Helmholtz Hodge decomposition of scalar optical fields

Bahl, Monika; Senthilkumaran, P.

doi:10.1364/josaa.29.002421

Cited by 25 publications

(8 citation statements)

References 26 publications

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“…Moreover, the superposition of positive and negative vortices produce circulating r/ x; y ð Þ transverse components that cancels out. These transverse components of k are responsible for internal energy flows within the transverse plane [30][31][32][33]. The electric field vector of a tilted interfering RCP/LCP beam, having propagation vector k making a small angle α with z-axis in the x-z plane, is given by:…”

Section: Phase Defectsmentioning

confidence: 99%

Singularities in cylindrical vector beams

Verma

Pal

Joshi

et al. 2015

Journal of Modern Optics

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Cylindrical vector beams with azimuthal and radial polarization distributions are studied for singularities. It is shown experimentally that these beams have screw dislocation as well as edge dislocation at the same time. The relation between phase and polarization of light beam is the key to understand this fact. We envisage that this has potential application in phase synthesis using polarization engineering. Further, the polarization singularities in these inhomogeneously polarized beams are examined by measuring Stokes parameters across the cross-section of these beams.

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Section: Phase Defectsmentioning

confidence: 99%

Singularities in cylindrical vector beams

Verma

Pal

Joshi

et al. 2015

Journal of Modern Optics

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“…This is a technique that can be used to analyze scalar optical fields [17], by separating them into solenoidal and irrotational components. Such fields are per se manifested in the interference and diffraction optics.…”

Section: Helmholtz-hodge Decompositionmentioning

confidence: 99%

“…The phase gradients at the focal plane are segmented into the solenoidal and irrotational components using the Helmholtz-Hodge decomposition (HHD) method [13][14][15][16][17]. The optical currents of the beam are clearly identified in the two components.…”

Section: Introductionmentioning

confidence: 99%

Internal energy flows of coma-affected singular beams in low-numerical-aperture systems

Bahl

Singh

et al. 2015

J. Opt. Soc. Am. A

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The circulating phase gradient component of a singular beam gets modified when focused by a low-numerical-aperature system suffering from coma aberration. The gradient due to this coma aberration splits the higher charge vortex into elementary vortices and distributes them spatially. This splitting depends on the charge and polarity of the incident singular beam as well as the sign and magnitude of the aberration coefficient. The transverse component of the Poynting vector field distribution at the focal plane is decomposed into the curl or solenoidal component and divergence or irrotational component using the Helmholtz-Hodge decomposition technique. The solenoidal component that relates to the orbital angular momentum carries the circulating energy, while the irrotational component shows the sources and sinks of the energy. Intriguing results of the study of energy flow around the edge dislocations apart from the point phase defects in the irrotational components are also presented.

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“…It had been applied to polarized vector fields and to reconstruct phase for wavefront distortions. We used HHD on scalar optical fields and studied the Orbital angular momentum (OAM) in diffraction optics that has been reported [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Data Visualization Using Hodge Decomposition - A Short Review

Bahl¹

2017

JNMR

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It has been seen that a vector field decomposition method called the Helmholtz Hodge Decomposition (HHD) can analyze scalar fields present universally in nature. It aids to reveal complex internal flows including energy flows in interference and diffraction optical fields. A gradient field defined in a region R, can be separated into solenoidal and irrotational components. HHD applied onto Magnetic Resonance Elasticity data can also aid to retain the curl field, while revealing the tissue elasticity in such medical measurements.

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Helmholtz Hodge decomposition of scalar optical fields

Cited by 25 publications

References 26 publications

Singularities in cylindrical vector beams

Singularities in cylindrical vector beams

Internal energy flows of coma-affected singular beams in low-numerical-aperture systems

Data Visualization Using Hodge Decomposition - A Short Review

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