Browsing by Subject "Numerical computations"
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Item Open Access Fast and accurate algorithm for the computation of complex linear canonical transforms(Optical Society of America, 2010-08-05) Koç A.; Özaktaş, Haldun M.; Hesselink, L.A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in ∼N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.Item Open Access Fast and accurate computation of two-dimensional non-separable quadratic-phase integrals(Optical Society of America, 2010-05-12) Koç A.; Özaktaş, Haldun M.; Hesselink, L.We report a fast and accurate algorithm for numerical computation of two-dimensional non-separable linear canonical transforms (2D-NS-LCTs). Also known as quadratic-phase integrals, this class of integral transforms represents a broad class of optical systems including Fresnel propagation in free space, propagation in gradedindex media, passage through thin lenses, and arbitrary concatenations of any number of these, including anamorphic/astigmatic/non- orthogonal cases. The general two-dimensional non-separable case poses several challenges which do not exist in the one-dimensional case and the separable two-dimensional case. The algorithm takes ∼ñ log ñ time, where ñ is the two-dimensional space-bandwidth product of the signal. Our method properly tracks and controls the space-bandwidth products in two dimensions, in order to achieve information theoretically sufficient, but not wastefully redundant, sampling required for the reconstruction of the underlying continuous functions at any stage of the algorithm. Additionally, we provide an alternative definition of general 2D-NS-LCTs that shows its kernel explicitly in terms of its ten parameters, and relate these parameters bidirectionally to conventional ABCD matrix parameters.Item Open Access Investigation of p-type depletion doping for InGaN/GaN-based light-emitting diodes(American Institute of Physics Inc., 2017) Zhang, Y.; Zhang Z.-H.; Tan S.T.; Hernandez-Martinez, P. L.; Zhu B.; Lu S.; Kang, X. J.; Sun, X. W.; Demir, Hilmi VolkanDue to the limitation of the hole injection, p-type doping is essential to improve the performance of InGaN/GaN multiple quantum well light-emitting diodes (LEDs). In this work, we propose and show a depletion-region Mg-doping method. Here we systematically analyze the effectiveness of different Mg-doping profiles ranging from the electron blocking layer to the active region. Numerical computations show that the Mg-doping decreases the valence band barrier for holes and thus enhances the hole transportation. The proposed depletion-region Mg-doping approach also increases the barrier height for electrons, which leads to a reduced electron overflow, while increasing the hole concentration in the p-GaN layer. Experimentally measured external quantum efficiency indicates that Mg-doping position is vitally important. The doping in or adjacent to the quantum well degrades the LED performance due to Mg diffusion, increasing the corresponding nonradiative recombination, which is well supported by the measured carrier lifetimes. The experimental results are well numerically reproduced by modifying the nonradiative recombination lifetimes, which further validate the effectiveness of our approach.Item Open Access Nonradiative recombination-Critical in choosing quantum well number for InGaN/GaN light-emitting diodes(Optical Society of American (OSA), 2015) Zhang, Y.P.; Zhang, Z.-H.; Liu W.; Tan, S.T.; Ju, Z.G.; Zhang X.L.; Ji, Y.; Wang L.C.; Kyaw, Z.; Hasanov, N.; Zhu, B.B.; Lu, S.P.; Sun X.W.; Demir, Hilmi VolkanIn this work, InGaN/GaN light-emitting diodes (LEDs) possessing varied quantum well (QW) numbers were systematically investigated both numerically and experimentally. The numerical computations show that with the increased QW number, a reduced electron leakage can be achieved and hence the efficiency droop can be reduced when a constant Shockley-Read-Hall (SRH) nonradiative recombination lifetime is used for all the samples. However, the experimental results indicate that, though the efficiency droop is suppressed, the LED optical power is first improved and then degraded with the increasing QW number. The analysis of the measured external quantum efficiency (EQE) with the increasing current revealed that an increasingly dominant SRH nonradiative recombination is induced with more epitaxial QWs, which can be related to the defect generation due to the strain relaxation, especially when the effective thickness exceeds the critical thickness. These observations were further supported by the carrier lifetime measurement using a pico-second time-resolved photoluminescence (TRPL) system, which allowed for a revised numerical modeling with the different SRH lifetimes considered. This work provides useful guidelines on choosing the critical QW number when designing LED structures. © 2014 Optical Society of America.Item Open Access Numerical computation of H∞ optimal controllers for time delay systems using YALTA(Elsevier B.V., 2016) Yeğin, M. O.; Özbay, HitayNumerical computation of H∞ controllers for time delay systems has been a challenge since 1980s. Even though significant techniques are developed to obtain direct optimal controllers, application of these methods may require manual computation depending on the plant. In this paper, an alternative computational technique is proposed for direct optimal controllers originally obtained by Toker and Özbay (1995). The new controller expression contains finite dimensional transfer functions and an infinite dimensional term, which is stable. Thus it is suitable for finite dimensional approximations and practical non-fragile implementations. In this method, in order to eliminate manual computation of the plant factorization for neutral and retarded delay systems YALTA (a tool developed at INRIA) is used. The new controller computation is implemented in Matlab, and it is illustrated on an example. © 2016