Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

Hernández-Aranda, Raúl I.; Gutiérrez-Vega, Julio C.; Guizar‐Sicairos, Manuel; Bandres, Miguel A.

doi:10.1364/oe.14.008974

Cited by 32 publications

(13 citation statements)

References 23 publications

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“…This possibility has been analyzed in many publications [8][9][10][11] where examples are included. Again, the full discussion of this problem is beyond the scope of this paper.…”

Section: Discussionmentioning

confidence: 99%

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The Equivalent of Fourier Holography at the Nanoscale

2008

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The paper deals with optical holographic interferometry at the nanometric scale. The observed objects are sodium chloride nanocrystals. The object illumination is done through the use of evanescent wavefronts. The observed crystals become self-luminous objects producing pseudo-non-diffracting wavefronts. The wavefronts emerging from the crystals are the result of electromagnetic resonances of the crystals. A microscope is utilized to register the wavefronts generated by the crystals. A 6 μm spherical particle made of polystyrene acts as a relay lens to collect the wavefronts that are recorded by a monochromatic CCD and a color camera attached to the microscope. The structure of the recorded images is determined through Fourier transform analysis. It is shown that the recorded images are lens holograms formed by the interference of the wavefronts generated by the crystals. Fourier transform algorithms and edge detection algorithms are utilized to obtain the dimensions of the crystals. The power of Gabor's idea when he invented holography is again proven in this study. If the problem of super-resolution is viewed from the point of view of the Theory of Communications, the fact that one can register both amplitude and phase of a signal of a self-luminous object provides the means of reaching spatial resolutions with average standard deviation of ±3 nm using helium-neon laser illumination of l=632.8 nm. The resolution that can be achieved depends on the structure of the observed material, in the present case ±5d, where d is the distance of the atomic planes of the NaCl. With improvements in the hardware and software higher resolutions may be feasible.

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“…This possibility has been analyzed in many publications [8][9][10][11] where examples are included. Again, the full discussion of this problem is beyond the scope of this paper.…”

Section: Discussionmentioning

confidence: 99%

“…The produced wavefronts can travel long distances or go through an optical system without the diffraction changes experienced by ordinary wavefronts [8][9][10][11]. For the validity of this statement we refer to the cited references and to the pertaining literature cited in those studies.…”

Section: Description Of the Experimental Proceduresmentioning

confidence: 99%

The Equivalent of Fourier Holography at the Nanoscale

2008

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“…It was first suggested in reference [15] that the number of ring dislocations appearing in the cross correlation function are in a one to one correspondence with the topological charge of a partially coherent vortex. This assertion was reported later in 2012 by Yang et al 10 Following the theoretical results reported in our previous works 9, 15 and also those given by Yang et al 10 suggesting that the singularities in the CCF of a partially coherent OV are directly related to the topological charge, we designed an experimental setup to demonstrate this direct relationship between the topological charge in a partially coherent vortex and the number of ring dislocations present in the CCF.…”

Section: Introductionmentioning

confidence: 99%

Determination of angular momentum content in partially coherent beams through cross correlation measurements

et al. 2013

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A means to measure orbital angular momentum in a partially coherent beam is demonstrated by using a wavefront folding interferometer. This interferometer allows us to study the cross correlation function of a partially coherent vortex beam. It is shown that the cross correlation function possesses ring dislocations which are related to the topological charge of the partially coherent vortex, exhibiting a one to one correspondence between the number of rings and the value of the topological charge, thus providing a direct measure of the orbital angular momentum.

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“…The propagation properties of several beams in GRIN lenses are discussed by researchers via the approach of Fractional Fourier transform (FrFT), such as cosh-Gaussian beams, Ince-Gaussian beams, HelmholtzGauss beams and etc. [5][6][7][8][9][10][11][12][13] . The FrFT approach treats the GRIN lens as a single-lens equivalent optical system of FrFT, which adopts the approximation of the first-order optics.…”

Section: Introductionmentioning

confidence: 99%

A method to calculate arbitrary linear polarized laser beam evolutions in GRIN lenses

Tsai

Chu

2013

Complex Light and Optical Forces VII

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This study proposed a method for calculating any arbitrarily linear polarization paraxial optical field propagation in Gradient-index (GRIN) lens. The proposed method uses multiple thin-phase sheets to approximate a GRIN lens. This study also compares the proposed method with the other well-known method. That is, using a single lens equivalent optical system of Fractional Fourier transform (FrFT) to simulate a GRIN lens. The evolution in GRIN lenses of many special beams have been calculated by the FRFT-method. This study use both methods to calculate the Helmholtz-Gauss beam evolution in GRIN lenses of a small and a high gradient constant, respectively. Numerical results shows that the differences between two calculation methods appeared while the GRIN lens of a high gradient constant. This study provides an alternative approach could calculate the linearly polarized field evolution in GRIN lenses with higher precision, which will be useful to the optical design of GRIN lens systems.

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Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

Cited by 32 publications

References 23 publications

The Equivalent of Fourier Holography at the Nanoscale

The Equivalent of Fourier Holography at the Nanoscale

Determination of angular momentum content in partially coherent beams through cross correlation measurements

A method to calculate arbitrary linear polarized laser beam evolutions in GRIN lenses

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