Arbeitsgruppe Lange und Ackemann
Nichtlineare Optik und Quantenoptik
Institut für Angewandte Physik
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Publications of the VCSEL group


Articles on polarization properties of small-area VCSELs

  • M. Giudici, S. Balle, T. Ackemann, S. Barland, J. R. Tredicce.

  • Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback: experiment and model.
    J. Opt. Soc. Am. B, 16, 2114-2113, 1999.
  • T. Ackemann, M. Sondermann.

  • cw and transient characteristics of polarization switching in vertical-cavity surface-emitting lasers.
    cw and transient features of polarization switching in VCSELs are investigated experimentally close to the threshold minimum in dependence of temperature and current in order to clarify the interplay of linear anisotropies and nonlinear dispersion.
    International Quantum Electronics Conference - IQEC 2000, Nice, France, September 10 - 15, 2000. IEEE Conference Digest, p.41, paper QTuD8
    (download pdf)
  • T.Ackemann, M.Sondermann.

  • Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers.
    Polarization selection in small-area vertical-cavity surface-emitting lasers (VCSELs) is studied experimentally in dependence of injection current and substrate temperature in the vincity of the minimum threshold condition. Polarization switching from the low to the high frequency fundamental spatial mode is demonstrated. The effective birefringence displays a minimum in the transition region. The observation of dynamical transition states hints to the relevence of nonlinear effects. A comparison to the predictions of the SFM-model based on phase-amplitude coupling is given.
    Appl.Phys.Lett. 78, 3574, 2001.

  • T.Ackemann, M.Sondermann.

  • Characteristics of polarization switching in vertical-cavity surface-emitting lasers.
    Polarization selection in small-area vertical-cavity surface-emitting lasers (VCSELs) is studied experimentally in dependence on injection current and substrate temperature in the vicinity of the minimum threshold condition. Different types of polarization switching (PS) are observed and analyzed: PS from the high to the low frequency mode, PS from low to high frequency and double switching (from high to low and back to high frequency). Whereas PS from the high to the low frequency mode due to a change in sign of linear dichroism, the optical spectra show dynamical transition states for the other case which hint to the relevence of nonlinear effects. A comparison to the predictions of the SFM-model based on phase-amplitude coupling is given. The interplay of spatial and polarization effects can depend strongly on the ambient temperature.
    Proc.SPIE. 4286, 44, 2001.
    (download pdf)
  • M. Sondermann, H. Bohnet, T. Ackemann.

  • Low Frequency Fluctuations and Polarization Dynamics in Vertical-cavity Surface-emitting Lasers with Isotropic Feedback.
    Phys. Rev. A 67, 021802(R)-1-4, 2003.
    (download pdf-file)
  • M. Sondermann, H. Bohnet, M. Weinkath, T. Ackemann.

  • Dynamics and polarization effects in small-area vertical-cavity surface-emitting lasers in free-running mode and with time-delayed feedback.
    Proc. SPIE 4942, 92, 2003.
    (download pdf-file)
  • A.V. Naumenko, N.A. Loiko, M. Sondermann, T. Ackemann

  • Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector.
    We analyze theoretically and experimentally the polarization dynamics of vertical-cavity surface-emitting lasers exposed to isotropic optical feedback. The theoretical investigations are based on a model that takes into account different inversion populations for charge carriers with opposite spin. In the deterministic case, we observe toruslike synchronized low-frequency fluctuations of one or both polarization modes in the vicinity of the solitary laser threshold, depending on the parameters and initial conditions. Both in experiment and in simulations including spontaneous emission noise, asymmetric low-frequency fluctuations are observed above and below the solitary laser threshold as well as a transition to coherence collapse further above threshold. The amount of excitation of polarization degrees of freedom and thus the occurrence of simultaneous lowfrequency fluctuations of both polarization modes is shown to depend on the magnitude of the dichroism. Apart from the correlation properties on the external-cavity time scale, we find a good qualitative agreement between experiments and simulations.
    Phys. Rev. A 68, 033805, 2003.
    (download pdf-file)
  • 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.
    (download pdf-file)

  • T. Ackemann, M. Sondermann, A. Naumenko, and N.A. Loiko

  • Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting lasers subjected to optical feedback.
    The dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback from a distant reflector is studied experimentally and numerically. Low-frequency fluctuations with sudden drop-outs of power are found to be qualitatively independent of the amount of excitation of the second polarization component. The latter is shown to be controlled to a great extent by the intrinsic dichroism of the solitary laser. The experimental findings are in very good qualitative agreement with simulations. The characteristic features of a doublet in the radio-frequency spectra around the external-cavity roundtrip frequency are discussed.
    Appl. Phys. B 77, 739-746, 2003.
    The copyright is owned by Springer-Verlag, the original publication is available at http://www.springerlink.com

  • M. Sondermann, T. Ackemann, S. Balle, J. Mulet, and K. Panajotov

  • Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers.
    The existence region of elliptically polarized dynamical states in the polarization dynamics of vertical-cavity surfaceemitting lasers is investigated experimentally and theoretically. These states can occur in the vicinity of a polarization switching from the fundamental transverse mode with lower emission frequency to the mode with higher frequency. It is demonstrated experimentally that these states may occur in a single as well as in a double switching scenario. The existence of the dynamical states is shown to be independent from the ellipticity of the state of polarization at the lasing threshold. Furthermore, the in.uence of the detuning between the band gap and the cavity resonance on the occurrence of the dynamical states is investigated.
    Opt. Commun. 235, 421-434, 2004.


  • M. Sondermann, M. Weinkath, and T. Ackemann

  • Polarization Switching to the Gain Disfavored Mode in Vertical-Cavity Surface-Emitting Lasers
    We report on the experimental observation of current-induced polarization switching in vertical-cavity surface- emitting lasers which is accompanied by a decrease of the total output power at the switching point. The relaxation oscillation frequency also decreases. This switching is interpreted as a switching event from the mode with higher (unsaturated) net gain to the gain disfavored mode. The experimental observations are in qualitative agreement with a nonlinear dynamical model taking into account spin degrees of freedom of carriers in a semiconductor quantum well. Within the framework of this model, we propose an explanation for the origin of a minimum in the effective dichroism observed at the switching point, which might also be relevant for other experiments.
    IEEE J. Quant. Electr. 40, 97-104, 2004.
    The copyright is owned by IEEE.
    (download pdf-file)
  • M. Sondermann and T. Ackemann

  • Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback
    We investigate experimentally the polarization dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback operating in the long-cavity regime. By means of an analysis of the correlation properties in the time domain and in the frequency domain a connection between a drift phenomenon and frequency components that deviate from the harmonics of the external cavity round-trip frequency is revealed. The latter frequency components are shown to result from an interaction of external cavity dynamics and relaxation oscillations. An analogy to the carrier-envelope effect in mode-locked lasers is drawn. Similar drift phenomena are observed also for other laser systems with delay.
    Opt. Exp. 13, 2707-2715, 2005.
    The original publication is available at http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2707


Articles on spatio-temporal structures in broad-area VCSELs

  • T. Ackemann, S. Barland, J.R. Tredicce, M. Cara, S. Balle, R. Jäger, M. Grabherr, M. Miller, and K.J. Ebeling.

  • Spatial structures in broad-area vertical-cavity regenerative amplifiers.
    We investigate the spatial structure of broad-area vertical-cavity regenerative amplifiers with injection of a homogeneous beam. The emerging patterns have a dominantly six-fold rotational symmetry verifying the recent prediction of hexagons. The length scale is controllable via the detuning and follows the prediction for tilted waves.
    Opt. Lett. 25, 814-816, 2000.
    (download pdf)
  • T. Ackemann, S. Barland, M. Cara, S. Balle, J.R. Tredicce, R. Jäger, M. Grabherr, M. Miller, and K.J. Ebeling.

  • Spatial mode structure of bottom-emitting broad-area vertical-cavity lasers.
    The spatial mode structure of circular broad-area bottom emitting VCSELs is investigated close to threshold. The devices display very high order flower-like Laguerre modes as well as structures with a cartesian symmetry in spite of the original O(2) symmetry. The latter resemble in some case tilted waves more than Hermite-Gaussian modes. Spatial structures appear for both sides of the detuning between gain peak and cavity resonance. The results indicate the necessity to refine the theoretical models to include realistic boundary conditions and inhomogeneities.
    J. Opt. B: Quantum Semiclass. Opt, 2, 406-412, 2000
    (Link to the Journal's web site at IOP)
  • T. Ackemann, S. Barland, M.Giudici, J.R. Tredicce, S. Balle, R. Jäger, M. Grabherr, M. Miller, and K.J. Ebeling.

  • Patterns in broad-area microcavaties.
    The emergence of spatial structures with an approximate hexagonal symmetry is observed in broad-area amplifying microcavaties with injection of a homogeneous beam. The length scale is controllable via the detuning. Optical bistability occurs close to the longitudinal resonance.
    phys.stat.sol.(b), 221, 133-136, 2000.
    (download ps)
  • T. Ackemann, W. Grosse-Nobis, G.L.Lippi.

  • The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their applications to resonance conditions in optical cavities
    An interpretation of the Gouy phase shift is proposed which relates the finite Gouy phase reduction of a Gaussian mode the the averaged phase retardation of the tilted waves in its Fourier spectrum compared to an on-axis plane wave. This provides a unified approach to resonance conditions in optical cavities with plane and curved mirrors. The possible relationship to pattern selection in nonlinear cavities is discussed.
    Opt.Commun. 189, 5, 2001.
    (download ps)
  • I.V. Babushkin, N.A. Loiko, and T. Ackemann.

  • Secondary bifurcations and transverse standing wave patterns in anisotropic microcavity lasers close to the first laser threshold.
    It is well known that in a laser-in the limit of an infinite extent of the transverse aperture-traveling tilted waves are excited at the laser threshold for positive detuning between the frequency of the gain maximum of the active medium and the cavity frequency [Phys. Rev. A 45, 8129 (1992)]. However, a transverse standing wave is unstable. In this paper, it is shown that in anisotropic lasers there can be a chain of secondary bifurcations very close to threshold, which stabilizes the standing wave and then destabilizes it again through a supercritical Hopf bifurcation. The parameter dependence of these bifurcations is discussed. The investigations are motivated by interest in pattern formation in vertical-cavity surface-emitting lasers in which the rotational symmetry is broken due to the dependence of the reflectance of the Bragg reflectors on the polarization vector of the field. The applicability of the results to other class-B lasers is discussed.
    Phys. Rev. A 67, 013813-1-8, 2003.
  • I.V. Babushkin, N.A. Loiko, and T. Ackemann.

  • Eigenmodes and symmetry selection mechanisms in circular large-aperture vertical-cavity surface-emitting lasers.
    The characteristics of the spatial eigenmodes of vertical-cavity surface-emitting lasers with a large circular aperture are considered close to the lasing threshold. Experiments yield patterns based on rotational symmetry ("flowerlike" patterns) or on Cartesian symmetry (stripelike patterns) for very close operating conditions. The former are compatible with the boundary conditions whereas the latter are expected in infinite devices. Theoretically, the problem is considered in the framework of an eigenmode analysis of a linear partial differential equation for the optical field valid at threshold. This formulation allows for a simple implementation of asymmetries due to the reflection properties of Bragg mirrors as well as of transverse variations of gain and refractive index due to the device structure or due to imperfections in the growth process. A sharp transition between flowerlike modes and stripelike modes is shown to occur, if the device aperture is increased.
    Phys. Rev. E 69, 066205-1-14, 2004.

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