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Near-field imaging by a micro-particle: a model for conversion of evanescent photons into propagating photons

Djenan Ganic, Xiaosong Gan, and Min Gu

Open Access Open Access

Abstract

In this letter we present a physical model, both theoretically and experimentally, which describes the mechanism for the conversion of evanescent photons into propagating photons detectable by an imaging system. The conversion mechanism consists of two physical processes, near-field Mie scattering enhanced by morphology dependant resonance and vectorial diffraction. For dielectric probe particles, these two processes lead to the formation of an interference-like pattern in the far-field of a collecting objective. The detailed knowledge of the far-field structure of converted evanescent photons is extremely important for designing novel detection systems. This model should find broad applications in near-field imaging, optical nanometry and near-field metrology.

©2004 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. (a) Schematic of our theoretical model for evanescent photon conversion. (b) Representation of the lens transformation process. (c) Experimental setup for recording the FID of converted evanescent photons, collected by a high NA objective.

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Fig. 2.
Fig. 2. Calculated FID in the image focal plane of a 0.8 NA objective. TE (top row) and TM (bottom row) incident illumination. (a) and (e) a=100 nm. (b) and (f) a=500 nm. (c) and (g) a=1000 nm. (d) and (h) a=2000 nm. Particle refractive index is 1.59, and illumination wavelength is 633 nm. All figures are normalised to 100.

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Fig. 3.
Fig. 3. Maximum intensity in the FID as a function of the particle radius near MDR for TE (a) and TM (b) illumination. Insets show the full normalized FID representing off and on resonance cases. Insets FID images are centered in the focal plane and their size is 220 µm×220 µm. Particle refractive index is 1.59, and illumination wavelength is 633 nm.

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Fig. 4.
Fig. 4. Calculated (top) and observed (bottom) FID in image focal plane of a 0.8 NA objective collecting propagating photons converted by a=240 nm polystyrene particle under TE (left column) and TM (right column) incident illumination.

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Fig. 5.
Fig. 5. Calculated and observed y axis scan through x=0, in image focal plane of a 0.8 NA objective collecting propagating photons converted by 1000 nm (radius) polystyrene particle under TE incident illumination. (a) Calculated results. (b) Observed results (full line) where the dotted line represents the convolution of the calculated results and the PSF of the imaging lens. Insets show the calculated and observed FID.

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Fig. 6.
Fig. 6. (a) A schematic diagram of a pinhole detection process. Only the rays coming from the front focal region are detected. (b) Detected signal intensity as a function of a pinhole radius, in optical coordinates, for uniformly illuminated objective. Assumed objective NA=0.8 in the front focal region, aperture size ρ a=3 mm and the back focal length of the objective f=160 mm.

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Fig. 7.
Fig. 7. Scattered level as a function of pinhole size (in optical coordinates) of a polystyrene particle for TE illumination (left column) and TM illumination (right column). Assumed objective NA=0.8 in the front focal region, aperture size ρ a=3 mm and the back focal length of the objective f=160 mm. (a) and (d) Particle radius 0.1 µm. (b) and (e) Particle radius 0.5 µm. (c) and (f) Particle radius 1.0 µm. Signal level is defined as the signal intensity normalized by the total signal intensity when pinhole radius R→∞.

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Equations (6)

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E S C ( r ) = ∑ lm { c β E ( l , m ) n ′ 2 ω l ( l + 1 ) h l ( 1 ) ( k ′ r ) r sin ⁡ θ [ ∂ ∂ θ ( ∂ Y lm ∂ θ sin ⁡ θ ) + 1 sin ⁡ θ ∂ 2 Y lm ∂ φ 2 ] r 1
+ [ ( − 1 ) β M ( l , m ) h l ( 1 ) ( k ′ r ) i sin ⁡ θ l ( l + 1 ) ∂ Y lm ∂ φ − c β E ( l , m ) n ′ 2 ω l ( l + 1 ) 1 r ∂ Y l m ∂ θ ∂ ∂ r ( r h l ( 1 ) ( k ′ r ) ) ] θ 1
+ [ β M ( l , m ) h l ( 1 ) ( k ′ r ) i l ( l + 1 ) ∂ Y l m ∂ θ − c β E ( l , m ) n ′ 2 ω l ( l + 1 ) 1 r sin ⁡ θ ∂ Y l m ∂ φ ∂ ∂ r ( r h l ( 1 ) ( k ′ r ) ) ] φ 1 } .
E ( r 2 , ψ , z 2 ) = i λ ∬ Ω ( − E r 1 r ̂ 2 + E θ 1 θ ̂ 2 + E φ 1 φ ̂ 2 ) exp [ − i k r 2 sin ⁡ θ 2 cos ⁡ ( φ 2 − ψ ) ]
× exp ( − i k z 2 cos ⁡ θ 2 ) sin ⁡ θ 2 d θ 2 d φ 2 ,
η = ∫ 0 R ∫ 0 2 π I ( r , ϕ ) rdrd ϕ ∫ 0 ∞ ∫ 0 2 π I ( r , ϕ ) rdrd ϕ ,
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