Browsing by Subject "Chirp"
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Item Open Access All-fiber all-normal-dispersion femtosecond laser with nonlinear multimodal interference-based saturable absorber(Institute of Electrical and Electronics Engineers Inc., 2019) Teğin, Uğur; Ortaç, BülendChong et al. demonstrated a stable passively mode-locked all-normal-dispersion fiber laser and pulse generation is attributed to the strong spectral filtering of chirped pulses, dissipative soliton pulses [1]. In the following years, with very-large-mode-area fibers the energy and power scalability of the dissipative soliton pulses is demonstrated. Recently, multimodal interactions are subject to device studies with various configurations. Nazemosadat et al. theoretically proposed a short graded-index multimode fiber segment in between single mode fiber as a saturable absorber [2]. On the other hand, with similar device structure an all-fiber bandpass filter is later presented both numerically and experimentally [3].Item Open Access Effect of fractional Fourier transformation on time-frequency distributions belonging to the Cohen class(Institute of Electrical and Electronics Engineers, 1996-02) Özaktaş, Haldun M.; Erkaya, N.; Kutay, M. A.We consider the Cohen (1989) class of time-frequency distributions, which can be obtained from the Wigner distribution by convolving it with a kernel characterizing that distribution. We show that the time-frequency distribution of the fractional Fourier transform of a function is a rotated version of the distribution of the original function, if the kernel is rotationally symmetric. Thus, the fractional Fourier transform corresponds to rotation of a relatively large class of time-frequency representations (phase-space representations), confirming the important role this transform plays in the study of such representations.Item Open Access Optical implementations of two-dimensional fractional Fourier transforms and linear canonical transforms with arbitrary parameters(Optical Society of America, 1998-04-10) Sahin, A.; Özaktaş, Haldun M.; Mendlovic, D.We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be controlled at the same time but are simpler and employ a fewer number of lenses. The variety of systems discussed and the design equations provided should be useful in practical applications for which an optical fractional Fourier transforming stage is to be employed.Item Open Access Optimal filtering in fractional Fourier domains(Institute of Electrical and Electronics Engineers, 1997-05) Kutay, M. A.; Özaktaş, Haldun M.; Arıkan, OrhanFor time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N/sup 2/) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N log N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained.Item Open Access Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations(SPIE - International Society for Optical Engineering, 2004) Onural, L.The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.