Browsing by Author "Umul, Yusuf Ziya"
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Article Citation Count: Umul, Y.Z. (2011). A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges. Optic Communications, 284(19), 4289-4294. http://dx.doi.org/10.1016/j.optcom.2011.06.045A hybrid Maliuzhinets/PO method for diffraction problems by impedance wedges(Elsevier Science Bv, 2011) Umul, Yusuf Ziya; 42699The solution of Maliuzhinets of the diffraction problem of waves by an impedance wedge is transformed into a physical optics integral. The resultant expression is suitable for the investigation of various diffraction problems having impedance wedges. The method is applied to the scattering of waves by an impedance spherical reflector with wedge structure at its discontinuity. The results are examined numerically.Article Citation Count: Umul, Yusuf Ziya, "A new approach to the Dirac equation", Optik, Vol. 181, pp. 524-527, (2019).A new approach to the Dirac equation(Elsevier GMBH, 2019) Umul, Yusuf Ziya; 42699Dirac equation is based on a novel method that expresses the roots of a square-root operation in terms of matrices. Instead of this technique we propose an alternative approach. The square-root expression is represented as a hypotenuse and it is written in terms of a trigonometric summation of the remaining two edges of a right-angle triangle. Both of the positive and negative energy terms are taken into account and a new matrix equation is obtained. The plane wave solutions of the new differential equation are studied.Article Citation Count: Umul, Y.Z. (2013). A new representation of the Kirchhoffs diffraction integral. Optic Communications, 291 48-51. http://dx.doi.org/10.1016/j.optcom.2012.11.038A new representation of the Kirchhoffs diffraction integral(Elsevier Science Bv, 2013) Umul, Yusuf Ziya; 42699The diffraction integral of Kirchhoff is rearranged according to its integral boundaries. The new approach is based on the theory of the edge dislocation waves and provides a more correct field representation for the semi-infinite and infinite integrals in the direct numerical computation. The integral is studied on the diffraction problem of plane waves by a perfectly conducting half-plane. The correctness of the scattering diagrams is compared with the classical approach and the Fresnel integral representation of the scattered waves numericallyArticle Citation Count: Umul, Yusuf Ziya (2021). "A new series solution associated with the quantum harmonic oscillator", Optik, Vol. 25.A new series solution associated with the quantum harmonic oscillator(2021) Umul, Yusuf Ziya; 42699In the non-relativistic case, the problem of quantum harmonic oscillator is solved by the aid of the Schro spacing diaeresis dinger equation. An additional term of potential energy that is related with the square of the spatial coordinate is also included in the equation. A second order linear differential equation is obtained in the stationary state. The direct solution gives the wave function in terms of the parabolic cylinder functions. This solution leads to the Hermite polynomials when the quantization of energy is considered. However, the derived expression of the wave function does not yield the correct functions for the limiting case, in which the potential energy is zero. We put forth an alternative solution for the second order linear differential equation. First of all, a new series expression is suggested as an ansatz for the power series solution of differential equations. The coefficients of the series are obtained in terms of recurrence relations. Some computational simulations are given.Article Citation Count: Umul, Yusuf Ziya (2021). "A relativistic electron interacting with electromagnetic waves", Optik, Vol. 231.A relativistic electron interacting with electromagnetic waves(2021) Umul, Yusuf Ziya; 42699A relativistic electron, in an electromagnetic wave is studied. The relativistic energy-momentum relation is taken into consideration for the derivation of a wave equation for spin-1/2 particle. The electromagnetic wave is represented by the electric scalar and magnetic vector potentials. Thus the spin information of the electron is integrated into the relativistic differential equation. A relativistic quantum wave equation is derived by using the derivatives with respect to time and spatial coordinates with respect to the kinetic energy and momentum of the electron. It is shown that the obtained relativistic equation directly reduces to the Pauli equation in the non-relativistic limit.Editorial Citation Count: Umul, Yusus Ziya, "A survey of the new proposal about the photon momentum", Optik, Vol.148, pp.342-343, (2017).A survey of the new proposal about the photon momentum(Elsevier GMBH, 2017) Umul, Yusuf Ziya; 42699Bahadoran et al. [1] proposed that the new approach to photon momentum, introduced by Umul [2], was not correct, because they obtained a negative energy expression for the absorbed photon. In this comment, we show that this proposal is wrong, since the related authors made a mistake in their derivations.Article Citation Count: Umul, Yusuf Ziya, "A survey on Klein paradox", Optik, Vol. 181, pp. 258-263, (2019).A survey on Klein paradox(Elsevier GMBH, 2019) Umul, Yusuf Ziya; 42699The solution of the relativistic tunneling problem with the aid of the Klein-Gordon and kinetic energy based wave equations are reviewed. The behaviors of the transmitted and reflected wave functions by the potential barrier are studied for different values of the barrier's energy. The reason of the Klein's paradox is put forth in terms of the structures of the wave equations.Article Citation Count: Umul, Y.Z. (2017). A uniform function for the diffraction of spherical waves. Optik, 130, 963-975. http://dx.doi.org/10.1016/j.ijleo.2016.11.032A uniform function for the diffraction of spherical waves(Elsevier GMBH, 2017) Umul, Yusuf Ziya; 42699A function which occurs in the scattering problem of the spherical waves by a perfectly conducting half-plane is introduced for constructing the transition functions of the uniform theory of diffraction and uniform asymptotic theory of diffraction. The important properties of the function, related with the geometrical optics and diffracted field components, are derived mathematically. A uniform asymptotic theory of wedge diffraction is introduced based on the new function. The resultant field expressions-are investigated numerically.Article Citation Count: Umul, Yusuf Ziya (2021). "Airy-type relativistic matter wave", Optik, Vol. 247.Airy-type relativistic matter wave(2021) Umul, Yusuf Ziya; 4269A new relativistic Airy-type matter wave is introduced as a solution of the kinetic energy based wave equation. The parametric solution of the related differential equation is obtained. The total energy and momentum of the relativistic particle are derived by using a Bohmian type of decomposition of the kinetic energy based equation. The acceleration of the particle is also evaluated. The behavior of the matter wave is investigated numerically. © 2021 Elsevier GmbHArticle Citation Count: Umul, Y.Z. (2008). Alternative interpretation of the edge-diffraction phenomenon. Journal of the Optical Society of America A-Optics Image Science and Vision, 25(3), 582-587. http://dx.doi.org/10.1364/JOSAA.25.000582Alternative interpretation of the edge-diffraction phenomenon(Optical Soc Amer, 2008) Umul, Yusuf Ziya; 42699An alternative interpretation of the phenomenon of edge diffraction is proposed according to a new separation of the Fresnel function. The subfields are investigated in the problem of diffraction of a plane wave by a perfectly conducting half-plane, and the results are compared numerically with other interpretationsArticle Citation Count: Umul, Y.Z. (2010). Apertured paraxial Bessel beams. Journal of the Optical Society of America A-Optics Image Science and Vision, 27(3), 390-398.Apertured paraxial Bessel beams(Optical Soc Amer, 2010) Umul, Yusuf Ziya; 42699The paraxial Bessel beam is obtained by applying an approximation in the wavenumbers. The scattering of the beams by a circular aperture in an absorbing screen is investigated. The scattered fields are expressed in terms of the Fresnel integrals by evaluating the Kirchhoff diffraction integral in the paraxial approximation. The results are examined numericallyArticle Citation Count: Umul, Y.Z. (2010). Application of the complex point source method to the Schrodinger equation. Optics and Laser Technology, 42(8), 1323-1327. http://dx.doi.org/10.1016/j.optlastec.2010.04.012Application of the complex point source method to the Schrodinger equation(Elsevier Science Ltd, 2010) Umul, Yusuf Ziya; 42699The paraxial wave equation is a reduced form of the Helmholtz equation. Its solutions can be directly obtained from the solutions of the Helmholtz equation by using the method of complex point source. We applied the same logic to quantum mechanics, because the Schrodinger equation is parabolic in nature as the paraxial wave equation. We defined a differential equation, which is analogous to the Helmholtz equation for quantum mechanics and derived the solutions of the Schrodinger equation by taking into account the solutions of this equation with the method of complex point source. The method is applied to the problem of diffraction of matter waves by a shutterArticle Citation Count: Umul, Yusuf Ziya,"Application of the Method of Transition Boundary To the Half-Planes With Mixed Boundary Conditions",Optik, Vol. 205, (2020).Application of the Method of Transition Boundary To the Half-Planes With Mixed Boundary Conditions(Elsevier GMBH, 2020) Umul, Yusuf Ziya; 42699The scattering problems of waves by soft-hard and hard-soft half-planes are investigated by the method of transition boundary. The functional values at the transition boundaries are found to be identical to the ones for the soft and hard half-screens. It is shown that the factorization process should be applied by also taking into account the boundary conditions besides the principle of reciprocity. The exact diffracted field expressions are obtained for both of the half-planes.Article Citation Count: Umul, Y.Z. (2011). Babinet's principle in the Fraunhofer diffraction by a finite thin wire.Optik, 122(16), 1434-1436. http://dx.doi.org/10.1016/j.ijleo.2010.09.023Babinet's principle in the Fraunhofer diffraction by a finite thin wire(Elsevier GMBH, 2011) Umul, Yusuf Ziya; 42699The scattered waves by a thin finite wire are evaluated by using the Rayleigh-Sommerfeld integral in the Fraunhofer approximation. The scattered fields by the complementary thin wire are also obtained with the aid of the Babinet's principle. The scattering integrals are evaluated directly. It is shown that Babinet's principle holds excellently for this problem. The scattered fields are examined numericallyArticle Citation Count: Umul, Y.Z. (2011). Babinet's principle in the Fraunhofer diffraction by a finite thin wire. Optik, 122(16), 1434-1436. http://dx.doi.org/ 10.1016/j.ijleo.2010.09.023Babinet's principle in the Fraunhofer diffraction by a finite thin wire(Elsevier GMBH, 2011) Umul, Yusuf Ziya; 42699The scattered waves by a thin finite wire are evaluated by using the Rayleigh-Sommerfeld integral in the Fraunhofer approximation. The scattered fields by the complementary thin wire are also obtained with the aid of the Babinet's principle. The scattering integrals are evaluated directly. It is shown that Babinet's principle holds excellently for this problem. The scattered fields are examined numericallyArticle Citation Count: Umul, Y.Z. (2015). Beam diffraction by a resistive half-plane. Applied Optics, 54(10), 2665-2671. http://dx.doi.org/10.1364/AO.54.002665Beam diffraction by a resistive half-plane(Optical Soc Amer, 2015) Umul, Yusuf Ziya; 42699The scattering of a Gaussian beam by a resistive half-screen is investigated. Far-field approximation is used in evaluation of geometrical optics and diffracted waves. The uniform expression of the diffracted waves by the resistive half-plane, which was found with the Sommerfeld-Maliuzhinets method, is obtained. The scattered fields for the case of the beam incidence are evaluated with the technique of a complex point source. The resultant wave expressions are examined numerically.Article Citation Count: Umul, Yusuf Ziya, "Boundary diffraction wave theory approach to corner diffraction", Optik, Vol. 183, pp. 200-202, (2019).Boundary diffraction wave theory approach to corner diffraction(Elsevier GMBH, 2019) Umul, Yusuf Ziya; 42699The scattering process of plane waves by a discontinuous edge contour is studied with the three dimensional boundary diffraction wave theory. The edge and corner diffracted fields are obtained from the stationary phase and edge point evaluations of the line integral. A new corner diffraction coefficient is derived. The behaviors of the uniform edge and corner diffracted waves are investigated numerically.Article Citation Count: Umul, Y.Z. (2012). Boundary diffraction wave theory of junctions between two surfaces with different face impedances. Optics and Laser Technology, 44(5), 1312-1317. http://dx.doi.org/10.1016/j.optlastec.2011.12.038Boundary diffraction wave theory of junctions between two surfaces with different face impedances(Elsevier Science Ltd, 2012) Umul, Yusuf Ziya; 42699The line integral of the boundary diffraction wave theory is derived for the diffraction process of waves by a junction between two surfaces with different face impedances. The exact solution of Maliuzhinets is used with this aim. The resultant integral is applied to the diffraction of waves by a circular junction between two impedance surfaces. The results are examined numerically.Article Citation Count: Umul, Y.Z. (2011). Boundary diffraction wave theory of resistive surfaces with edge discontinuities. Optics Communications, 284(22), 5269-5274. http://dx.doi.org/10.1016/j.optcom.2011.07.068Boundary diffraction wave theory of resistive surfaces with edge discontinuities(Elsevier Science Bv, 2011) Umul, Yusuf Ziya; 42699The line integral of the boundary diffraction wave theory is derived by considering the exact diffracted fields of a resistive half-plane. The line integral is generalized for arbitrary resistive surface with edge discontinuity. The method is applied to the diffraction problem of waves by a convex resistive spherical reflector and the resultant field expressions are investigated numericallyArticle Citation Count: Umul, Y.Z. (2009). Closed form series solution of the diffraction problem of plane waves by an impedance half-plane. Journal of Optics A-Pure and Applied Optics, 11(4). http://dx.doi.org/10.1088/1464-4258/11/4/045709Closed form series solution of the diffraction problem of plane waves by an impedance half-plane(IOP Publishing Ltd, 2009) Umul, Yusuf Ziya; 42699The scattering problem of plane waves by an impedance half-plane is solved by using the method of separation of variables, and a closed form series expression, which separately reduces to the cases of soft and hard half-planes, is obtained. The results are investigated numerically and compared with the solutions in the literature
