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Photothermally induced transparency

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Science Advances  21 Feb 2020:
Vol. 6, no. 8, eaax8256
DOI: 10.1126/sciadv.aax8256
  • Fig. 1 Experimental setup and detection configuration.

    (A) Experimental setup. A laser (1064 nm) is split into a strong laser (control) and a weak laser (probe) with their frequencies being modulated by two AOMs, respectively. The two lasers are recombined by a 50:50 split and then coupled to a linear optical cavity. The substrate (made from fused silica) of the cavity front mirror is placed inside the cavity such that the photothermal effects are are enhanced. The polarization of the laser is tuned by a half-wave plate (HWP) to avoid birefringence effects. A laser window is used to pick up the cavity reflection (blue detector) and the reference signal (green detector). The transmitted power of the cavity is also detected by a photodiode (red). (B) The strong laser is partially absorbed by the cavity mirrors, leading to the expansion of the mirror surfaces and the refractive index change of the substrate. The front mirror is orientated such that its high-reflectivity (HR) coating faces outward, and its anti-reflectivity (AR) coating faces inward. The end mirror attaches a piezoelectric actuator (PZT) used to scan the cavity length. (C and D) Reference (green), reflection (blue), and transmission (red) signals detected by the three optical detectors. The left panels present the spectral configuration of control and probe lasers. The middle panels show the detector signals normalized to cavity resonance. Each dataset (dots) is fitted using a sine wave (solid lines). The curves on the right panels are shifted for clarity, which allows us to see the phase shift relative to the reference signal. The probe frequency relative to control frequency is set as Ωp = 2π × 8 kHz and Ωp = 2π × 5 Hz for (C) and (D), respectively. The signals are measured at a control power of about 90 mW and effective control detuning of about 2π × 140 kHz.

  • Fig. 2 Stability of the system induced by the photothermal effects.

    (A) The stability map of the system, with the blue region being the bistability and yellow region being single stability. The parameter regime enclosed with solid curves corresponds to the one of Fig. 6. The green line represents the transition between single stability and bistability. (B) Experimental observation of optical bistability induced by the photothermal effects. At a control power of 160 mW, the cavity response depends on the scanning direction. We observe the self-locking effect when moving the cavity mirror outward and anti–self-locking effect when moving the mirror inward.

  • Fig. 3 Observation of the PTIT and an intuitive picture on self-locking.

    (A) PTIT observed in measured cavity transmission (dots) at a control power of about 90 mW. We set Δ0 = 0.28 κ by manually tuning the piezoelectric actuator. Solid lines correspond to the model fits of experimental data. We observe a sharp transmission dip in the amplitude response Tamp of the dominant time-varying cavity transmission (top panels). The phase ϕT of the transmission is greatly altered (bottom panels), implying a strong dispersion behavior of the system. (B) The diagram of the “beat-locking” picture. The fluctuation of intracavity power induced by the probe field tends to converge in the blue-detuned regime and diverge in the red-detuned regime. The insets illustrate the diagrams of transmission dip and amplification peak present at blue and red detunings, respectively. Note that the red-detuned cavity can be stable only in the single-stability regime. Given that our experiment run in the bistable regime, the relevant amplification process is not observed for the red-detuned case.

  • Fig. 4 Theoretical and experimental results of the power dependence of the transparency bandwidth.

    (A) The bandwidth of transmission dip as a function of control laser power for several different control detunings. The bandwidth is obtained by fitting the dip to a Lorentzian function. Solid curves represent the model, and the points with error bars are the experimental results. Error bars indicate the 95% confidence interval. (B to C) Cavity transmission at high power of 160 mW (red error bar). At high powers, the experimental result starts to deviate from the theory (B) as the increase of mirror temperature gives an increase of the photothermal coefficient. When taking into account the change of the photothermal coefficient, we can still fit the model to the data (C) and obtain a new photothermal coefficient.

  • Fig. 5 The probe transmission and group delay modified by a strong control field.

    (A) Probe transmission as a function of probe frequency (Ωp/2π), including theoretical results (solid lines) and calibrated data (dots). Both a peak and a dip are present in a given control detuning. (B) The phase response of probe transmission. Alteration of phase at Ωp ≈ 0 signifies strong cavity dispersion. (C) Group delay of probe transmission. A positive value of delay implies a slow light effect, while a negative one implies causality-preserving superluminal effect. Pcon ≈ 90 mW and Δ0 ≈ 0.28 κ are used for all panels.

  • Fig. 6 Theoretical predictions of group delay and advance.

    Theoretical prediction of group delay (A) and advance (B) as a function of control powers and effective control detunings (Δ0). The blue dots correspond to the experimental description in Fig. 5. Here, we take the absolute value for group advance. Both delay and advance are tunable via control detuning and power. The green curves indicate the boundary between single stability and bistability, as mentioned in Fig. 2.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Modeling
    • Section S2. Shape of the transparency window of the cavity transmission
    • Section S3. Calibration of probe transmission
    • Section S4. A simplified solution

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