Exploring the Photon-Number Distribution of Bimodal Microlasers with a Transition Edge Sensor

A photon-number-resolving transition edge sensor (TES) is used to measure the photon-number distribution of two microcavity lasers. The investigated devices are bimodal microlasers with similar emission intensity and photon statistics with respect to the photon autocorrelation. Both high-$\beta$ microlasers show partly thermal and partly coherent emission around the lasing threshold. For higher pump powers, the strong mode of microlaser $\mathit{A}$ emits Poissonian distributed photons, while the emission of the weak mode is thermal. By contrast, laser $\mathit{B}$ shows a bistability resulting in overlayed thermal and Poissonian distributions. While a standard Hanbury Brown and Twiss experiment cannot distinguish between the simple thermal emission of laser $\mathit{A}$ and the temporal mode switching of the bistable laser $\mathit{B}$, TESs allow us to measure the photon-number distribution, which provides important insight into the underlying emission processes. Indeed, our experimental data and their theoretical description by a master equation approach show that TESs are capable of revealing subtle effects like the mode switching of bimodal microlasers. As such, we clearly demonstrate the benefit and importance of investigating nanophotonic devices via photon-number-resolving transition edge sensors.

Figure 1

Sketch of the experimental setup. The microlaser sample is operated in a He-flow cryostat at 15 K and is excited by a pulsed electrical voltage supply. The emitted light is analyzed by a spectrometer or the TES or, alternatively, by a standard HBT setup. SPCM denotes single-photon counting module.

Figure 2

(a) Intensity-bias voltage characteristic of laser $\mathit{A}$. The strong mode (the blue squares) shows an $\mathsf{S}$-shaped behavior, while the weak mode (the orange circles) saturates in intensity (given as the number of photons inside the cavity, set to 1 at the laser threshold) above the threshold. (b)–(d) Photon statistics at three bias voltages, indicated by the red arrows. The bars correspond to the statistics measured with the TES; the dots, connected by a line, correspond to the theory. (b) For low bias voltage ($V_{\mathrm{bias}}=3.9\mathrm{V}$), both modes possess a Poissonian distribution. (c) Above threshold ($V_{\mathrm{bias}}=4.4\mathrm{V}$), the photon statistics exhibits a transient distribution which is partly thermal and partly Poissonian. (d) For high voltage ($V_{\mathrm{bias}}=6.0\mathrm{V}$), the weak mode shows a thermal distribution, whereas the strong mode exhibits a Poissonian distribution.

Figure 3

Laser $\mathit{A}$. (a) The second-order autocorrelation function at zero-time delay $g^{(2)}(0)$ determined by the TES (the small, darker symbols) is in very good agreement with the one determined by the HBT (the big, brighter symbols) and the theory (the dashed curves). The strong mode shows a transition from thermal to coherent emission. The weak mode increases in $g^{(2)}(0)$ to values slightly above the thermal limit. The dashed lines indicate the respective thermal values $k!$. (b) The third and fourth orders of the autocorrelation function $g^{(n)}(0)$ from the same TES measurements exhibit behavior analogous to that of $g^{(2)}(0)$.

Figure 4

Laser $\mathit{B}$. The photon-number distributions of the (a) weak mode and (b) strong mode at $V_{\mathrm{bias}}=5.4\mathrm{V}$ can best be described by an overlay of a thermal distribution with a low mean photon number $⟨n⟩$ and a Poissonian distribution with a high $⟨n⟩$ value. [Inset of (a)] The input-output characteristic and [inset of (b)] $g^{(2)}(0)$ values of laser $\mathit{B}$ are similar to laser $\mathit{A}$ (cf. Figs. 2 and 3).