SPIE Proceedings [SPIE SPIE Photonics Europe - Brussels, Belgium (Monday 16 April 2012)]...

Optical injection locking of polarization modes and spatial modes in single-aperture VCSELs and VCSEL arrays emitting at 1.3 µm

E. Lamothe*a, C. Longa, A. Mereutab, A. Calimanb, A. Sirbua, V. Iakovleva, G. Suruceanub and E. Kapona

aEcole Polytechnique Federale de Lausanne, Laboratory of Physics of Nanostructures, 1015 Lausanne, Switzerland

bBeamExpress, 1015 Lausanne, Switzerland

ABSTRACT

We report the injection locking of specific spatial modes and polarization modes of 1.3µm wavelength vertical surface emitting lasers (VCSELs) in single-aperture devices and phase-coupled arrays. The optical injection is realized using a master laser (ML) VCSEL, the beam of which is directed onto the output facet of the slave laser (SL) VCSEL or VCSEL array. We measured the emission spectra of the SL as the ML operating conditions (frequency, power) were varied systematically, and present the results on two-dimensional stability maps of power versus detuning of the ML from the injected modes.

In single-aperture devices, the high degree of circular symmetry allows the support of two modes with orthogonal polarizations with ~75 GHz frequency difference. With optical injection, we could induce a polarization mode switching and decrease the power of the free running mode by 25 dB. Model calculations confirm injection locking and specify the stability region. In a 1×2 VCSEL array defined by tunnel junction patterning and biased below threshold, we injection locked the fundamental mode (1×2 mode) and a « broad area » mode (1×3 mode). The spatial overlap between the ML spot and the array mode is shown to be a key factor in injection locking. Locking of the non-lasing 1×3 mode results in suppressed output power of the free running 1×2 mode. These studies are useful for understanding the mode structure of these VCSELs and suggesting ways for their discrimination.

Keywords: vertical surface emitting laser (VCSEL), injection locking, long wavelength VCSEL, polarization mode, spatial mode, VCSEL array, mode control, stability map.

1. INTRODUCTION Optical injection locking of semiconductor lasers is a topic that has garnered much interest from the scientific community over the past few decades [1]. In particular, injection locking of single-mode [2,3], multi-mode [4], polarization bistable [5-7], and arrayed VCSELs [8-10] has had a prominent place. Besides interest in the fundamental physics of locking and synchronizing oscillators [11], optical injection locking has been explored and exploited for a variety of applications, including characterization of the SL device parameters [12], enhancement of its optical properties – with benefits seen in decreasing laser linewidth and noise levels, increasing modulation bandwidth, and supressing signal distortion [13,14] – and as a platform for all-optical signal processing [15,16].

In optical injection locking, light from an external master laser (ML) is directed onto the facet of a second slave laser (SL). Depending on the power and frequency of the incident light, it is possible for the SL to lock to the ML so that both operate at the same frequency at a fixed phase difference. When the master laser is detuned from stable injection conditions, the SL responds by exhibiting rich nonlinear characteristics such as resonant oscillations and chaotic behavior before becoming fully unlocked [17]. The physics of injection locking can be described using the usual laser rate equations with an extra term to describe the injection locking, as given below. They treat the real and imaginary parts of the laser master equation separately so that they can individually describe the laser’s photon number S and phase φ, and carrier number N:

*[email protected]

Semiconductor Lasers and Laser Dynamics V, edited by Krassimir Panajotov, Marc Sciamanna, Angel Valle, Rainer Michalzik,

Proc. of SPIE Vol. 8432, 84321V · © 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.922138

Proc. of SPIE Vol. 8432 84321V-1

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dSdt

= Γυggn N − Ntr( )

1+εS− 1

τ p

⎡

⎣⎢⎢

⎤

⎦⎥⎥S + βB

Va

N 2 + 2κ SinjS cos φ(t)−φinj (t)( ) (1)

dφdt

= α2

Γυggn N − Ntr( )

1+εS− 1

τ p

⎡

⎣⎢⎢

⎤

⎦⎥⎥−κ

Sinj

Ssin φ(t)−φinj (t)( ) − 2πΔf (2)

dNdt

= Ibias

q− N

τ N

− Γυggn N − Ntr( )

1+εSS (3)

Formal definition of variables will be given in the discussion section below, but here a qualitative description is illustrative. Equation (1) describes the rate of change of the photon number. The three terms on the right tell us that the photon number depends on laser gain and loss mechanisms, spontaneous emission into the mode, and externally injected photons from the ML, respectively. Equation (2) describes the rate of change of the phase, or frequency of the laser. The first term on the right describes a change due to a shift in the cavity resonance with carrier number because of the coupling α (linewidth enhancement factor) between the laser amplitude and phase. The second term describes a change due to coupling of the internal and external fields, which depends on the instantaneous value of the phase. And the third term describes the frequency detuning ∆ν=νML-νSL of the injected ML and free running SL. A concise description of optical injection is contained in this equation [18]: when the first two terms sum to the ML detuning frequency the net phase change is equal to zero, and we can state that the laser is injection locked. Equation (3) describes the rate of change for the carrier number N. The first term represents the injected carriers from the bias current, the second describes the loss of carriers to non-radiative processes, and the third is the loss due to stimulated emission.

A coupling rate term defined as κ=υg/2Lcav describes the duration it takes for the incident ML light to distribute itself along the length of the SL cavity Lcav. The boundaries to stable injection locking can be found by considering steady-state solutions to the rate equations and solving for the limiting values for the frequency detuning. This leads to a locking range given by

−κSinj

S0

1+α 2 ≤ 2πΔf ≤ κSinj

S0

. (4)

Thus, the linewidth enhancement factor α leads to asymmetry in the locking region, and 2D maps of the response of the lasers versus ML injection power and detuning will reflect this asymmetry.

Injection locking is of special interest in VCSELs for which the discrimination among lasing modes is weak and prevents sufficient mode stability that is important for reduced partition noise, error-free large signal modulation, or maintaining specific spatial and polarization modes throughout the range of operating paramaters (e.g., current, temperature). This is particularly the case for single mode VCSELs that suffer from polarization mode switching or instability [7, 19], and for multi-mode VCSEL such as VCSEL phase-locked arrays, in which mode discrimination is inherently poor [8]. Recent reports have illustrated the rich dynamics taking place due to polarization mode competition in injection-locked long wavelength VCSELs, observed in time resolved experiments [20]. In the current paper we report on the characteristics of 1.3µm injection-locked single- and multi-spatial mode VCSELs analyzed by measuring and simulating their spectral stability maps.



2. INJECTION LOCKING SETUP

Fig. 1 | Optical injection locking setup. ML – Master Laser, iso – optical isolator, atte – optical attenuator, PC – polarization

controller, splitter – 10/90 fiber splitter, pol – polarizer, BS – beamsplitter, M – mirror, Flip M – flip mirror, O – microscope objective, L – coupling lens, SL – slave laser, OSA – optical spectrum analyzer, CCD – charge-coupled device.

The optical injection properties of the VCSEL under test are recorded using a pair of optical spectrum analyzers (OSAs) (see Fig. 1). The ML we use is a commercially available VCSEL emitting in the 1.3 μm band that is packaged with a fiber pigtail; it has a threshold current of 1.8 mA and operates single mode (single mode suppression ratio >30dB) until approximately 5 mA (Pout ≈ 0.4 mW). The signal passes through an optical isolator (> 50 dB isolation) to prevent backscattered light from entering the ML and so ensures unidirectional coupling between lasers. Next, light passes through a manual optical attenuator, a polarization controller and fiber optic splitter with a 10/90 split ratio. The 10% port is used as a monitor and sent to the first OSA. The main path exits the fiber through an output coupler with 5-axis motion and passes through a 50/50 non-polarizing beam splitting cube. The signal is directed through a microscope objective toward the SL that is placed on a temperature-contolled stage. Emitted light from the SL (and backscattered light of the ML) is collected by the microscope objective and passes through the beam splitter a second time. At the output the light is analyzed by a second OSA, a CCD camera, or a photodiode.

We measure the response of the SL as the ML bias current (frequency) and attenuation levels (power) are varied, and present the power in a given mode on two-dimensional maps of power versus detuning of the ML. The set up is implemented such that both the SL emission and ML spot can be imaged to verify proper spatial overlap. The placement is further refined by maximizing the optical response of the SL while adjusting the ML spot location. We estimate the size of the ML spot to be 4 μm in diameter, slightly smaller than the SL waist.



3. VCSEL DEVICE STRUCTURE

Fig. 2 | Schematic structure of wafer-fused 2x1 VCSEL array with patterned tunnel junction, and an optical micrograph of

the device.

A schematic of the VCSELs used in this study is shown in Fig. 2, alongside a micrograph of a 1×2 VCSEL array. The VCSEL active region consists of six strained InGaAs/InAlGaAs quantum wells grown on InP and optimized for emission at 1320 nm. A tunnel junction layer is patterned and regrown to provide current injection into a confined area, and defines the spatial extent of the laser waist. The distributed Bragg reflectors (DBRs) are made of alternating layers of AlGaAs and GaAs and grown on a separate wafer. The final wafer structure is complete when the separate pieces are fused together [21]. For the experiments with single-spatial mode VCSELs, the devices have tunnel junction diameters of 6 μm to ensure single-transverse mode operation. For the 1×2 VCSEL arrays, the active region consist of two 6µm diamater tunnel junction mesas with a center-to-center spacing of 8 μm [22]. Individual array elements are biased through a common contact. The single-aperture VCSELs show a threshold current of 2.7 mA and maximum output power of 4.4 mW at room temperature; the VCSEL arrays display threshold currents between 1 and 3 mA, with a peak output power of 2 to 3 mW.

4. EXPERIMENTAL RESULTS 4.1 Injection locking of polarization modes of single-aperture VCSELs

The single-aperture VCSELs are typically linearly polarized along the crytallographic direction [110] or [1-10], when free running. The particular VCSEL studied lased with linear polarization parallel to the [110] crystallographic direction, referred to here as the parallel mode, with a threshold current of 2.7mA. The orthogonal polarization state, orthogonal mode, is polarized along the [1-10] crytallographic direction, and has a threshold of 7 mA. The device undergoes a polarization flip at 9 mA, after which power in the orthogonal mode exceeds the parallel mode by several (>5) dB. A higher-order transverse mode begins to lase at 15 mA (see LI curves in Fig. 3).

Fig. 3 | Polarization resolved LI-characteristics. Threshold current Ith =2.7 mA.

The spectrum of this SL VCSEL, biased at I=2.9 mA(=1.04×Ith), shows the two polarization states separated by ∼0.5 nm (75 GHz), see black trace in Fig. 4(a) and (c). The parallel mode oscillates at 1317.6 nm and dominates by 20 dB over the orthogonal mode. The optical injection of the SL is realized by sweeping the ML frequency over the entire frequency



range with the ML beam polarized in the parallel or orthogonal polarization and varying the power of the ML VCSEL at each spectral detuning, as shown in Fig. 4. The red traces in the emission spectra represent spectra under optimal injection locking. A 5 dB enhancement can be reached for parallel polarization mode injection, as shown in Fig. 4(a). It is also possible to induce a polarization switching within the VCSEL by injecting the SL at the orthogonal polarization mode, see Fig. 4(c). In this case, the power in the free-running mode (parallel mode) has decreased by 25 dB whereas the orthogonal polarization mode has enhanced by the same quantity; this is a strong indication that injection locking occurs. The two dimensional stability maps in Fig. 4(b) and (d) (parallel and orthogonal polarizations) are built from “injected” spectra measured over a wide range of ML frequency detuning and power. Each point indicates the peak power of the measured spectrum of the corresponding polarization mode for the indicated detuning and power of the ML; the color code employed for displaying the peak intensity is also indicated . The detuning and the power changes are implemented by increasing the ML current in steps of 0.05 mA and by attenuating the signal in steps of -1 dB. These stability maps demonstrate that injection locking is possible within a finite range of ML-SL detuning and with sufficient injected power.

In Fig. 5, the stability maps are compared for three different biased currents above the threshold I1 = 2.9 mA (=1.04×Ith), I2=3.0 mA (=1.07×Ith) and I3=3.3 mA (=1.18×Ith), for the same VCSEL device. Left and right columns correspond to parallel and orthogonal polarization of the ML source, respectively. Furthermore, instead of showing the absolute value of the SL peak power PSL, we subtract from it the maximum power, i.e PSL - Plock,max, in order to get the same reference level at 0 dB. The color scale units are now in dB. The power enhancement of the injection locked free-running mode (parallel mode) decreases from 5.0 dB (Fig. 5(a)) to 0.8 dB (Fig. 5(c)) when the SL biased current increases from I1=1.04× Ith to I3=1.18× Ith. Such decrease in the power enhancements is also observed for orthogonal injection of the orthogonal mode. In this case, it falls from 8 dB to 3.5 dB for the same current range, see Fig 5(d)-(f). The contour lines are plotted at different fraction of the maximum injection locked power Plock, max: 92% - full traces, 70% - dashed traces and 50% - dotted traces. In the case of the perpendicular injection, Fig. 5(d)-(f), the blue traces correspond to the contour lines of the power fractions of the orthogonal mode whereas the black traces correspond to the parallel mode output power at the corresponding levels. Comparing the contour lines at 0.92×Plock,max, we observe an expansion of the injection locked bandwidth for both cases parallel and perpendicular injection with increasing injected power.



Fig. 4 | Optical spectra and stability maps of the single-aperture VCSEL biased at 2.9 mA (1.04×Ith), undergoing injection

locking of parallel (a)-(b) and orthogonal (c)-(d) polarization states. The black traces correspond to the free-running spectra, the red traces to the optimum injection locked spectra. Zero frequency detuning refers to the wavelength of the free running parallel polarization mode.



Fig. 5 | Stability maps of the single-aperture VCSEL of Fig. 3, biased at 2.9, 3.0 and 3.3mA (Ith = 2.7 mA), undergoing

injection locking of the parallel (a)-(c) and orthogonal (d)-(f) polarization states. Note the different intensity scale as compared to Fig. 3 (see text).

4.2 Injection locking of VCSEL array modes

Laser arrays are frequently employed in applications requiring high output power. Because of their large size, the cavities often support multiple oscillating modes with weak mode discrimination. Injection locking of array modes [23] has been used by many researchers to stabilize a specific array mode and consequently control the far field pattern of the devices. Here we present the modal patterns and stability maps of an optically injected VCSEL array emitting near 1300 nm [22]. The particular device studied supports a fundamental mode that matches the array pixelation, i.e., the tunnel junction (TJ) pattern, and also higher order « broad area » modes, with threshold currents of 3, 10 and 12 mA for the 1×2, 1×3and 1×4 modes, respectively. Here, “N” in 1xN indicates the number of near field lobes in the corresponding mode. With optical injection, we can induce the device to lase on these higher order modes, even biased significantly below their threshold in the free running device.



Near field and far field patterns

In this experiment, we optically injected two of the spatial modes of a 1×2 phase-coupled VCSEL array and captured the near field (NF) and far field (FF) images with a CCD camera. For comparison, the spectrally resolved NF patterns of the free-running modes are measured by sampling optical spectra at different locations in space, and shown in Fig. 6. Similar images taken for the FF patterns indicate that individual lobes are coupled out-of-phase for all current bias levels, producing an on-axis null.

Fig. 6 | Optical spectrum and near field patterns of three spatial modes of a 1×2 VCSEL array biased at I=15mA=5×Ith .

The array was biased at threshold for the free running 1×2 array mode, and the ML spot focused onto one of the two array elements of the SL. The ML frequency was then tuned via temperature bias near the SL free-running mode resonances, centered at λ1x2=1317 nm and λ1x3=1316.4 nm (Δfmode = 104 GHz). Fig. 7 shows the evolution of the NF and the FF patterns of these modes (1×2 and 1×3) when the ML frequency is swept onto and out of resonance with the mode. The ML frequency is increased progressively in each panel, but incident power is maintained at 2.9 μW. When the ML moves closer to the 1×2 mode resonance, we induce the array mode to lase, as evidinced by emission from the second array element (Fig. 7 (a)-panel 0.17GHz). As the frequency detuning is further increased, the light emitted by the second array element is extinguished and all that is visible is the ML spot. This behavior is consistent with the expected behavior of injection locking rather than an optical pumping process. When we observe the FF patterns under the same ML injection conditions, we see two off-axis lobes in the FF (see Fig. 7(b)) that indicate out-of-phase coupling between the VCSELs.

The measurement was repeated with the ML tuned to the 1×3 VCSEL mode, see Fig. 7(c) and (d). The ML spot is placed slightly above the center of the array element in order to maximize the spatial overlap between the ML spot and the 1×3 free running mode. When we induce the 1x3 mode to lase, the intensity of the spatial mode is enhanced at the expense of the free running 1×2 mode, see Fig. 7(c). The corresponding FF patterns are presented in Fig. 7(d). In the first panel, primarily the FF of the 1×2 array mode is apparent, but as the 1×3 mode appears, the FF pattern expands and the central lobe begins to form. It comes out of the upper lobe, sweeps across the center and then joins the lower lobe as the ML frequency moves off resonance. A similar effect was reported by Hohimer, et al. [24] for injection locked arrays of gain-guided edge emitting lasers, and was attributed to nonuniform gain across the array that produced a tilted phase front on the emitted beam.



Fig. 7 | Near field (NF) and far field (FF) patterns of 1×2 and 1×3 modes when injected at the upper array element as a

function of the ML detuning at constant power. Above each panel, the ML detuning frequency is noted in GHz. The white circles represent the locations of both array elements (TJ apertures) and of the ML spot. (a) 1×2 mode NF patterns, (b) 1×2 mode FF patterns, (c) 1×3 NF patterns and (d) 1×3 mode FF patterns.

Stability maps of different spatial modes

Fig. 8 | 1×2 VCSEL array biased below the threshold (I=2.8mA) - (a) Free-running spectrum , (b) two dimensional stability

map showing optical injection for the 1×2 and 1×3 modes separated by 100 GHz.



In Fig. 8 we present the power map of the injection locked array modes when biased below threshold with the ML spot positioned over one of the tunnel junction apertures. In order to capture both modes in the plot, we record the strongest peak in each optical spectrum. There are two regions that show enhanced light output, indicating injection into the 1×3 mode (at -100 GHz) and the 1x2 mode (at 0 GHz). Under injection locking, we see a power increase of nearly 15 dB, and the enhancement is still visible down to -35 dBm of incident ML power. The bandwidth of the 1×2 stable injection region is broader because of its lower threshold and increased overlap (coupling) with the ML spot. Injection of the other modes is possible with further detuning of the ML frequency.

5. DISCUSSION Simulations of optical injection locking were carried out using the rate equation approach [25] whereby the differential equations describing the temporal evolution of the photon number and phase of the lasing modes and the carrier number are evaluated at different instances of time. Similar to Ref. [26] we add two additional equations to describe optical injection locking when two modes are present, but have them coupled to the same carrier population. In the case of polarization mode injection, we can set the appropriate coupling constant to zero so that we inject only one mode. In this way, one mode responds to the injected power, and the other responds indirectly through the carrier response. For example, when we simulate injection of the non-lasing orthogonal mode, it reduces the carrier number below the threshold level and decreases the power in the lasing mode. The equations are given below, with definitions and nominal values used in the simulation listed in Table 1. Equations (5) and (7) describe the photon population in the parallel and orthogonal modes, equations (6) and (8) describe the phases of their respective modes, and equation (9) describes the carrier population.

dS1

dt= Γυg

gn N − Ntr( )1+ε11S1 +ε12S2

− 1τ p1

⎡

⎣⎢⎢

⎤

⎦⎥⎥S1 + βB

Va

N 2 + 2κ1 SinjS1 cos φ1(t)−φinj (t)( ) (5)

dφ1

dt= α

2Γυg

gn N − Ntr( )1+ε11S1 +ε12S2

− 1τ p1

⎡

⎣⎢⎢

⎤

⎦⎥⎥− 2πΔf −κ1

Sinj

S1

sin φ1(t)−φinj (t)( ) (6)

dS2

dt= Γυg

gn N − Ntr( )1+ε22S2 +ε21S1

− 1τ p2

⎡

⎣⎢⎢

⎤

⎦⎥⎥S2 + βB

Va

N 2 + 2κ2 SinjS2 cos φ2 (t)−φinj (t)( ) (7)

dφ2

dt= α

2Γυg

gn N − Ntr( )1+ε22S2 +ε21S1

− 1τ p2

⎡

⎣⎢⎢

⎤

⎦⎥⎥− 2π Δf − Δfsplit( ) −κ2

Sinj

S2

sin φ2 (t)−φinj (t)( ) (8)

dNdt

= Ibias

q− N

τ N

− Γυggn N − Ntr( )

1+ε11S1 +ε12S2

S1 − Γυggn N − Ntr( )

1+ε22S2 +ε21S1

S2 (9)



Table 1 List of Simulation Parameters

Symbol Value Name Symbol Value Name

Γ 0.0265 mode confinement factor υg [27] 8.3 cm/ns group velocitygn 3.6x10-16 cm2 differential gain τN 0.21 ns carrier lifetimeVa 1x10-12 cm3 active region volume Ntr 1 x 10-18 cm3 transparency carrier number B [28] 8x10-20 cm3/ns recombination coefficient β [28] 1x10-4 cm3/ns spontaneous emission rate τp1 4.8 ps mode 1 photon lifetime τp2 0.995 x τp1 mode 2 photon lifetime ε11 7.2815x10-7 mode 1 self-gain-saturation ε22 0.97 x ε11 mode 2 self-gain-saturation ε21 1.3 x ε11 cross-gain saturation ε12 0.95 x ε12 cross-gain saturation

Simulation values not otherwise referenced were measured for the VCSEL sample through static and dynamic characterization [28]. The photon lifetime of the second mode is chosen so that the side-mode suppression between the two is similar to the observed spectrum, and the cross gain saturation coefficients set such that a polarization switch occurs at the same bias current as observed in a polarization-resolved light-current (LI) measurement.

The equations are solved using the Runge-Kutta method with Matlab’s built-in differential equation solvers ODE23 and ODE45. We first establish the free-running conditions by evaluating the rate equations without the injection term for a long time (10 ns), and then we introduce the injection terms and run the simulation for an additional 10 ns. Optical injection locking is determined by verifying that the amplitudes of the two modes have reached a steady-state value and the point-to-point variance has decreased significantly. We repeat this measurement for a range of detuning frequencies and attenuation levels of the ML light and compare them alongside the experimental data.

We verify the simulation parameters for this particular laser sample by creating an LI plot and set simulation parameters that predict the threshold and the polarization switching currents seen experimentally. The value for the coupling coefficient κ based on round trip time in the cavity is in reference to light that is injected into the cavity, so is dependent on many experimental parameters that can be difficult to estimate. The value shown in Table I is lowered by small amount to account for the coupling of external to internal fields, and provides a better fit between experiment and analytical expressions. Further refinement of the coupling factor would account for the cavity effects of the VCSEL resonator [29].

A comparison of experimental and simulated data is shown in Fig. 9 for the injection locking properties of the single-aperture VCSEL when biased at 3.0 mA (Ith = 2.7 mA). The contour lines shown on the experimental data represent the edges of the stable injection as predicted by (4). The boundary is drawn at the edge of the region that shows enhancement over the free-running field. Using α = 1.0 gives the proper asymmetry to the stable injection locking region, and a coupling parameter of κ1 =0.45 × κ gives the proper bandwidth to the data. At low injection powers, the power enhancement diminishes as the SL unlocks from the ML. The map of the simulated data shows the power enhancement over the free running laser power in a dB scale normalized to the maximum. The first contour line (black) shows the locking boundary extracted from the experimental data set, and the second (blue) is based on the time domain variation of the photon number S1. Differences in the power enhancement are attributed to interference between the backscattered ML light and the injection locked SL light, which can interfere coherently due to the injection-locked



phase difference between the two sources [30]. Given this situation, we emphasize and compare the locking boundaries rather than the color scale.

(a) (b)

Fig. 9 | Experimental (left) and simulated (right) stability maps for a VCSEL biased near threshold undergoing injection of the parallel mode, with contour line showing the borders of the stable injection region. This data is a subset of that shown in Fig. 5(b).

We next simulate the optical injection of the orthogonal mode. As above, we set the bias current to 3.0 mA, threshold for the parallel mode, but then we set κ1 to zero and κ2 to 0.38×κ to inject only the orthogonal mode. All other parameters are kept the same. We present the peak power of the parallel mode for the experimental and simulated data in Fig. 10. A contour line is drawn around the region where the peak power has decreased by 20 dB. This minimum is centered near -75 GHz, and the power change occurs symmetrically at the low and high frequency borders. Simulations show that this behavior is consistent with low values of α: for higher values (>3) the system slowly enters the injection region from the high frequency side and quickly snaps out on the low frequency side. In the right panel of Fig. 10 we see that the simulated data (continuous data) predicts a similar locking range as the experimental data set (small squares), but again the locking range extends to very low levels of injected power and predicts a greater diminution of the parallel mode. The inner (black) contour line is the locking region from the experimental data, and the outer (blue) contour line is the region where the simulation predicts >20 dB suppression ratio between the parallel and orthogonal modes. The experimental stability region appears offset from the simulated data by about 2 GHz, which is within the expected error in calibrating the two OSAs.

Looking at the experimental locking ranges, we see that the SL locking region is 18 GHz for parallel injection with a ML power of -23 dBm (see dashed line, Fig. 5b), and the SL responds to power levels down to -30 dBm. Comparatively, the locking range for orthogonal injection is only 4 GHz at -23 dBm injection power (see dashed line, Fig. 5c), with a lower border for injection locking that occurs soon thereafter. If we instead consider the change in power of the parallel mode when injecting the orthogonal mode, the bandwidth of the response is increased to 11 GHz at -23 dBm, and the minimum power for a response is -30 dBm. For both polarizations, the linewidth enhancement factor is near unity, giving a stability map that is nearly symmetric with frequency detuning. Fig. 5 shows that greater asymmetry develops when we bias the SL at higher currents, similar to what was reported in ref [20].

In our simulations, we attribute this difference in response to a difference in the efficiency of coupling external light into the SL mode, which decreases κ by approximately 15%. Another possibility is that it is due to material properties of the device itself, such as polarization-dependent gain. Further investigation is necessary to elucidate this difference.



Fig. 10 | Experimental (dots on top of the simulations) and simulated (solid) stability maps of a VCSEL biased near

threshold unergoing injection of the orthogonal mode, with contour lines showing the borders of the stable injection region. This data is a different subset of that shown in Fig. 10(b) and (e).

6. SUMMARY In summary, we present the optical injection locking properties of 1.3-μm wavelength VCSELs, including their stability maps for stable injection locking and the NF and FF images of array devices. Polarization mode and transverse mode injection locking are presented, and we show that optical injection locking is useful for selecting single operational modes when multiple possibilities exist, and for changing the far field beam patterns. The devices are modeled using the rate equation approach, and it is seen that the VCSELs response is slightly asymmetric, which is attributed to a linewidth enhancement parameter of 1. Future work will be to further explore polarization switching in VCSELs, where injection locking can be used to quantify the strength of the mode discrimination.

7. ACKNOWLEDGEMENTS The authors would like to thank the Fond National Suisse (FNS) for supporting this project.

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