Periodic superradiance in an Er:YSO crystal

We observed periodic optical pulses from an Er:YSO crystal during irradiating with a continuous-wave excitation laser. We refer to this phenomenon as “periodic superradiance.” This periodicity can be understood qualitatively by a simple model, in which a cyclic process of a continuous supply of population inversion and a sudden burst of superradiance is repeated. The excitation power dependences of peak interval and the pulse area can be interpreted with our simple model. In addition, the linewidth of superradiance is much narrower than an inhomogeneous broadening in a crystal. This result suggests that only ${\mathrm{Er}}^{3+}$ ions in a specific environment are involved in superradiance.

Figure 1

(a) Energy diagram of ${\mathrm{Er}}^{3+}$ ion doped in YSO crystal. The dashed rounded square shows an enlarged view of the ${}^4\mathrm{I}_{15/2}$ ground state. (b) Experimental setup. PBS; polarization beam splitter. HWP; half-wave plate. BS; beam sampler. PD; photodetector. InGaAs; InGaAs photodetector.

Figure 2

(a) Example of waveform of observed periodic pulses in the middle 3 ms of excitation and from 1 ms before the excitation laser is turned off. The excitation laser is turned on for 40 ms from $t=0$. (b) Histogram of the peak interval between neighboring pulses. The red line is the Gaussian fit. (c) Example of observed single pulse. The red crosses are the data points. The blue solid line is the fit by a sech-squared function.

Figure 3

(a) Peak interval at various excitation laser power. The blue circles represent the averages. The error bars indicate the standard deviations, not the statistical errors. The red line is the fit of $\left(\mathrm{interval}\right)=A\times ln(P/P_{\mathrm{th}})/(P-P_{\mathrm{th}})$ to the data. (b) Pulse area at various excitation laser power. The blue circles and the error bars indicate the averages and the standard deviations, respectively. The red line is the fit of $\left(\mathrm{area}\right)=B\times ln(P/P_{\mathrm{th}})$ to the data. The threshold power $P_{\mathrm{th}}$ is common to both fits.

Figure 4

Linewidth measurement of SR using a confocal cavity. The cavity length is scanned by changing a PZT voltage. The red line is the Gaussian fit. The inset shows an enlargement of one of the peaks.

Figure 5

(a) Relationship between pulse duration and peak height of each pulse. The data points are taken only after $t=10$ ms. The blue circles represent the average of pulse duration in a certain peak height range. The error bars indicate the standard deviations, not the statistical errors. The red solid line is the power fit of $\left(\mathrm{duration}\right)=A\times {\left(\mathrm{height}\right)}^{\alpha }$ to the data. (b) Relationship between pulse area and peak height of each pulse. The green diamonds and the error bars represent the average of pulse area in a certain peak height range and the standard deviations, respectively. The black dashed line is the power fit of $\left(\mathrm{area}\right)=A\times {\left(\mathrm{height}\right)}^{\alpha }$ to the data.