This study summarizes the theory of laser-amplifier noise based on the master equation, the quantum-mechanical Langevin equation, and the rate equation. The three approaches are used differently depending on the application. Laser-amplifier noise in the direct-detection receiver is described by the master equation. Meanwhile, the quantum-mechanical Langevin equation is most effective for analyzing noise appearing in coherent optical communication systems. The rate equation approach provides a clear understanding of the intensity-noise characteristics of laser oscillators, including the amplitude squeezing.

Using computer simulations, we analyze the bit-error rate (BER) characteristics of the optical transmission system repeated by erbium-doped fiber amplifiers (EDFAs) and two-mode phase-sensitive optical parametric amplifiers (PSAs), where  phase-conjugated (PC) twin waves are co-propagating through the link. We focus on the 256 quadrature-amplitude-modulation (QAM) format, whose transmission characteristics are seriously affected by fiber nonlinearity because the required power is significantly high. Changing the repeater spacing and group-velocity dispersion (GVD) of fibers for transmission in the two-mode PSA-based system, we calculate the BERs as a function of the launched power. When the repeater spacing and  GVD value of fibers are properly designed, the two-mode PSA-based system can mitigate nonlinear impairments more effectively than the EDFA-based PC twin system.

Using computer simulations,  we  analyze the bit-error rate (BER) characteristics of a high-order QAM  optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers (PSAs).  In this  system, an idler, which is a phase-conjugated twin of a signal, propagate through the link together with the signal. One advantage of this system is that the  noise figure of two-mode PSAs used as repeaters can approach 0 dB. The other advantage is that  two-mode PSAs cancel out self-phase modulation of the signal at each repeater through the interaction between the transmitted  signal and idler. Owing to these advantages, the BER characteristics  of 16, 64, and 256QAM signals are significantly improved compared with the system using erbium-doped fiber amplifiers and phase-conjugation twin waves, provided that dispersion-shifted fibers are employed for transmission.

We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.

This study develops a theory of noise in optical parametric amplifiers (OPAs) based on the quantum-mechanical Langevin equations. We derive theoretical expressions for the spontaneous emission factor of OPAs for the first time. This enables analyzing the effect of internal loss on the noise characteristics. In addition, we analyze the noise figures of the laser amplifier, phase-insensitive OPA, and phase-sensitive OPA.