3.1.1 Theory：Injection Locking Theorem
A rate equations based model is usually used to describe the interaction between photons and carriers inside a laser cavity. When an additional light source is injected into the cavity, the system preserves the general form of the original equations, but with extra terms describing the effects of the injection [1]. These extra terms play an important role in this nonlinear dynamic system and the equations are shown below.
n
In these equations, S,φ, and N denote the photon number, the phase, and the carrier number inside the follower laser cavity, respectively. G0 denotes the gain coefficient, N0 is the transparency carrier number, τp and τn are the photon and carrier lifetimes, respectively, I is the follower laser bias current, ε is the gain compression factor, and α is the linewidth-enhancement factor. Rsp is the spontaneous emission rate and the
(3-1)
Langevin noise terms F are also added for completeness. And ∆φ(t)=φinj-φ(t) The follower laser locks to the master only for a certain combination of the injection power and frequency detuning. The stable locking condition can be found as [2]
S k S S w
kc Sinj + <∆ < c inj
− 1 α2
rThe presence of the linewidth-enhancement factor makes the follower laser easier to lock to a master laser at the red side and, therefore, the locking range is asymmetric in frequency detuning. Also, a higher injection power results in a larger locking range. If the detuning range is mapped out for different injection powers, we obtain the locking range of the system.
We begin by assuming a steady-state value for each of the variables with a small signal modulation term, at the optical frequency
jwt
Substituting (3.2) into (3.1),
Only considering the small- signal modulation terms in (3.2) for the photon part,
)
Similarly, for the phase term, considering the small-signal modulation terms in (3.2),
)
)
Equations (3.3), (3.4), (3.5) can now be written in matrix form:
⎥⎥
The small-signal modulation response can also be found from this system by considering I as the small signal modulation current.
⎥⎥
The modulation response transfer function will be
)
Based on the above analysis, the small signal modulation response of the injection locked laser has been shown to be of the same form as that of a free-running laser with an additional 1st order pole :
γ
In this equation, s = jw and K represents he 1st order pole introduced by the injection, wR the resonance and the damping term. The coefficients ai and bi are functions of the laser parameters and injection conditions [3].
The frequency response of this system is simplified considerably when Sinj=0 (i.e. no injected light). In this case, a0=b0=0, and the frequency response in equation (3-6) is
reduced to . a directly modulated laser and the relaxation oscillation frequency is
P N
r b a S
f =(2π)−1 1 ~(2π)−1 τ
On the other hand, when Sinj/S is very large, b0 becomes negligible compared to the other terms in the denominator of the transfer function, which is once again reduced
to a two-pole function, .
)
fr = . This is very interesting as it seems to indicate that with strong injection fr can be increased indefinitely.
3.1.2 Experimental Setup：Injection Locking System
The experimental setup is schematically illustrated in Fig.3-1. The QD VCSEL is used as the slave laser while a DFB laser is used as the master laser. The injection power is varied by a variable optical attenuator at the output of the DFB laser. The polarization of the DFB laser is adjusted using a polarization controller before injecting into the QD VCSEL. The adjusted DFB laser signal injects into the port 1 of optical circulator then injecting into QD VCSEL at the port 2. The QD VCSEL is directed modulated by vector network analyzer. The light output at port 3 of optical circulator is divided into 2 parts. 90% of the light signal is transmitted into photo detector then convert into electrical signal amplified by RF amplifier and sent into vector network analyzer to measure frequency response. 10% of the light signal is connected to optical spectrum analyzer to observe the locking condition. In the experiment, the polarization and the center wavelength of DFB laser are adjusted that the QD VCSEL has the most significant enhancement in the frequency response. The wavelength detuning is adjusted by changing the temperature and bias current of DFB laser.
3.1.3 Results and Discussion
The free running frequency response of the QD VCSEL is shown as Fig.3-2 and the inset of Fig.3-2 shows the spectra of QD VCSEL. Fig. 3-3 shows the frequency response of the QD VCSEL with light injection and the QD VCSEL is biased at 4 mA.
The detuning wavelength (λDFB-λQD VCSEL) is 0.128nm. This figure clearly shows that external light injection can achieve a significant enhancement in frequency response. When the power injection is 6dBm, the 3-dB frequency is from 1.75GHz to 7.44GHz which is the most improved bandwidth. The inset of Fig.3-3 is the spectra of QD VCSEL with and without light injection. After injection locking, the wavelength
QD VCSEL and the power level of QD VCSEL light output is enhanced by external light injection. We plot the 3dB frequency verses injection power as shown in Fig. 3-4.
In this figure, we can observe that the 3dB frequency is enhanced by injection power of DFB laser. This is because external light injection in the active region of QD VCSEL makes the photon number increase thus improving the 3dB bandwidth. To prove the improved bandwidth can be utilized, we also demonstrated that this enhancement of the frequency response can greatly improve the performance of SCM system based on direct modulation of QD VCSELs.
. Fig. 3-5 shows the experimental setup for the injection locking of QD VCSEL in a SCM system. A 50 Mb/s non-return-to-zero (NRZ) pseudo-random binary sequence (PRBS) data with 231 – 1 pattern length from a pattern generator is mixed with a 7 GHz RF carrier. The resulting data signal is then used to directly modulate the QD VCSEL. Fig.3-6 shows the electrical spectra of QD VCSEL with and without light injection at point A. Light injection technique leads to 33 dB improvement in the SCM system. The 7-GHz 50-Mb/s is down converted using a mixer, where it is mixed with the same RF carrier generated by the signal generator. The variable phase shifter is used to adjust the carrier’s phase. The corresponding eye diagrams are shown in Fig.
3-7. The improvement in system performance can be clearly seen when light injection technique is employed. The QD VCSEL without light injection cannot generate 7-GHz 50-Mb/s data due to the limited frequency response.