Fig. 1. Realization and characterization of the super-bunching laser. (a) Schematic of the optical setup for the realization and measurement of the super-bunching laser. PCF, photonic crystal fiber; BF, bandpass filter; Att, attenuation; BS, beam splitter; SPD, single-photon detector; TCSPC, time-correlation single-photon counting system. The insert shows the cross-sectional profile of the PCF. Typical second-order correlation, g⁽²⁾(τ), for a coherent laser (b) and the super-bunching laser (c), with the normalized g⁽²⁾(0) to be 1 and 340, respectively. The repetition frequency of the two lasers was 5 MHz. The insert shows the enlargement of the dashed area. (d) Photon number probability distribution for the coherent laser (hollow symbols) and the super-bunching laser (histogram) under different mean numbers per pulse, ⟨n⟩. (e) Enhancement of the probability between the super-bunching laser and the coherent laser under different ⟨n⟩ values.

Fig. 2. Experimental implementation of CPI. (a) Schematic of the optical setup for underwater CPI. SBL, super-bunching laser; SPD_r, single-photon detector as a reference. Both SBL and SPD_r are maintained in a dark environment. M, mirror; NL, natural light; GM, galvo mirror; SPD_s, single-photon detector as a signal; PC, personal computer. (b) Principle of the noise-resistant CPI. The two photon sequences are detected from the reference (SPD_r) and signal beam (SPD_s). The red, blue, and green balls are electric responses from the super-bunching laser, natural light, and dark noise of the SPD. T and Δt are the time interval between the pulse and gate time to count the correlated biphoton, which are 200 and 1 ns in our experiment, respectively. (d) Coincidence rates of the biphoton (N_c) from the super-bunching laser as functions of reference beam intensity (N_r), under different signal beam intensities (N_s). The dashed circle represents N_s = N_r = 7 kcps (thousand counts per second), and N_c = 922 cps (counts per second). (e) Coincidence rates of the biphoton functions of reference beam intensity (N_r), under different noise intensities (N_n). The signal intensity was fixed at 150 kcps. The insert shows the enlargement of the dashed rectangle.

Fig. 3. Comparison between CPI and SPI under different NSRs. (a)–(d) SPI via counting the signal photons detected by SPDs per integral time per pixel under different NSRs. The average intensity of the signal without external noise was about 60 kcps. (a) NSR = 0 (i.e., without external noise), (b) NSR = 3, (c) NSR = 100, and (d) NSR = 1000. Considering that under NSR = 1000, the estimated counting rates [about 60 Mcps (million counts per second)] have exceeded the maximum rates of SPD (about 20 Mcps), in this case, both the signal and the noise have been attenuated 20 times to perform imaging. (e)–(h) CPI via the super-bunching laser under different NSRs. (e) NSR = 0, (f) NSR = 3, (g) NSR = 100, and (h) NSR = 1000. (i)–(l) CPI via a coherent laser (PicoQuant, 5 MHz) under different NSRs. (i) NSR = 0, (j) NSR = 3, (k) NSR = 100, and (l) NSR = 1000. (m) Calculated CNR as a function of NSR for different imaging schemes. (n) Enhancement of CNR between CPI and SPI (both via the super-bunching laser), as well as enhancement of CNR for CPI between the super-bunching laser and a coherent laser.

Fig. 4. Comparison between underwater CPI and SPI under different NSRs. (a)–(d) Underwater SPI under different NSRs with the attenuation coefficient of the tap water about 0.062 m⁻¹. (a) NSR = 0, (b) NSR = 3, (c) NSR = 100, and (d) NSR = 500. Compared with Fig. 3, the power of the super-bunching laser was increased by 10-fold. (e)–(h) CPI via the super-bunching laser under different NSRs. (e) NSR = 0, (f) NSR = 3, (g) NSR = 100, and (h) NSR = 500. (i)–(l) CPI via a coherent laser under different NSRs. (i) NSR = 0, (j) NSR = 3, (k) NSR = 100, and (l) NSR = 500. (m) Calculated CNR as a function of NSR for different imaging schemes. (n) Enhancement of CNR between CPI and SPI, as well as that between the super-bunching laser and a coherent laser.

Fig. 5. Underwater CPI with different NSRs and attenuation coefficients (α). (a)–(d) Underwater CPI without external noise under different attenuation coefficients. (a) α = 0.062 m⁻¹, (b) α = 0.098 m⁻¹, (c) α = 0.144 m⁻¹, and (d) α = 0.176 m⁻¹. (e)–(h) Underwater CPI with NSR = 30 under different attenuation coefficients. (e) α = 0.062 m⁻¹, (f) α = 0.098 m⁻¹, (g) α = 0.144 m⁻¹, and (h) α = 0.176 m⁻¹. (i-l) Underwater CPI with NSR=150 under different attenuation coefficients. (i) α = 0.062 m⁻¹, (j) α = 0.098 m⁻¹, (k) α = 0.144 m⁻¹, and (l) α = 0.176 m⁻¹. (m) Profiles of the target of the interesting areas [highlighted by dashed rectangles in (i)–(l)]. (n) Calculated CNR as a function of NSR under different attenuation coefficients. The shadows indicate the areas with CNR < 1. (o) Calculated CNR as a function of attenuation coefficients under NSR = 0 and NSR = 150; the solid lines are the linear fit.