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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2476–2484
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Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers

Lukasz Olejniczak, Krassimir Panajotov, Hugo Thienpont, Marc Sciamanna, Alex Mutig, Friedhelm Hopfer, and Dieter Bimberg  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2476-2484 (2011)
http://dx.doi.org/10.1364/OE.19.002476


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Abstract

We show experimentally that polarization mode hopping in quantum dot vertical cavity surface emitting lasers (VCSELs) takes place between nonorthogonal elliptically polarized modes. In contrast to quantum well VCSELs the average dwell time decreases with injection current. This decrease is by 8 orders of magnitude: from seconds to nanoseconds and is achieved without any modifications of the VCSEL internal anisotropies. The observed scaling happens in a range of currents as wide as 8 times the threshold value.

© 2011 Optical Society of America

1. Introduction

Many dynamical systems under the influence of noise show bistable hopping between two metastable states [1

1. P. Hänggi, P. Talkner, and M. Borkovec, “Reaction-rate theory: fifty years after Kramers,” Rev. Mod. Phys. 62, 251–341 (1990). [CrossRef]

]. Classical picture of such a behavior is given by the Kramers escape over a potential barrier [2

2. H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7, 284–304 (1940). [CrossRef]

]. Since detail studies on polarization switching in quantum well (QW) vertical-cavity surface-emitting laser (VCSELs) show that it is often accompanied by a noise-driven polarization mode hopping (PMH) [3

3. C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Polarisation characteristics of quantum well vertical cavity surface emitting lasers,” Electron. Lett. 27, 163–165 (1991). [CrossRef]

5

5. K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization Behavior of Vertical-Cavity Surface-Emitting Lasers: Experiments, Models and Applications,” Proc. AIP 560, 403–417 (2001). [CrossRef]

], these devices represent an ideal system for experimental study of such noise effects. Indeed, this issue has already been investigated for solitary devices [6

6. M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization Switching of a Vertical-Cavity Semiconductor Laser as a Kramers Hopping Problem,” Phys. Rev. Lett. 82, 4815–4818 (1999). [CrossRef]

10

10. B. Nagler, M. Peeters, J. Albert, G. Verschaffelt, K. Panajotov, H. Thienpont, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Polarization-mode hopping in single-mode vertical-cavity surface-emitting lasers: Theory and experiment,” Phys. Rev. A 68, 013813 (2003). [CrossRef]

] as well as for QW VCSELs subject to feedback [11

11. J. Houlihan, D. Goulding, Th. Busch, C. Masoller, and G. Huyet, “Experimental Investigation of a Bistable System in the Presence of Noise and Delay,” Phys. Rev. Lett. 22, 050601 (2004). [CrossRef]

13

13. K. Panajotov, M. Sciamanna, A. Tabaka, P. Megret, M. Blondel, G. Giacomelli, F. Marin, H. Thienpont, and I. Veretennicoff, “Residence time distribution and coherence resonance of optical-feedback-induced polarization mode hopping in vertical-cavity surface-emitting lasers,” Phys. Rev. A 69, 011801 (2004). [CrossRef]

] and optical injection [14

14. I. Gatare, M. Triginer, H. Thienpont, K. Panajotov, and M. Sciamanna, “Experimental study of polarization switching and polarization mode hopping induced by optical injection in VCSELs,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Ghent, 143–146 (2004).

]. The general conclusion is that the average dwell time between consecutive polarization hops depends on the potential barrier between the wells corresponding to distinct polarization states, and the strength of the spontaneous emission noise initiating the hopping. From an application point of view, polarization mode hopping is a source of polarization noise which introduces excess intensity noise and unwanted jitter thus degrades the system performance in terms of its bit-error-rate [15

15. U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission,” IEEE Photon. Technol. Lett. 8, 746–748 (1996). [CrossRef]

, 16

16. T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga, “Excess intensity noise originated from polarization fluctuation in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 7, 1113–1115 (1995). [CrossRef]

].

Polarization mode hopping in QW VCSELs, if present, is only observed when the laser is biased in the vicinity of the current of an abrupt polarization switching. Since the polarization switching current changes from device to device, the average dwell time can be of the order of nanoseconds in devices showing polarization switching close to the lasing threshold but can also reach few seconds far from threshold, where the emission is dominated by the stimulated recombination. Consequently, the polarization switching current and the average dwell time can be regarded as still another parameters characterizing a particular device.

Current dependence of the average dwell time has been validated experimentally by external manipulation of the linear anisotropy [6

6. M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization Switching of a Vertical-Cavity Semiconductor Laser as a Kramers Hopping Problem,” Phys. Rev. Lett. 82, 4815–4818 (1999). [CrossRef]

,10

10. B. Nagler, M. Peeters, J. Albert, G. Verschaffelt, K. Panajotov, H. Thienpont, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Polarization-mode hopping in single-mode vertical-cavity surface-emitting lasers: Theory and experiment,” Phys. Rev. A 68, 013813 (2003). [CrossRef]

] that determine the current at which the polarization switching between two orthogonal, linearly polarized states occurs. The results show that the average dwell time increases by 8 orders of magnitude when the polarization switching current is being shifted to larger values [6

6. M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization Switching of a Vertical-Cavity Semiconductor Laser as a Kramers Hopping Problem,” Phys. Rev. Lett. 82, 4815–4818 (1999). [CrossRef]

, 10

10. B. Nagler, M. Peeters, J. Albert, G. Verschaffelt, K. Panajotov, H. Thienpont, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Polarization-mode hopping in single-mode vertical-cavity surface-emitting lasers: Theory and experiment,” Phys. Rev. A 68, 013813 (2003). [CrossRef]

].

Much less is known for quantum dot (QD) VCSELs. In our last report [17

17. L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, and D. Bimberg, “Polarization Switching in Quantum-Dot Vertical-Cavity Surface-Emitting Lasers,” IEEE Photon. Technol. Lett. 211008–1010 (2009). [CrossRef]

] we have shown that these devices also exhibit polarization switching. Its characteristics, however, are in contrast to what is commonly observed in QW VCSELs. Here we show that the polarization mode hopping that accompanies the observed switching is also different: it takes place in an exceptionally wide range of currents and when the current is increased the average dwell time decreases by 8 orders of magnitude without any external manipulation of the inherent anisotropies. To our best knowledge, this is the first observation of such a diversified, in terms of dwell time scaling, dynamics of polarization mode hopping in a single VCSEL.

2. Results

The structure and composition of submonolayer (SML) QD VCSELs used in our experiment are described in detail in [18

18. F. Hopfer, A. Mutig, A., M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106–141106 (2006). [CrossRef]

]. The emitted light is first collimated by an antireflection-coated aspherical lens with a focal length of 3.1 mm and then it is reflected by a mirror and passes through a polarizer to analyze its polarization properties. Finally, the light is coupled into a multimode fiber. To avoid feedback from its facet we use an optical isolator. The temperature of the wafer is actively stabilized up to a few milli Kelvin. Thermal variation of the laser wavelength is of 0.07 nm/K while the variation of the threshold current is of 0.009 mA/K. Out of 26 single-transverse mode devices, 7 exhibit very stable and reproducible polarization switching, which essentials are reflected in the polarization resolved power versus current characteristics shown in Fig. 1. The total output power is represented by black squares. Close to the lasing threshold the laser emits linearly polarized light along the P0-direction (LP1-mode, open circles; polarization angle is denoted as a subscript, e.g. P0 means 0 deg with respect to the y axis. When the current is increased, at a point IA the power measured at the P90-direction (black triangles) starts growing. As shown later, point IA indicates the onset of stable, elliptically polarized emission (EP1). When the current is further increased the polarization ellipse of the EP1-mode rotates gradually, such that at point IS its major axis is aligned with P−20-direction. Likewise, its ellipticity, calculated as the ratio of the power corresponding to the minor and major axes of the polarization ellipse, increases gradually to 10%. At the point IS another elliptically polarized mode EP2 appears and region of PMH between these two EP modes starts. The major axis of EP2 is aligned with P20-direction, which shows that the modes EP1 and EP2 are non-orthogonal [17

17. L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, and D. Bimberg, “Polarization Switching in Quantum-Dot Vertical-Cavity Surface-Emitting Lasers,” IEEE Photon. Technol. Lett. 211008–1010 (2009). [CrossRef]

]. The amplitude of switching changes as a function of polarizer orientation and achieves maximum at P45- and P−45-directions. The power-current characteristics measured at these directions are represented in Fig. 1 by gray triangles and squares, respectively. The region of PMH extends to a point IR.

Fig. 1 Polarization resolved power-current characteristics of the investigated QD VCSEL. The inset shows schematically the orientation of elliptically polarized states after point IS.

Fig. 2 Polarization resolved optical spectra at I = 1.85 mA for different orientations of the polarizer (P). The inset in panel a) shows RF spectrum captured at P45. Polarization angle is denoted as a subscript, e.g. P20 means 20 deg with respect to the y axis.

As already mentioned, the main spectral component in Fig. 2 possesses low-amplitude, equidistant sidebands. They appear near the IS point, which is manifested by a strong peak at 8 GHz in the radio frequency spectrum (RF), see the inset in Fig. 2a. Note, that similar observations have been reported for polarization switching involving dynamical states in QW VCSELs [19

19. M. Sondermann, T. Ackemanna, S. Balleb, J. Muletb, and K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004). [CrossRef]

], i.e. the increase of the ellipticity angle close to the switching point has been accompanied by the appearance of sidebands in the optical spectrum. Their frequency has been attributed to an effective birefringence expressed as the sum of the linear birefringence observed at the lasing threshold and the non-linear contributions due to saturable dispersion and spin dynamics [19

19. M. Sondermann, T. Ackemanna, S. Balleb, J. Muletb, and K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004). [CrossRef]

]. In our SML QD VCSELs, however, the sidebands in the optical spectra in PMH regime have different origin as shown hereafter.

In Fig. 3 we show the relaxation oscillation frequency (fRO) as a function of the square root of the pump current above threshold. A linear interpolation of the experimental data with:
fRO=AIITH
(1)
gives a proportionality constant A of 5.71±0.03 GHz/mA0.5. We then use Eq. (1) to extrapolate the value of the relaxation oscillation frequency at the current of 1.85 mA. The value of 7.31 GHz is close to the frequency of 8 GHz of the RF peak in Fig. 2a and, therefore, we attribute the spectral sidebands to a low-amplitude time dependent modulation of the laser response at the frequency of the relaxation oscillations excited by polarization instabilities.

Fig. 3 Relaxation oscillation frequency (black squares) as a function of the square root of the pump current. The solid gray curve is a linear fitting and the gray circle is extrapolation giving fRO = 7.31 GHz at I=1.85 mA.

As already mentioned, the region of PMH starts at the point IS and extends over a wide range of currents up to IR. This is in sharp contrast to PMH in QW VCSELs, which occurs only when the laser is biased close to the abrupt polarization switching [10

10. B. Nagler, M. Peeters, J. Albert, G. Verschaffelt, K. Panajotov, H. Thienpont, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Polarization-mode hopping in single-mode vertical-cavity surface-emitting lasers: Theory and experiment,” Phys. Rev. A 68, 013813 (2003). [CrossRef]

]. Another distinctive feature is its dynamics. Examples of time traces captured at the polarizer orientation of P45 and different currents are shown in Fig. 4. Just after IS, at I = 1.81 mA, polarization mode hopping is asymmetric, i.e. the laser stays most of the time in one EP mode and exhibits rapid switches to the other mode every few seconds, see Fig. 4a. At around I = 2.0 mA PMH becomes symmetric, while the average dwell time decreases to microseconds, see Fig. 4b. At still larger currents the average dwell time decreases to nanoseconds (see Fig. 4c,d,e), although there is also a subtle increase at around I = 3.2 mA (see Fig. 4d).

Fig. 4 Time traces at the current of a) 1.81 mA, b) 2.0 mA, c) 2.6 mA, d) 3.2 mA, e) 3.6 mA at the polarizer direction corresponding to the maximum amplitude of switching, i.e. P45.

Current dependence of the dynamics of the observed PMH is summarized in Fig. 5. Contrary to the scaling of the dwell time in QW VCSELs, the average dwell time in QD VCSELs decreases with injection current. This decrease is by 8 orders of magnitude: from seconds to nanoseconds and is achieved without any modifications of the internal anisotropies. The observed scaling happens in polarization mode hopping range of currents as wide as 8 times the threshold current.

Fig. 5 Experimental data for the current dependence of the average dwell time for both EP modes calculated from the time traces captured at the polarizer orientation of P45.

After the point IR polarization mode hopping disappears, but, unlike in the polarization switching involving dynamical states in QW VCSEls, the laser does not switch to the LP2 mode, i.e. polarization mode that is suppressed close to threshold. Instead, it exhibits two-mode emission with dominant LP1, which also dominates before the onset of elliptically polarized emission, and weaker LP2, see Fig. 6. Moreover, each LP mode is accompanied by a single low-amplitude peak of the same polarization. The RF spectrum shown in the inset of Fig. 6 includes two strong beating signals. One of them, at 4.8 GHz, corresponds to the frequency splitting between the two dominating LP modes that in the FP spectrum are split by 5.58 GHz. The difference between the RF beat and the mode interval in FP spectra results from the limited resolution of the FP interferometer. The frequency of 4.8 GHz can be regarded as corresponding to the birefringence splitting between the two polarization modes. The remaining spectral component appears at 9.8 GHz and corresponds to the frequency splitting between LP mode and a small-amplitude peak of the same polarization, which again we interpret as slightly excited relaxation oscillations at this current (the relaxation oscillation frequency at 4.45 mA estimated from Eq. (1) amounts to 11.75 GHz).

Fig. 6 Polarization resolved optical spectra at I = 4.45 mA. The inset shows RF spectrum captured at P45.

3. Conclusion

In this paper we show experimental characterization of optical spectra and dynamics of polarization mode hopping in QD VCSELs. In contrast to what is observed in QW VCSEls, polarization mode hopping takes place between nonorthogonal elliptically polarized modes with frequency splitting smaller than 2 GHz and is observed in an exceptionally wide range of currents. Similarly to polarization switching involving dynamical states in QW VCSEL, the increase of the ellipticity of the lasing polarization component close to the point at which polarization switching starts is accompanied by the appearance of sidebands in the optical spectrum. We attribute these sidebands to a low-amplitude time dependent modulation of the laser response at the frequency of the relaxation oscillations excited by polarization instabilities.

Another striking difference between the observed scenario and polarization switching in QW VCSELs involving dynamical states is that instead of switching to the LP mode that is suppressed close to threshold, after the region of polarization mode hopping the laser exhibits two-mode emission with dominant LP mode that lases also before the onset of elliptically polarized emission, and a weaker orthogonal one. The frequency splitting between these two modes can be regarded as a measure of birefringence and is of 4.8 GHz. Each LP mode is accompanied by a single low-amplitude peak of the same polarization split in frequency by 9.8 GHz, which we again interpret as excitation of relaxation oscillations at this current.

Another distinctive feature of the observed polarization mode hopping is its dynamics. The average dwell time decreases when the current is increased. This decrease is by 8 orders of magnitude: from seconds to nanoseconds. Interestingly, such behavior is observed without any external manipulation of the VCSEL anisotropies. To our best knowledge, this is the first observation of such a diversified, in terms of time scaling, dynamics of polarization mode hopping in a single VCSEL.

We would like to stress that the reported polarization instabilities are important for applications of QD-VCSELs in optical telecom and datacom systems. Indeed, it has been shown that polarization mode hopping in QW VCSELs is a source of polarization noise which introduces excess intensity noise and unwanted jitters [15

15. U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission,” IEEE Photon. Technol. Lett. 8, 746–748 (1996). [CrossRef]

, 16

16. T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga, “Excess intensity noise originated from polarization fluctuation in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 7, 1113–1115 (1995). [CrossRef]

]. Ultimately, these effects will degrade the system performance in terms of its bit-error-rate [15

15. U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission,” IEEE Photon. Technol. Lett. 8, 746–748 (1996). [CrossRef]

].

Acknowledgments

We are grateful to A. R. Kovsh with Innolume GmbH for the wafer growth. The authors acknowledge the financial support of Conseil Regional de Lorraine, BELSPO IAP 6/10, FWO-Vlaanderen, OZR-VUB for the GOA and IOF Projects, COST MP0702.

The authors acknowledge the financial support of Conseil Regional de Lorraine, BELSPO IAP 6/10, FWOVlaanderen, OZR-VUB for the GOA and IOF Projects, COST MP0702, by the Deutsche Forschungsgemeinschaft (Sfb 787), by the State of Berlin (100 x 100 Optics) and BMBF via DLR.

References and links

1.

P. Hänggi, P. Talkner, and M. Borkovec, “Reaction-rate theory: fifty years after Kramers,” Rev. Mod. Phys. 62, 251–341 (1990). [CrossRef]

2.

H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7, 284–304 (1940). [CrossRef]

3.

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, and N. G. Stoffel, “Polarisation characteristics of quantum well vertical cavity surface emitting lasers,” Electron. Lett. 27, 163–165 (1991). [CrossRef]

4.

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995). [CrossRef]

5.

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization Behavior of Vertical-Cavity Surface-Emitting Lasers: Experiments, Models and Applications,” Proc. AIP 560, 403–417 (2001). [CrossRef]

6.

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization Switching of a Vertical-Cavity Semiconductor Laser as a Kramers Hopping Problem,” Phys. Rev. Lett. 82, 4815–4818 (1999). [CrossRef]

7.

G. Giacomelli and F. Marin, “Statistics of polarization competition in VCSELs,” Quantum Semiclass. Opt. 10, 469–476 (1998). [CrossRef]

8.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two frequency emission and polarization dynamics at lasing threshold in vertical- cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003). [CrossRef]

9.

J. Kaiser, C. Degen, and W. Elsasser, “Polarization-switching influence on the intensity noise of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 19, 672–677 (2002). [CrossRef]

10.

B. Nagler, M. Peeters, J. Albert, G. Verschaffelt, K. Panajotov, H. Thienpont, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Polarization-mode hopping in single-mode vertical-cavity surface-emitting lasers: Theory and experiment,” Phys. Rev. A 68, 013813 (2003). [CrossRef]

11.

J. Houlihan, D. Goulding, Th. Busch, C. Masoller, and G. Huyet, “Experimental Investigation of a Bistable System in the Presence of Noise and Delay,” Phys. Rev. Lett. 22, 050601 (2004). [CrossRef]

12.

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543–1545 (2003). [CrossRef] [PubMed]

13.

K. Panajotov, M. Sciamanna, A. Tabaka, P. Megret, M. Blondel, G. Giacomelli, F. Marin, H. Thienpont, and I. Veretennicoff, “Residence time distribution and coherence resonance of optical-feedback-induced polarization mode hopping in vertical-cavity surface-emitting lasers,” Phys. Rev. A 69, 011801 (2004). [CrossRef]

14.

I. Gatare, M. Triginer, H. Thienpont, K. Panajotov, and M. Sciamanna, “Experimental study of polarization switching and polarization mode hopping induced by optical injection in VCSELs,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Ghent, 143–146 (2004).

15.

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission,” IEEE Photon. Technol. Lett. 8, 746–748 (1996). [CrossRef]

16.

T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga, “Excess intensity noise originated from polarization fluctuation in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 7, 1113–1115 (1995). [CrossRef]

17.

L. Olejniczak, M. Sciamanna, H. Thienpont, K. Panajotov, A. Mutig, F. Hopfer, and D. Bimberg, “Polarization Switching in Quantum-Dot Vertical-Cavity Surface-Emitting Lasers,” IEEE Photon. Technol. Lett. 211008–1010 (2009). [CrossRef]

18.

F. Hopfer, A. Mutig, A., M. Kuntz, G. Fiol, D. Bimberg, N. N. Ledentsov, V. A. Shchukin, S. S. Mikhrin, D. L. Livshits, I. L. Krestnikov, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Single-mode submonolayer quantum-dot vertical-cavity surface-emitting lasers with high modulation bandwidth,” Appl. Phys. Lett. 89, 141106–141106 (2006). [CrossRef]

19.

M. Sondermann, T. Ackemanna, S. Balleb, J. Muletb, and K. Panajotov, “Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers,” Opt. Commun. 235, 421–434 (2004). [CrossRef]

OCIS Codes
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Optoelectronics

History
Original Manuscript: November 4, 2010
Revised Manuscript: December 16, 2010
Manuscript Accepted: December 19, 2010
Published: January 25, 2011

Citation
Lukasz Olejniczak, Krassimir Panajotov, Hugo Thienpont, Marc Sciamanna, Alex Mutig, Friedhelm Hopfer, and Dieter Bimberg, "Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers," Opt. Express 19, 2476-2484 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2476


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References

  1. P. Hänggi, P. Talkner, and M. Borkovec, "Reaction-rate theory: fifty years after Kramers," Rev. Mod. Phys. 62, 251-341 (1990). [CrossRef]
  2. H. A. Kramers, "Brownian motion in a field of force and the diffusion model of chemical reactions," Physica 7, 284-304 (1940). [CrossRef]
  3. C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, and N. G. Stoffel, "Polarisation characteristics of quantum well vertical cavity surface emitting lasers," Electron. Lett. 27, 163-165 (1991). [CrossRef]
  4. K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers," IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995). [CrossRef]
  5. K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, "Polarization Behavior of Vertical-Cavity Surface-Emitting Lasers: Experiments, Models and Applications," Proc. AIP 560, 403-417 (2001). [CrossRef]
  6. M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, "Polarization Switching of a Vertical-Cavity Semiconductor Laser as a Kramers Hopping Problem," Phys. Rev. Lett. 82, 4815-4818 (1999). [CrossRef]
  7. G. Giacomelli and F. Marin, "Statistics of polarization competition in VCSELs," Quantum Semiclass. Opt. 10, 469-476 (1998). [CrossRef]
  8. M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, "Two frequency emission and polarization dynamics at lasing threshold in vertical- cavity surface-emitting lasers," Phys. Rev. A 68, 033822 (2003). [CrossRef]
  9. J. Kaiser, C. Degen, and W. Elsasser, "Polarization-switching influence on the intensity noise of vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 19, 672-677 (2002). [CrossRef]
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  11. J. Houlihan, D. Goulding, Th. Busch, C. Masoller, and G. Huyet, "Experimental Investigation of a Bistable System in the Presence of Noise and Delay," Phys. Rev. Lett. 22, 050601 (2004). [CrossRef]
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