Far-field diffraction characteristics of a time-variant Gaussian pulsed beam propagating from a circular aperture

Side-lobeless far-field spectrum of a short pulse from a circular aperture with Gaussian form of transmittance

“…(10).Fig. 3illustrates this property for different values of source bandwidth g( ¼ 1/o 0 t), and this property also can be found under other aperture dispersion cases[1][2][3][4][5][6][7][8][9][10][11][12][13]. The blue shift of the maximum of the spectral intensity I(0,o) is dependent on the source bandwidth g( ¼ 1/o 0 t).…”

“…In this work, we study the spectral characteristics of a time-dependent Gaussian pulse when it is incident on a circular aperture function with Gaussian form transmittance. It can be shown that the resultant diffracted intensity is completely free of the side-lobes, which appear in most of the aperture dispersion cases [1][2][3][4][5][6][7][8][9][10][11][12][13]. This side-lobeless effect can give important applications for optical engineering or optical communication where the side-lobes are not wanted.…”

“…It also includes the red or blue shift of the spectrum maximum or the distortion of the incident pulse's spectrum [1][2][3][4][5][6][7][8][9][10][11][12][13]. However, due to the oscillating properties of the aperture function in the spectral domain, as explained later, there are always some side-lobes found in the resultant diffraction spectrum [3][4][5][6][7][8][9][10][11][12][13].…”

“…It is also noted that Eq. (1) is usually used for a monochromatic incident field, U 0 (p 0 ,t) ¼ U 0 (p 0 ,o)e Àjot , with a single frequency o and the constant complex amplitude U 0 (p 0 ,o), but it is also applicable for a broad-band incident pulse [1][2][3][4][5][6][7][8][9][10][11][12][13], which can be superposed by monochromatic fields via the Fourier integral [15]. For a circular aperture with Gaussian form of transmittance, as shown in Fig.…”

“…For a comparison, the resultant spectral intensity I na (y,o) for a normal circular aperture with unit transmittance and radius a is [11] I na ðy; oÞ ¼ A 0 o 2 exp½Àðo À o 0 Þt 2 J 1 ðao sin y=cÞ ao sin y=c 2 , where A 0 ¼ t 2 a 4 /2pc 2 R 2 and the subscript na in I na (y,o) indicates the normal aperture.…”