Using a k.p model for the electrons in a Bi_{2}Se_{3} slab to second order in the wave vector and first order in strain we calculate the optical absorbance of the surface state electrons. The absorbance, defined as the ratio of absorbed intensity to the incident light intensity, is shown in the figure for a 2 QL slab. The band gap and the band edge absorbance are significantly increased with increasing tensile strain, and for ε_{zz}=6% the band gap occurs at a finite wave vector giving a divergent band edge absorbance and a discontinuous decrease at the larger gap at zero wave vector.

At the NUSOD 2017 conference further details on the model will be presented as well as results for shear strain, which breaks the isotropy of the Dirac cone leading to a polarization dependent change in the absorbance (talk TuA2).

[1] Xia et al, Nat. Nanotech. 4, 839 – 843 (2009)

[2] Zhang et al, Phys. Rev. B 82, 245107 (2010)

]]>For a targeted design of such structures and a deeper understanding of the complex QCL dynamics, a detailed theoretical model is required. We have developed a multi-domain simulation approach, which couples a Maxwell-Bloch type description of the light-matter interaction with advanced ensemble Monte Carlo (EMC) carrier transport simulations to eliminate empirical electron lifetimes [5]. In the figure, simulation results for a QCL-based terahertz frequency comb source [3] are presented. The laser dynamics gives rise to a two-lobed power spectrum consisting of equidistant discrete comb lines [Fig. (a)]. Furthermore, a periodic temporal shifting of the power between the two spectral lobes is observed [Fig. (b)]. The two-lobed comb spectrum and the associated temporal switching dynamics have also been observed in experiment [3,5], validating our simulation model.

At the NUSOD 2017 conference in Copenhagen, we will present a further developed approach based on density matrix EMC simulations of the carrier transport, yielding both the electron lifetimes and dephasing times and thus rendering our simulation model completely self-consistent (talk FA1).

[1] C. Y. Wang et al., Phys. Rev. A **75**, 031802(R) (2007).

[2] A. Hugi et al., Nature **492**, 229 (2012).

[3] D. Burghoff et al., Nature Photon. **8**, 462 (2014).

[4] C. Y. Wang et al., Opt. Express **17**, 19929 (2009).

[5] P. Tzenov et al., Opt. Express **24**, 23232 (2016).

The Fano laser (fig. 1) consists of a line-defect waveguide in a 2D photonic crystal membrane coupled to a nearby point-defect, with active material embedded directly in the membrane. This coupling yields a strong, narrowband suppression of transmission, due to the interference of the continuous waveguide modes with the discrete mode of the nanocavity, effectively forming the right-most laser mirror at the symmetry line, with the left formed by termination of the waveguide [2].

The system is modelled by a combination of coupled-mode theory and conventional rate equations, in order to describe the complex interference between the nanocavity and waveguide fields, while also accounting for the laser dynamics of the waveguide field and the saturable absorption of the nanocavity.

The laser has either continuous wave (CW) or pulsed output, depending on both passive system parameters and the driving current, as shown in fig. 2, where yellow represents self-pulsing, blue is CW output, and insets show the temporal output power evolution.

Due to the active material in the nanocavity the reflection coefficient depends upon the nanocavity free carrier density, meaning that a spike in laser intensity leads to a decrease in nanocavity absorption due to saturation, which in turn yields a larger reflection coefficient, allowing the laser field to increase, further saturating the nanocavity absorption. In this way the nanocavity functions as a highly-dispersive semiconductor saturable absorber mirror, which forms a positive feedback loop for the laser field, allowing for passive pulse generation and existence of a dynamical lasing equilibrium with pulse repetition rates on the order of 10 GHz and pulsewidths around 10 ps.

The stability of this feedback loop depends sensitively on several system parameters, which define the phase space of self-pulsing operation, as in fig. 2. Furthermore, dynamical perturbations of the system, e.g. tuning of the nanocavity resonance frequency or varying the drive current, can result in phase transitions between CW and pulsed output (figs. 3 and 4), so that the type of laser output can be controlled dynamically.

Additional details of the theoretical model, the self-pulsing mechanism and the dynamical phase transitions will be presented at NUSOD 2017, as well as some perspectives for applications such as sub-picosecond pulse generation and transistor-like operation (paper TuA1).

[1]: Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, Nat. Photon. **11**(2), 81–84 (2017), Letter.

[2]: J. Mork, Y. Chen, and M. Heuck, Phys. Rev. Lett. 113(Oct), 163901 (2014).

]]>The problem of circuit control can be particularly challenging in high-index-contrast photonic platforms, due to the large sensitivity of the optical parameters of the devices even to tiny geometrical variations occurring during fabrication, mainly inducing random phase errors. This is particularly true for high-order coupled microring resonator filters. The use of these devices cannot be addressed without proper tuning and locking techniques that can be significantly more complex than the approaches required for the control of a single ring, due to the larger number of degrees of freedom, the existence of non-negligible coupling between rings and the risk of trapping in sub-optimal local solutions. Common tuning strategies presented in literature explore iterative approaches to overcome this problem. These sequential tuning algorithms are based on sweeping the resonance of each microring individually (generally through thermo-optic actuators) until reaching an optimal working point for the entire filter. On the other hand, the use of thermo-optic actuators leads almost unavoidably to the problem of handling thermal cross-talk that causes unwanted phase changes in adjacent rings close to the one under control. Thermal cross-talk may hence make sequential methods inefficient in locking schemes. We propose here a novel method (transformed coordinate method) for the tuning and locking of a coupled microring resonator filter. With this technique, the thermal phase controller of all the rings that realizes the filter are tuned simultaneously at each iteration of the algorithm to minimize the target error function. The effectiveness of this technique is demonstrated by experimentally tuning a 3rd order microring-based filter fabricated in SiON platform starting from five different randomly perturbed conditions [Fig. (a)]. Using transformed coordinate method in all of the cases fine-tuned filters were obtained and such status was maintained via locking scheme in presence of perturbations [Fig. (b)]. More details will be presented at the NUSOD 2017 conference in Copenhagen (talk WB1).

]]>Microcavity exciton-polaritons have numerous advantages over bare photons and excitons. For instance, due to the excitonic component, they exhibit weaker diffraction and tighter localisation, and the strong interparticle interactions result in lower operational powers ~fJ/mm^{2 }and faster switching speeds ~a few ps. Polariton waves can be confined in structures with sub-micron size, which opens up possibilities for fabrication of polaritonic integrated circuits based on structured semiconductor microcavities on a chip. Laterally etched microcavity wires [1] (Fig. 1a) enhance further the polaritonic nonlinearities and thus are a particularly promising integration platform due to broad transparency window, mature fabrication technology and the possibility of monolithic integration with semiconductor diode lasers and VCSELs. In this respect, new theories and numerical methods are needed to model the nonlinear polariton dynamics in non-planar microcavity wires.

This work is focused on the largely unexplored nonlinear functionality of polaritons and the potential of self-organised structures, such as bright polariton solitons [2], to be exploited for signal processing in polaritonic networks on a chip. We aim at designing novel polariton devices based on polariton soliton logic.

We have developed a driven-dissipative mean-field model of the polariton nonlinear dynamics in non-planar microcavity wires [3]. For a realistic microcavity wire, we found that the conventional for planar microcavities bistability evolves into complex multistability [Fig. 1b] and discussed its origin in detail. In contrast to the single-mode polariton solitons in planar microcavities, polariton solitons in microcavity wires exhibit a complex spatial multi-mode structure. Under suitable conditions, different modes within the polariton soliton wave packet interact among themselves in such a way as to give rise to a self-localisation mechanism that prevents the pulse from broadening (Fig. 1c). We have developed a modal expansion method [4] to investigate the nonlinear mechanisms behind localisation, and attempt to find a means to leverage the inter-modal interactions for the development of polaritonic integrated circuits. The multi-mode solitons deserve special attention, since they are capable of propagating further along an imperfect microcavity wire than their single-mode counterparts.

Using our 2D model, we investigate polariton soliton propagation in microcavity wires with different widths — with a view to designing integrated polaritonic devices [5]. We simulate polariton soliton propagation in tilted and tapered microcavity wires, and determine the maximum tilt angle for which the soliton persists. Finally, we demonstrate numerically a new coherent propagation phenomenon of a radiating polariton soliton exhibiting periodic collapses and revivals, and identify regimes for existence of this new class of polariton solitons.

Further details will be presented at the NUSOD 2017 conference in Copenhagen (paper ThA1).

[1] E. Wertz et al., Nat. Phys. **6**, 860 (2010)

[2] M. Sich et al., Nat. Photonics, **6**, 50 (2012)

[3] G. Slavcheva, A. V. Gorbach, A. Pimenov, A. G. Vladimirov, and D. V. Skryabin, Opt. Lett. **40**, 1787 (2015)

[4] G. Slavcheva, A. V. Gorbach, and A. Pimenov, Phys. Rev. B **94,** 245432 (2016)

[5] G. Slavcheva, M. V. Koleva, and A. Pimenov, J. of Optics **19**, 065404 (2017)