A9.1 Introduction

There are at least three 'different' principles that can be used to calculate the spontaneous emission in a laser:

1. the method given in Section 2.4.1;

2. a method which considers the spontaneous emission which has to occur in an ideal waveguide amplifier to obtain the correct 'noise' output [1, 2]. This amplifier can also be turned into an attenuator to see that the results are still consistent; and

3. the spontaneous emission which can also be found by the Einstein treatment of counting photon states [3].

All these methods are tied together to show consistency with one another. The appendix is concluded with essential material for interpreting the spontaneous emission in a numerical formalism.

The appendix first considers thermal and quantum noise and the ideal signal-to-noise power ratio that can be measured using a 100%-efficient photodetector. An ideal optical amplifier followed by an ideal detector is then considered. At the output of this ideal amplifier, the signal-to-noise-power ratio depends on the spontaneous emission and it is argued that this ratio has to be the same as the signalto-noise-power ratio for the ideal direct detection of optical fields at the input. The ideal amplification cannot improve (or worsen) the signal-to-noise ratio. This argument gives one measure of the spontaneous emission. The same device considered as an attenuator in thermal equilibrium with its surrounds gives yet another measure of spontaneous emission, and finally spontaneous emission can be estimated through counting photon states.

A9.2 Thermal and Quantum Noise

Thermal noise at microwave frequencies...