# Precise Photon Correlation Measurement of a Chaotic Laser
## 4 Experimental Results  
The chaotic laser was firstly attenuated by a variable attenuator and then passed through the HBT setup. In the photon detection system, an internal clock triggered two channel gates simultaneously. When a photon was detected on one channel, the arriving time was recorded. During the same clock period, a subsequent photon was received from another channel and then the time interval was measured. The desired distribution was obtained with many records, and if the detection quantum efficiency was higher, the better the photon pair distribution was close to the real light source distribution. Otherwise, the single photon detector would mistake dark noise for photon signals. Moreover, as the incident photon number increased, the noise level would be higher due to the after pulsing effect. In that case, the time interval distribution of photon pairs was also affected by noise. When the coherence time of light source was short, high resolution time was required in the detection. Besides, the unbalance of the two light intensities after the BS had an adverse effect on the acquired distribution. It was difficult to obtain an accurate time interval distribution of photon pairs with a very low quantum efficiency. In our experiment, the detection quantum efficiency was 25%. We investigated how different average photon intensity and coherence time affected the accuracy of different order corrections. We used the relative error to compare different high order corrections with the ideal second order photon correlation. According to Equation (2), we calculated \(P_{9}(\tau)\) with high order terms and omitted the terms higher than ninth order. Likewise, we took the photon pair time interval distribution \(D_{1}(\tau)\) and then convolved \(D_{1}(\tau)\) to \(D_{9}(\tau)\). The terms higher than ninth order were also omitted. Using Equation (17) we obtained a different high order correction of \(g^{(2)}(\tau)\) with experimental data. The influences of different average photon intensity and the coherence time were investigated theoretically. At 1.5 times the threshold current (\(\mathrm{J=1.5J_{th}}\)) and 25 \({}^{\circ}\)C temperature (\(\mathrm{T=25}\,^{\circ}\)C), central wavelength was stabilized near 1548 nm. We adjusted the attenuator VA1 and polarization controller to accurately control the optical feedback strength. The feedback strength \(\eta\) was obtained as the ratio of the feedback power to the output power of the laser. With the increase of the feedback strength, the laser experienced a transition from period-1 and period-2, to the steady chaos oscillation. Among them, we selected three typical states, including period-2 (weak chaos) with the feedback strength \(\eta\) of 2.66%, the intermediate chaotic state (chaos) with \(\eta\) of 8.87%, and steady chaotic oscillation state (strong chaos) with \(\eta\) of 30.31%. Figure 2a shows the three typical frequency spectrums of the chaotic laser. To quantify the bandwidth of the chaotic laser, we used the definition that is expounded as the frequency spectrum region the DC and the frequency where 80% of the energy is contained within [46]. According to the 80% bandwidth definition, the bandwidth of the chaotic laser was 4.98 GHz, 9.84 GHz, and 11.71 GHz, respectively. Figure 1: Schematic diagram of the experimental setup for measuring photon correlation \(g^{(2)}(\tau)\) of a chaotic optical-feedback laser. DFB-LD: distributed feedback 1550 nm laser diode; PC: polarization controller; OC: optical circulator; VA1 and VA2: variable optical fiber attenuator; FC1 and FC2: fiber coupler; PD: high-speed photodetector; L1, L2 and L3: aspheric lens collimator; BS: beam splitter; F: optical filter; SPD: single photon detector; TDC: time to digital converter; LC: laptop computer; OSC: oscilloscope; TTC: thermoelectric temperature controller; CSC: current source controller. Figure 2b is the optical spectrum of the chaotic laser. Environmental changes slightly influenced the optical feedback strength and the coherence length [47].