**2. Basic concepts of injection locking**

Rate equations of the injection locking are given below. Optical injection eventually introduces an extra degree of freedom, and due to the low facet reflectivity of the semiconductor, and perturbation from outside will alter the gain of the laser and may induce nonlinear dynamics. As a point of view, this nonlinear dynamics may be a candidate to chaotic system. The illustration of optical injection is shown in figure 1. A master laser, optically isolated from the slave laser, will inject its single-frequency output into the active region of the slave laser. This optical injection has a variety of effects on the operating characteristics of the slave laser that will be discussed here.

**Figure 1.** Schematic of optical injection.

The optical injection when it has to be in the locking range, the master and slave lasers have to be precisely identical and have the same oscillation frequencies. The frequency detuning must be within several GHz [11]. Once the appropriate conditions of frequency detuning and the optical injection strength have been achieved, a synchronization state of the two lasers is reached. Optical injection locking will be reached under these conditions, i.e., when the slave laser is forced to oscillate at the injected signal frequency from the master laser and is locked to its phase.

The operating principles of semiconductor laser are similar to those of any other laser system, except the linewidth enhancement factor, which arises because the real refractive index in the active laser medium varies with changing carrier density. The injected carrierinduced refractive index change is associated with the change in the gain, the differential gain. This factor plays an important role in the optical injection regimes of semiconductor lasers. Strong optical injection is usually used in the rate equations so that the impact of the noise and the spontaneous emission rate coupled to the lasing mode are negligible [12].

The rate equations of strong optical injection locking are [13]:

114 Optical Communication

known for a single-mode laser [9,10].

chaotic transmitter is the major objective.

without extra protection afforded by other means.

characteristics of the slave laser that will be discussed here.

**2. Basic concepts of injection locking** 

**Figure 1.** Schematic of optical injection.

is locked to its phase.

of FP-LD that is submitted to optical injection, it is so-called injection map, which is well

The maximum available modulation frequency of the laser is in the vicinity of the relaxation oscillation frequency. Optical injection can enhance the relaxation oscillation frequency of the slave laser, and hence the bandwidth. So we would expect higher-speed transmitter for optical communication. On the other hand, a laser with controlled chaos could be obtained. The bandwidth-enhancement of the semiconductor laser by optical injection as well as a

This chapter will focus on the improvements of semiconductor lasers by the optical injection locking regimes and its applications for secure optical communication networks. The injection locked semiconductor laser, utilizing such applications, noise properties are of vital importance especially, the relative intensity noise (RIN). The aspects of noise influence on the dynamical operation of the laser with injection locking will be emphasized. The deployment of such a high bandwidth and chaotic carrier transmitter will be feasible

Rate equations of the injection locking are given below. Optical injection eventually introduces an extra degree of freedom, and due to the low facet reflectivity of the semiconductor, and perturbation from outside will alter the gain of the laser and may induce nonlinear dynamics. As a point of view, this nonlinear dynamics may be a candidate to chaotic system. The illustration of optical injection is shown in figure 1. A master laser, optically isolated from the slave laser, will inject its single-frequency output into the active region of the slave laser. This optical injection has a variety of effects on the operating

The optical injection when it has to be in the locking range, the master and slave lasers have to be precisely identical and have the same oscillation frequencies. The frequency detuning must be within several GHz [11]. Once the appropriate conditions of frequency detuning and the optical injection strength have been achieved, a synchronization state of the two lasers is reached. Optical injection locking will be reached under these conditions, i.e., when the slave laser is forced to oscillate at the injected signal frequency from the master laser and

The operating principles of semiconductor laser are similar to those of any other laser system, except the linewidth enhancement factor, which arises because the real refractive

$$\frac{dP(t)}{dt} = \left\{ G(N) - \frac{1}{\tau\_p} \right\} P(t) + 2\tau\_m \sqrt{P(t)P\_{\text{up}}} \cos\left(\phi\_l(t) - \phi(t)\right) \tag{1}$$

$$\frac{d\,\phi(t)}{dt} = \alpha\_o(N\,) - \alpha\_{\rm inj} - \frac{\alpha}{2} \Big( G(N\,) - \frac{1}{\tau\_{\rho}} \Big) + \tau\_{\rm in} \sqrt{\frac{P\_{\rm inj}}{P(t)}} \sin \left( \phi\_i(t) - \phi(t) \right) \tag{2}$$

$$\frac{dN\ \left(t\right)}{dt} = J - \frac{N\ \left(t\right)}{\pi\_{sp}} - G\left(N\ \right)P\left(t\right) \tag{3}$$

where is the angular optical frequency (carrier dependent) of the slave laser, is of the injected signal, is the injected signal power, is the carrier dependent gain, is the carrier lifetime, is the linewidth enhancement factor, is the injection current, and is the phase difference between the injected and the free-running laser fields. ( ) *<sup>O</sup> N inj Pinj G N*( ) *sp J <sup>i</sup>*() () *t t*

The frequency detuning between the master and slave lasers is defined as 2 . *inj o f* 

The injection ratio is defined as the ratio of optical powers of the master and free-running slave laser inside the slave laser cavity . *Pinj P*

The static state of the slave laser can be found from solving the steady solutions in the above equations by setting the time derivatives to zero and this will lead to the state of locking frequency within the master-slave frequency detuning. This static locking range is:

$$-\frac{1}{2\pi\,\tau\_{\rm in}}\sqrt{\frac{P\_{\rm inj}}{P}}\sqrt{1+\alpha^{2}} < \Delta f \quad < \frac{1}{2\pi\,\tau\_{\rm in}}\sqrt{\frac{P\_{\rm inj}}{P}}\tag{4}$$

Equation (4) gives the locking range of the slave laser and is increased with the injection ratio and is also inversely proportional to the slave laser cavity round-trip time . The locking frequencies depend strongly on the linewidth enhancement factor. Figure 2 shows the locking range of the slave laser. Asymmetric locking range is obvious from the graph. This can be interpreted as; the locking properties depend on the gain profile of the salve laser supporting many longitudinal modes, and when injection occurs at frequency close to the side mode instead of the free-running dominant mode of the slave laser. Now, gain is carrier density dependent, and refractive index also depends on carrier density the in the active region which results in this asymmetry in the locking curve. *in* 

**Figure 2.** Locking characteristics of the slave laser showing the stable (locking) and unlocking regions for two values of linewidth enhancement factor.
