1,376 research outputs found
Photonic Anomalous Quantum Hall Effect
We experimentally realize a photonic analogue of the anomalous quantum Hall
insulator using a two-dimensional (2D) array of coupled ring resonators.
Similar to the Haldane model, our 2D array is translation invariant, has zero
net gauge flux threading the lattice, and exploits next-nearest neighbor
couplings to achieve a topologically non-trivial bandgap. Using direct imaging
and on-chip transmission measurements, we show that the bandgap hosts
topologically robust edge states. We demonstrate a topological phase transition
to a conventional insulator by frequency detuning the ring resonators and
thereby breaking the inversion symmetry of the lattice. Furthermore, the
clockwise or the counter-clockwise circulation of photons in the ring
resonators constitutes a pseudospin degree of freedom. We show that the two
pseudospins acquire opposite hopping phases and their respective edge states
propagate in opposite directions. These results are promising for the
development of robust reconfigurable integrated nanophotonic devices for
applications in classical and quantum information processing
Some Contiguous Relation on k-Generalised Hypergeometric Function
In this research work our aim is to determine some contiguous relations and some integral transform of the k-generalised hypergeometric functions, by using the concept of “k-Gamma and k-Beta function”. “Obviously if k approaches 1”, then the contiguous function relations become Gauss contiguous relations
Photonic quadrupole topological phases
The topological phases of matter are characterized using the Berry phase, a
geometrical phase, associated with the energy-momentum band structure. The
quantization of the Berry phase, and the associated wavefunction polarization,
manifest themselves as remarkably robust physical observables, such as
quantized Hall conductivity and disorder-insensitive photonic transport.
Recently, a novel class of topological phases, called higher-order topological
phases, were proposed by generalizing the fundamental relationship between the
Berry phase and the quantized polarization, from dipole to multipole moments.
Here, we demonstrate the first photonic realization of the quantized quadrupole
topological phase, using silicon photonics. In this 2nd-order topological
phase, the quantization of the bulk quadrupole moment in a two-dimensional
system manifests as topologically robust corner states. We unambiguously show
the presence of localized corner states and establish their robustness against
certain defects. Furthermore, we contrast these topological states against
topologically-trivial corner states, in a system without bulk quadrupole
moment, and observe no robustness. Our photonic platform could enable the
development of robust on-chip classical and quantum optical devices with
higher-order topological protection
Topological photonics: fundamental concepts, recent developments, and future directions
Topological photonics is emerging as a new paradigm for the development of
both classical and quantum photonic architectures. What makes topological
photonics remarkably intriguing is the built-in protection as well as intrinsic
unidirectionality of light propagation, which originates from the robustness of
global topological invariants. In this Perspective, we present an intuitive and
concise pedagogical overview of fundamental concepts in topological photonics.
Then, we review the recent developments of the main activity areas of this
field, categorized into linear, nonlinear, and quantum regimes. For each
section, we discuss both current and potential future directions, as well as
remaining challenges and elusive questions regarding the implementation of
topological ideas in photonics systems
Some results on k-hypergeometric function
In this paper, we establish integral representation and differentiation formulas for k-Gauss hypergeometric function 2F1,k(a, b; c; z) and develops a relationship with k-Confluent hypergeometric function 1F1,k(a, b; c; z), which are based properties defined by Rao and Shukla. Our study is to identify the integral as well differential representation of 2F1,k(a, b; c; z) and also find the inverse Laplace transform on it
ON EXTENSION OF MITTAG-LEFFLER FUNCTION
In this paper, we study the extended Mittag -Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag -Leffler functions have also be given
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