Exact analytical method for planar optical waveguides with arbitrary index profile

Cao, Zhang; Jiang, Yi; Shen, Qing; Dou, Xiaoming; Chen, Yingli

doi:10.1364/josaa.16.002209

Cited by 67 publications

(19 citation statements)

References 6 publications

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“…The quantity φ i in (1) represents the phase contribution from the turning point x i . The phase contribution φ i is typically assumed to be a constant value of π/4 [4], which is a good approximation for the thick-film case. However, for the case of thin films (< 1µm thick) relevant to the IM-IWKB method and many thin-film photovoltaics, φ i must be modified, especially for modes that have turning points near the cover interface [5].…”

Section: Methodsmentioning

confidence: 99%

Measuring refractive index profiles within thin-film photovoltaics with high spatial resolution using the modified IM-IWKB method

Pang

Eisaman

2014

2014 IEEE 40th Photovoltaic Specialist Conference (PVSC)

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We derive a correction to the phase contribution for the reconstruction of refractive index profiles within thin-film photovoltaics using the Index Matched Inverse Wentzel-Kramers-Brillouin (IM-IWKB) Method. We quantify the improvement of the refractive-index reconstruction due to this modification for structures typical of organic photovoltaics. Near the low-index surface of the photoactive layer, this modification reduces the fractional error in the reconstructed profile by a factor of ten, resulting in a highly accurate refractive index reconstruction throughout the entire film thickness. This technique is applicable to the reconstruction of the refractive index profiles within any thin-film photovoltaic material.

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Section: Methodsmentioning

confidence: 99%

Measuring refractive index profiles within thin-film photovoltaics with high spatial resolution using the modified IM-IWKB method

Pang

Eisaman

2014

2014 IEEE 40th Photovoltaic Specialist Conference (PVSC)

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“…Analytical relationships for modes propagating in graded-index planar waveguides were derived in [16,17]. A general constraint of the above works has been the assumption on the existence of one [16] or two [17] turning points of the refractive index profile of the planar waveguide.…”

Section: Introductionmentioning

confidence: 99%

“…A general constraint of the above works has been the assumption on the existence of one [16] or two [17] turning points of the refractive index profile of the planar waveguide. We have derived extended analytical relationships for mode …”

Section: Introductionmentioning

confidence: 99%

High Resolution through Graded-Index Microoptics

Kotlyar

Kovalev

Nalimov

2012

Advances in Optical Technologies

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By solving Helmholtz equations, relationships to describe propagating modes in an arbitrary graded-index planar waveguide are derived. We show that in the quadratic-and secant-index waveguides a minimal mode width is 0.4λ/n, where λ is the wavelength in free space and n is the refractive index on the fiber axis. By modeling in FullWAVE, we show that the high-resolution imaging can be achieved with half-pitch graded-index Mikaelian microlenses (ML) and Maxwell's "fisheye" lenses. It is shown that using a 2D ML, the point source can be imaged near the lens surface as a light spot with the full width at half maximum (FWHM) of 0.12λ. This value is close to the diffraction limit for silicon (n = 3.47) in 2D media FWHM = 0.44λ/n = 0.127λ. We also show that half-pitch ML is able to resolve at half-maximum two close point sources separated by a 0.3λ distance.

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“…[3][4][5] Among them, the most popular methods are the inverse WKB method, [6][7][8] and the improved IWKB method. 9 The inverse analytical transfer matrix ͑ATM͒ was represented afterward by Ding et al 10 who induced the ATM method 11 into the iterative method.…”

Section: Introductionmentioning

confidence: 99%

Improved method for recovering graded-index profile of isotropic waveguide by cubic spline function

2010

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An improved method for recovering the refractive index profile of an isotropic graded-index waveguide is presented on the basis of the cubic spline interpolation method. The surface refractive index of the waveguide can be obtained by using a polynomial function that is related with the parameters of all modes. The simulation results of several typical index distributions show that this method can be employed to recover a graded-index profile well.

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Exact analytical method for planar optical waveguides with arbitrary index profile

Cited by 67 publications

References 6 publications

Measuring refractive index profiles within thin-film photovoltaics with high spatial resolution using the modified IM-IWKB method

Measuring refractive index profiles within thin-film photovoltaics with high spatial resolution using the modified IM-IWKB method

High Resolution through Graded-Index Microoptics

Improved method for recovering graded-index profile of isotropic waveguide by cubic spline function

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