In this work we provide a new short proof of closed formulas for the n-th derivative of the cotangent and secant functions using simple operations in the context of the Zeon algebra. Our main ingredients in the proof comprise a representation of the ordinary derivative as an integration over the Zeon algebra, a representation of the Stirling numbers of the second kind as a Berezin integral, and...

By employing the Gaussian decomposition method, the analytical formulas of the Gaussian-beam Z-scan traces have been derived for an optically thin material exhibiting both refractive and absorptive parts of third-order nonlinearity, with Gaussian or hyperbolic secant squared laser pulses of femtosecond duration. The formulas have been verified experimentally with femtosecond-pulsed Z scans on a...

A method is proposed for the optical rotation of the spin of an electron in a quantum dot using excited trion states to implement operations significantly faster than those of most existing proposals. Key ingredients are the geometric phase induced by 2pi hyperbolic secant pulses, use of coherently trapped states and use of naturally dark states. Our proposal covers a variety of quantum dots by...

We report experimental evidence of the propagating capillary solitary waves generated by a localized water surface perturbation. Solitons are formed at the air-water interface with a solid plunger and then propagate with velocities proportional to their amplitudes. The shape of the forward front of such solitons is independent of the plunger shape and is given by the hyperbolic secant profile. ...

The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In add...

Fig. 2 Results for three HS pulses: a high bandwidth pulse (row 1), a reduced bandwidth pulse (row 2), and an optimized pulse with reduced bandwidth (row 3). Flip-angle maps are calculated on the grid of targeted static and RF field variations (column 1) and within an axial slice of the human brain (column 2). Frequency profiles for B1/ B1,nom intensities of 0.35, 0.50, 0.75, and 1.00 are shown...

Abstract New families of complex-valued refractive-index profiles the hyperbolic-secant type are constructed by means factorization method. These included in class widely-studied PT -symmetric ones and a generalization well-known (real-valued) profiles. Also, analytic expressions for corresponding modal fields obtained interlacing zeroes real imaginary parts is elucidated. In addition, bi-ortho...