High Resolution through Graded-Index Microoptics

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 t...

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Bibliographic Details
Published in:Advances in optical technologies 2012, Vol.2012 (2012), p.1-9
Main Authors: Kotlyar, Victor V., Kovalev, Alexey A., Nalimov, Anton G., Stafeev, Sergey S.
Format: Article
Language:English
Subjects:
Composite materials
Diffraction
Experiments
Helmholtz equations
Imaging
Lasers
Lenses
Mathematical models
Point sources
Two dimensional
Wave propagation
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Summary: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.
ISSN:1687-6393
1687-6407
DOI:10.1155/2012/647165