Ray refraction in uniaxial crystals by Fermat’s principle

Wang, Pengqian

doi:10.1364/ao.57.004950

Cited by 6 publications

(3 citation statements)

References 26 publications

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“…However, it is not until recently that the equivalence between methods that use the electromagnetic wave theory and Huygens principle was formally shown [Wan18a]. Additional relevant work employs Fermat's principle [Wan18b] to derive ray directions and considers absorption in conductive crystals [WLXW08].…”

Section: Related Workmentioning

confidence: 99%

Analytic Spectral Integration of Birefringence‐Induced Iridescence

Steinberg¹

2019

Computer Graphics Forum

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Optical phenomena that are only observable in optically anisotropic materials are generally ignored in the computer graphics. However, such optical effects are not restricted to exotic materials and can also be observed with common translucent objects when optical anisotropy is induced, e.g. via mechanical stress. Furthermore accurate prediction and reproduction of those optical effects has important practical applications. We provide a short but complete analysis of the relevant electromagnetic theory of light propagation in optically anisotropic media and derive the full set of formulations required to render birefringent materials. We then present a novel method for spectral integration of refraction and reflection in an anisotropic slab. Our approach allows fast and robust rendering of birefringence‐induced iridescence in a physically faithful manner and is applicable to both real‐time and offline rendering.

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Section: Related Workmentioning

confidence: 99%

Analytic Spectral Integration of Birefringence‐Induced Iridescence

Steinberg¹

2019

Computer Graphics Forum

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“…The physics is a little bit complicated, and the corresponding mathematics is also some certain troublesome, especially when considering that LN crystal and many other nonlinear crystals are anisotropic materials rather than simple isotropic materials. There have existed some schemes that extensively only investigate the reflection and transmission of incident wave from isotropic medium to uniaxial crystal interface, [31][32][33][34][35][36][37][38][39] such as the classical electromagnetic theoretical analysis method. [37][38][39] However, the implementation of a specific SHG in PPLN crystal usually utilizes the collinear configuration where the pump FW light and generated SHW light beam is parallel.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution to incident angle quasi-phase-matching engineering for second harmonic generation in a periodic-poled lithium niobate crystal

Hong 洪,

Qiu 邱,

Li 李

et al. 2024

Chinese Phys. B

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Phase matching or quasi-phase matching (QPM) is of significant importance to the conversion efficiency of second harmonic generation (SHG) in artificial nonlinear crystals like lithium niobate (LN) crystal or microstructured nonlinear crystals like periodic-poled lithium niobate (PPLN) crystals. In this paper, we propose and show that the incident angle of pump laser light can be harnessed as an alternative versatile tool to engineer QPM for high-efficiency SHG in a PPLN crystal, in addition to conventional means of period adjusting or temperature tuning. A rigorous model is established and analytical solution of the nonlinear conversion efficiency under the small and large signal approximation theory is obtained at different incident angles. The variation of phase mismatching and walk-off length with incident angle or incident wavelength are also explored. Numerical simulations for a PPLN crystal with first order QPM structure are used to confirm our theoretical predictions based on the exact analytical solution of the general large-signal theory. The results show that the narrow-band tunable SHG output covers a range of 532-552.8 nm at the ideal incident angle from 0° to 90°. This theoretical scheme, fully considering the reflection and transmission at the air-crystal interface, would offer an efficient theoretical system to evaluate the nonlinear frequency conversion and help to obtain the maximum SHG conversion efficiency by selecting an optimum incident wavelength and incident angle in a specially designed PPLN crystal, which would be very helpful for the design of tunable narrow-band pulse nanosecond, picosecond, and femtosecond laser devices via PPLN and other microstructured LN crystals.

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“…Wang used the essential axiom in optical Fermat's principle to calculate the propagation of light, but the physical images were not explicitly shown. [13] For these reasons, in this paper we attack these shortcomings and difficulties by taking a different point of view. We intentionally only consider a simple model where the optical axis of the birefringent crystal is perpendicular to the crystal surface and focus on the propagation of the TM polarization light (i.e., extraordinary light) in the crystal, but neglect the TE polarization light as this case is just identical to the ordinary isotropic medium.…”

Section: Introductionmentioning

confidence: 99%

A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

Pan¹,

Chen²,

Hong³

et al. 2022

Chinese Phys. B

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Birefringence production of light by natural birefringent crystal has long been studied and well understood. Here, we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way. This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal, but also discloses many relevant physical and optical quantities that are rarely studied and less understood. We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal. We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index. We find big difference between them, where the phase refractive index satisfies the classical index of ellipse and Snell’s law, while the ray refractive index does not. Moreover, we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection. For better concept demonstration, we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations. In addition, we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle. Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals, and may greatly facilitate people to find rigorous solution to many light-matter interaction processes happening within birefringent crystals, e.g., nonlinear optical interactions, with electromagnetic theory.

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Ray refraction in uniaxial crystals by Fermat’s principle

Cited by 6 publications

References 26 publications

Analytic Spectral Integration of Birefringence‐Induced Iridescence

Analytic Spectral Integration of Birefringence‐Induced Iridescence

Analytical solution to incident angle quasi-phase-matching engineering for second harmonic generation in a periodic-poled lithium niobate crystal

A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

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