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Optical injection locking of 1.3-µm phase-locked VCSEL arrays defined by patterned tunnel junctions and wafer fusion is investigated experimentally and theoretically. The impact of the overlap between the master laser injection beam and the injected modes is demonstrated and explained with a rate equation model that incorporates the spatial variations.
© 2014 Optical Society of America
1. Introduction
Increasing the output power of vertical-cavity surface-emitting lasers (VCSELs) requires the use of larger cavity apertures in broad area or array configurations [1]. However, the resulting multitude of transverse modes reduces the VCSEL coherence and single mode power, and may introduce undesirable static and dynamic instabilities [2]. A useful approach for mode selection and stabilization in lasers is optical injection locking (OIL), in which photons from a master laser (ML) are injected into the optical cavity of the slave laser (SL) to change its operation. Contrary to built-in modifications of the VCSEL cavity for transverse mode discrimination [3], this approach provides dynamic selectivity and also gives access to operation domains such as periodic oscillations, pulsations and chaos, otherwise not available [4-7]. Previous studies of OIL in multimode VCSELs have clarified the role of mode competition [8] and polarization [9], and distinguished between mode selection and full locking [10], and shown OIL to a higher-order transverse mode [11, 12]. In the analysis of a single mode laser, the coupling efficiency due to spatial overlap of the ML beam and SL mode is commonly suppressed, but analysis of multimode lasers requires careful attention to the overlap factor [7,9]. By exploiting this spatial dependence, it is possible to optimize the ML beam location to select different spatial modes and change the laser response [13].
Here we present the results of spatially resolved optical injection locking of coupled VCSEL arrays emitting in the 1300-nm waveband. We find that selective, single-mode operation can be achieved by proper choice of the ML frequency detuning, power level, and spatial overlap with the SL modes. A rate equation model that includes the spatial distribution of the beams yields stability boundaries that well fit the experimental values, and reproduces the proper modal selection process.
2. Experiment
The investigated 3 × 1 VCSEL array emitting near 1320 nm [14] was fabricated by wafer fusion (100 wafer orientation) of two AlGaAs/GaAs distributed Bragg reflectors (DBRs) with a gain wafer comprising six InP/InAlGaAs quantum wells (QWs) [15]. The three VCSEL apertures were defined by regrown TJ mesas with 6-µm diameters placed on Λ = 8 µm centers [Fig. 1] and common electrical contacts [16]. The transverse mode structure of the arrays was characterized using spatial scanning of an optical fiber in the image plane of the near field and connected to an optical spectrum analyzer (OSA) [17]. The device under investigation had a threshold current of 4.0 mA, operating single-transverse-mode until 6 mA, where higher-order modes spaced by ~80 GHz appear [Fig. 1]. The observed transverse modes can be classified into two groups: (i) supermode-like modes corresponding to linear combinations of the individual VCSEL modes [18], see modes 1 × 1 and 3 × 1; and (ii) higher order modes confined by a broad-area like gain distribution brought about by the weak spatial modulation of the optical gain introduced by the TJ patterning, see modes 4 × 1 and 5 × 1 [19]. All modes were linearly polarized stably along the [110] crystal axis.
Fig. 1 (left) Schematic drawing of the components of the 3 × 1 coupled VCSEL array, (top right) optical spectrum and (bottom right) near field intensity mode patterns at 8 mA bias. White circles indicate TJ boundaries, and yellow scale bars correspond to 5 μm.
For OIL experiments we used the setup presented in Fig. 2 [20]. The ML is a fiber pigtailed DFB laser (NEL NLK1B5EAAA), frequency tuned through temperature and current bias. Its beam is focused to a spot of 3.4-µm diameter on the VCSEL array chip. For each ML detuning frequency, the applied optical attenuation is decreased from 35 to 0 dB in 1-dB steps and spectra are recorded with the OSA. The array was biased at 4.8 mA and optically injected at seven sites, corresponding to the maxima of the 3 × 1 and 4 × 1 spatial modes [Fig. 3(a)]. The injected spatial modes resemble the free running modes shown in Fig. 1, but in some cases the power in the different lobes may vary. By proper positioning and frequency tuning of the ML beam we could select subthreshold spatial modes and extinguish the free running mode. In Fig. 3(b) are representative optical spectra for the free running and injected SL when the ML spot is aligned to the outer maximum of the 4 × 1 mode (site 7); in this case the array operates on only this mode with over 30 dB side mode suppression ratio (SMSR).
Fig. 2 OIL setup. ML: master laser, Iso: optical isolator, Atten: automatic attenuator, PC: polarization controller, BSC: beamsplitter cube, DMM: digital multimeter, SL: slave laser, Pol: polarizer, M: mirror, CCD: IR CCD camera, OSA: optical spectrum analyzer, and L: lens.
Fig. 3 (a) Near field images of the VCSEL array, 0) spontaneous emission showing the TJ locations, 1)-7) injected modes for various sites of the ML spot, shown in dark red (false color intensity scale). (b) Typical optical spectra of the free running and stably injected SL when the ML is detuned by −6 GHz from the target mode with an injection ratio of 3.6 dB.
The power-detuning injection maps depicted in Fig. 4 show the optical power of the targeted and non-targeted spatial modes for each power and frequency detuning of the ML. In this case, the ML is focused onto the smaller of the outer lobes of the 3 × 1 mode (site 2), for which all three spatial modes have significant overlap with the ML spot. When injecting about the lasing 3 × 1 resonance, [Fig. 4(e)] the SL displays the typical behavior of a single-mode laser with nonzero linewidth enhancement [4]: stable injection at negative detuning (−5 to 0 GHz), with greater bandwidth at increasing injected power. At moderate power levels (−15 to 0 dB) near 0 GHz, we see diminished optical power due to unresolved nonlinear behavior that disappears with higher injection. Complimentary features are apparent in the non-targeted spatial modes [Fig. 4(d) and 4(f)], which couple through the common carrier pool. A SL operating in a stable locking region requires less gain to lase and so the carrier density decreases, but when running in a nonlinear dynamic region, mode competition releases the gain clamping and the carrier density rises. For the non-targeted modes, the output power decreases in regions where the 3 × 1 mode power level increases (becomes stably injected), and increases on average when the SL transitions to a nonlinear state.
Fig. 4 Measured power-detuning maps of modal power for injection into site 2 (see Fig. 3). Rows are for injection targeting different modes and columns are the responses of different modes, as indicated. Contour lines in (e) mark the calculated locking regions: solid red, stable injection; dashed red, phase locked operation; solid black, all modes stably injected. Frequency spacing between data points is unequal because of inconsistent detuning with ML bias.
When targeting the 4 × 1 (non-lasing) mode [Fig. 4(i)], we see a region of increased output power that is triangular and centered at the free-running modal frequency. For positive detuning frequency, the power level increases continuously with injection level. For negative detuning, power increases slowly at first, then abruptly jumps to higher levels. The monotonic increase in power implies the SL undergoes stable injection locking without significant regions of dynamic oscillations at this site. Targeting the mode from its other maxima, however, could produce strong variations in output power for detuning of −6 to + 1 GHz, indicating the appearance of new dynamic states (not shown). Figure 4(h) shows a typical reaction of the 3 × 1 mode for all sites. The minimum power for mode selection occurs near 75 GHz (−6 GHz from 4 × 1 resonance), and the single-mode region expands from this detuning frequency. Outside of this region, the power decreases only slightly, but in good agreement with the augmented power of the 4 × 1 mode. The response of the 1 × 1 mode [Fig. 4(g)] follows the 3 × 1 mode. For targeting the 1 × 1 mode, we again see quiet operation in a stably locked state [Fig. 4(a)]. The power increases monotonically, with a discontinuity seen for negative detuning. Mode selection is achieved at −10 GHz, where the corresponding power in the 3 × 1 mode abruptly drops [Fig. 4(b)]. The 4 × 1 mode [Fig. 4(c)] shows new behavior in that its power increases with increasing 1 × 1 modal power, which stems from the poor spatial overlap between modes.
Figure 5 presents the response for optical injection of the 4 × 1 mode at different sites, highlighting the effect of ML spatial overlap with the SL mode. Mode selection is defined to be when the power in the 3 × 1 peak is decreased by 20 dB from its initial value, and indicated by a contour line in the figure. We select the 4 × 1 mode when injecting into either of the lobes, with a minimum occurring near −5 GHz in both cases [Fig. 5(a) and 5(b)]. Injecting into the large outer lobe [Fig. 5(a)] is the most efficient method, with mode selection seen by −5.5 dB and producing a large locking region. Injection into the array center [Fig. 5(c)] shows almost no response as this location corresponds to a null of the target mode. Spatial mode asymmetries and coupling into non-targeted modes allow small input coupling, but mode selection is not achieved.
Fig. 5 (a)-(c) Measured power-detuning maps showing the SL response for injection of mode 4 × 1 into sites 1, 3 and 4, respectively.
3. Modeling and analysis
We model our OIL experiments using rate equations [21] for the carrier number N, photon number Sμ, and phase ϕμ for each mode μ. In particular, we take into account the spatial variation of the photon number along the linear VCSEL array by writing [22], where ψμ is proportional to the intensity of the mode, normalized such that
and 2Wact is the width of the active region. The carrier number distribution is approximated by a Fourier series expansion:Integrating over the device and exploiting the orthogonality of cosine functions yields the following set of rate equations [7] The usual rate equation variables are identified in Table 1. The parameters hμmp and gp, resulting from spatial averaging, are defined as: where f(x) represents the current distribution, assumed to be 1 inside the TJ region and 0 elsewhere.
Table 1. OIL simulation parameters
The last terms in Eqs. (3) and (4) are due to OIL. The ML operates at a frequency Δν from the lowest-order SL mode. The injection rate κ depends on the cavity round-trip time τRT, and also includes injection efficiency due to partial reflection at the SL facet (with reflectivity R) and incomplete mode matching between the ML and SL [7,23]:
The prime symbols denote terms proportional to the field of the mode, and the absolute value is taken to remove a relative phase of π that can occur with higher-order modes.We implement this model using analytical functions to represent the spatial modes (SL: 1 × 1, 3 × 1, 4 × 1 Hermite-Gaussian modes, with 6.0-μm waist; ML: Gaussian with 2.8-μm waist) and a truncated series to represent the carrier distribution (m<5). Overlaps gp and hμmp are evaluated for 2Wact = 3Λ and are shown in Table 2 for modes 1 × 1, 3 × 1, and 4 × 1. The simulation is run using a Runge-Kutte time-stepping algorithm to evolve the 11 rate equations for 20 ns using a maximum step size of 1.2 ps, and data from the second half of the simulation are used in the analysis. We optimize input parameters to model the free running laser and present them in Table 1. Laser threshold is used to find the carrier lifetime and transparency carrier number. The slope efficiency and relaxation oscillation frequency are used to iteratively determine the photon lifetime of the 3 × 1 mode and laser gain. We then set the photon lifetime of other modes such that they reach threshold at their measured values. The round-trip time is estimated from the VCSEL layer structure using an assumed group velocity and including penetration depth into the DBRs.
Table 2. Overlap factors for current and SL modes with carrier expansion terms
We calculate hML for alignment to an outer lobe of the 3 × 1 mode and then create maps of the average output power and dynamic stability versus detuning and injection level. Stable injection locking of a mode (SIL1) occurs when the standard deviation of its phase is less than 1 radian, and the relative standard deviation of its photon number is less than 0.01. For the appropriate input parameters all modes can become stably locked to the ML (SIL2). We first target the 3 × 1 mode and plot the stability regions on top of the measured data in [Fig. 4(e)]. A linewidth enhancement factor of α = 4.75 gives stability regions in good agreement with the areas of the map where the SL displays increased output power. This value is greater than what was found previously for a single VCSEL on this wafer [20], and the difference is attributed to the increased bias point of the array, as α has been shown to increase with current [24]. A narrow tail of SIL extends from near 0 GHz to −5 GHz with increasing injection ratio (red contour, 3 × 1 mode injected), and then it gradually expands (black contour, all modes injected). The dashed line encloses areas where the phase of the SL is locked to the ML. Here, the mean intensity increases but full stable locking is not achieved. The fit could be improved using the actual beam shapes instead of approximate functions. Next we target the 4 × 1 mode, and plot the change in modal power and stability boundaries in Fig. 6. The mode becomes stably locked (SIL1) at low injection levels, giving increased output across most of the map [Fig. 4(i)]. For Δν≈200 GHz and moderate injection ratio, new peaks appear in the optical spectrum spaced by the relaxation oscillation frequency, indicating a nonlinear (NL) dynamic state. The power in the 3 × 1 mode is unaffected by the changes in the 4 × 1 mode at low injection ratio. But when the ML reinforces the 4 × 1 mode sufficiently to overcome its disadvantage in gain, a sharp jump in the 4 × 1 power occurs accompanied by a small decrease in the 3 × 1 mode, similar to Fig. 4(h). At sufficiently high injection level and negative relative detuning, the power in the 3 × 1 mode drops, and it becomes stably locked through intermodal injection locking (SIL2) [25].
Fig. 6 Simulation response for injection targeting 4 × 1 mode at site 2, showing change in output level of the 3 × 1 and 4 × 1 modes. NL: nonlinear region of operation, SIL1: stable injection locking of the 4 × 1 mode, and SIL2: stable injection of all spatial modes.
4. Summary and conclusion
We presented the OIL response of a long-wavelength coupled VCSEL array, and find features that are due to the ML overlap with the different SL modes. The experimental measurements were carried out on a wafer-fused 1.3-µm wavelength VCSEL array. The OIL process was modeled using a modified rate equation approach that includes spatial features of the system, such as ML/SL mode matching, SL mode shape, and carrier distribution. Comparison between the measured and the calculated power-detuning maps allowed evaluating the main characteristics of the OIL process in these multimode systems. As expected, we find that OIL is most efficient when injecting into the large anti-nodes of a spatial mode, as these locations will maximize the ML overlap with the SL. However, our analysis reveals finer details of the OIL process, including regimes of stable injection locking of a single mode, stable injection locking of multimodes, and indications of nonlinear and instability regimes. All these results give insight on the modal interactions in this complex system and suggest ways for achieving OIL of specific modal configurations. In particular, it allows design of multimode VCSELs in which higher-power single mode operation can be obtained via efficient OIL.
Acknowledgment
This work was supported by the Swiss National Science Foundation.
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