Optical response of a single spherical particle in a tightly focused light beam: Application to the spatial modulation spectroscopy technique

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 25, Issue 2, 2008, Pages 493-514

  Lermé, Jean ^a   Bachelier, Guillaume ^a   Billaud, Pierre ^a   Bonnet, Christophe ^a   Broyer, Michel ^a   Cottancin, Emmanuel ^a   Marhaba, Salem ^a   Pellarin, Michel ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION SPECTRA; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIELECTRIC MATERIALS; MATHEMATICAL MODELS; NUMERICAL METHODS;

MIE THEORY; OPTICAL RESPONSE; PLANE-WAVE DECOMPOSITION;

LIGHT SCATTERING;

EID: 41549168327     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.25.000493     Document Type: Article

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75. In general a0/2 is small as compared with the second term in the denominator of Eq. (51).
76. All the calculations have been performed with a standard PC (Intel Pentium 4 processor with 3.2 GHz clock speed, computational code written in the C language). Typically the spectra or error parameter curves (as a function of λ) displayed in the manuscript involve roughly Nλ=280 wavelengths and a maximum order Nmax in the expansion of the fields equal to 15 i n=1,2,3,..., Nmax in Eqs. (B1)-(B3)]. Actually this large Nmax value is not necessary for particles of radius equal to or smaller than 100 nm. Besides the Lorenz-Mie coefficients [Eqs. (B4)-(B7)] the present theory requires the Bessel functions Jm(x =kpp sin(2q)) and Legendre polynomials Pnm(θ) to be computed for each θ value in the integral of Eq. (32). Typically 800-1200 θ values are retained, depending on the parameter kpp in the argument of the Bessel function Jm (and also on kpp in the exponential factor), though this quite large number is unnecessary in most cases of interest. Thanks to efficient recurrence relations obeyed by the Bessel functions and the Legendre polynomials [64], a spectrum is obtained within 3-4 s for an arbitrary particle location (pp ≠ 0; zp ≠ 0). This time obviously depends on the Nλ, Nmax, and θ step values that are selected. This high speed is rooted in the simple mathematical ingredients (standard analytical functions) involved in the theory.