Jan Wiersig

Otto-von-Guericke-Universität Magdeburg, Magdeburg, Saxony-Anhalt, Germany

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Publications (125)335.35 Total impact

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    Henning Schomerus, Jan Wiersig
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    ABSTRACT: Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., nonhermitian degeneracies at which not only the frequencies and decay rates coalesce but also the eigenmodes themselves. The non-hermitian corrections to the group velocity are largest in the regions around the exceptional points.
    Physical Review A 09/2014; 90(5). DOI:10.1103/PhysRevA.90.053819 · 2.99 Impact Factor
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    Raktim Sarma, Li Ge, Jan Wiersig, Hui Cao
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    ABSTRACT: We demonstrate in open microcavities with broken chiral symmetry, quasi-degenerate pairs of co-propagating modes in a non-rotating cavity evolve to counter-propagating modes with rotation. The emission patterns change dramatically by rotation, due to distinct output directions of CW and CCW waves. By tuning the degree of spatial chirality, we maximize the sensitivity of microcavity emission to rotation. The rotation-induced change of emission is orders of magnitude larger than the Sagnac effect, pointing to a promising direction for ultrasmall optical gyroscopes.
    Physical Review Letters 04/2014; DOI:10.1103/PhysRevLett.114.053903 · 7.73 Impact Factor
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    ABSTRACT: The effect of Kerr-nonlinearity on coupled whispering gallery modes is studied. As a model system, we choose an add-drop filter, which comprises a circular microcavity and two side-coupled wave guides. The coupling of counter propagating whispering gallery modes is achieved by evanescent field's scattering on the waveguides, and this coupling leads to doublets of whispering gallery modes. By numerically computing the transmission of the add-drop filter, the formation of a doublet whispering gallery mode is verified. With increase of Kerr-nonlinearity in the cavity, the doublets of whispering gallery modes exhibit the bistable transition in the beginning. However, when the nonlinearity surpasses a certain level, an unexpectedly low transmission is generated between the two transmission peaks of the doublet, which we name `anomalous transmission'. In order to analyse the anomalous transmission, the system is modelled by coupled mode theory and analysed in terms of nonlinear dynamics. This analysis reveals that the stable- and the unstable branches of a WGM doublet are merged at the frequency where the anomalous transmission occurs, as the nonlinearity exceeds a certain limit. From this observation, we can find a clue, that this merger can locally break the stability and cause the observed anomalous transmission.
  • Marcus Kraft, Jan Wiersig
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    ABSTRACT: In recent experiments it has been demonstrated that wavelength-scale microdisk lasers with the shape of a limaçon can support high-quality whispering-gallery modes with a regular nodal line structure. Here, we show that these modes can be accurately described by a perturbation theory for slightly deformed microdisk cavities. Our results reveal that the performance of the perturbation theory can be considerably improved by a suitable choice of the origin around which the perturbation series is expanded.
    Physical Review A 01/2014; 89(2). DOI:10.1103/PhysRevA.89.023819 · 2.99 Impact Factor
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    ABSTRACT: We present a new method to formulate equations of motion for open quantum many-particle systems. Our approach allows for a numerically exact treatment as well as for approximations necessary in large systems and can be applied to systems involving both bosonic and fermionic particles. The method generalizes the cluster expansion technique by using expectation values instead of correlation functions. The use of expectation values not only makes the equations more transparent but also considerably reduces the amount of algebraic effort to derive the equations. The proposed formulation offers a unified view on various approximation techniques presented recently in the literature. The microscopic semiconductor model for quantum-dot-based microcavity lasers is extended to higher-order photon-autocorrelation functions and the validity of the cluster expansion is shown for this system. We study photon-autocorrelation functions up to fifth order and monitor the onset of lasing in quantum-dot-based microcavity lasers. We observe a successive vanishing of photon bunching in the higher-order photon-autocorrelation functions with increasing pump rates. Our results reveal that the laser threshold is not only softened in microcavity laser systems but is centered around different pump rates with respect to the photon-autocorrelation functions.
    Physical Review B 01/2014; 89(8). DOI:10.1103/PhysRevB.89.085308 · 3.66 Impact Factor
  • Raktim Sarma, Li Ge, Jan Wiersig, Hui Cao
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    ABSTRACT: We propose a novel and ultrasensitive scheme of rotation sensing by measuring farfield intensity from an asymmetric microcavity laser. We optimize the cavity shape and show the farfield sensitivity is enhanced by introducing structural chirality.
    CLEO: Applications and Technology; 01/2014
  • Jan Wiersig
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    ABSTRACT: We study the properties of energy eigenstates in open quantum systems in which clockwise and counterclockwise traveling waves are weakly coupled. We show that under rather general conditions the energy eigenstates of such systems can appear in pairs of nonorthogonal, copropagating traveling-wave states. The relation to exceptional points of the effective non-Hermitian Hamiltonian is discussed.
    Physical Review A 12/2013; 89(1). DOI:10.1103/PhysRevA.89.012119 · 2.99 Impact Factor
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    ABSTRACT: Resonant modes with high-Q factors in a two-dimensional deformed microdisc cavity are analyzed by using a dynamical and semiclassical approach. The analysis focuses particularly on the ultra-small cavity regime, where the scale of a resonant free-space wavelength is comparable with that of the microdisc size. Although the deformed microcavity has strongly chaotic internal ray dynamics, modes with high-Q factors in this regime show unexpectedly regular distributions in configuration space and adiabatic features in phase space. By tracing the evolution process of such high-Q modes through the deformation from a circular cavity, it is uncovered that the high-Q modes are formed adiabatically on cantori. Due to the openness of microcavities, such adiabatic formation of high-Q modes around cantori is enabled, in spite of strong chaos in ray dynamics. Since the cantori are in close contact with short periodic orbits, their influence on the modes, such as localization patterns in phase space, can be also clarified. In order to quantitatively analyze the spectral range where high-Q modes appear, the phase space section of the deformed microcavity is partitioned by partial barriers of short periodic orbits, and the semiclassical quantization scheme is applied to the partitioned areas and their action fluxes. The derived spectral ranges for the high-Q modes show a good agreement with a numerically observed spectrum. In the course of semiclassical quantization, it is shown that the chaotic diffusion in the system that we investigate can be resolved by the scale of a quarter effective Planck's constant, and the topological structure of the manifolds in phase space allows for this resolution higher than a Planck constant scale. By analyzing flux Farey trees, the role of short periodic orbits in chaotic diffusion and their connection to cantori are verified.
    New Journal of Physics 11/2013; 15:113058. DOI:10.1088/1367-2630/15/11/113058 · 3.67 Impact Factor
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    Jeong-Bo Shim, Jan Wiersig
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    ABSTRACT: When two microdisks are placed close to each other and the evanescent fields of their whispering gallery modes are overlapped, a strong coupling can be induced in the modes and lead to a doublet state. We attempt to evaluate the frequency splittings of the doublets by applying a semiclassical analysis in the regime of small wavelengths. Since a whispering gallery mode in a microdisk is a leaky mode, an established semiclassical method that deals with coupled closed systems is modified. As a result, we attain an analytic formula which can conveniently compute the frequency splittings of coupled whispering gallery modes. The derived formula is verified by demostrating a perfect agreement with numerical solutions of Maxwell's equations.
    Optics Express 10/2013; 21(20):24240-24253. DOI:10.1364/OE.21.024240 · 3.53 Impact Factor
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    ABSTRACT: We show that coupling among multiple resonances can be conveniently introduced and controlled by boundary wave scattering. This is demonstrated in optical microcavities of quasicircular shapes, where the couplings of multiple modes are determined by the scattering from harmonic boundary deformations. We analyze these couplings using a perturbation theory, which gives an intuitive understanding of the lowest-order and higher-order scattering processes. Different scattering paths between two boundary waves can either enhance or reduce their coupling strength. The effect of controlled multimode coupling is most pronounced in the direction of output from an open cavity, as the coupling can cause a dramatic change of the external cavity field distribution.
    Physical Review A 10/2013; 88(4). DOI:10.1103/PhysRevA.88.043801 · 2.99 Impact Factor
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    ABSTRACT: We present a theoretical study of a quantum-dot-based microcavity laser where two nearly degenerate high-Q modes are involved in the laser dynamics. To analyze the coupled carrier-photon system we have extended a single mode microscopic semiconductor theory to the case of two modes and have also taken the crosscorrelation functions into account.Our theoretical results show that the mode which loses the mode competition exhibit super-thermal photon bunching (). This interesting feature is traced back to mode coupling induced by the gain medium.The strong correlation between the two modes is revealed by calculation of the photon cross correlation functions.
    physica status solidi (b) 09/2013; 250(9). DOI:10.1002/pssb.201200715 · 1.61 Impact Factor
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    ABSTRACT: We outline a new formulation of the cluster expansion to derive equations of motion for open quantum systems. Our method uses expectation values instead of correlation functions. The algebraic effort to derive the equations is reduced and the approach is more intuitive.We demonstrate the efficiency of our method by applying it to the damped Jaynes-Cummings model. This model is a good starting point to investigate quantum dot based laser systems. Further we will examine the convergence properties of the cluster expansion for various orders. (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
    physica status solidi (c) 09/2013; 10(9). DOI:10.1002/pssc.201200711
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    Qinghai Song, Li Ge, Jan Wiersig, Hui Cao
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    ABSTRACT: The recent progresses in single crystalline wide bandgap hexagonal disk have stimulated intense research attention on pursuing ultraviolet (UV) laser diodes with low thresholds. While whispering-gallery modes based UV lasers have been successfully obtained in GaN, ZnO nanorods, and nanopillars, the reported thresholds are still very high, due to the low-quality (Q) factors of the hexagonal resonances. Here we demonstrate resonances whose Q factors can be more than two orders of magnitude higher than the hexagonal modes, promising the reduction of the energy consumption. The key to our finding is the avoided resonance crossing between superscar states along two sets of nearly degenerated triangle orbits, which leads to the formation of hexagram modes. The mode couplings suppress the field distributions at the corners and the deviations from triangle orbits simultaneously and therefore enhance the Q factors significantly.
    Physical Review A 08/2013; 88(2). DOI:10.1103/PhysRevA.88.023834 · 2.99 Impact Factor
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    ABSTRACT: Within this paper a novel method for selecting certain lasing modes from a whispering gallery mode (WGM) spectrum of electrically pumped microrings is presented. Selection is achieved by introducing sub-wavelength sized notches of about 50nm width and 500nm depth to the sidewalls of ring shaped quantum dot micro cavities with 80µm diameter and ridge widths below 2µm. It is shown that the notches act as scattering centers, suppressing modes that have maxima in intensity at the notch position. By a variation of the angle between the notches, different repetitive patterns of lasing modes and suppressed modes are conceivable.
    Optics Express 07/2013; 21(13):15951-15958. DOI:10.1364/OE.21.015951 · 3.53 Impact Factor
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    ABSTRACT: We show that coupling among multiple resonances can be conveniently introduced and controlled by boundary wave scattering. We demonstrate this principle in optical microcavities of quasi-circular shape, where the couplings of multiple modes are determined by the scattering from different harmonic boundary deformations. We analyze these couplings using a perturbation theory, which gives an intuitive understanding of the first-order and higher-order scattering processes. Different scattering paths between two boundary waves can either enhance or reduce their coupling strength. The effect of controlled multimode coupling is most pronounced in the direction of output from an open cavity, which can cause a dramatic change of the external cavity field distribution.
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    ABSTRACT: An equation-of-motion based theory for the description of light emission from multilevel semiconductor quantum dots (QDs) is presented. It accounts for electronic excitations in the presence of Coulomb interaction, leading to multiexciton states, and their coupling to the quantized electromagnetic field. The two key aspects of this work concern (i) the combination of an exact treatment of the electronic degrees of freedom with an approximate approach for the photonic degrees of freedom that is based on the cluster expansion technique and (ii) the consistent incorporation of scattering and dephasing due to the coupling to delocalized electronic states and phonons into the equations of motion via Lindblad terms. Differences to previously used theories are discussed and results of the theory are shown for free-space emission, where multiexciton spectra are shown, and for emission into a single high-Q cavity mode. In the latter case, a full solution of the von-Neumann equation is used to benchmark the proposed theory, which we term “finite-size hierarchy” (FSH) method.
    Physical review. B, Condensed matter 04/2013; 87(16). DOI:10.1103/PhysRevB.87.165306 · 3.66 Impact Factor
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    ABSTRACT: We report on strong mode coupling in closely spaced GaInP microdisk dimer structures including InP quantum dots as the active medium. Using electron beam lithography and a combination of dry- and wet-etch processes, dimers with inter-disk separations down to d < 100 nm have been fabricated. Applying a photo-thermal heating scheme, we overcome the spectral mode detuning due to the size mismatch between the two disks forming the dimer. We observe signatures of mode coupling in the corresponding photoluminescence spectra with coupling energies of up to 0.66 MeV. With the aid of a numerical analysis, we specify the geometrical and physical factors of the microdisk dimer precisely, and reproduce its spectrum with good agreement.
    New Journal of Physics 01/2013; 15(1):013060. DOI:10.1088/1367-2630/15/1/013060 · 3.67 Impact Factor
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    ABSTRACT: We investigate correlations between orthogonally polarized cavity modes of a bimodal micropillar laser with a single layer of self-assembled quantum dots in the active region. While one emission mode of the microlaser demonstrates a characteristic s-shaped input-output curve, the output intensity of the second mode saturates and even decreases with increasing injection current above threshold. Measuring the photon auto-correlation function g^{(2)}(\tau) of the light emission confirms the onset of lasing in the first mode with g^{(2)}(0) approaching unity above threshold. In contrast, strong photon bunching associated with super-thermal values of g^{(2)}(0) is detected for the other mode for currents above threshold. This behavior is attributed to gain competition of the two modes induced by the common gain material, which is confirmed by photon crosscorrelation measurements revealing a clear anti-correlation between emission events of the two modes. The experimental studies are in excellent qualitative agreement with theoretical studies based on a microscopic semiconductor theory, which we extend to the case of two modes interacting with the common gain medium. Moreover, we treat the problem by an extended birth-death model for two interacting modes, which reveals, that the photon probability distribution of each mode has a double peak structure, indicating switching behavior of the modes for the pump rates around threshold.
    Physical Review A 01/2013; 87(5). DOI:10.1103/PhysRevA.87.053819 · 2.99 Impact Factor
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    ABSTRACT: We experimentally demonstrate directional far field emission from whispering gallery modes (WGMs) in electrically driven quantum dot micropillar lasers. In-plane directionality of whispering gallery mode emission is obtained by patterning micropillars with Limacon-shaped cross-section and an upper air-bridge contact for current injection. The micropillar lasers with radii R-0 down to 4.5 mu m show Q-factors of 40 000 and threshold currents of 40 mu A at low temperature. We achieved a far field divergence of about 30 degrees and a directionality of 1.67 +/- 0.15 for an optimal Limacon deformation factor epsilon approximate to 0.5. Parameter dependent studies of the directional emission as a function of epsilon reveal good qualitative agreement with theoretical predictions. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4733726]
    Applied Physics Letters 07/2012; 101(2). DOI:10.1063/1.4733726 · 3.52 Impact Factor

Publication Stats

2k Citations
335.35 Total Impact Points


  • 2008–2014
    • Otto-von-Guericke-Universität Magdeburg
      • Institute of Theoretical Physics (ITP)
      Magdeburg, Saxony-Anhalt, Germany
  • 2013
    • Harvard University
      • School of Engineering and Applied Sciences
      Cambridge, Massachusetts, United States
  • 1996–2009
    • Universität Bremen
      • Institute of Solid State Physics
      Bremen, Bremen, Germany
  • 2007
    • Universität Stuttgart
      • Institute of Physics
      Stuttgart, Baden-Württemberg, Germany
  • 2000–2007
    • Max Planck Institute of Physics
      München, Bavaria, Germany
  • 2003
    • Max Planck Institute for the Physics of Complex Systems
      Dresden, Saxony, Germany
  • 1999
    • University of London
      Londinium, England, United Kingdom