Abstract

Similar to edge-emitting lasers, vertical cavity surface emitting lasers (VCSELs) subjected to optical feedback are known for exhibiting erratic fluctuations of their optical power at slow and fast time scales; these are called low-frequency fluctuations (LFF). Here, we demonstrate both experimentally and numerically that the chaotic itinerancy in phase space associated with LFF has a deep connection with the creation of non-local correlations at multiple time scales between the two linear polarization modes. Our result provides a novel framework to interpret the unknown origin of spectral signatures in the optical power of chaotic lasers with optical feedback, which were observed in the past two decades.

© 2017 Optical Society of America

1. Introduction

Thanks to their numerous advantages, vertical cavity surface emitting lasers (VCSELs) overcome edge-emitting lasers (EEL) in several applications such as optical communications and sensing [1]. In addition, VCSELs are known to exhibit interesting properties related to polarization competition: although the light emitted at threshold is linearly polarized (LP), increasing the current may lead to polarization switching [2–4] and instabilities including deterministic polarization chaos [5].

When VCSELs are subjected to optical feedback, they undergo similar regimes of instabilities to those encountered in EELs [6], however with an additional interplay between the two competing linearized polarization modes (X- and Y-LP) and the optical feedback. This can unlock new dynamical behaviors that cannot be observed in conventional EELs, such as bistable polarization mode hopping [7], polarization coherence resonance induced by time-delay [8], polarization self-modulation leading to square waveforms [9,10], and vectorial dissipative solitons [11].

A chaotic dynamical regime of interest is the so-called low-frequency fluctuations (LFF). This consists of irregular power dropouts at a slow time scale [12]. The peculiarity of LFF in VCSELs is that two types of LFFs (Type I and II) can be observed depending on the competition between the X and Y-LP modes [13, 14]. In Type-I LFF, both modes shares approximately the same mean power and are correlated at the average LFF modulation time scale [14, 15]. In the case of Type-II LFF, however, the two modes are anti-correlated at that time scale, implying that one mode is dominant and shows sudden drops, while the other one is depressed and bursts from its quiescent state [13,16].

These correlation properties occurring on a slow time scale manifest themselves by a strong peak in the cross-spectral density (CSD) between the two LP modes. In addition, a double-peak structure appears in the vicinity of the external cavity frequency and seems to be also a generic feature of LFF regimes [17, 18], since it has been also documented in the RF spectrum of EEL with optical feedback [19–22, 27]. These time (resp. spectral) correlations are referred to as non-local in time as they results from the nonlinear interaction of optical fields and their delayed versions [23]. Multiple assumptions have been made as for the origin of the double-peak non-local correlation [18, 19, 27]. In Ref. [19], the double-peak power spectrum is explained by the influence of multiple round-trips in a slightly misaligned external cavity. In Ref [27], the same feature is explained by a competition between longitudinal modes. However, to the best of our knowledge, a detailed physical explanation of this deterministic phenomenon has remained elusive for more than a decade, thus motivating further theoretical and experimental exploration. In particular, the link between the double peak power spectrum and the properties of the deterministic chaotic dynamic remains to be elucidated.

We demonstrate here that the origin of the double-peak non-local correlation between the two LP modes in the LFF regimes results from chaotic itinerancy in phase space and depends on the type of LFF and hence the type of competition between the two LP modes. Finally, we provide a physical interpretation of these particular features and connect them with the trajectory of the system in the vicinity of ruins of stable and unstable external cavity modes. We perform a detailed study of the parametric influence (pumping current and time delay) and show that our interpretation for the double-peak holds also for EELs.

2. Experimental results

We design an experiment to measure the polarization dynamics within a large frequency range that encompasses the bandwidths of the chaotic dynamics and the relaxation oscillation frequency. The experimental setup, shown in Fig. 1(a), comprises an AlGaAs/GaAs VCSEL emitting at 850 nm with a solitary threshold current of Jths=0.45mA at 15°C, which was measured under controlled thermal fluctuations within ±0.01°C. The output beam shows a single transverse mode with Gaussian profile in the range of currents where we operate the VCSEL i.e. up to 0.9 mA. The laser beam is collimated by a microscope objective before reaching a first 50/50 beam splitter. The first arm corresponds to the external cavity and uses a 99.9% reflectivity mirror and a variable attenuator to control the feedback strength. The measurement arm comprises a 50/50 beam-splitter, two polarizers and optical isolators to separate the two LP modes before coupling into two single-mode optical fibers. The measurement arm is designed so that we can guarantee a balanced coupling efficiency and identical traveling distances from the laser source. Finally, the two LP modes are measured by two identical photodiodes LeCroy OE425 with 4.5 GHz bandwidth and two Newport 1554-B with 12 GHz bandwidth which are connected to either a 4 GHz Lecroy Waverunner 640Zi oscilloscope with 40 GSamples/s or a 26.5 GHz Rohde & Schwarz FSW26 spectrum analyzer. The VCSEL emits in its Y-LP mode at threshold and switches to X-LP at pumping current 0.75 mA. X-(Y-) LP mode is the low (high) frequency mode hence the switching is of type I [2]. In the following, we shall operate in the range 0.48–0.56 mA, well below the switching point.

 figure: Fig. 1

Fig. 1 (a) Experimental setup. C: collimating microscope objective, BS: beam-splitter, P: polarizer, ISO: isolator, SMF: single mode fiber, M: mirror, PD: photodiode. (b) Intensity time series of the Y-LP mode and (c) X-LP mode of VCSEL LFF Type-II regime at pumping current 1.2Jths=0.54mA, time delay τ≈5 ns, temperature 15°C, and 14% threshold reduction.

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We select an external cavity length of Lext≈75 cm corresponding to a time-delay of τ = 2Lext/c ≈ 5 ns. This ensures the so-called long cavity regime, where the external cavity frequency fEC = 1/τ is much smaller than the relaxation oscillation fRO of the free-running VCSEL, which has been estimated to be about 1.37 GHz at 0.48 mA by relative intensity noise (RIN) measurements. In these experimental conditions with a pumping current range [0.43 mA, 0.6 mA], the VCSEL exhibits LFF dynamics, as shown in Fig. 1(b) and 1(c). We observe a typical instance of Type-II LFF which we can most likely attribute to the large dichroism of our device [13]. Anti-correlation between the LP mode dynamics manifests itself on a slow time scale as confirmed by CSD calculation in Fig. 2(d) at ∼20 MHz, which is mathematically defined by

CSD(f)=I˜x(f)I˜y*(f)+I˜y(f)I˜x*(f),
with Ĩx(f) (resp. Ĩy(f)) the Fourier Transform of the X-LP (resp. Y-LP) intensity and * denotes the complex conjugate. At a frequency ffEC, the CSD also shows an anti-correlated behavior. Most importantly, the CSD shows a double-peak structure with two peaks labeled f and f+ in the spectral vicinity of fEC. The frequency separation of Δf = f+f is about 20 MHz. The CSD confirms that the dynamics at these two frequencies are anti-correlated between the two LP modes.

 figure: Fig. 2

Fig. 2 Spectrogram of the Y-LP mode in the frequency range (a) f ∈ [200 MHz, 400 MHz] as function of the external cavity delay (b) f ∈ [0 MHz, 70 MHz] and (c) f ∈ [170 MHz, 240 MHz] as function of the pumping current. (d) CSD between X-LP and Y-LP modes. f and f+ are the two main components of the discussed double-peak structure. The fixed parameters are identical to those used in Fig. 1.

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This result differs from previous studies [18] on Type-I LFF, where it was found that the X-LP and Y-LP modes are correlated at the second frequency f+. This positive correlation was interpreted as the result of an unspecified mixing between fEC and fRO for VCSEL [18].

The double peak structure observed in the CSD can also be retrieved from the respective RF spectra of each LP mode. In Fig. 2(a–c), we analyze the dependence of the structure at (f, f+) by measuring the experimental power spectrum of the Y-LP mode (dominant LP mode) as a function of the external cavity delay [Fig. 2(a)] and the pumping current [Fig. 2(b) and 2(c)]. The spectrogram in Fig. 2(b) and 2(c) shows that the lowest frequency peak f is not affected by an increase of pumping current, while the highest one at f+ shifts towards higher frequencies when increasing the current. Interestingly, the frequency deviation of f+ evolves similarly to that of the average modulation LFF frequency (close to ∼20 MHz) with varying pumping current. The two f± evolve similarly when varying the time-delay [Fig. 2(a)].

3. Numerical results

To gain additional insight, we have first verified that our experimental findings are reproducible by numerical simulations. Our model is based on the spin-flip model (SFM) [24], which is modified to account for optical feedback:

E˙x,y=κ(1+iα)[(N1)Ex,y+inEy,x](γa+iγp)Ex,y+Fx,y+ηEx,y(tτ)exp(iϕ0),
N˙=γn[Nμ+N(|Ex|2+|Ey|2)+in(EyEx*ExEy*)],
n˙=γsnγn[n(|Ex|2+|Ey|2)+iN(EyEx*ExEy*)],
where Ex,y are the complex slow-varying amplitudes of the (X,Y)-LP modes, N is the carrier difference between the conduction and valence bands, and n is the difference between the population inversions of the spin up and down radiation channels. κ is the field decay rate, γn is the decay rate of N, γs is the spin-flip relaxation rate, α is the linewidth enhancement factor, μ is the normalized injection current, γa is the linear dichroism and γp is the linear birefringence. τ is the external cavity delay, η is the feedback rate, and ϕ0 = ω0τ is the feedback phase, where ω0 is the optical frequency of the polarization mode in the absence of birefringence and feedback. Spontaneous emission noise is taken into account through the terms Fx = [βsp(N + n)/2]1/2ξ1 + [βsp(Nn)/2]1/2ξ2 and Fy = iFx. βsp is the spontaneous emission rate and ξ1,2 are two complex uncorrelated white Gaussian noises with zero mean and unitary variance.

It is known that the VCSEL dynamics and its the polarization properties with optical feedback depend both on the laser and feedback parameters. Here, we choose τ = 5 ns to match the experimental condition. γp = 5 rad.ns−1 corresponds to the experimentally measured frequency splitting between the X- and Y-LP modes, i.e. 2γp/2π = 1.59 GHz. We consider γa = 0.5 rad.ns−1 and γs = 5 ns−1 so that the model reproduces LFF Type-II which is the dynamic observed experimentally. Finally, η and μ are our bifurcation parameters. The other parameters have numerical values that can be found in the literature [13–15,28] : γn = 1 ns−1, βsp = 10−4 ns−1, α = 3. LFF Type-II polarization dynamics is shown in Fig. 3(a)and 3(b). The corresponding power spectra are plotted in Fig. 3(c) and 3(d). The power spectra of the X- and Y-LP modes show also a double peak signature close to fEC = 200 MHz. In Fig. 3(e), our model predicts that both peaks of the double peak structure leads to an anti-correlated polarization mode dynamics. Qualitatively similar observations can be made by adjusting the γa (resp. γs) value between 0.01 rad.ns−1 and 0.7 rad.ns−1 (resp. 2 ns−1 and 11 ns−1). For larger values of γa and γs, the system still operates in LFF Type-II regime as defined in [13]. However, is that case, the X-LP mode is too depressed and therefore the computed CSD doesn’t show a discernible double-peak. We are also able to induce LFF Type-I (not shown here) by adjusting the VCSEL parameters (for example with γa = 0.001 rad.ns−1 and γp = 0.01 rad.ns−1 and the other parameters identical to those of Fig. 3). In LFF Type-I, we find a strong correlation at low frequency and also at f+, in agreement with Ref. [18].

 figure: Fig. 3

Fig. 3 Numerical LFF Type-II time traces of (a) the X-LP mode, (b) the Y-LP mode, the corresponding RF spectrum for (c) X- and (d) Y-LP mode and the resulting cross-spectral density μ = 1.02, η = 9 GHz, τ = 5 ns, κ = 300 GHz, α = 3, ϕ0 = 6 rad, γn = 1 ns−1, γs = 5 ns−1, βsp = 10−4 ns−1, γa = 0.5 rad.ns−1, γp = 5 rad.ns−1.

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Additional insight into the physical origin of the double peak can be provided by analyzing the VCSEL dynamics in the projection of the infinite dimension phase space. Figure 4(b) shows the projection of the trajectory in the plane (|Ey(t)|, ϕy(t) − ϕy(tτ) + ϕ0) where ϕy(t) is the phase of the dominent Y-LP mode and ϕy(t) − ϕy(tτ) + ϕ0 is the phase difference between the Y-LP mode and its time-delayed version. As demonstrated theoretically for EELs [12,25,26], the LFF trajectory in phase space corresponds to a chaotic itinerancy among destabilized external-cavity modes (ECMs). Numerically, the clearest insight is obtained when the system shows a limited set of ECMs and when the trajectory stays long enough around each ECM. These conditions can be achieved for a value of η (γs) slightly smaller (larger) than the one used in Fig. 3. As mentioned in the previous paragraph, for the value of γs = 50 ns−1, the dynamic is still an LFF Type-II but the X-LP mode is highly depressed. Therefore, we focus the following study on the dominant mode only, i.e. the Y-LP mode. Its power spectrum associated with this complex trajectory in phase space shows clearly a double-peak structure at frequency close to fEC [Fig. 4(a)]. We observe that the chaotic trajectory is attracted towards the ECM with maximum gain corresponding to the largest phase difference but visits a set of other ECMs. While pulsating around the position of the maximum gain mode (represented by a diamond in Fig. 4(c)), the trajectory is repelled by the close proximity of a saddle-type ECM called anti-mode [represented by a square in Fig. 4(c)].

 figure: Fig. 4

Fig. 4 (a) Numerical RF spectrum of the intensity of the Y-LP mode in external cavity frequency window, (b) trajectory in the phase space and (c) a zoom into the attractor of highest phase shift, (d) the histogram showing the number of points as function of the phase shift and (e) its corresponding zoom into the attractor of highest phase shift region. The parameters are identical to those used in Fig. 3 except for η = 3 GHz and γs = 50 ns−1.

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To give a dynamical interpretation to the observed double-peak structure, we analyze the frequency content of phase space trajectories that remain in the vicinity of either the maximum gain mode or the antimode. Figure 5(a) shows a typical drop-out event of LFF dynamics associated with the trajectory in the projected phase space of Fig. 4(b). Similar time-traces can be found at different time-locations in the numerical simulation as the system encounters many times similar trajectories in phase space after a drop-out. All of these typical time traces have two distinct dynamical behaviors marked by the orange and green time-windows : the orange window displays a dynamics corresponding to the trajectory around the maximum gain mode [orange trajectories in 4(c)] whereas the green window shows the typical time evolution around the corresponding antimode. In Fig. 5(b), we show the RF spectrum obtained by computing the concatenation of a large number of such orange time-windows. We notice the complete suppression of the peak at f in the double peak structure. In contrast by considering the additional green time-windows, the f component of the double-peak structure arises in Fig. 5(c). In Fig. 5(d) and 5(e), we further increase the window size in the phase-space and, thus, consider more points in the time-domain. Doing so, we recover the original double-peak structure shown in Fig. 4(a).

 figure: Fig. 5

Fig. 5 (a) Typical time trace of a LFF drop-out event of the Y-LP mode. RF spectra computed by considering different window sizes in the phase space in Fig. 4(b). For ϕY(t)−ϕY(tτ)+ϕ0 range : (b) from −35 to −31 rad, (c) from −35 to −27 rad, (d) from −35 to −16 rad, (e) from −35 to −0 rad.

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Finally, we show in Fig. 6 that the double-peak structure studied numerically behaves similarly as in the experiment when varying the parameters τ and μ. Indeed, in Fig. 6(a), the double peak structure follows the external cavity frequency when varying the delay. Furthermore, Fig. 6(b) show that when increasing the pumping current, the first frequency component f of the double peak structure remains unchanged while the second frequency component f+ shifts to higher values. This is also the case for the low frequency modulation. For higher values of current μ > 1.025, the dynamic of the system moves from LFF regime towards the so called coherence-collapse regime with no clear low frequency signature which is translated in the spectrogram by a slow fading of the low frequency component. Numerical simulations and experiments confirm that there is a strong link between the low frequency component corresponding to power dropouts and the the highest frequency f+ of the double peak structure. Indeed, (anti-)correlation at the low frequency leads to (anti-)correlation at f+ and when the low frequency shifts with varying the parameters, f+ also shifts in frequency.

 figure: Fig. 6

Fig. 6 Spectrograms of Y-LP mode as a function of (a) the delay τ and (b) the current μ. Other parameters are the same as in Fig. 4.

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4. Discussion

In this work, we have analyzed in detail how polarization mode competition in VCSEL interplays with optical feedback induced instabilities. The polarization mode competition manifests itself as a correlation or anticorrelation at the low frequency of LFF dynamics, as already evidenced in separated experiments [16, 18], but we unveil a new feature, which is the dependence of the correlation (or anticorrelation) between the slow-time scale of the LFF and a faster time scale close to the external cavity frequency. This complex interplay at multiple time scales yields a double-peak structure in both the CSD and the power spectrum with correlation properties depending on the type of polarization competition.

Appart from the correlation analysis, similar double-peak spectral signatures have been reported in previous studies on external-cavity laser diode in different dynamical regimes. This naturally raises the question of the generality of such spectral properties and their physical interpretation. For example, in Ref. [19], the explanation of the double-peak signature relied on multiple round-trips in the external cavity of a chaotic VCSEL. In Ref. [27], the authors based their explanation on the competition between longitudinal modes of an EEL subjected to a weak feedback. Finally, in Ref. [18], it was proposed that a still unexplained nonlinear mixing between the external-cavity frequency and the relaxation-oscillation frequency of a VCSEL was responsible for the appearance of the double-peak structure.

Here, we provide an alternative explanation relying on the chaotic itinerancy in the phase space due to the interplay between stable and unstable ECMs in LFF regime. Interestingly, and by contrast to these earlier explanations, this explanation does not require the inclusion of longitudinal mode competition or multiple round trips in cavity. This is evidenced in Fig. 7(b) where we simulate the single-mode LK equations with a single round-trip feedback [28,29] :

E˙(t)=1/2(1+iα)(GN,|E|21/τp)E(t)+γeiω0τE(tτ),
N˙(t)=pJthN/τsGN,|E|2|E(t)|2,
GN,|E|2=GN(NN0)/(1+|E|2),
where E(t) =|E(t)|e(t) is the slowly varying envelop of the complex electric field, N is the carrier density in the active region, GN,|E|2 is the optical gain, α is the linewidth-enhancement factor, is the saturation coefficient, N0 is the carrier density at transparency, GN is the differential gain, ω0 is the angular frequency of the solitary laser, γ is the feedback rate, τp is the photon lifetime, τs is the carrier lifetime, Jth is the threshold current, p is the pumping factor and τ the external cavity delay. Used parameters are listed in the caption of Fig. 7 and lead to a chaotic LFF dynamics. Except for the specific correlation properties driven by the VCSEL polarization competition in Fig. 3, the double peak structure is well reproduced numerically.

 figure: Fig. 7

Fig. 7 Numerical (a) time trace of the output intensity and (b) power spectrum for τp = 1.66 ps, τs = 1 ns, α = 3, = 5 × 10−7 m3, GN = 1.5 × 104 m3 · s−1, N0 = 1.5 × 108 m−3, Jth = 1.9 × 1017 m−3 · s−1, p = 1, γ = 3 GHz, τ = 5 ns, ω0τ = 0 rad.

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Our work therefore confirms that the dynamical scenario leading to the double-peak structure in both the CSD and power spectrum is the manifestation of the combined attraction and repelling motions of ruins of modes and antimodes, respectively. In VCSELs the polarization competition however leads to an interesting unique feature: the correlation (anticorrelation) at the low-modulation frequency yields the correlation property at the shifted frequency f+.

5. Conclusion

In summary, we have analyzed both numerically and experimentally the spectral properties of the linearly polarized modes of a chaotic VCSEL with optical feedback. The polarization mode competition, which interplays with the feedback instability, is known to impact the intermodal correlation properties at a slow time scale in the LFF regimes: (i) correlation with Type-I LFF or (ii) anti-correlation with type-II LFF. However, what we discover is that these correlation properties at the slow time-scale are transported to a faster time-scale located close to the vicinity of the external cavity frequency. This multiple time scales transport yields a so-called double-peak correlation signature in both the cross-spectral density (intermodal spectral information) and the individual power spectrum of each polarization modes. Furthermore, we show that the origin of this double peak could be explained by the chaotic itinerancy in LFF regimes occurring in the vicinity of the ruins of modes and anti-modes. Our study also shows that a simple model of an EEL with optical feedback is sufficient to observe the appearance of the double peak structure.

Acknowledgments

C.H.U., D.R., S.B. and M.S. acknowledge the support of the Conseil Regional de Lorraine, the Préfecture de Lorraine, the Fondation Supelec, the Fond Europeen pour le Developpement Regional (FEDER) through the projects PHOTON (FEDER, 2014–2015) and APOLLO (FEDER and FNADT, 2015–2016), the Inter-University Attraction Pole (IAP) program of BEL-SPO through the project Photonics@be grant number IAP P7/35, and the Agence Nationale de la Recherche (ANR) through project TINO (ANR-12-JS03-005).

References and links

1. R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).

2. K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998). [CrossRef]  

3. K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995). [CrossRef]  

4. M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000). [CrossRef]   [PubMed]  

5. M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013). [CrossRef]  

6. J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997). [CrossRef]  

7. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003). [CrossRef]   [PubMed]  

8. M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

9. S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993). [CrossRef]  

10. H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998). [CrossRef]  

11. M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015). [CrossRef]  

12. T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994). [CrossRef]   [PubMed]  

13. M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003). [CrossRef]  

14. M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003). [CrossRef]  

15. A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003). [CrossRef]  

16. M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999). [CrossRef]  

17. A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006). [CrossRef]  

18. M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005). [CrossRef]   [PubMed]  

19. P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994). [CrossRef]  

20. M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997). [CrossRef]  

21. L. Langley, J. Mørk, and K. Shore, “Dynamical and noise properties of laser diodes subject to strong optical feedback,” Opt. Lett. 19(24), 2137–2139 (1994). [CrossRef]   [PubMed]  

22. J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989). [CrossRef]   [PubMed]  

23. B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001). [CrossRef]  

24. M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995). [CrossRef]   [PubMed]  

25. C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994). [CrossRef]   [PubMed]  

26. C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998). [CrossRef]  

27. M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994). [CrossRef]  

28. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980). [CrossRef]  

29. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009). [CrossRef]  

References

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  1. R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).
  2. K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
    [Crossref]
  3. K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
    [Crossref]
  4. M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
    [Crossref] [PubMed]
  5. M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
    [Crossref]
  6. J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
    [Crossref]
  7. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
    [Crossref] [PubMed]
  8. M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).
  9. S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
    [Crossref]
  10. H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
    [Crossref]
  11. M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
    [Crossref]
  12. T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
    [Crossref] [PubMed]
  13. M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
    [Crossref]
  14. M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
    [Crossref]
  15. A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
    [Crossref]
  16. M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
    [Crossref]
  17. A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
    [Crossref]
  18. M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005).
    [Crossref] [PubMed]
  19. P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
    [Crossref]
  20. M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
    [Crossref]
  21. L. Langley, J. Mørk, and K. Shore, “Dynamical and noise properties of laser diodes subject to strong optical feedback,” Opt. Lett. 19(24), 2137–2139 (1994).
    [Crossref] [PubMed]
  22. J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
    [Crossref] [PubMed]
  23. B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
    [Crossref]
  24. M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
    [Crossref] [PubMed]
  25. C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
    [Crossref] [PubMed]
  26. C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
    [Crossref]
  27. M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
    [Crossref]
  28. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
    [Crossref]
  29. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
    [Crossref]

2015 (1)

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

2013 (1)

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

2009 (1)

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

2007 (1)

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

2006 (1)

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

2005 (1)

2003 (4)

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
[Crossref]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

2001 (1)

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

2000 (1)

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (3)

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

1997 (2)

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

1995 (2)

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

1994 (5)

C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
[Crossref] [PubMed]

L. Langley, J. Mørk, and K. Shore, “Dynamical and noise properties of laser diodes subject to strong optical feedback,” Opt. Lett. 19(24), 2137–2139 (1994).
[Crossref] [PubMed]

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

1993 (1)

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

1989 (1)

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

Abraham, N.

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

Abraham, N. B.

Ackemann, T.

M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005).
[Crossref] [PubMed]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

Agrawal, G. P.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

Ait-Ameur, K.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Arteaga, M. A.

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Balle, S.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

Barland, S.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

Besnard, P.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Bezruchko, B. P.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Blondel, M.

Bohnet, H.

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

Choquette, K. D.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Citrin, D. S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Dagenais, M.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Danckaert, J.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Elsäßer, W.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Elsässer, W.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

Feng, Q.

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

Fischer, I.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Gavrielides, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Giacomelli, G.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Giudici, M.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Göbel, E. O.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

Green, C.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Hendriks, R.

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Hohl, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Hou, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Javaloyes, J.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

Jiang, S.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Karavaev, A. S.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

Kojima, K.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

Langley, L.

Law, J. Y.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

Lear, K. L.

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Leibenguth, R. E.

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Li, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Locquet, A.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Loiko, N.

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

López-Amo, M.

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Marconi, M.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

Masoller, C.

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
[Crossref]

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
[Crossref] [PubMed]

Mégret, P.

Meziane, B.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Michalzik, R.

R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).

Moloney, J.

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

Morgan, R.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Mørk, J.

Naumenko, A.

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

Nespolo, U.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Pan, Z.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Panajotov, K.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Peeters, M.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Peil, M.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Ponomarenko, V. I.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Prokhorov, M. D.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Rogister, F.

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Ryvkin, B.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Sacher, J.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

San Miguel, M.

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

Sano, T.

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

Schneider, R.

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Sciamanna, M.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

Shore, K.

Sondermann, M.

M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005).
[Crossref] [PubMed]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

Stephan, G.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Tabaka, A.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Thienpont, H.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Tredicce, J.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Tredicce, J. R.

Valencia, M.

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Van der Poel, C.

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Van Exter, M.

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Veretennicoff, I.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Virte, M.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

Willemsen, M.

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

Woerdman, J.

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Appl. Phys. Lett. (2)

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

IEEE J. Quantum Elect. (2)

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

IEEE J. Sel. Top. Quant. (2)

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

IEEE Journal of Quantum Electronics (1)

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

IEEE Photonic. Tech. Lett. (1)

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Photonics (2)

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Optics communications (1)

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Phys. Rev. A (7)

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
[Crossref] [PubMed]

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

Phys. Rev. E (2)

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Phys. Rev. Lett. (3)

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Other (1)

R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).

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Figures (7)

Fig. 1
Fig. 1 (a) Experimental setup. C: collimating microscope objective, BS: beam-splitter, P: polarizer, ISO: isolator, SMF: single mode fiber, M: mirror, PD: photodiode. (b) Intensity time series of the Y-LP mode and (c) X-LP mode of VCSEL LFF Type-II regime at pumping current 1.2 J th s = 0.54 mA , time delay τ≈5 ns, temperature 15°C, and 14% threshold reduction.
Fig. 2
Fig. 2 Spectrogram of the Y-LP mode in the frequency range (a) f ∈ [200 MHz, 400 MHz] as function of the external cavity delay (b) f ∈ [0 MHz, 70 MHz] and (c) f ∈ [170 MHz, 240 MHz] as function of the pumping current. (d) CSD between X-LP and Y-LP modes. f and f+ are the two main components of the discussed double-peak structure. The fixed parameters are identical to those used in Fig. 1.
Fig. 3
Fig. 3 Numerical LFF Type-II time traces of (a) the X-LP mode, (b) the Y-LP mode, the corresponding RF spectrum for (c) X- and (d) Y-LP mode and the resulting cross-spectral density μ = 1.02, η = 9 GHz, τ = 5 ns, κ = 300 GHz, α = 3, ϕ0 = 6 rad, γn = 1 ns−1, γs = 5 ns−1, βsp = 10−4 ns−1, γa = 0.5 rad.ns−1, γp = 5 rad.ns−1.
Fig. 4
Fig. 4 (a) Numerical RF spectrum of the intensity of the Y-LP mode in external cavity frequency window, (b) trajectory in the phase space and (c) a zoom into the attractor of highest phase shift, (d) the histogram showing the number of points as function of the phase shift and (e) its corresponding zoom into the attractor of highest phase shift region. The parameters are identical to those used in Fig. 3 except for η = 3 GHz and γs = 50 ns−1.
Fig. 5
Fig. 5 (a) Typical time trace of a LFF drop-out event of the Y-LP mode. RF spectra computed by considering different window sizes in the phase space in Fig. 4(b). For ϕY(t)−ϕY(tτ)+ϕ0 range : (b) from −35 to −31 rad, (c) from −35 to −27 rad, (d) from −35 to −16 rad, (e) from −35 to −0 rad.
Fig. 6
Fig. 6 Spectrograms of Y-LP mode as a function of (a) the delay τ and (b) the current μ. Other parameters are the same as in Fig. 4.
Fig. 7
Fig. 7 Numerical (a) time trace of the output intensity and (b) power spectrum for τp = 1.66 ps, τs = 1 ns, α = 3, = 5 × 10−7 m3, GN = 1.5 × 104 m3 · s−1, N0 = 1.5 × 108 m−3, Jth = 1.9 × 1017 m−3 · s−1, p = 1, γ = 3 GHz, τ = 5 ns, ω0τ = 0 rad.

Equations (7)

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CSD ( f ) = I ˜ x ( f ) I ˜ y * ( f ) + I ˜ y ( f ) I ˜ x * ( f ) ,
E ˙ x , y = κ ( 1 + i α ) [ ( N 1 ) E x , y + i n E y , x ] ( γ a + i γ p ) E x , y + F x , y + η E x , y ( t τ ) exp ( i ϕ 0 ) ,
N ˙ = γ n [ N μ + N ( | E x | 2 + | E y | 2 ) + i n ( E y E x * E x E y * ) ] ,
n ˙ = γ s n γ n [ n ( | E x | 2 + | E y | 2 ) + i N ( E y E x * E x E y * ) ] ,
E ˙ ( t ) = 1 / 2 ( 1 + i α ) ( G N , | E | 2 1 / τ p ) E ( t ) + γ e i ω 0 τ E ( t τ ) ,
N ˙ ( t ) = p J t h N / τ s G N , | E | 2 | E ( t ) | 2 ,
G N , | E | 2 = G N ( N N 0 ) / ( 1 + | E | 2 ) ,

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