Sampling rules in the frequency domain for numerical propagation of ultrashort pulses through linear dielectrics

Veetil, Suhas P.; Vijayan, C.; Sharma, Diksha; Schimmel, Hagen; Wyrowski, Frank

doi:10.1364/josab.23.002227

Cited by 5 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have, for example, considered propagation in free space only and therefore assumed a constant, wavelength-independent, refractive index. The different spectral components that make up a pulse, traveling, for example, in an optic fiber, "see" different refractive indices [15,16]. This will change sampling conditions derived here.…”

Section: Resultsmentioning

confidence: 99%

“…We do note that a sampling rule is presented in [15] stipulating that the phase difference between subsequent spectral components may not exceed 2. We believe the analysis presented in this paper complements that in [15], providing an intuitive graphical picture that describes how undersampling the pulse results in numerical artifacts in the spatial domain.…”

Section: Resultsmentioning

confidence: 99%

“…(1a) [15,16,22]. Using the retarded time is also advantageous from a numerical point of view, since removing the linear phase term can greatly reduce the number of samples required to represent the signal [15,16,22]. Also, we note that with z = 0, the time t R = t =0 refers to that instant when the peak pulse amplitude fills the aperture.…”

Section: Theoretical Analysismentioning

confidence: 99%

“…These pulses are in common use in areas such as optical coherence tomography, confocal microscopy, terahertz (THz) generation and detection, and spectroscopy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Pulses generated in fs sources tend to have a broad spectrum ͑ϳ20 nm͒ consisting of many different wavelengths and so differ from the approximately monochromatic light produced by most standard lasers.…”

Section: Introductionmentioning

confidence: 99%

“…The diffracted spatial-temporal pulse is then found by performing an inverse Fourier transform (with respect to the temporal frequency) on this spatial-spectral distribution [11,13,14]. In some cases, analytical expressions describing the spatialtemporal distribution exist [13], however, in order to analyze general diffraction problems, it is important to develop complementary numerical techniques [15,16,22]. Since many different spectral components contribute to a pulse's diffraction pattern, a fast numerical technique for calculating the diffraction pattern formed by a single wavelength is clearly important.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Numerical sampling rules for paraxial regime pulse diffraction calculations

et al. 2008

View full text Add to dashboard Cite

Sampling rules for numerically calculating ultrashort pulse fields are discussed. Such pulses are not monochromatic but rather have a finite spectral distribution about some central (temporal) frequency. Accordingly, the diffraction pattern for many spectral components must be considered. From a numerical implementation viewpoint, one may ask how many of these spectral components are needed to accurately calculate the pulse field. Using an analytical expression for the Fresnel diffraction from a 1-D slit, we examine this question by varying the number of contributing spectral components. We show how undersampling the spectral profile produces erroneous numerical artifacts (aliasing) in the spatial-temporal domain. A guideline, based on graphical considerations, is proposed that determines appropriate sampling conditions. We show that there is a relationship between this sampling rule and a diffraction wave that emerges from the aperture edge; comparisons are drawn with boundary diffraction waves. Numerical results for 2-D square and circular apertures are presented and discussed, and a potentially time-saving calculation technique that relates pulse distributions in different z planes is described.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Theoretical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical sampling rules for paraxial regime pulse diffraction calculations

et al. 2008

View full text Add to dashboard Cite

show abstract

Fast numerical algorithm for ultrashort THz pulse diffraction

et al. 2007

View full text Add to dashboard Cite

Gaussian pulsed beam decomposition for propagation of ultrashort pulses through optical systems

Worku

Groß

2019

J. Opt. Soc. Am. A

View full text Add to dashboard Cite

Many applications of ultrashort laser pulses require manipulation and control of the pulse parameters by propagating them through different optical components before the target. This requires methods of simulating the pulse propagation taking into account all effects of dispersion, diffraction, and system aberrations. In this paper, we propose a method of propagating ultrashort pulses through a real optical system by using the Gaussian pulsed beam decomposition. An input pulse with arbitrary spatial and temporal (spectral) profiles is decomposed into a set of elementary Gaussian pulsed beams in the spatiospectral domain. The final scalar electric field of the ultrashort pulse after propagation is then obtained by performing the phase correct superposition of the electric fields all-Gaussian pulsed beams, which are propagated independently through the optical system. We demonstrate the application of the method by propagating an ultrashort pulse through a focusing aspherical lens with large chromatic aberration and a Bessel-X pulse generating axicon lens.

show abstract

Sampling rules in the frequency domain for numerical propagation of ultrashort pulses through linear dielectrics

Cited by 5 publications

References 16 publications

Numerical sampling rules for paraxial regime pulse diffraction calculations

Numerical sampling rules for paraxial regime pulse diffraction calculations

Fast numerical algorithm for ultrashort THz pulse diffraction

Gaussian pulsed beam decomposition for propagation of ultrashort pulses through optical systems

Contact Info

Product

Resources

About