A novel model including the interference effect of master laser reflection is established for reflection-mode optical injection locking. This model sheds insight on the physical origin of some rather distinct but unexplained modulation characteristics of optical injection-locked vertical-cavity surface-emitting lasers (VCSELs), including data pattern inversion in on-off keying modulation, a large RF gain at low frequency, and an anomalous DC-suppression under small signal modulation, in specific locking conditions. Excellent agreement is obtained between the simulation and experiment results.
©2010 Optical Society of America
Optical injection locking (OIL) has been shown to greatly enhance the performance of a directly-modulated laser [1–8]. Resonance frequency greater than 100 GHz and an intrinsic 3 dB bandwidth up to 80 GHz have been demonstrated for directly modulated vertical-cavity surface-emitting laser (VCSEL) under strong OIL . In this regard, similar behavior is found between injection locking of a VCSEL and an edge-emitting distributed feedback (DFB) laser . Recently, we reported an interesting data pattern inversion and the corresponding chirp polarity inversion in both single transverse mode and multi-transverse mode OIL-VCSELs. This leads to a ten-fold and ninety-fold increased single-mode fiber transmission distance respectively [2,3]. This never-predicted-before phenomenon has only been observed in VCSELs. In addition, there are two other anomalies in small-signal modulation characteristics (S21) of OIL-VCSELs that cannot be explained by standard OIL rate equations [6–10]. First, a large 20 dB RF gain at low frequency can be obtained for OIL-VCSEL at certain detuning values (wavelength difference between the master and the free-running slave laser) . Second, under certain other detuning values, a dip or “zero” occurs at very low frequency, herein referred as DC-suppression.
In this paper, we establish a novel model [11,12] which includes the interference effect of the master laser reflection for the first time. This interference was completely ignored in all the prior analyses of the modulation characteristic of reflection-mode OIL-lasers. With the inclusion of this interference, the distinct modulation features of OIL-VCSELs can be fully explained and excellent agreements are obtained with experimental results. The model established in this paper will be suitable for all reflection-mode OIL-lasers including VCSELs and some edge-emitting lasers. The reflection not only differentiates the reflection-mode OIL-lasers from the transmission-mode OIL-lasers, but can be leveraged for further performance improvements, which is also discussed here.
2. Theoretical modeling and simulation
Figure 1 shows the schematic of an OIL-VCSEL. The master laser field Em impinges onto the front facet of the slave VCSEL and is divided into transmission and reflection. The transmission interacts with the VCSEL cavity, described by the standard rate equations [6–10]. A steady state is reached inside the cavity and its output Es is phase coherent with Em, with a phase shift φs ranging from −0.5π to cot−1α [6,9], where α is the linewidth enhancement factor. φs is determined by the detuning Δλ = λm - λs, where λm and λs are the wavelength of the master laser and the free-running slave VCSEL respectively.
The total output field Etotal is the sum of Es and the reflection of the master laser Emr, where r is the reflectivity of the top facet of the VCSEL, with a phase shift φr depending on VCSEL’s top DBR structure and λm. φr is around π in general. In previous models, only transmitted light was considered and, hence, the interference between Es and Emr was ignored. The total output power Ptotal of the steady state can be written as,
Figure 2a shows the output power in the locking map for a transmission-mode OIL-laser , while Fig. 2b shows the output power for a reflection-mode OIL-laser where the interference effect of master laser reflection is taken into account. The total output power increases with injection ratio (defined as 20log10(|Em|/|Efr|), where E fr is the electric field of the free-running slave laser light), which is the same in both cases. In the reflection-mode OIL, however, Ptotal decreases with detuning, opposite to the case of the transmission-mode OIL [6,13]. This is because φs increases from −0.5π to cot−1α, leading to a more destructive interference and thus a lower total output power.
Small signal analysis is then performed based on the rate equations [6,7,9,10] with the reflection model. Both |E s|2 and phase φs have a response under the small-signal modulation, written as Δ|Es|2 and Δφs respectively, which are superimposed on the steady state solution. Based on Eq. (1), the total output power is written as,
With the main simulation parameters listed in Table 1 in Appendix, the typical frequency response of ΔPtotal is simulated for different detuning values under a strong injection ratio. The results are shown in Fig. 3 , where the amplitude response |ΔPtotal|2 (the square converts optical domain into electrical domain, known as S21) is normalized to the free-running case. It is clearly seen that there is a DC-suppression in the amplitude response as the detuning increases from blue (Δλ<0) to red (Δλ>0). This DC-suppression corresponds to a π phase change in the phase response (phase of ΔPtotal). It is the destructive interference between the OIL-VCSEL internal output field Es and the master laser reflection light Emr that leads to this DC-suppression and phase change. We will show later that this corresponds to the transition point for data pattern inversion in large signal modulation. As the detuning value increases further, the DC-dip disappears and a very large RF gain is obtained, again due to the interference effect.
Data pattern under on-off keying (OOK) large-signal modulation is simulated by fourth-order Runge-Kutta method. Extinction ratio re is defined as 10log10(P1/P2), where P1 and P2 are the OIL-VCSEL output powers corresponding to the high and low level of the modulation current. Thus a negative extinction ratio indicates data pattern inversion. Figure 4 shows the typical 1 Gb/s data patterns for different detuning values, with a fixed injection ratio. The average total output power decreases with detuning, as predicted by Fig. 2b. With increasing detuning, the data pattern changes from normal to transition state, and then to inverted.
Next, we compare simulation results for small- and large- signal modulation response by sweeping the parameter space of injection ratio and detuning value. Figure 5 shows the RF response at 1 GHz and the extinction ratio of the 1 Gb/s data pattern on the same locking map. The locking range of the large-signal modulation is slightly smaller than that of the small-signal modulation, due to the larger perturbation to the system in the large-signal modulation. It is interesting to note that the DC-suppression in Fig. 5a is at the same parameter space with the transition state at which the extinction ratio is zero in Fig. 5b, confirming a strong correlation between them. For a certain injection ratio at the red detuning side, the interference effect makes P1 into a very small value, resulting in a very large (in magnitude), and desirable extinction ratio with data pattern inverted. This is indeed the regime of interests for greatly increased fiber transmission distance [2,3].
Detailed experiments on 1.55 μm buried-tunnel-junction (BTJ) VCSELs  were performed to verify the simulation results and, in particular, the correlation between small- and large- signal modulation.
The VCSEL and experimental setup were similar to that reported elsewhere . The VCSEL was biased at 4 mA, 2.5 times threshold current, with −3 dBm free-running output power. The small-signal modulation response of the OIL-VCSEL was measured at a fixed injection ratio of 20 dB for different detuning values, shown in Fig. 6 . At blue detuning (e.g. Δλ = −0.759 nm), a high resonance frequency of 100 GHz was attained, similar to what was reported . The large damping at lower frequencies is due to the parasitic RC of the VCSEL. Increasing the detuning to 0.149 nm, a large DC-dip was seen, which was not reported before. Further detuning to the red side, the DC-dip disappeared and a large RF gain 12.5 dB at low frequency was obtained. Similar observation with >20 dB gain was reported in Ref. 4.
Figure 7 shows experimental results of OIL-VCSEL under 1 Gb/s OOK modulation at different detuning values, with the injection ratio optimized at 12.9 dB for good extinction ratios. With increasing detuning, the data pattern changes from normal, transition state, to inversion. The typical top DBR mirror field reflectivity of the VCSEL is higher than 99%, resulting in a strong reflection and interference effect of the master laser light. Extinction ratio as high as 12 dB with a 3.6 dB signal amplification compared to the free-running case was achieved with the 1.036 nm detuning.
The RF response at 1 GHz and the extinction ratio of the 1 Gb/s data pattern were measured at different points in the same parameter space for another VCSEL (5 mA bias current which is 3 times threshold current, −0.7 dBm free-running output power), with the results shown in Fig. 8 . The strong correlation between the DC-suppression in small-signal modulation and transition state in large-signal modulation is clearly seen. All these results agree very well with the simulation.
The reflection-mode OIL model would find its great application in optical communication and optical data processing. It predicts the conditions of data pattern inversion and the corresponding chirp polarity inversion, which is exactly the region where the greatly increased single-mode fiber transmission distance was achieved in the OIL-VCSELs [2,3]. Furthermore, since the OIL-VCSEL can operate either in normal data state or inverted data state, it is possible to develop some optical switching applications. For example, a frequency-modulated master laser can be used to modulate the detuning value of the OIL-VCSEL, and thus the switching can occur between the normal data state and inverted date state. Alternatively, an intensity-modulated master laser can be used to control the injection power and thus the switching. However, as seen in Fig. 5 and Fig. 8, the transition line is very flat with respect to the injection ratio, making this switching difficult. On the other hand, by adjusting the VCSEL’s front DBR reflectivity and phase, it is possible to tilt the transition line. Figure 9 shows the same simulations as Fig. 5, except that the front DBR’s field reflectivity is changed from 0.9968 to 0.9962 while the reflection phase from 1.000π to 0.970π at 1550 nm. The transition line is tilted, and the output of the VCSEL can switch between normal state and inverted state by different injection powers from the master laser. Reference  shows the initial experimental switching results, and this may be possibly further developed into an optical logic gate.
The proposed model incorporates the interference effect of the master laser reflection into the total output of the reflection-mode OIL-lasers. This reflection, which once was considered detrimental for practical applications, is shown to be a key to explain the rather distinct modulation characteristics of OIL-VCSELs. The small-signal RF response is strongly correlated to the data patterns in large-signal modulation. The distinct DC-suppression reflects itself into the transition state in large-signal modulation. The large RF gain at low frequency is both seen in simulation and experiment. This model will not only be useful to optimize the conditions for OIL-VCSEL-based optical communication, but also expand OIL-VCSELs applications into multi-level modulation, photonic switching and logic gates.
Simulation parameters of the slave VCSEL are listed in the following table.
The authors thank M. C. Amann and W. Hofmann for providing the 1.55 μm VCSELs, and the support from National Security Science and Engineering Faculty Fellowship. The authors were made aware of an independent work  with relevant similarities after the submission of this manuscript.
References and links
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