The beam transfer matrix, often called the ABCD matrix, is one of the essential mathematical instruments in optics. It is a unimodular matrix whose determinant is 1. If all the elements are real with three independent parameters, this matrix is a 2 x 2 representation of the group Sp(2). It is shown that a real ABCD matrix can be generated by two shear transformations. It is then noted that, in ...

The ABCD matrix is one of the essential mathematical instruments in optics. It is the two-by-two representation of the group Sp(2), which is applicable to many branches of physics, including squeezed states of light, special relativity and coupled oscillators. It is pointed out that the shear representation is oriented to binary logic which may be friendly to computer applications. While this i...

Expressions are derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model beam propagating through a paraxial ABCD system. Using the recently developed unified theory of coherence and polarization of electromagnetic beams and the ABCD matrix for gradient-index fibers, we study the changes of the spectral density, of the spectral degree of polarization, and of the...

Propagation of stochastic electromagnetic beams through paraxial ABCD optical systems operating through turbulent atmosphere is investigated with the help of the ABCD matrices and the generalized Huygens-Fresnel integral. In particular, the analytic formula is derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model (EGSM) beam. We applied our analysis for the A...

It is shown that every ray transfer matrix, often called the ABCD matrix, can be written as a similarity transformation of one of the Wigner matrices that dictate the internal space-time symmetries of relativistic particles, while the transformation matrix is a rotation preceded by a squeeze. The implementation of this mathematical procedure is described, and how it facilitates the calculations...

studying gaussian beam is a method to investigate laser beam propagation and abcd matrix is a fast and simple method to simulate gaussian beam propagation in different mediums. of the abcd matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. however in previous work the incident beam and the principle axis of surface are in parallel...

Due to their hilarious properties, carbon nanotubes (CNTs) with different varieties have been suggested as potential alternatives for interconnects in many industrial applications related Artificial Intelligence. This work made an overview of the various models resistive effect inside several CNT based interconnects. In addition, it has studied propagation delay interconnect by comparing two va...

Background Prevalence of subungual melanoma (SUM) in Asian population is relatively high and early clinical detection improves both quality of life and survival. Objective We sought to establish screening strategy for SUM in situ. Methods We retrospectively reviewed medical records of 8 patients pathologically diagnosed as SUM in situ between January 2015 and September 2016. Results All p...

The evolution and propagation of a partially coherent matter wave (PCMW) is investigated theoretically by the correlation function method. The ABCD matrix formalism previously used for a fully coherent matter wave is extended to the PCMW domain. A new ABCD law is derived, using a tensor method to describe the evolution of a PCMW. An analytical solution of the first-order correlation function is...

OVERVIEW In 2013, the ABCD published 'Matrix vaccination guidelines: ABCD recommendations for indoor/outdoor cats, rescue shelter cats and breeding catteries' in a Special Issue of the Journal of Feline Medicine and Surgery (Volume 15, Issue 7, pages 540-544). The ABCD's vaccination recommendations were presented in tabulated form, taking into account that there is no universal vaccination prot...