26 Fundamentals of Optical Devices This effect turns out to be much stronger than the direct phase noise process illustrated in Figure 1.1.13, and the overall linewidth expression of a laser diode is Do ¼ R sp ð1 þ a 2 Þ lw 2P ð1:1:51Þ where the second term is the contribution of the photon density-dependent refractive index. This is where the term linewidth enhancement factor came from. For typical semiconductor lasers, the value of a lw varies between 2 and 6; there- fore, it enhances the laser linewidth by 4 to 36 times [2]. 1.1.6.3.6.3 Mode Partition Noise The output from a semiconductor laser can have multiple longitudinal modes as shown in Figure 1.1.9 if the material gain profile is wide enough. All these longitudinal modes compete for carrier density from a common pool. Although several different modes may have similar gain, the winning mode will consume most of the carrier density and thus the power of other modes will be sup- pressed. Since the values of gain seen by different modes are not very different, spontaneous emission noise, external reflection, or temperature change may introduce a switch from one mode to another mode. This mode hopping is ran- dom and is usually associated with intensity fluctuation. In addition, if the external optical system has wavelength-dependent loss, this mode hopping will inevitably introduce additional intensity noise for the system. 1.1.7 Single-Frequency Semiconductor Lasers So far we have only considered the laser diode where the resonator consists of two parallel mirrors. This simple structure is called a Fabry-Perot resonator and the lasers made with this structure are usually called Fabry-Perot lasers, or simply FP lasers. An FP laser diode usually operates with multiple longitu- dinal modes because a phase condition can be met by a large number of wave- lengths and the reflectivity of the mirrors is not wavelength selective. In addition to mode partition noise, multiple longitudinal modes occupy wide optical bandwidth, which results in poor bandwidth efficiency and low tolerance to chromatic dispersion of the optical system. The definition of a single-frequency laser can be confusing. An absolute sin- gle-frequency laser does not exist because of phase noise and frequency noise. A single-frequency laser diode may simply be a laser diode with a single longi- tudinal mode. A more precise definition of single-frequency laser is a laser that not only has a single mode but that mode also has very narrow spectral