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The experiment

The experimental setup was as shown in Figure. The VCSEL^2.1 was an AlGaAs quantum well structure emitting at 830 nm and was mounted on a temperature controlled stage. The VCSEL was DC biased with a low noise battery power supply. As we were examining the intensity noise spectrum it was vital that the laser should suffer no optical feedback. Therefore the laser output was collimated by a lens, and passed through two optical isolators. The isolators were both Faraday rotators with input and output linear polarisors giving a total of 60 dB reverse isolation. A $\lambda/2$ plate was inserted before the isolators so that either polarisation could be transmitted through the input linear polariser. The optical spectrum was analysed with a plane-plane scanning Fabry-Perot whose finesse was $\sim 100$ when its free spectral range (FSR) was $\sim 250$ GHz, and was less for smaller FSR's. The laser light was focussed by a $\times 10$ microscope objective onto the photodiode, an InGaAs Schottky diode (New Focus model 1435), of bandwidth 25 GHz. The photodiode signal was amplified by two low noise amplifiers of bandwidth 10 GHz yielding an amplification of 46.4 dB. The intensity noise spectrum was recorded on the electronic spectrum analyser (ESA), bandwidth 20 GHz.

How this arrangement could yield information about the relaxation oscillation frequency $\nu_r$ seems worth an explanation. Every laser has what can be described as a small signal transfer function from pump amplitude modulation to light intensity modulation. This function is (depending on electrical parasitics) nearly flat in frequency from DC until $\nu_r$ is reached, whereupon the transfer function peaks and then falls sharply and monotonically on the high frequency side of $\nu_r$ . Thus by examining this transfer function, one can identify the (average pump dependent) relaxation oscillation frequency. This experiment would be very involved and would require one to package the VCSEL so as to avoid electrical parasitics and other electrical effects.

An alternative approach to finding $\nu_r$ is to realise that there is what amounts to a weak white noise source inside the laser as random spontaneous emission events in the laser constantly modulate the carrier number and the laser intensity. If one examines the intensity noise spectrum, at $\nu_r$ the intensity noise is only weakly damped and a clear peak in the spectrum can be discerned, yielding $\nu_r$ . This was the method used in these experiments to find the relaxation oscillation frequency.

Several different VCSELs from this chip were tested and the results reported below for one of them at a particular heat-sink temperature were qualitatively the same for different VCSELs and for the same VCSEL at different heat-sink temperatures. Figure shows the polarisation resolved light-current (L-I) characteristic of the VCSEL. At threshold two modes were discernable in the optical spectrum and they were spectrally separated by 5.3 GHz. Both were orthogonally polarised fundamental transverse modes and are labelled here v and h. Until a current of 4.6 mA $\sim 1.5 I_{th}$ the lower frequency v-polarisation was dominant and the h-polarisation latent. That this mode was not lasing was indicated by its linewidth, which was on the order of 1 GHz.

**Figure:** Polarisation resolved L-I curve for implanted VCSEL. The hollow squares correspond to v-polarised power and the asterisks to h-polarised power. The onset of multimode operation occurs at 5.2 mA. As can be seen from the curve, the higher order transverse modes are orthogonally polarised to the fundamental.
$\begin{figure} \centerline{ \epsfxsize=16.0 truecm \epsffile {polar/figs/li.ps} }\end{figure}$

**Figure:** Optical spectra of VCSEL obtained using the scanning Fabry Pérot spectrometer both below (upper spectrum) and above (lower spectrum) the switching current, obtained with nearly maximum attenuation for the dominant mode in each case. Note that the spectral width of the latent mode below switching indicates moded spontaneous emission, but not lasing.
$\begin{figure} \centerline{ \epsfxsize=14.0 truecm \epsffile {polar/figs/fpspectra.eps} }\end{figure}$

At 4.6 mA an abrupt transition occurred where most of the power switched into the h-polarisation. The non polarisation resolved L-I was smooth despite this switching. There was no evidence for hysteresis in the switching in this device. At the switching point the frequency of the v-polarisation reduced by 1.2 GHz and that of the h-polarisation reduced by 2.6 GHz, giving a splitting after the switching of 3.9 GHz. See Figure for optical spectra before and after switching, and for a zoom on the latent h-polarised mode before switching. At an injection current of 5.2 mA the VCSEL began to emit multiple transverse modes. We shall not be concerned here with this region of operation of the laser.

**Figure:** Intensity noise spectra of the VCSEL as a function of current. The half wave plate is oriented so as to pass both polarisations equally, allowing one to see the relaxation oscillation both before and after the switching. This also causes the two polarisation modes to beat in the photodiode, so the polarisation splitting is simultaneously visible. This is very obvious on this graph after the switching, the beat frequency is at 3.9 GHz. The relaxation oscillation is small after the switching, linear stability analysis of the laser rate equations predicting that the relaxation oscillation damping should increase with injection current.
$\begin{figure} \centerline{ \epsfxsize=18.0 truecm \epsffile {polar/figs/rfspectra.ps} }\end{figure}$

**Figure:** A plot of the relaxation oscillation frequency versus normalised injection, r=(i-i_th/i_th. As predicted by the rate equations, $\nu_{r}^{2} \propto r$ , but in the vicinity of $\nu_d$ , the beating frequency of the polarisation modes, $\nu_r$ locks to $\nu_d$ . Unlocking occurs when the VCSEL polarisation switches and the new $\nu_d$ is less than $\nu_r$ . $\nu_r$ then returns to its predicted behaviour.
$\begin{figure} \centerline{ \epsfxsize=14.0 truecm \epsffile {polar/figs/reson.eps} }\end{figure}$

Figure contains a rainbow plot of VCSEL RF noise intensity versus frequency squared for different values of the injection current. The uppermost plot was taken close to threshold where $\nu_r$ was on the order of hundreds of megahertz. As the pump was increased, $\nu_r$ increased and the resonance became broader as the damping increased. This is in accordance with a linear stability analysis of the laser rate equations [20] which predicts $\nu^2_r \propto r$ , where $r=\frac{i-i_{th}}{i_{th}}$ is the pumping parameter, and that the damping rate $\Gamma \propto r$ . The beat frequency of the orthogonal polarisations, $\nu_d$ , was visible at 30 GHz² and became strongly enhanced when $\nu_r\approx\nu_d$ and the relaxation oscillation locked to the polarisation mode beat frequency. The relaxation oscillation remained locked for a range of current, until the polarisation switching current was reached and the h-polarisation became dominant. $\nu_{d}^{2}$ was reduced to 16.2 GHz², as is very clear from Figure. $\nu_r$ then unlocked from $\nu_d$ and returned to its pre-locking trajectory. This was difficult to see from Fig, as the relaxation oscillation was very damped, so the behaviour is clarified in Fig, which plots $\nu_{r}^{2}$ versus r. As can be seen, the linear dependence of $\nu_r$ on r was very well obeyed outside the locking range, until the onset of multimode operation. This behaviour was observed for different VCSELs on the same chip and for the same VCSEL at different heat sink temperatures. A change in the heat sink temperature changed the frequency splitting of the two modes, and locking was observed for splittings between 4-6 GHz. However when the splitting was reduced to 1.5 GHz, no interaction was observed between the two peaks.

Next: Discussion Up: Polarisation in VCSELs Previous: Introduction