Photon statistics of amplified spontaneous emission noise in a 10 Gb/s optically pre-amplified lightwave direct detection receiver

Abstract

The determination of receiver sensitivity and bit-error rate (BER) is important in the design of high bit rate optical digital communication systems at the 1.5 pm wavelength, where the most sensilive receivers use optical preamplification. There exists two classes of models for the analysis of optically amplified signals. The first class uses the semiclassical square-law model for detection, resulting in a gaussian distribution for the photocurrent [ 11. The second class uses quantum mechanics to treat spontaneous and stimulated processes in the optical amplifier [2]. The advantages of the semiclassical models are simplicity and the fact that it yields an analytical expression for the BER, while the advantage of the quantum mechanical model is its correctness in describing the physical processes. In this paper, we show that the photon distribution of the ZEROS obtained experimentally is indeed Bose-Einstein distributed. We then demonstrate that we can predict the sensitivity of the receiver based on the quantum mechanical model.The ASE noise of an optical amplifier is Bose-Einstein distributed [3]. For polarized light incident on a photodetector, if the optical filter bandwidth is g times wider than the inverse response time of the photodetector, the Bose-Einstein process becomes g-fold degenerate. The resulting photon probabillity distribution is then the convolution of the individual distributions over m, which can be stated in closed form as [2] For an optical amplifier with a power gain of G , the mean photon number in each mode is E = x(G -l), where x is the noise enhancement factor for incomplete inversion of the gain medium.We set up the receiver, as shown in Fig. 1, to measure the photon statistics of the ASE noise. The receiver consists of an optical pre-amplifier pumped at 980 nm, an optical bandpass filter with center wavelength 1550 nm and bandwidth 1.3 nm to provide rejection of out-of-band noise, a 20 GHz pin detector with a quantum efficiency of 0.8, and a dc-coupled digital sampling oscilloscope. To calibrate our measurement, we measure the detector noise by blocking the input to the pin detector and obtaining the distribution of rf voltages on the oscilloscope. As shown in Fig. 2 in a logarithmic scale, the histogram of voltages, in the absence of incident light, agrees very well with a gaussian fit of zero mean and a standard deviation of 0.54 mV, which is expected because thermal circuit noise is gaussian [4].The photon distribution of ASE noise of the pre-amplifier on the oscilloscope is obtained by blocking the incident light on the receiver and unblocking the pin detector. Using the previously measured circuit noise distribution, the theoretical distribution of the ASE noise is computed by convolving the degenerate Bose-Einstein distribution in Eq. (4) with the gaussian distribution obtained in Fig. 2. The ASE histogram data, collected with 9x10' hits, is then fitted with this composite distribution, shown in Fig. 3(a) in ai logarithmic scale. The two degrees of freedom used in fitting are t...