The use of the stationary phase method as a mathematical tool to determine the path of optical beams

Carvalho, Silvânia A.

doi:10.1119/1.4898044

Cited by 27 publications

(29 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Observing that and this is exactly the prediction of Geometric Optics by using the Snell and reflection laws [7]. Is is also interesting to observe that for an incidence greater than the critical one the Fresnel coefficient gains an additional phase…”

Section: Fresnel Coefficients and Optical Phasesupporting

confidence: 71%

“…Due to the fact that the left (AB) and right (CD) interfaces have discontinuities along the z-axis (the perpendicular direction to the left/right prism boundaries), it is convenient, as it is used to be done in Quantum Mechanics [7], to introduce, for the transversal block [see Fig. 1(a)] the coordinate system (x , y , z).…”

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

“…The same can be done for the up (BC) and down (AD) dielectric/air discontinuities whose normal is along the z * -axis, by introducing the coordinate system (x , y * , z * ). The changes in the wave number components occur in the direction perpendicular to the discontinuity and the reflection and transmission coefficients obtained by a like potential step analysis [7]. These reflection and transmission coefficients have to reproduce the well-known Fresnel coefficients in the plane wave limit and contain the information on the geometrical structure of the block in their geometrical phase coming from the position in which the air/dielectric or dielectric/air interface are located.…”

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

“…Let us now obtain the geometrical optical phase. When doing it, we have to observe that the continuity equation for the electric field imposes the presence of exponential factors in the reflection and transmission coefficients, taking into account the normal distance between the discontinuities [7]. For the reflection coefficient the exponential factor contains the term 2 × reflection wave number × normal distance = 2 q z * AB √ 2 and for the transmission coefficient…”

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

“…for detail see refs. [7,11]. Finally, the geometrical phase for the transversal bock [TB] is given by…”

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

See 4 more Smart Citations

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

Carvalho¹

2018

Journal of Modern Optics

Self Cite

View full text Add to dashboard Cite

When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Hänchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay. arXiv:1901.07279v1 [physics.optics]

show abstract

Section: Fresnel Coefficients and Optical Phasesupporting

confidence: 71%

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

“…for detail see refs. [7,11]. Finally, the geometrical phase for the transversal bock [TB] is given by…”

Section: Fresnel Coefficients and Optical Phasementioning

confidence: 99%

See 3 more Smart Citations

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

Carvalho¹

2018

Journal of Modern Optics

Self Cite

View full text Add to dashboard Cite

show abstract

Optimizing Weak Measurements to Detect Angular Deviations

Araújo

Maia

2017

Annalen der Physik

Self Cite

View full text Add to dashboard Cite

Optimizing weak measurements to detect angular deviationsW e analyze and compare the angular deviations for an optical beam reflected by and transmitted through a dielectric triangular prism. The analytic expressions derived for the angular deviations hold for arbitrary incidence angles. For incidence approaching the internal and external Brewster angles, the angular deviations transverse magnetic waves present the same behavior leading to the well-known giant Goos-Hänchen angular shift. For incidence near the critical angle a new region of large shift is seen both for transverse magnetic and transverse electric waves. While a direct measuring procedure is better in the vicinity of the Brewster region, a weak measurement breaks off the giant Goos-Hänchen effect, preserving the amplification in the critical region. We discuss under which conditions it is possible to optimize the amplification and we also determine when a weak measurement is preferred to a direct measuring procedure.

show abstract

Ferroelectric perovskites as electro-optic switching devices, modulators and optical memory

Mitra

Prusty

Manju

2023

Perovskite Metal Oxides

View full text Add to dashboard Cite

The use of the stationary phase method as a mathematical tool to determine the path of optical beams

Cited by 27 publications

References 37 publications

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

Optimizing Weak Measurements to Detect Angular Deviations

Ferroelectric perovskites as electro-optic switching devices, modulators and optical memory

Contact Info

Product

Resources

About