Elements of Photonics, Volume II

Iizuka, Keigo

doi:10.1002/0471221376

Cited by 78 publications

(42 citation statements)

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“…The reason for this is that the mathematics used to describe skew rays is difficult. [5][6][7] The study of geometric optics ray tracing for skew rays is still an important problem for two reasons. The first is pedagogical: skew ray tracing for laser light in large fibers, e.g., HeNe laser in 1 cm diameter glass fiber, can be used to verify the helical properties of skew rays in a student laboratory.…”

Section: Introductionmentioning

confidence: 99%

Skew ray tracing in a step-index optical fiber using geometric algebra

2015

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We used Geometric Algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the law of refraction, and the juxtaposed vector product form for the law of reflection. In particular, the exponential forms of the vector rotations enables us to take advantage of the addition or subtraction of exponential arguments of two rotated vectors in the derivation of the ray tracing invariants in cylindrical and spherical coordinates. We showed that the light rays inside the optical fiber trace a polygonal helical path characterized by three invariants that relate successive reflections inside the fiber: the ray path distance, the difference in axial distances, and the difference in the azimuthal angles. We also rederived the known generalized formula for the numerical aperture for skew rays, which simplifies to the standard form for meridional rays.

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Section: Introductionmentioning

confidence: 99%

Skew ray tracing in a step-index optical fiber using geometric algebra

2015

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“…It would be possible to compensate for distortion as a post-processing step (not done in this work). Noise performance of APDs is an important consideration [191], as it limits the minimum optical intensity which can be accurately detected. Sensitivity at low incident power is limited by detector (thermal) noise, and at higher power levels by shot noise.…”

Section: 4: Scanners and Scan Mirrorsmentioning

confidence: 99%

GDx-MM: An Imaging Mueller Matrix Retinal Polarimeter

Twietmeyer

2007

Frontiers in Optics 2007/Laser Science XXIII/Organic Materials and Devices for Displays and Energy Conversion

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“…Let r and θ be the polar coordinates in the plane of incidence and assuming there to be no component of the field varying in the direction perpendicular to the plane of incidence (say, y-direction). Therefore, the propagation of e.m. radiation at the carrier wavelength λ in such a waveguide can be described by the Helmholtz equation [17] …”

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confidence: 99%

“…Here for definiteness, we use even integer m for even TE/TM modes (ϕ m = 0) and odd m for odd TE/TM modes (ϕ m = π/2) [17]. Under the circumstances, the propagation constant β in the r direction, defined through ψ m (r, θ) = Ψ(r, θ) exp(iβr) (here Ψ(r, θ) is the mode amplitude), can be found from the asymptotic expansion of H [19].…”

mentioning

confidence: 99%