Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?

Sze, Michelle Wynne C.; Sugon, Quirino M.; McNamara, Daniel J.

doi:10.1364/josaa.27.002468

Cited by 2 publications

(6 citation statements)

References 6 publications

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“…As the near-field amplitude at the gap increases, therefore, the destructive interference of the reflected beam from metal and diffracted beam from the gaps in turn leads to a larger decrease in the zeroth-order reflection from the incident side. While there are reports on nonconservation of energy-momentum under oblique superposition of two out-of-phase waves [38], it would be more reasonable to understand the observed extinction in terms of change in the phase relation creating another path where the two beams constructively interfere, leading to energy transfer into other directions that the detection scheme cannot collect. This interpretation suggests an interesting possibility for the case of nanogaps coupled with an absorbing material.…”

Section: Q K L Tmentioning

confidence: 97%

Anomalous extinction in index-matched terahertz nanogaps

et al. 2017

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Slot-type nanogaps have been widely utilized in transmission geometry because of their advantages of exclusive light funneling and exact quantification of near-field enhancement at the gap. For further application of the nanogaps in electromagnetic interactions with various target materials, complementary studies on both transmission and reflection properties of the nanogaps are necessary. Here, we observe an anomalous extinction of terahertz waves interacting with rectangular ring-shaped sub-30 nm wide gaps. Substrate works as an index matching layer for the nanogaps, leading to a stronger field enhancement and increased nonlinearity at the gap under substrate-side illumination. This effect is expressed in reflection as a larger dip at the resonance, caused by destructive interference of the diffracted field from the gap with the reflected beam from the metal. The resulting extinction at the resonance is larger than 60% of the incident power, even without any absorbing material in the whole nanogap structure. The extinction even decreases in the presence of an absorbing medium on top of the nanogaps, suggesting that transmission and reflection from nanogaps might not necessarily represent the absorption of the whole structure.

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Section: Q K L Tmentioning

confidence: 97%

Anomalous extinction in index-matched terahertz nanogaps

et al. 2017

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“…Maxwell's equation for electromagnetic fields in free space can be expressed in geometric algebra as a single equation [29,30]:…”

Section: A Maxwell's Equationmentioning

confidence: 99%

“…are the electromagnetic field [29,31] and the space-time derivative operator, respectively. Distributing the space-time derivative operator and applying the definition of the geometric product to the nabla operator, we get…”

Section: A Maxwell's Equationmentioning

confidence: 99%

“…Because ω=c ¼ k by the wave condition [29] and We may also rewrite Eq. (42) in a coordinate-free way as…”

Section: B Circularly and Elliptically Polarized Electromagnetic Wavesmentioning

confidence: 99%

“…In general, the solution to Maxwell's equation with frequency ω is a linear superposition of wave functionsψ −1 andψ [29]:…”

Section: Representations Of Polarization Ellipsementioning

confidence: 99%

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Polarization ellipse and Stokes parameters in geometric algebra

2011

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In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

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Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?

Cited by 2 publications

References 6 publications

Anomalous extinction in index-matched terahertz nanogaps

Anomalous extinction in index-matched terahertz nanogaps

Polarization ellipse and Stokes parameters in geometric algebra

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