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Digital spiral imaging

Lluis Torner, Juan P. Torres, and Silvia Carrasco

Open Access Open Access

Abstract

A major application of optics is imaging all types of structural, physical, chemical and biological features of matter. Techniques based on most known properties of light have been developed over the years to remotely acquire information about such features. They include the spin angular momentum, encoded in the polarization, but not yet the orbital angular momentum encoded in its spiral spectrum. Here we put forward the potential of such spiral spectra. In particular, we use several canonical examples to show how the orbital angular momentum spectra of a light beam can be used to image a variety of intrinsic and extrinsic properties encoded, e.g., in phase and amplitude gradients, dislocations or delays.

©2005 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Intensity distribution of two different LG modes: (a) LG 00 (m=0, p=0), and (b) LG 20 (m=2, p=0).

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Fig. 2.
Fig. 2. Spiral spectra of the output field reflected/refracted from a target imprinting a π phase dislocation across in the center of the illuminating beam. The transfer function of such a target has the form: R(x,y)=1 for x<0, and R(x,y)=-1 otherwise. The input field is a Gaussian beam (pure LG 00 mode).

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Fig. 3.
Fig. 3. (a) Spiral spectra of the output field reflected/refracted from a target imprinting a ϕ phase dislocation across in the center of the illuminating beam for four selected values of the phase dislocation. (b) Weight of the central (n=0), P 0 and the first adjacent (n=±1) sidelobes, P 1+P (-1) versus the normalized phase dislocation ϕ/π. The transfer function of the target has the form: R(x,y)=1 for x<0, and R(x,y)=eiϕ otherwise. The input field is a Gaussian beam.

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Fig. 4.
Fig. 4. Weight of the central (n=0), P 0 and the first adjacent (n=±1) sidelobes, P 1+P (-1) for a Gaussian beam of beam waist η=1 illuminating an off-axis π phase dislocation placed at a distance D from the center of the beam.

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Fig. 5.
Fig. 5. Output intensity distributions (left column), and spiral spectra (right column) for a Gaussian beam of beam waist η=1 illuminating a target imprinting a comb of π phase dislocations. Each row displays a different value D of the separation between the edges. Top row, D=1; middle row, D=0.5; bottom row, D=0.25.

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Fig. 6.
Fig. 6. Spiral spectra of the output field for a Gaussian beam of beam waist η=1 illuminating a target featuring an antisymmetric phase gradient across the input beam for different selected strengths α of the phase gradient. The transfer function of the target has the form R(x,y)=eiαπx/η .

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Fig. 7.
Fig. 7. Same as in Fig. 6, for a symmetric phase gradient target of the form R(x,y)=eiαπ|x|/η .

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Fig. 8.
Fig. 8. Intensity distributions (left column), and spiral spectra (right column) of the output field reflected from a perfect mirror with a blocking strip of different widths D placed in the center of the illuminating beam. The transfer function of such a target has the form R(x, y)=1 for |x|>D/2, and R(x,y)=0 otherwise. The input beam is a pure LG mode with m=2, and a beam waist η=1.

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Equations (3)

Equations on this page are rendered with MathJax. Learn more.

L G m , p ( ρ , φ ) = ( 2 p ! π ( ∣ m ∣ + p ) ! ) 1 2 1 η ( 2 ρ η ) ∣ m ∣ L p ∣ m ∣ ( 2 ρ 2 η 2 ) exp ( − ρ 2 η 2 ) exp ( i m φ ) ,
u ( ρ , φ ; z ) = 1 2 π ∑ n = − ∞ n = ∞ a n ( ρ , z ) exp ( i n φ ) ,
P n = C n ∑ q = − ∞ ∞ C q
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