Quantum noise in optical communication systems

Abstract

It is noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, which, as an extra source of noise, could become comparable to the amplified-spontaneous-emission noise of optical amplifiers. The optical noise in random loss/gain has a quantum origin, as a manifestation of the corpuscular nature of electromagnetic radiation. This paper adopts the Schrödinger representation, and uses a density matrix in the basis of photon number states to describe the optical signals and their interaction with the environment of loss/gain media. When the environmental degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism provides an intuitive interpretation of the quantum-optical noise as the result of a classical Markov process in the space of the photon number states. The formulism would be more convenient for practical engineers, and should be sufficient for fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Even better, the model admits analytical solutions to the photon-number distribution of the optical signals.In modern fiber transmission lines, the optical signals experience alternating loss and gain. The amplified spontaneous emission (ASE) of the in-line amplifiers is usually blamed and considered as the sole source of noise that corrupts the optical signals. However, it should be noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, namely, an extra source of noise, which could become comparable to the commonly blamed ASE noise. It is therefore necessary to understand and include this noise in system design and performance evaluation. Fundamentally, the optical noise in random loss/gain has a quantum origin, incurred as a result of the corpuscular nature of electromagnetic radiation. Such quantum noise is often treated in the Heisenberg representation, and interpreted as the result of a Langevin noise operator, 1 or vacuum field operators, 2, 3 added to the Heisenberg field operator of the signal. This paper adopts the Schrödinger representation, and uses a density matrix in the basis of photon number states to describe the signal field, the medium reservoir, and their interactions. When the medium degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism is sufficient for practical fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Furthermore, our formulism...