### Abstract

Original language | English |
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Publisher | Technical University of Denmark |
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Number of pages | 159 |

Publication status | Published - 2019 |

### Cite this

*Active nanophotonic antenna arrays for effective light-matter interactions*. Technical University of Denmark.

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*Active nanophotonic antenna arrays for effective light-matter interactions*. Technical University of Denmark.

**Active nanophotonic antenna arrays for effective light-matter interactions.** / Kaminski, Piotr Marek.

Research output: Book/Report › Ph.D. thesis › Research

TY - BOOK

T1 - Active nanophotonic antenna arrays for effective light-matter interactions

AU - Kaminski, Piotr Marek

PY - 2019

Y1 - 2019

N2 - We have investigated novel phenomena such as bound state in the continuums (BICs), Dirac cones and exceptional points in photonic crystal (PhC)-based lasers. We found that the extent of the ring of exceptional points can be controlled with thickness of the PhC slab. For a speciﬁc thickness, the extent of the ring can be reduced almost to a point. Then, large Q-factor values are found over the broad region of the Brillouin zone (BZ). These results were used in the design of high Q-factor,small footprint PhC-based resonators that could be used in photonic crystal surface-emitting lasers (PCSELs). Furthermore, we found that elliptical air-holes introduce frequency separation between the two large Q-factor bands leading to the uniform ﬁeld proﬁle without ﬁeld localization eﬀects. The dispersion of the PhC with elliptical air-holes is radically diﬀerent along the high symmetry directions and is signiﬁcantly altered by a sheer rotation of the air-hole. This may allow to easily control band curvature along speciﬁc directions and thus control mode spacing in ﬁnite size structures. Moreover, we have investigated the dynamic model of the self-pulsing Fano laser. We observed that the laser dynamics are conﬁned to the curved surface after the initial transition stage. We proved that after the initial transition stage, the original ﬁve dimensional (5D) model can be reduced to only one-dimensional (1D) in the limited region of the parameter space and that the system evolves into two-dimensional (2D) beyond the exceptional point when the steady-state eigenvalues transition from being purely real to a complex conjugate pair. We have used the simpliﬁed 2D model to associate the unknown origin of instability with a new unstable periodic orbit separating the stable steady-state from the stable periodic orbit. We have classiﬁed the bifurcation standing behind the two orbits and an equilibrium point (steady-state) as a Bautin bifurcation. Furthermore, the instantaneous eigenvalues have been found to form a complex conjugate pair within the pulse, which is bounded by two exceptional points. In total, four exceptional points are found to be crossed within a single loop in the phase space. Finally, we have demonstrated that the intervals of the solution following the adiabatic prediction are interrupted by abrupt nonadiabatic transitions when the state is at the periodic orbit. These transitions have been observed in close vicinity of the pulse. To the best of author’s knowledge, this is the ﬁrst time when the nonadiabatic phenomena are observed in the complex Fano laser system in which the exceptional points are crossed due to the self-modifying behaviour, without any need for an external parameter variation.

AB - We have investigated novel phenomena such as bound state in the continuums (BICs), Dirac cones and exceptional points in photonic crystal (PhC)-based lasers. We found that the extent of the ring of exceptional points can be controlled with thickness of the PhC slab. For a speciﬁc thickness, the extent of the ring can be reduced almost to a point. Then, large Q-factor values are found over the broad region of the Brillouin zone (BZ). These results were used in the design of high Q-factor,small footprint PhC-based resonators that could be used in photonic crystal surface-emitting lasers (PCSELs). Furthermore, we found that elliptical air-holes introduce frequency separation between the two large Q-factor bands leading to the uniform ﬁeld proﬁle without ﬁeld localization eﬀects. The dispersion of the PhC with elliptical air-holes is radically diﬀerent along the high symmetry directions and is signiﬁcantly altered by a sheer rotation of the air-hole. This may allow to easily control band curvature along speciﬁc directions and thus control mode spacing in ﬁnite size structures. Moreover, we have investigated the dynamic model of the self-pulsing Fano laser. We observed that the laser dynamics are conﬁned to the curved surface after the initial transition stage. We proved that after the initial transition stage, the original ﬁve dimensional (5D) model can be reduced to only one-dimensional (1D) in the limited region of the parameter space and that the system evolves into two-dimensional (2D) beyond the exceptional point when the steady-state eigenvalues transition from being purely real to a complex conjugate pair. We have used the simpliﬁed 2D model to associate the unknown origin of instability with a new unstable periodic orbit separating the stable steady-state from the stable periodic orbit. We have classiﬁed the bifurcation standing behind the two orbits and an equilibrium point (steady-state) as a Bautin bifurcation. Furthermore, the instantaneous eigenvalues have been found to form a complex conjugate pair within the pulse, which is bounded by two exceptional points. In total, four exceptional points are found to be crossed within a single loop in the phase space. Finally, we have demonstrated that the intervals of the solution following the adiabatic prediction are interrupted by abrupt nonadiabatic transitions when the state is at the periodic orbit. These transitions have been observed in close vicinity of the pulse. To the best of author’s knowledge, this is the ﬁrst time when the nonadiabatic phenomena are observed in the complex Fano laser system in which the exceptional points are crossed due to the self-modifying behaviour, without any need for an external parameter variation.

M3 - Ph.D. thesis

BT - Active nanophotonic antenna arrays for effective light-matter interactions

PB - Technical University of Denmark

ER -