We have studied experimentally effects of two-frequency optical injection on a multimode vertical-cavity surface-emitting laser (VCSEL). The injected signal comes from another VCSEL. Polarization switching (PS) with and without frequency locking occurs for relatively small frequency detuning. Outside the regime of polarization switching, the VCSEL demonstrates two types of instabilities. The instability regions and boundaries of PS of each transverse mode are mapped in the parameter plane of frequency detuning versus injected power.
©2011 Optical Society of America
Vertical-cavity lasers have proven to be very useful in optical data communications, optical switching, and other applications because of their advantages over edge-emitting lasers (EELs), such as single-longitudinal-mode operation, low threshold current, circular beam profile, high modulation bandwidth, and easy fabrication of two-dimensional arrays . Though VCSELs are in single-longitudinal-mode operation intrinsically due to its short resonant cavity, they often operate with several transverse modes when the injection current is high . Multi-transverse-mode VCSELs have lower modal noise than EELs and are used in multimode fiber links. At the same time, the onset of transverse modes increased complexity of the behaviors of VCSELs . Another complexity of VCSELs is their polarization property. Even when lasing in the fundamental mode, VCSELs usually have two orthogonally polarized components with slightly different frequencies. VCSELs can switch between these two polarizations when the bias current or substrate temperature is changed . When higher order transverse modes start emission, their polarizations can be perpendicular  or parallel  to that of the fundamental mode.
Similar to EELs, VCSELs are sensitive to injected signal coming from another laser. Optical injection cannot only improve the performance of semiconductor lasers [7–9], but also induce rich dynamical phenomena in them [10–12]. One commonly used configuration in the study of optical injection is termed orthogonal injection , in which the polarization of the injected signal is perpendicular to that of the laser that receives the injection. If the polarization of the injected signal is parallel to that of the laser, it is named parallel injection. In VCSELs, optical injection can cause polarization switch, frequency locking, bistability, periodic fluctuations, and chaotic instabilities [6,13–19]. It can be used to reduce chirp and nonlinearity , enhance resonance frequency and modulation bandwidth , achieve mode selection in a multimode VCSEL [6,17], and to obtain chaos synchronization [22,23]. Single-mode VCSEL-by-VCSEL optical injection locking has been recently studied as a first step for obtaining integrated low-cost high-speed communications modules .
In most studies on optical injection, the injected signal comes from an external laser (named transmitter or master laser) that operates with a single frequency. Much less attention was paid to the injection of more than one frequency. Since optical injection changes the coupling characteristics between the electric field in the laser cavity and the charge carriers, the dynamics of a laser subject to more than one injected frequency will be much more complicated. Recently, some theoretical and experimental studies have been extended to optical injection of more than one frequency on EELs [25–29]. From the applications point of view, dual-beam optical injection is of special interest since photonic generation of broadly tunable microwave signals has been obtained by using a DFB laser . Optical injection of more than one frequency, however, has not been applied to VCSELs yet.
In this paper we report our experimental study of a multi-transverse mode VCSEL subject to two-frequency optical injection. To our knowledge, this is the first study of optical injection of more than one frequency applied to VCSELs. The two-frequency optical injection is applied by using another multi-transverse mode VCSEL. Thus, we consider partially coherent optical injection in contrast to [26,27,29], where a DFB laser was optically injected by using two different master lasers.
2. Experimental setup
In our experiment, a proton-implanted VCSEL, V1 (receiver), emitting at 847 nm receives a two-frequency injected signal provided by another VCSEL, V2 (transmitter), of the same model, as shown in Fig. 1 . The temperatures of the two VCSELs are stabilized at 24.01 °C and 32.02 °C separately by temperature controllers of same model (Thorlabs TEC2000). Their bias currents are controlled by current drivers (Thorlabs LDC200C) with accuracy 0.001 mA. The dominant polarization of both VCSELs is parallel to the optical table, which is termed X polarization. The polarization perpendicular to the optical table is termed Y polarization. The X polarization of the transmitter is selected by a polarizing beam splitter (PBS) and sent through an optical isolator (ISO). Since the isolator makes the polarization rotated 45°, a half-wave plate (HWP) is placed behind the isolator to rotate the polarization of the transmitted light by another 45°, becoming perpendicular to the optical table. Now the polarization of the injected light is orthogonal to the dominant polarization of the receiver. The injection is sent into the receiver by mirror M2 and a nonpolarizing plate beamsplitter M1. We obtain the optimal alignment when the injection power necessary to induce polarization switching is minimized at the boundary of the PS region.
For the purpose of observation and measurement, the output of V1 is split at M1: the transmitted part is sent to a Fabry-Perot (F-P) spectrum analyzer (FSR 300 GHz) and a charge-coupled device (CCD) camera, the reflected light is sent to a one-meter spectrometer (Jobin Yvon 1000m) and a fast detector (Newport 1580B, 12 GHz) which can be connected to an RF spectrum analyzer (Agilent EXA N9010A, 9 kHz to 26.5 GHz) or a digital oscilloscope (Tektronix DPO 7254, 2.5 GHz). With the aid of another PBS and a half-wave plate, we can detect spectrum and dynamics of each polarization of V1 as well as its power. The power of each polarization is measured with a power meter. We can also set up two fast detectors to observe temporal behaviors of the X and Y polarizations simultaneously. Half of the beam from the transmitter V2 can be sent to the spectrometer or to the F-P spectrum analyzer and the CCD camera. In order to send the light of V2 to the F-P spectrum analyzer, we use a mirror, M3, installed on a translational stage. M3 and the PBS that reflects the output of V2 are carefully aligned to get the frequency structure of V2 at the F-P spectrum analyzer. The frequency (wavelength) detuning is obtained from the F-P spectrum analyzer (spectrometer). The neutral density filter is used to adjust the injection power. The power of the injected signal is measured in front of the collimating lens of V1.
The solitary V1 is dominantly polarized in the X direction, and no polarization switching (PS) is observed within the current range we used in the experiment. From threshold I1=2.51 mA to 3.35 mA, the VCSEL operates in fundamental mode (LP01 mode). The second mode, a higher-order transverse mode, starts lasing from 3.35 mA. Its beam profile indicates that it can be described as a LP11s mode. The frequency difference between the LP11s mode and the fundamental mode is 63 GHz. From 3.50 mA to 4.75 mA, the VCSEL operates with three transverse modes. The third mode is a LP11c mode. The frequency of its X polarization is 15 GHz less than that of the LP11s mode. The fourth transverse mode is on from 4.75 mA. In our experiment, the VCSEL operates in the three-transverse-mode regime. The injected light includes two lasing modes: a fundamental mode and a first-order mode. Their frequency difference is 61 GHz. The spectrum and beam profile of each transverse mode of both receiver (V1) and transmitter (V2) are given in Fig. 2 .
We obtained frequency difference between the modes with the same transverse profile for V1 by analyzing polarization resolved optical spectra from the F-P spectrum analyzer. For the two modes with the fundamental profile, one is slightly elliptically polarized and the other is Y polarized. The Y polarized mode is 9 GHz higher than the elliptical polarized. However, since the intensity of the X component of the elliptical polarization is much stronger, the mode is essentially X polarized. The polarization feature of the LP11s profile is similar; it includes an essentially X polarized mode and a nonlasing Y polarized mode that is ~7 GHz away. For the LP11c profile, the difference between the X and Y polarized modes is 7 GHz. For both first-order profiles, the Y polarized mode has the higher frequency.
We define frequency detuning, ∆ν, as the frequency difference between the fundamental mode of the injected light, ν2f, and the Y polarization of the fundamental mode of the solitary V1, ν1fY. We change ∆ν by varying I1, the bias current of the receiver. Another control parameter is the injected power. For the results presented below, the bias current of V2 is 4.200 mA. When ∆ν is changed, the injected power, Pinj, is kept constant. The injected power is adjusted by using a neutral density filter (NDF).
We have observed polarization switching (PS) in each transverse mode for a certain range of the frequency detuning and injected power. For a fixed frequency detuning, PS may occur when the injected power is strong enough. Figure 3 (left) shows how the total power of each polarization varies with the injected power when the frequency detuning is set at −1.8 GHz. The total power has PS when the injected power is greater than 38 μW. Figure 3 (right) illustrates modal intensities versus frequency detuning, in which the three transverse modes switch simultaneously for ∆ν to be ~-2 GHz but do not switch back together. Therefore, we have observed that the polarized total power has an abrupt change on one side of the PS regime and a gradual variation on the other side.
The dynamics of the VCSEL subject to the two-frequency injection is mapped in Fig. 4 . It shows that in a wide range of the injected power, the three transverse modes have PS simultaneously but switch back for different values of detuning. Switching occurs in the fundamental mode for negative detuning in most cases, whereas the detuning can be both positive and negative for the first order modes. When ∆ν is about 0 GHz, both the fundamental mode and the LP11s mode have PS with minimum injected power. That is, the minimum power for switching is obtained when the X polarization of the fundamental mode is about 9 GHz less than the fundamental mode of the injected signal. This frequency difference is the splitting between the X and Y polarization of the fundamental mode of the receiver. This is similar to  in which the minimum switching power is obtained for a detuning corresponding to the frequency splitting between the two components of the fundamental mode. The optical spectra (not shown) manifest that for both the LP01 mode and the LP11s mode, their wavelengths are locked to the corresponding injected modes. The switching in the LP11c mode is not related to wavelength locking. It is probably caused by polarization competition. For a chosen value of Pinj, as the detuning is increased from −12 GHz toward the PS regime, the VCSEL demonstrates fluctuations which we classify as type 1 and type 2 instabilities. Type 1 instability includes a sharp peak and a low frequency shoulder in the rf power spectrum (Fig. 5(a) ) of both polarizations of the VCSEL. Its frequency is very close to the frequency difference between the X polarization of the fundamental mode, ν1fX, and ν2f. We measured the frequency of the first type of instability versus ν2f–ν1fX. The result shows a good linear relation (not shown), and the slope of the best fitting line is very close to 1. Therefore, the peak in the first type of instability is the periodic fluctuation caused by ν2f–ν1fX. Type 2 instability (Fig. 5(b)) occurs when the frequency detuning is close to the boundary of PS. It always starts with a peak in the power spectrum at around 2 GHz. As the frequency detuning is increased a little, this frequency decreases slightly with an increasing intensity. The bandwidth of the peak as well as the low frequency shoulder in the power spectrum is wider than that of the first type of instability. This instability suddenly disappears when the three modes have PS simultaneously. Its origin is to be explored. For these instabilities, we take the peak in the rf power spectrum into account when its intensity is greater than 3 dB. Figure 5(c) gives the power spectrum in the stable PS regime in the stability map, in which the sharp peaks in the low frequency region are external noise. Given the coexistence of three transverse modes in this regime, there should be oscillations at the beat frequencies of the modes. Those frequencies are not observed because they are higher than the bandwidth of our detectors. Figure 5(d) is in the unstable PS regime, where the fundamental mode is out of the PS regime but the two first-order modes have not. The peak in the power spectrum is very close to the frequency detuning and the low frequency part is due to polarization hopping.
Our results show that the partially coherent, two-frequency injection can induce PS in the total power of a multi-transverse mode VCSEL. The physical mechanisms of PS are frequency locking for the two strong transverse modes and polarization competition for the weakest mode. This extends injection-induced PS to multi-transverse mode regime of both transmitter and receiver and may be useful for development of tunable multimode light source. The feature that the width of modal PS regime is different can be used for transverse mode selection. Instabilities include unstable PS when the three modes do not switch simultaneously and periodic oscillations before the receiver enters the stable PS regime.
H. Lin acknowledges support from the National Science Foundation under Grant No. PHY-1068789. A. Quirce thanks support from the Spanish Research Council (Consejo Superior de Investigaciones Cientificas (CSIC)) and from Ministerio de Ciencia e Innovación, Spain, under project TEC2009-14581-C02-02. H. Lin also thanks Y. Hong for useful suggestions on some experimental methods.
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