Sharif Digital Repository

We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I-V characteristics are also found under non-zero external bias  

In this paper, the equivalent medium of Schwarzschild metric is discussed. The corresponding ray-tracing equations are integrated for the equivalent medium of the Schwarzschild geometry, which describes the curved space around a spherically symmetric, irrotational, and uncharged blackhole. We make comparison to the well-known expression by Einstein. While Einstein's estimate is reasonably good for large closest distances of approach to the star, it disregards the optical anisotropy of space. Instead, Virbhadra's estimate which takes the effects of anisotropy of Schwarzschild metric is shown to be more consistent with numerical simulations. Hence, a true physical anisotropy in the velocity of... 

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The results for real-valued systems are simplified 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 findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples  

The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that this postulation is in fact unnecessary and may be replaced by a few deeper concepts, which ultimately lead to the derivation of Poisson bracket. One would only need to use Fourier transform pairs and Kramers- Kronig identities in the complex domain. We present a definition of Hermitian time-operator and discuss some of its basic properties. © Electronic Journal of Theoretical Physics  

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While the zeroth order linearization approximation to the operators is normally used, here, first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches √6 - 2, in good... 

The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order interactions, do not vanish under any possible choice of canonical parameters, and lead to coupling of momentum and field. The existence of quadratic mechanical parametric interaction is then demonstrated rigorously, which has been so far assumed phenomenologically in previous studies. Corrections to the quadratic terms are particularly significant when the mechanical frequency is of the same order or larger than the electromagnetic frequency. Further discussions... 

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time... 

A system scheme is presented, which allows non-reciprocal wave transmission or directional amplification of electromagnetic signals, using a boxed four-node method. Edges represent strong hopping interactions and diagonals stand for weak parametric interactions. Using careful optimization of values for design parameters, we are able to obtain non-reciprocity in excess of 12 and 130 dB for intrinsic and extrinsic configurations at identical input/output frequencies. For the directional amplification, an isolation as high as 40 dB is demonstrated with the forward/backward gains of ±20 dB. Cascading two such systems potentially can offer high isolations at high gains. © 1965-2012 IEEE  

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer two-dimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX2 with M = Mo, W and X = S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear and nonlinear surface susceptibility tensors with ωΣ = ωr + ωs + ωt. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two... 

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 monolayer graphene, supported by observations of dominant role of out-of-plane excitons in polycyclic aromatic hydrocarbons. In this paper, 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... 

We discuss the deflection of light and Shapiro delay under the influence of gravity as described by Schwarzschild metric. We obtain an exact expression based on the coordinate velocity, as first set forth by Einstein, and present a discussion on the effect of velocity anisotropy. We conclude that the anisotropy in the coordinate velocity, as the velocity apparent to a distant observer, gives rise to a third order error in the deflection angle, so that the practical astronomical observations from gravitational lensing data remain inconclusive on the anisotropy. However, measurement of Shapiro delay provides a fairly convenient way to determine whether the spacetime is optically anisotropic... 

Most electromechanical devices are in two-dimensional metallic drums under high tensile stress, which causes increased mechanical frequency and quality factor. However, high mechanical frequencies lead to small zero-point displacements xzp, which limits the single-photon interaction rate g0. For applications which demand large g0, any design with increased xzp is desirable. It is shown that a patterned drum by a spiral shape can resolve this difficulty, which is obtained by a reduction of mechanical frequency while the motion mass is kept almost constant. An order of magnitude increase in g0 and agreement between simulations and interferometric measurements is observed. © 2018 Author(s)  

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... 

It is has been long known that the curved space in the presence of gravitation can be described as a non-homogeneous anisotropic medium in flat geometry with different constitutive equations. In this article, we show that the eigenpolarizations of such medium can be exactly solved, leading to a pseudo-isotropic description of curved vacuum with two refractive index eigenvalues having opposite signs, which correspond to forward and backward travel in time. We conclude that for a rotating universe, time-reversal symmetry is broken. We also demonstrate the applicability of this method to Schwarzschild metric and derive exact forms of refractive index. We derive the subtle optical anisotropy of... 

Using a simple nonlinear model based on rate equations, and by employing a harmonic balance method, we develop a theory of optimal mixing in directly modulated semiconductor laser diodes. We perform a consistent numerical solution to the mixing in laser diodes to the arbitrary accuracy and intermodulation index (m, n). Through numerical computations we demonstrate that there is an optimal bias in mixing, corresponding to a relaxation frequency, fr, coinciding with the subcarrier frequency, f1, at which the mixing power is maximized nearly simultaneously for all intermodulation products, fmn. In terms of increasing the signal's current amplitude, it will be shown that it would result in a...