Differential-Transfer-Matrix Based on Airy's Functions in Analysis of Planar Optical Structures With Arbitrary Index Profiles

2016

Scientia Iranica

Abstract. The Di erential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The results for real-valued systems are simpli ed and a pair of basis functions are found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The ndings of this paper allow explicit evaluation of eigenvalues of con ned modes with high precision, as demonstrated by few examples.

Section: Basis Functionsmentioning

confidence: 99%

New basis functions for wave equation

2016

Scientia Iranica

“…2, depends not only on the thickness of the potential barrier but also on the applied electric field. A detailed treatment of the problem of finding the field-assisted tunneling probability in such a system using transfer matrix formalism [30,31] combined with expansion on Airy's functions [32] is briefly explained here.…”

Section: Structure and Calculationsmentioning

confidence: 99%

Tunable Spontaneous Emission From Layered Graphene/Dielectric Tunnel Junctions

IEEE J. Quantum Electron.

2014

There has been a rapidly growing interest in optoelectronic properties of graphene and associated structures. Despite the general belief on absence of spontaneous emission in graphene, which is normally attributed to its unique ultrafast carrier momentum relaxation mechanisms, there exist a few recent evidences of strong optical gain and spontaneous light emission from mono-layer graphene, supported by observations of dominant role of out-of-plane excitons in polycyclic aromatic hydrocarbons. In this article, we develop a novel concept of light emission and optical gain from simple vertical graphene/ dielectric tunnel junctions. It is theoretically shown that the possible optical gain or emission spectrum will be easily tunable by the applied voltage. We present details of quantum mechanical calculations and perform an exact analysis of field-assisted tunneling using transfer matrices combined with expansion on Airy's functions.

“…The previous formulations of DTMM [1,4] would fail at zeros of ˧{˲{. The method of Airy functions [5] and generalized DTMM [2] are able to respectively pass over and remove certain types of these singularities. This extended method, however, effectively works out such singular points, since the arising singularities are now located at zeros of ˧{ˮ{ˤˮ ˲ 0 instead of ˧{˲{, and furthermore the only singular expression corresponds to {ʽ{˲{{.…”

Section: Reduction To the Real-axismentioning

confidence: 99%

Basis functions for solution of non-homogeneous wave equation

Karimi

2013

SPIE Proceedings

In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of equations having a rank twice the size of the real-valued problem. The method discussed in this paper also successfully removes the problem of dealing with essential singularities, which was present in the earlier formulations. Then we simplify the result for real-valued problems and obtain a new set of basis functions, which may be used instead of the WKB solutions. These basis functions not only satisfy the initial conditions perfectly, but also, may approach the turning points without the divergent behavior, which is observed in WKB solutions. Finally, an analytical transformation in the form of a matrix exponential is presented for improving the accuracy of solutions.