Elektronik ve Haberleşme Mühendisliği Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/260
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Article Diffraction in Time of Matter Waves Located in a Confined Region(Springer Heidelberg, 2022) Umul, Yusuf Z.The process of diffraction in time of a standing matter wave is studied. This case occurs generally when a quantum particle is confined in a trap or infinite potential well. First of all, the wave-function of a classical time diffracted matter wave is studied by considering a separation of the Fresnel function in terms of geometrical optics and diffracted waves. The behavior of the matter wave which is the counterpart of a geometrical optics field is investigated. Then a confined particle in a one-dimensional infinite potential well is taken into account. One of the walls of the trap is remained at an initial time and the process of diffraction in time is formulated by using the information, obtained from the geometrical optics fields. Some numerical results are given. This paper proposes two original approaches. The first one is the application of the optical diffraction theory to quantum physics. This is the separation of the scattered field into geometric optics and diffracted wave components. The second novelty is the addition of the effects of both of the traveling waves, which compose the standing wave, to the scattering integral.Article Citation - WoS: 31Citation - Scopus: 36Beam Wander of Dark Hollow, Flat-Topped and Annular Beams(Springer Heidelberg, 2008) Cil, C. Z.; Eyyuboglu, H. T.Benefiting from the earlier derivations for the Gaussian beam, we formulate beam wander for dark hollow (DH) and flat-topped (FT) beams, also covering the annular Gaussian (AG) beam as a special case. Via graphical illustrations, beam wander variations of these beams are analyzed and compared among themselves and to the fundamental Gaussian beam against changes in propagation length, amplitude factor, source size, wavelength of operation, inner and outer scales of turbulence. These comparisons show that in relation to the fundamental Gaussian beam, DH and FT beams will exhibit less beam wander, particularly at small primary beam source sizes, lower amplitude factors of the secondary beam and higher beam orders. Furthermore, DH and FT beams will continue to preserve this advantageous position all throughout the considered range of wavelengths, inner and outer scales of turbulence. FT beams, in particular, are observed to have the smallest beam wander values among all, up to certain source sizes.Article Citation - WoS: 10Citation - Scopus: 12Scintillation Behavior of Cos, Cosh and Annular Gaussian Beams in Non-Kolmogorov Turbulence(Springer Heidelberg, 2012) Eyyuboglu, H. T.For a non-Kolmogorov spectrum, scintillation aspects of cos, cosh and annular Gaussian beams are investigated. The appropriate mathematical formulation is developed, the derived scintillation index is evaluated and its variation is plotted in graphs. We find that, when the values of the power coefficient of the spectrum are just above 3, low scintillation is encountered, then as the power coefficient is increased, rises will occur with a peak being reached around 3.21. From there onwards, scintillation will drop, as the power coefficient approaches a value of 5. For extreme off-axis positions, there will be slight increases in scintillation at high power coefficient values. At points near on-axis and when the beams have small width sizes, cosh Gaussian beam having a bigger displacement parameter will offer the lowest scintillation. At large width sizes, this advantage will switch to the side of the cos Gaussian beam. In this study, the variation of scintillation with other sources and propagation parameters is examined as well.Article Citation - WoS: 24Citation - Scopus: 27Partially Coherent Airy Beam and Its Propagation in Turbulent Media(Springer Heidelberg, 2013) Sermutlu, Emre; Eyyuboglu, Halil T.The properties of partially coherent Airy beam propagating in turbulent media are investigated. Firstly the variations in the intensity profile and the location of the Airy beam peak with respect to dislocation and width parameters are examined. On the source plane, it is shown that there is a threshold value of the dislocation parameter which determines whether the beam peak will lie on the negative or positive side of the axis. The changes in source beam power and source beam size with respect to dislocation and width parameters are also examined. Then analysis is made for partially coherent Airy beam propagating in turbulence against variations in propagation distance, dislocation and width parameters, structure constant and partial coherence. It is found that the peak of the Airy beam will always shift to the right for increasing propagation distance. But this shift will become less as the dislocation and width parameters are increased. Finally it is shown that higher levels of turbulence and partial coherence will lead to more spreading and shift the beam peak more toward the on-axis position.Article Citation - WoS: 5Citation - Scopus: 6Effect of Spatial Coherence on the Scintillation Properties of a Dark Hollow Beam in Turbulent Atmosphere(Springer Heidelberg, 2013) Yuan, Yangsheng; Chen, Yahong; Liang, Chunhao; Cai, Yangjian; Baykal, YahyaWith the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.Article Citation - WoS: 5Citation - Scopus: 6Scintillations of Multiwavelength Gaussian, Cos, Cosh and Annular Gaussian Beams(Springer Heidelberg, 2012) Eyyuboglu, Halil T.We provide the scintillation formulation for a multiwavelength source. Within this context, the scintillation aspects of Gaussian, cos, cosh and annular Gaussian beams are investigated. For all situations examined, it is found that for a source comprising many wavelengths, there will be less scintillations as compared to a single wavelength source of the lowest wavelength and but the reverse will be true if the comparison is with respect to the single wavelength source of the highest wavelength. The same is observed at all propagation distances, source sizes, on-axis and off-axis positions considered. Additionally, it is seen that the scintillation characteristics of multiwavelength sources will follow similar trends of single wavelength sources. The analysis is based on the Rytov approximation, therefore our results are valid for conditions of weak atmospheric turbulence.Article Citation - WoS: 16Citation - Scopus: 16Annular, Cosh and Cos Gaussian Beams in Strong Turbulence(Springer Heidelberg, 2011) Eyyuboglu, Halil T.For the strong atmospheric turbulence regime, the asymptotic on-axis scintillation behavior of annular, cosh and cos Gaussian beams is theoretically derived and illustrated with numerical examples. It is observed from the plots that annular Gaussian beams exhibit more scintillations than a Gaussian beam, regardless of the amplitude coefficient and source size settings. For small source sizes, cosh Gaussian beams seem to have an advantage over Gaussian beams in terms of reduced scintillation, but for large source sizes a switchover occurs where cos Gaussian beams assume the advantage. Analysis of the effect of inner scale value shows that scintillations increases for all beams as the inner scale increases.Article Citation - WoS: 33Citation - Scopus: 39Turbulence Distance of Radial Gaussian Schell-Model Array Beams(Springer Heidelberg, 2010) Li, X.; Ji, X.; Eyyuboglu, H. T.; Baykal, Y.The effect of turbulence on the spreading of radial Gaussian Schell-model (GSM) array beams is studied quantitatively by examining the mean-squared beam width. The analytical expression for the turbulence distance z (T) of radial GSM array beams is derived by using the integral transform technique, which indicates within what ranges radial GSM array beams will be less affected by turbulence. It is shown that the effect of turbulence on the spreading of radial GSM array beams can be reduced by choosing the suitable array beam parameters and the type of the beam superposition. In addition, a comparison with the previous work is also made.Article Citation - WoS: 13Citation - Scopus: 15Partially Coherent Elegant Hermite-Gaussian Beams(Springer Heidelberg, 2010) Cai, Y.; Eyyuboglu, H. T.; Baykal, Y.; Cil, C. Z.; Wang, F.Elegant Hermite-Gaussian beams (EHGBs) are extended to the partially coherent case. An explicit and analytical formula is derived for the cross-spectral density of a partially coherent EHGB propagating through an aligned or misaligned paraxial ABCD optical system. The propagation properties of a partially coherent EHGB in free space and its focusing properties through a thin lens are studied numerically, and are compared to those of a partially coherent standard Hermite-Gaussian beam (SHGB). It is found that the propagation and focusing properties of a partially coherent EHGB are closely related to its initial coherence. A partially coherent EHGB spreads slower than a partially coherent SHGB in free-space propagation. A partially coherent EHGB can be focused more tightly than a partially coherent SHGB.Article Citation - WoS: 11An Analysis on Radius of Curvature Aspects of Hyperbolic and Sinusoidal Gaussian Beams(Springer Heidelberg, 2010) Eyyuboglu, H. T.; Ji, X.The effective radius of curvature of hyperbolic and sinusoidal Gaussian beams in free space and turbulent atmosphere is studied analytically and numerically. It is shown that the radius of curvature rises with growing source size, and changes slowly with wavelength. In general, given the same source and propagation settings, the beams can be listed in descending order of radius of curvature magnitudes as sinh Gaussian, cosh Gaussian, sine Gaussian, pure Gaussian and cos Gaussian beams. However, the radius of curvature and the difference of the radius of curvature between the different beams reduce with growing strength of turbulence because the beam's spatial phase distribution is destroyed by turbulence.