Propagation of polychromatic Gaussian beams through thin lenses

Abstract

The transformation by a lens of a polychromatic laser beam composed of on-axis superposed monochromatic TEM00 Gaussian modes in the paraxial approximation is studied. The chromatic aberrations are described by allowing the waist position on the z axis and the Rayleigh range to depend on wavelength. The beam radius, the far-field divergence, the Rayleigh range, the beam product, the beam propagation factor, and the kurtosis parameter are calculated. The relationship between the fourth-order and the second-order moments of Hermite-Gaussian and Laguerre-Gaussian modes is obtained and is used for calculating kurtosis parameter. The results are generalized to polychromatic modes of higher orders. It is shown that the on-axis superposition of monochromatic TEM00 modes with no chromatic aberration is leptokurtic.

Beam propagation ratios measurement based on transmissive liquid crystal spatial light modulator

“…However, by geometrical transformations, the beam propagation ratios (M 2 ) can be calculated by the parameters related to the incident and emergent Gaussian beam. As the theory mentioned by Luis [12], an input Gaussian beam, with squared waist radius 2 0 w , Rayleigh range R z and waist position on z axis w z is transformed by a thin lens. As is shown in Figure 4, the waist position on the z axis ws z , the Rayleigh range RS z and the squared waist radius 2 0S w can be given by the formulas…”

“…Lens Therefore, by combining the expressions (8)- (12), the squared beam radius of Gaussian beam in a plane located at a distance z from the lens can be given by       2 2 2 2 2 2 2 , , , , , , 2 2 2 2 , , , …”

Femtosecond filamentation in sapphire with diffractive lenses

“…In order to account for the beam quality we estimated the quality factor, M 2 , following the procedure ISO/DIS 11146. For a real beam transformed by a lens, the radius at 1∕e 2 of intensity along the propagation axis (which can be easily related to the FWHM) changes according to the following equation [29]:…”

“…For the estimation of M 2 we have chosen λ 440 nm (the central wavelength of the peaked blue structure). A rigorous analysis for polychromatic light can be found in [29].…”

Free-Motion Beam Propagation Factor Measurement by Means of a Liquid Crystal Spatial Light Modulator

“…We are interested in how the changes in the focal length affect to beam parameters after the lens and how to express these changes in terms of the input beam parameters. By geometrical transformations, it is straightforward to obtain the formulas that relate the parameters of the incident beam to those of the beam that emerges from the lens (with "s" subscript) [1,18]. In this way, we find for both the horizontal and the vertical directions…”