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2017 ; 7
(ä): 44995
Nephropedia Template TP
Martin L
; Mardani D
; Kondakci HE
; Larson WD
; Shabahang S
; Jahromi AK
; Malhotra T
; Vamivakas AN
; Atia GK
; Abouraddy AF
Sci Rep
2017[Mar]; 7
(ä): 44995
PMID28344331
show ga
Interferometry is one of the central organizing principles of optics. Key to
interferometry is the concept of optical delay, which facilitates spectral
analysis in terms of time-harmonics. In contrast, when analyzing a beam in a
Hilbert space spanned by spatial modes - a critical task for spatial-mode
multiplexing and quantum communication - basis-specific principles are invoked
that are altogether distinct from that of 'delay'. Here, we extend the
traditional concept of temporal delay to the spatial domain, thereby enabling the
analysis of a beam in an arbitrary spatial-mode basis - exemplified using
Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays
correspond to optical implementations of fractional transforms; for example, the
fractional Hankel transform is the generalized delay associated with the space of
Laguerre-Gaussian modes, and an interferometer incorporating such a 'delay'
obtains modal weights in the associated Hilbert space. By implementing an
inherently stable, reconfigurable spatial-light-modulator-based
polarization-interferometer, we have constructed a 'Hilbert-space analyzer'
capable of projecting optical beams onto any modal basis.
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