Polarization competition and noise properties of VCSELs

Transcription

1 15 January 1998 Optics Communications Polarization competition and noise properties of VCSELs G. Giacomelli 1, F. Marin 2, M. Gabrysch 3, K.H. Gulden 4, M. Moser 4 Istituto Nazionale di Ottica, Largo E. Fermi 6, Florence, Italy, and INFM, Sezione di Firenze, Florence, Italy Received 1 July 1997; accepted 9 September 1997 Abstract A detailed experimental characterization of the dynamics of Vertical Cavity Surface Emitting Lasers VCSELs is presented. Evidence of strong anticorrelations between the different states of linear polarization of the field is given. As a consequence, it is shown that the noise of the single states of polarization is much higher than the total intensity noise. The dynamics of the polarizations is studied, showing that the statistics of the fluctuations is non-gaussian in the competition regime. q 1998 Elsevier Science B.V. PACS: Sf; Sa; p The Vertical Cavity Surface Emitting Laser Ž VCSEL. is a novel laser source which appears quite promising both for basic research Ž spectroscopy, quantum optics. and for industrial applications Žcommunications, imaging, molecular sensing.. In fact, it shows many advantages with respect to the previous standard semiconductor laser architectures, e.g. the improved spatial quality of the beam and the very reduced pump threshold w1,2 x. This last property seems to assure, together with the high pump rate attainable, a very high efficiency which makes the VCSEL a good candidate to easily obtain amplitude-squeezed states wx 3. On the other hand, the VCSEL shows several behaviours which are not completely understood. Among them, the competition between different states of polarization of the field and the role of the transverse modes which are easily excited w4,5 x. A thorough undestanding of these 1 Corresponding author. gianni@ino.it. 2 Also at Dipartimento di Fisica, Universita di Firenze, Largo E. Fermi 2, Florence, Italy. 3 European Laboratory for Nonlinear Spectroscopy Ž LENS., Largo E. Fermi 2, Florence, Italy and Physikalisches Institut, Universitat Heidelberg, Philosophenweg 12, Heidelberg, Germany. 4 CSEM Zurich Ž formerly Paul-Scherrer Institut., Badenerstrasse 569, 8048 Zurich, Switzerland. features, together with the amplitude fluctuations and noise, is important for all the above mentioned applications. Anticorrelated fluctuations among longitudinal modes wx 6 have been shown to influence the amplitude noise up to the quantum regime for multimode wx 7 and nearly singlewx 8 semiconductor lasers. Kilper et al. wx 9 have mode observed an increase of about 2 db in the amplitude noise by selecting the polarization of a diode laser at cryogenic temperatures. Some investigations on the intensity noise properties of VCSELs have been published, showing the effects of mode hops w10x and polarization stability w11 x. In this work, we present a detailed experimental characterization of the role of anticorrelations in the polarization fluctuations on the amplitude noise. We show also non- Gaussian behaviour of the fluctuation statistics due to polarization and mode competition. The design and fabrication of the VCSELs investigated in this work is described for example in Ref. wx 1. The air post VCSELs have an emission wavelength of 765 nm and they operate in a single longitudinal mode. The same results have been obtained using different lasers in a reproducible way. Two perpendicular linear polarizations are defined, parallel and perpendicular to the ² 110: crystal direction wx 4. The laser is housed in a copper block, collimated and thermally stabilized within 1 mk. The homemade power r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S

2 G. Giacomelli et al.roptics Communications supply has a current noise below 70 par' Hz in the range 1 khz 3 MHz. The threshold current is 5.4 ma and the differential efficiency is 0.1 WrA near threshold. The maximum power is 0.82 mw at 17 ma. A polarizer and a half-wave plate Ž HWP. permit to select and analyze the different polarization components of the laser emission. The laser amplitude noise has been measured with an avalanche photodiode and a balanced homodyne detection setup. The former is a fast Ž more than 2 GHz bandwidth. Mitsubishi PD-1002 avalanche photodiode Ž APD.. The latter is performed by splitting the beam into two parts by means of an HWP and a polarizing beamsplitter Ž PBS.. The signals are then detected using two PIN photodiodes Ž EG& G model FND-100. with a total detection quantum efficiency of 70% and amplified using two homemade amplifiers with a bandwidth of 30 MHz. The sum and the difference of the signals are obtained using a combination of power splitters. The total common mode rejection ratio is better than 25 db over the whole bandwidth, while the overall detection noise corresponds to an input current noise of 20 par' Hz. The difference of the two signals allows an accurate calibratation of the shot noise level w12 x. The signals have been analyzed in the time domain, using a digital scope Ž 1 GHz bandwidth, 4 Gsamplesrs., and in the frequency domain with a spectrum analyzer. The optical spectrum has been analyzed using a confocal Fabry-Perot, with a FSR of 1.5 GHz and a finesse of about 300, while the spatial structure of the transverse modes has been displayed using a CCD camera. Fig. 1. Experimental setup. POL: polarizer, BS: beamsplitter, OI: optical isolator, FP: Fabry-Perot analyzer, CCD: video camera, HWP: half-wave plate, PBS: polarizing beamsplitter, D1, D2: PIN photodiode with amplifier, APD: avalanche photodiode, SD: sum and difference device, SA: spectrum analyzer. Fig. 2. Laser intensity in the main Ž. a and in the secondary polarization Ž. b versus pump current. The regions I IV are defined by the vertical lines at the currents Is9.8 ma, 12.8 ma and 14.3 ma. The setup is depicted in Fig. 1. The behaviour of the laser changing the pump current can be divided into four regions Ž see Fig. 2a.. In the region Ž.Ž I up to 9.8 ma. the laser is strongly linearly polarized Ž better than 97%. and in a single TEM00 mode. In the region Ž II. Ž between 9.8 ma and 12.8 ma., a few different near-threshold transverse modes Žup to 20% of the total power. appear in the secondary polarization Ž see Fig. 3.. In region Ž III. Ž between 12.8 ma and 14.3 ma., several transverse modes are excited in the main polarization. As a consequence, the fraction of power in the secondary polarization is rapidly reduced. Finally, in the region Ž IV. Ž above 14.3 ma., the laser is again polarized but now the power is distributed among several different transverse modes. As we will show in the following, the laser displays very different dynamics in these four regions. We have first investigated the laser amplitude noise spectrum. In Fig. 4 we show the behaviour of the noise versus pump current at 5 MHz. Curve Ž. b represents the total noise, while curve Ž. a is the noise in the main polarization. We stress that if the polarization of the field is not defined, a balanced detection using a PBS would not give the correct result. Indeed, curve Ž. b is referred to the shot noise level measured in the main polarization, corrected to keep into account the slightly higher total emission. We notice that in region Ž. I the noise level is nearly the same for the two curves, while the main polarization exhibits a larger excess noise in the other regions. The analysis of the optical spectrum during the pump scan reveals how the increase of the single polarization noise is related to the appearance of other transverse modes in the secondary polarization Žregion Ž II... The growth of transverse modes in the main polarization Žregion Ž III.. leads first to a strong increase, then, as the secondary polarization intensity depresses, to a reduction of the noise.

3 138 G. Giacomelli et al.roptics Communications Fig. 4. Noise with respect to shot noise at 5 MHz versus pump current. The resolution bandwidth is 100 khz. Curve Ž. a is the noise in the main polarization, while curve Ž. b is the total noise. In the inset the values of y10 log Ž1qC Ž 0.. Ž see text. ps with the same axis units are reported. The vertical lines are defined as in Fig. 2. Fig. 3. Transverse modes of the laser in region II Ž see text.. The pattern in Ž. a refers to the main polarization and shows a TEM 00 mode, while in Ž. b a higher order mode in the secondary polarization is shown. The behaviour of the total intensity noise in regions Ž II IV. Žup to more than 25 db less than that of the main polarization. represents a clear evidence that the fluctuations in the two polarizations are strongly anti-correlated. In order to investigate such a phenomenon, we have adjusted the HWP to separate and detect simultaneously the two polarizations on the PIN photodiodes. In Fig. 5 we report the temporal behaviour of the intensity fluctuations detected by the two photodiodes at Is13.1 ma. We notice that, in spite of the different power level in the two polarizations, the two signals display opposite amplitude fluctuations and are indeed anticorrelated. To better quantify such a behaviour, we introduce the cross-correlation function of the two polarization intensities ² D I Ž tyt. D I Ž t. : p s CpsŽ t. s, Ž 1. ² 2 :² 2 D I Ž. t D I Ž. t : ( p s where D IsIy² I :, the subscripts p and s refer to the principal and secondary polarization respectively and ²: denotes time average. The two photodiode signals contain some amount of electronic noise, uncorrelated with each other and with the laser fluctuations. Such a noise gives no contribution to the numerator of ŽEq. Ž 1.., while the denominator was corrected subtracting the measured variances of the electronic noise from the ones of the signals. In the inset of Fig. 4, we plot 1qC Ž. ps 0 on a log-scale versus the pump current to compare with the behaviour of the noise in the main polarization. In fact, in the case of strongly anti-correlated signals with a flat spectrum, the quantity 1qCŽ. 0 is equivalent to the ratio SŽ I. rsž I., Fig. 5. Temporal behaviour of the polarizations at Is13.1 ma. Curve Ž a. ŽŽ b.. refers to the secondary Ž principal. polarization. The Ž arbitrary. vertical scales are the same. tot p

4 G. Giacomelli et al.roptics Communications where I si qi is the total intensity and SŽ I. tot s p is the noise spectrum of I. By observing the temporal series of Fig. 5, we notice that the fluctuations are not symmetric. This behaviour is characteristic of region Ž III., while in the other regions, even in the presence of strong excess noise, the temporal statistics is Gaussian. To investigate this behaviour, we plot in Fig. 6 the histograms of the intensity signal in the main polarization, for different values of the pump current. They are obtained from the APD signal, sampled at 2 Gsamplesrs, using 2.5=10 5 samples. In region Ž. I, the laser is single-mode and its fluctuations are Gaussian. In region Ž II., several transverse modes appear in the secondary polarization; they do not compete with the mode of the principal polarization Ž TEM. 00 and the fluctuations are again almost Gaussian Ž Fig. 6a, 6b., while they are strongly anti-correlated. In region Ž III., the same transverse modes start to move to the principal polarization. The distribution due to the competition adds to the usual Gaussian distribution of fluctuations, and the overall statistics displays therefore the two-peaks structures of Fig. 6c 6f. Finally, in region Ž IV. the laser is well-polarized and the different transverse modes are in the principal polarization, with Gaussian fluctuations. Moreover, while the spectrum of the Gaussian fluctuations is almost flat up to the frequency of the relaxation oscillations ŽFig. 7b, region Ž II.., in region Ž III. we observe a cut at about 50 MHz Ž Fig. 7a.. That is, the polarization competition has a characteristic time longer than the relaxation time of the laser. Indeed, the measured autocorrelation function decays with a time constant of 3.3 ns at Is13.1 ma. Fig. 7. Spectrum of the fluctuations in the main polarization detected with the APD and recorded with a spectrum analyzer. Curve Ž. a is within the competition regime Ž Is13.1 ma., while curve Ž. b is in the quasi-gaussian regime Ž Is12.4 ma.. A theoretical model for investigating VCSELs polarization states and dynamics has been recently developed by San Miguel and co-workers w13,14 x. They were indeed able to explain the switching between the two steady-states of the polarization Ž see Fig. 2. and the appearance of higher order modes increasing the pump current. Some of their results are very similar to those here reported, however, the dynamics of competition and the noise-reduction effects we have found are not reproduced, thus requiring a further theoretical work. In conclusion, we have shown how a VCSEL exhibits a strong noise reduction for a large interval of pump currents. This phenomenon is due to the competition between the two states of linear polarization which are anti-correlated. The amount of anti-correlation is closely related to the noise reduction measured using a balanced homodyne technique. The statistics of the polarization dynamics is given, which is non-gaussian in the regime of polarization competition. Acknowledgements We acknowledge the very useful technical support by Sergio Acciai and Massimo D Uva. This work was partially supported by EEC contract no. CI1)CT References Fig. 6. Histograms of the intensity signal for the principal polarization at different values of the pump current: Is10.9 ma Ž. a, 12.4 ma Ž. b, 12.8 ma Ž. c, 13.0 ma Ž. d, 13.1 ma Ž. e and 13.5 ma Ž. f. The histograms are normalized in such a way that the area is the relative noise. wx 1 K.H. Gulden, M. Moser, S. Luscher, H.P. Schweizer, Electron. Lett. 31 Ž wx 2 R.S. Geels, S.W. Corzine, L.A. Coldren, IEEE J. Quantum Electron. 27 Ž , and references therein. wx 3 S. Machida, Y. Yamamoto, Y. Itaya, Phys. Rev. Lett. 58 Ž

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