2013
DOI: 10.1016/j.optcom.2012.11.085
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Study of internal energy flows in dipole vortex beams by knife edge test

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Cited by 19 publications
(5 citation statements)
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“…We numerically calculated and experimentally obtained the intensity patterns of the modified BG vortex beam in the far field with various phase terms using Equation ( 3 I(x, y) and ⃗ ∇𝜃(x, y) are the intensity and the transverse phase gradient, respectively. [55] The energy flows also transformed into spiral forms as m ′ is increased, and the distributions of the flows are consistent with the intensity patterns. In Figure 3a1-a5, the density of distribution and the size of the arrows represent the intensity of the focused beam.…”
Section: Simulation and Experimentssupporting
confidence: 66%
“…We numerically calculated and experimentally obtained the intensity patterns of the modified BG vortex beam in the far field with various phase terms using Equation ( 3 I(x, y) and ⃗ ∇𝜃(x, y) are the intensity and the transverse phase gradient, respectively. [55] The energy flows also transformed into spiral forms as m ′ is increased, and the distributions of the flows are consistent with the intensity patterns. In Figure 3a1-a5, the density of distribution and the size of the arrows represent the intensity of the focused beam.…”
Section: Simulation and Experimentssupporting
confidence: 66%
“…An analogy between azimuthons (found in nonlinear media) and rotating transverse energy flow structures in paraxial beams is demonstrated in [241]. Patterns of energy flows in dipole vortex beams were studied using a knife-edge test [242]. Effect of astigmatism [243] and coma [244] on the transverse energy distributions was also investigated.…”
Section: Literature Survey Of Phase and Polarization Singularitiesmentioning
confidence: 99%
“…For positive TCs, the intensity and phase gradients have opposite directions, whereas for negative TCs, the directions are the same. [ 55 ] The energy flows are computed as transverse components of the Poynting vector as follows: [ 56 ] 〈〉J=c4πεD×Bnewline=c8πεiωEEEE+2ωk||E2trueez$$\begin{eqnarray} \left\langle {\vec{J}} \right\rangle &=& \frac{c}{{4\pi \varepsilon }}\left\langle {\vec{D} \times \vec{B}} \right\rangle\nonumber\\ &=& \frac{c}{{8\pi \varepsilon }}\left( {i\omega \left( {E{\nabla }_ \bot {E}^* - {E}^*{\nabla }_ \bot E} \right) + 2\omega k{{\left| E \right|}}^2{{\vec{e}}}_z} \right) \end{eqnarray}$$where c denotes the speed of light in vacuum, ε is the permittivity, D$\vec{D}$ and B$\vec{B}$ represent the electric and magnetic fields, respectively, =exx+eyy${\nabla }_ \bot = {\vec{e}}_x\frac{\partial }{{\partial x}} + {\vec{e}}_y\frac{\partial }{{\partial y}}$ is used to calculate the transverse gradient of E , and E${E}^ * $ denotes the complex conjugate beam of E . The energy flow of the HO‐OVL was numerically simulated using Equation (10).…”
Section: Resultsmentioning
confidence: 99%
“…For positive TCs, the intensity and phase gradients have opposite directions, whereas for negative TCs, the directions are the same. [55] The energy flows are computed as transverse components of the Poynting vector as follows: [56] ⟨…”
Section: Resultsmentioning
confidence: 99%