Abstract

A theoretical and numerical investigation is devised for resonant light scattering of an off-axis normally incident Gaussian beam by two parallel nonabsorbing cylinders based on the related beam theory developed in J. Opt. Soc. Am. A 14, 640 (1997). By varying the half-beam width, we show that the multireflection process between the two scatterers can be minimized. Moreover, the study is an attempt to understand the underlying physics present in the process of resonance excitation by evanescent wave coupling.

© 2002 Optical Society of America

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References

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  1. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
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  5. H. A. Yousif, S. Köhler, “Scattering by two penetrable cylinders at oblique incidence. I. The analytical solution,” J. Opt. Soc. Am. A 5, 1085–1096 (1988).
    [CrossRef]
  6. T. Tsuei, P. W. Barber, “Multiple scattering by two parallel dielectric cylinders,” Appl. Opt. 27, 3375–3381 (1988).
    [CrossRef] [PubMed]
  7. M. Yokota, T. Takenaka, O. Fukumitsu, “Scattering of Hermite–Gaussian beam mode by parallel dielectric circular cylinders,” J. Opt. Soc. Am. A 4, 580–586 (1986).
    [CrossRef]
  8. J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997).
    [CrossRef]
  9. J. A. Lock, “Morphology dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
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    [CrossRef]
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  13. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
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    [CrossRef] [PubMed]
  15. H. M. Nussenzweig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992).

1998

1997

1995

1992

1988

1987

1986

M. Yokota, T. Takenaka, O. Fukumitsu, “Scattering of Hermite–Gaussian beam mode by parallel dielectric circular cylinders,” J. Opt. Soc. Am. A 4, 580–586 (1986).
[CrossRef]

1955

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Arnold, S.

Barabás, M.

Barber, P. W.

Chang, R. K.

Chowdhury, D. Q.

de Mendonça, J. P. R. F.

Fukumitsu, O.

M. Yokota, T. Takenaka, O. Fukumitsu, “Scattering of Hermite–Gaussian beam mode by parallel dielectric circular cylinders,” J. Opt. Soc. Am. A 4, 580–586 (1986).
[CrossRef]

Griffle, G.

Guimarães, L. G.

Hill, S. C.

Khaled, E. E. M.

Köhler, S.

Lock, J. A.

Nussenzweig, H. M.

H. M. Nussenzweig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992).

Poon, A. W.

Serpengüzel, A.

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Takenaka, T.

M. Yokota, T. Takenaka, O. Fukumitsu, “Scattering of Hermite–Gaussian beam mode by parallel dielectric circular cylinders,” J. Opt. Soc. Am. A 4, 580–586 (1986).
[CrossRef]

Tsuei, T.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Yokota, M.

M. Yokota, T. Takenaka, O. Fukumitsu, “Scattering of Hermite–Gaussian beam mode by parallel dielectric circular cylinders,” J. Opt. Soc. Am. A 4, 580–586 (1986).
[CrossRef]

Yousif, H. A.

Appl. Opt.

Can. J. Phys.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

H. M. Nussenzweig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

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Figures (5)

Fig. 1
Fig. 1

Scattering geometry of an off-axis normally incident Gaussian beam by two parallel nonabsorbing cylinders with separation distance d, refractive indices N1 and N2, and radii a1 and a2. The refractive index of the surrounding medium is N0. The half-beam width w0 is located a distance y0 from the z axis of the cylinder O1.

Fig. 2
Fig. 2

(a) Situation in which the cylinders are touching and there is a Gaussian beam with spot size values that range from a tightly to a nonfocused half-beam width, (b) BSC dependency on the angular momentum n for different values of the half-beam width w0, (c) numerical test on the BSC.

Fig. 3
Fig. 3

Sequence of plotted values of the squared modulus of the scattering coefficient [|Ans(β)|2] for fixed values of D (Dd/a). The dotted curves correspond to the pump coefficients, and the solid curves correspond to the probe coefficients.

Fig. 4
Fig. 4

(a) Equivalent single-cylinder results for Gaussian beam illumination. The dotted curve inside corresponds to the size of the focal plane of the beam. The solid curves represent the cylinder’s respective source function. (b) Source function for D=3. The main contribution is at the pump, while at the probe a competition between background and resonance contribution prevails. The shadowed region between the two cylinders, indicated by MWI, corresponds to the maximum width of intersection resulting from caustic–caustic overlapping. (c) Corresponding source function for D=2.7, where MWI=0.4a. It is interesting to note the slight enhancement of the related EM energy density at the pump’s cavity. (d) Results for D=2.6, where the probe’s resonance contribution reaches a maximum.

Fig. 5
Fig. 5

(a) Shifted resonance curves for Dc. The blueshift (redshift) corresponds to an increase (decrease) in the radius of the probe, while the refractive index is varied to keep the product aNprobe constant. (b) Plot of the resonance width Γ against the separation distance D. The inset shows an interpolating parabola (dashed curve) in which an estimation of the minimum position of Γ is given at Dmin. (c) Ray interpretation of the twin-cylinder resonant mode.

Tables (1)

Tables Icon

Table 1 Related Resonance Position β and Respective Width Γ as a Function of the Interdistance D=d/a for Pump and Probe Cylinders

Equations (27)

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Ez=E0 exp{-w0-2[(y-y0)2+(z-z0)2]}exp[ikx(x-x0)]uˆz,
Einc=Exuˆx+Ezuˆz.
ψij=-+dkzin=-FnjAnj(kz)Zn(ρ(ki2-kz2)1/2)exp(inϕ)exp(ikzz),
An(h)14πs2(1-h2)exp-h24s2-+dhy×exp-hy24s2+qhy,
An(h)12π1/2s(1-h2)1/2×exp-s2k0y0+n(1-h2)1/22-h24s2.
nmax=-k0y0(1-h2)1/2-h(1-h2)1/22s2.
Anmax(h)=12π1/2s(1-h2).
An(h)Anmax(h)2=14π1/2s(1-h2).
nbl=nnor-h2s2,
h=2s2(nnor-nbl).
S=12[(EzHy*)uˆx+(EzHx*-ExHz*)uˆy+(ExHy*)uˆz].
EzHy*=F2E02ω-2iδ(kx)μ0w02+i4(z-z0)2δ(kx)μ0w04-kx exp(-ikxx)μ0exp(ikxx),
EzHx*=F2E02ω-i(y-y0)μ0w02,
ExHz*=F2E02ω-8i(z-z0)2(y-y0)μ0w06exp(-ikxx),
ExHy*=F2E02ωδ(kx)(z-z0)×-4iδ(kx)μ0w04+8i(z-z0)2δ(kx)μ0w06-kx exp(-ikxx)w02μ0,
Sw0=12(EzHy*)uˆx=k0E022ωμ0uˆx,
Etotal,z=Einc,z+Escattpump,z+Escattprobe,z.
Hl(ρ2k˜0)exp(ilϕ2)=q=-Zq-l(dk˜0)Yq(ρ1k˜0)exp(iqϕ1),
k=-δn,k-TnO2q=-i(k-n)TqO1Hk-n(1)(dk˜0)×Hq-n(1)(dk˜0)Ak,O2s,μ
=TnO2An,O2μ+TnO2q=-iq-nTqO1Aq,O1μHq-n(1)(dk˜0)
×exp[ik0h(z1-z2)],
TnOi=2iDi1ui2π[Hn(ui)]2Di1Di2-(nh)2×1ui2-1vi22-1-Jn(ui)Hn(ui),
Di1(2)=Hn(ui)uiHn(ui)-μiμ0i0Jn(vi)viJn(vi),
Δya2πβ2/3.
|Ans,μ(β)|2C(Γnμ)2(β-βnμ)2+(Γnμ)2+P˜(β),
Siz(ρ)=12πSinc02πdϕ|Eiz|2,
ΔNprobe=-ΔaNprobea.

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