We present experimental results of output power bistability in a vertical-cavity surface-emitting laser under optical injection induced by frequency detuning or power variation of the master laser. An ultra-wide hysteresis cycle of 3.7 nm (473.3 GHz) is achieved through frequency detuning, which is more than 11 times wider than that achieved in the state-of-the-art (37 GHz). Furthermore, the width of injection power induced hysteresis cycle we achieved is as large as 7.3 dB. We theoretically analyzed the hysteresis cycles based on standard optical injection locking rate equations including the interference effect of master laser reflection and found excellent agreement with experimental results.
© 2013 OSA
Vertical-cavity surface-emitting lasers (VCSELs) have been proven to have a number of unique advantageous features over other types of semiconductor lasers. These advantages include cost efficiency, easiness for fiber coupling and intrinsically single longitudinal mode. Optical injection locking (OIL) of VCSELs has demonstrated significant performance improvement over directly modulated VCSELs in experiments [1–3], which are well analyzed and explained from a theoretical point of view [4–6]. Optical injection of VCSELs is also an attractive method to obtain polarization bistability [7–9] which is promising for optical communication, optical switching, and optical data processing .
In this paper, we report ultra-wide hysteresis cycles of OIL-VCSEL power as a function of master laser frequency and power. Super wide hysteresis cycle of 473.3 GHz is achieved through high injection power (14 dBm), which is more than 11 times wider than that achieved in the state-of-the-art (37 GHz) . We provide theoretical analysis of the wide hysteresis cycles based on standard optical injection locking rate equation  including the interference effect of master laser reflection  for the first time. The changed trend of output power and the shape of hysteresis cycles are calculated. The simulation results show excellent agreement with our experimental results.
2. Experimental setup
The experimental setup is shown in Fig. 1(a) . A commercial high power tunable laser is used as the master laser. The slave laser is a single-mode 1.55 μm VCSEL designed with buried tunnel junction (BTJ) structure to confine both current and light . The master laser injection-locks the slave laser through an optical circulator (OC). Polarization controller (PC) is used to match the master polarization with the VCSEL’s preferred polarization. An optical spectrum analyzer (OSA) is used to monitor the locking condition and an optical power meter is used to monitor the total optical power.
The VCSEL is biased at 7.0 mA to yield −5.0 dBm free-running output power at room temperature 294.0 K. Figure 1(b) shows the optical spectrum of this VCSEL. Two polarization modes are 0.28 nm apart from each other (λ∥ = 1531.30 nm, λ⊥ = 1531.02 nm) with 30 dB side mode suppression ratio. The polarization of master laser is controlled by PC to match the strong polarization mode (λ∥) of VCSEL.
3. Experimental results
3.1 Hysteresis cycles achieved by sweeping wavelength detuning
We investigate the locking range and output power of an OIL-VCSEL as a function of the direction of sweep of the master laser wavelength. The master laser sweeping from a wavelength shorter than that of the slave laser, the locking range is significantly larger than the other way around. Figures 2(a) and 2(b) show the locking maps of VCSEL as a function of wavelength detuning and injection power ratio. Figure 2(a) shows the master wavelength increasing from a value shorter than VCSEL wavelength, and the other way around in (b). The total VCSEL output power is shown as color contours. In this experiment, the injection power of master laser is changed from 10.0 dBm to 15.0 dBm, so injection ratio (Rinj = PMaster/PSlave) changes from 15.0 dB to 20.0 dB correspondingly. Wavelength detuning (Δλ = λMaster–λSlave∥) changes from −1.2 nm to 5.4 nm. The locking cut-off wavelengths on the blue side (short) are nearly the same. However, the red edges of the locking ranges are significantly different due to the slave laser cavity resonance shift with strong light injection [4,12].
The hysteresis of output power under three specific conditions (Rinj = 16.0 dB, 17.5 dB, 19.0 dB) are plotted in Fig. 3 , which correspond to straight lines at fixed x-axis in Figs. 2(a) and 2(b). In Fig. 3(a), injection ratio is fixed at 16.0 dB. The output power is 4.4 dBm when the slave laser is unlocked. When detuning is increased to −0.62 nm, VCSEL is injection locked. The total output power decreases with a further detuning. The minimum output power goes to −2.2 dBm when the VCSEL is locked. As red detuning of master laser wavelength continues, VCSEL is suddenly unlocked and the output power returns to 4.4 dBm. The black dashed curve exhibits the output power when wavelength detuning direction is reversed. Under this condition, locking range shrinks from 2.2 nm to 0.8 nm, so the width of this hysteresis cycle is 1.4 nm (= 2.2 nm - 0.8 nm).
When injection ratio is increased, the width of the hysteresis cycle increases. The widths are 2.3 nm and 3.7 nm respectively in Figs. 3(b) and 3(c), corresponding to Rinj = 17.5 dB and 19.0 dB. They all display anticlockwise optical bistability under these three conditions.
In our experiment, the polarization of master laser matches the strong polarization mode (λ∥) of VCSEL. It should be pointed out that similar results can be obtained with optical injection to match the weak polarization mode (λ⊥) of VCSEL.
3.2 Hysteresis cycles achieved by sweeping injection ratio
When wavelength detuning is fixed, hysteresis cycles can be obtained by sweeping injection ratio. This corresponds to lines at fixed y-values in Figs. 2(a) and 2(b). In Fig. 4(a) , when injection ratio increases to 15.7 dB, VCSEL is switched from free running condition to injection locked condition. The output power changes from 4.0 dBm to 2.4 dBm. When injection ratio decreases, the switch point of injection ratio from locking to free running is at 11.6 dB. At this point, output power suddenly increases from −7.3 dBm to 0.7 dBm. The width of the hysteresis cycle is 4.1 dB (= 15.7 dB - 11.6 dB).
Figure 4 compares the wavelength detuning dependence of the hysteresis cycles. When the detuning increases from 0.25 nm to 0.44 nm, the width of the cycles increases from 4.1 dB to 7.3 dB. They are all clockwise optical bistability cycles under these three conditions.
4. Theory and simulation results
4.1 Simulate hysteresis phenomenon based on standard OIL rate equations
Hysteresis cycles can be easily explained by frequency pulling effect in a very intuitive way. However, this hysteresis phenomenon has never been analyzed by standard OIL rate equations. We present the hysteresis cycle simulated based on these equations for the first time. The standard OIL rate equations are used for numerical simulation as follows :
When these equations are solved in the time domain, the initial values: S0 (photon number), ϕ0 (relative phase difference) and N0 (carrier number) should be set. The equations are solved in time domain to examine the convergence of three values after a reasonable long period of time (usually chosen to be 10 ns). The most important part of our simulation is how to set the initial values of S, ϕ and N in equations. For example, if the red point (in Fig. 5 : Rinj = 15.0 dB, Δλ = 1.6 nm) is to be calculated under increased wavelength detuning condition, the previous black point should be calculated at first. If the previous black point is locking stable, the black point’s stable values (S0, ϕ0, N0) can be used as red point’s initial values of S, ϕ and N. If the black point is unstable, then free running stable values should be used as red point’s initial values of S, ϕ and N. So, all the points’ calculation is based on the calculation result of their preceding points. In this simulation, the step of wavelength detuning is chosen at 20 GHz (0.16 nm) in this simulation.
Based on this method, the obtained hysteresis cycle by sweeping wavelength detuning is plotted in Fig. 5. When the slave laser is injection locked, the larger detuning is, the higher output power will be. We notice that this result is surprisingly different from the experimental results shown in Fig. 3. Based on our previous research , the interference effect of master laser reflection from the front facet of the slave VCSEL should be included to calculate the total output power of OIL-VCSEL. Since the output power in Fig. 5 doesn’t include this interference effect, we label the vertical axis as “Power without Interference (dBm)”. The details of this interference effect are described and discussed in the following subsection.
The locking state of black point in Fig. 5 is stable in our calculation, so the black point’s stable values of S0, ϕ0 and N0 are achieved and act as red point’s initial values. For the red point’s calculation, Figs. 6(a) to 6(c) show the evolution of S, ϕ and N in time domain based on standard OIL rate Eqs. (1) to (3). These three values are converged after 0.05 ns as is depicted in Figs. 6(a) to 6(c), which means the locking condition is stable at this red point. In order to clearly and distinctly see how these three values become stable, Fig. 6(d) is plotted. Horizontal dimension of Fig. 6(d) is corresponding to light field complex plane which can be calculated by S and ϕ in Figs. 6(a) and 6(b). Vertical dimension of Fig. 6(d) is corresponding to the carrier number which is the same as Fig. 6(c). Thus the convergence trajectory is easily verified, and the coordinate point converges to a stable red point in Fig. 6(d).
For decreasing wavelength detuning condition, the locking state of gray point is unstable in our calculation, so the free running stable values should be used as blue point’s initial values. For the blue point’s calculation, Figs. 7(a) to 7(c) show the evolution of S, ϕ and N in initial 0.1 ns. Phase value of Fig. 7(b) is limited between 0 and 2π. These three values are not converged in 10.0 ns based on our calculation which means the locking condition is unstable at this blue point. The divergent trajectory is easily verified in Fig. 7(d), and the coordinate point doesn’t converge to a stable point during a reasonable long period of time. The frequency of this oscillation is corresponding to the frequency difference between the master and the slave laser (beating frequency: f = Δλ = 200 GHz). The average output power in time domain is fixed after a reasonable long period of time (2 ns in the blue point calculation), and the average output power is used to plot the hysteresis cycle in Fig. 5.
Based on above analysis, the red and the blue points’ locking states are different, even though they are under the same locking condition (Rinj = 15.0 dB, Δλ = 1.6 nm). This leads to the hysteresis of OIL-VCSEL output power.
4.2 Calculate the hysteresis cycle including the interference effect
To explain the discrepancy between Fig. 5 and Fig. 3, we must discuss the reflection-mode OIL-VCSEL model established in our previous publication . The light of master laser is divided into two parts. One part transmits into the cavity of the slave laser, and the other part is reflected by the front facet of the slave laser. These two parts are phase coherent, so the total output power is calculated based on interference of these two parts. The simulation result in Fig. 5 doesn’t include the reflected master laser power by the front facet of the slave laser. Taking into account the interference effect, the hysteresis cycle is replotted in Fig. 8 . This simulation result is now consistent with our previous experimental results in Fig. 3.
5. Discussion: an intuitive explanation of hysteresis cycles based on ellipse model
After simulating hysteresis cycles based on standard OIL rate equations, an intuitive visualization and simple explanation can be provided based on the ellipse model . We previously reported a new graphical tool to analyze OIL-VCSELs. It predicts the cavity mode behavior for VCSELs under injection locking. Figure 9(a) shows the positions of master laser’s wavelength and slave laser’s cavity mode under different locking conditions with increased wavelength detuning. When λmaster = λi, the slave laser is not locked and stays at the origin which is set to be λslave0. The locking starts when λmaster increases further to y = λii, which intercepts with the ellipse at point a. This continues until the master wavelength increases beyond point b. Before point b, master laser’s wavelength pushes the slave laser’s cavity mode to red shift which is called frequency pulling effect . Figure 9(b) shows the other condition with decreasing wavelength detuning. When λmaster = λiv, the slave laser is not locked and stays at the origin λslave0. The locking starts when λmaster decreases further to y = λiii, which intercepts with the ellipse at points b’ and c’. In the beginning of this locking, the slave laser’s cavity mode is located at point c’. The ϕ of this point on the ellipse is π/2. However, only when ϕ falls in the range from -π/2-π/2 to cot−1α (α: linewidth enhancement factor) can the slaved laser reach a steady locking state [4, 5]. So the cavity mode of slave laser will red shift from point c’ to point b’, and reach a steady locking state on the ellipse. This continues until the master wavelength decreases below point a’.
Based on our previous research , the area of the ellipse is proportional to Rinj. When Rinj is higher, the ellipse is larger, which means the hysteresis cycle is wider. This is consistent with our experimental results. We believe that the width of detuning-induced hysteresis cycle is only limited by injection ratio. Also, the linewidth enhancement factor of the slave laser determines the eccentricity e of the ellipse. This is coherent with Ref : the larger α, the wider bistable region. This ellipse model can also explain injection power induced hysteresis cycles by changing the size of the ellipse. More details of this ellipse model could be found in Ref .
In summary, the hysteresis phenomenon of optical injection VCSEL is experimentally and theoretically analyzed. An ultra-wide hysteresis cycle of 3.7 nm (473.3 GHz) is achieved by varying the wavelength detuning at a fixed injection ratio of 19 dB. This is more than 11 times wider than previous report . A width of 7.3 dB in output power can also be achieved by sweeping injection ratio at a fixed detuning of 0.44 nm. Theoretical work is presented to explain the shape of the hysteresis cycles. This theoretical explanation will be useful to optimize the conditions for application of VCSEL in optical communication, optical switching, and optical data processing.
The authors wish to acknowledge the support of the National Basic Research Program of China (973 Program 2012CB315606 and 2010CB328201), the State Key Laboratory of Advanced Optical Communication Systems and Networks, China. CCH acknowledges support by the US Department of Defense National Security Science and Engineering Faculty Fellowship N00244-09-1-0013, and Chang Jiang Scholar Endowed Chair Professorship. The authors thank Ms. Rongrong Gu for correcting the English manuscript.
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