around 37 MHz). $\Gamma =45$.

Figure 7

(a) Signal to noise ratio of the first peak in the electrical spectrum (at around 37 MHz) as a function of the input noise. (b) Area of the first peak of the JRTD plotted as a function of the input noise. The background has been subtracted before the calculation of the area is made. In (a) and (b), $\Gamma =7.5$. (c) Intensity of injected noise at which the resonance condition according to the SNR indicator is achieved for different values of the LP mode asymmetry factor $\Gamma$.