Measuring absolute spectral radiance using an erbium-doped fiber amplifier

We describe a method to measure the spectral radiance of a source in an absolute way without the need of a reference. Here we give the necessary detail to allow for the device to be reproduced from standard fiber-optic components. The device is suited for fiber-optic applications at telecom wavelengths and calibration of power meters and spectrometers at light levels from 1 nW to 1 $\mu$W.

Figure 1

Experimental setup. A stable ASE source is filtered and injected into a fully inverted erbium-doped fiber. At the output of this fiber the spectrum is measured with a spectrometer. The power of the source is controlled by a variable attenuator which also contains a shutter. The diode symbols represent optical isolators which both stop back-reflections and remove any remaining 980 nm light.

Figure 2

Fiber source of spontaneous emission. An erbium-doped fiber is backwards pumped. The amplified spontaneous emission counterpropagating to the pump is separated with a wavelength division multiplexer (WDM). Any residual pump light is removed using an isolator which has very strong attenuation for the pump light.

Figure 3

Saturation of the atomic medium. As the pump laser power $P_{\mathrm{p}}$ is increased the spontaneous emission power $P_{\mathrm{ASE}}$ increases as $P_{\mathrm{ASE}}\propto P_{\mathrm{p}}/(P_{\mathrm{p}}+C)$ (fitted curve). The slope $\partial P_{\mathrm{ASE}}/\partial P_{\mathrm{p}}$ becomes 2000 times smaller as the pump laser power reaches 400 mW.

Figure 4

Amplified spontaneous emission spectrum. A peak is present at 1530 nm and a flat region between 1540 nm and 1544 nm.

Figure 5

Linearity of the power meter measured by METAS, the Swiss federal office of metrology. The linearity has a deviation of only $0.4\%$ between 0 dBm and $-$65 dBm. The last point, at $-$70.1 dBm, has a deviation of $1.3\%$ mainly due to the background noise of the power meter.

Figure 6

Spectrometer calibration curve vs a wave meter. The calibration error is of the order of ${10}^{-4}$. Once calibrated (linear fit) the standard deviation of the residuals is 2 pm.

Figure 7

In order to calibrate the input loss of the EDF at connector C2 one injects light backwards through connector C3 and measures the amount of light $P_2$ out of the EDF at C2. After this, one makes the connection at C2 and measures the amount of light $P_1$ coming out of C1. The input loss is then $P_1/P_2$. This characterization is made only once since C2 will remain connected during the entire experiment.

Figure 8

Connection statistics. Making a connection without measuring its loss each time will result in a random error. We measured this random error to be $0.4\%$. However it can be reduced by only accepting connections with the highest values of transmission. Rejecting values below a certain threshold we improve the repeatability to $0.16\%$.

Figure 9

Relative spectra of the source light and spontaneous and stimulated emissions.

Figure 10

Comparison between the spectral radiance measured with the power meter and with the radiometer.

Figure 11

Linearity of our radiometer. Number of photons per mode measured by our radiometer versus transmission of the variable attenuator (linear scale). Residuals are magnified 100$\times$ and show no sign of saturation.

Figure 12

Stability over a period of two hours: The Allan deviation drops to a value of ${10}^{-4}$.

Figure 13

Power spectral density function $I\left(\nu \right)$ for a small frequency element $\Delta \nu$ centered at ${\nu }_0$.