Package 'mie'

Mie theory

Description

Scattering of light by a spherical object

Author(s)

baptiste Auguie [email protected]

References

Etchegoin, P. Le Ru, E., Principles of Surface-Enhanced Raman Spectroscopy, Elsevier, Amsterdam (2009). L. Novotny, E. Hecht, Principles of Nano-optics Cambridge University Press, 2006

See Also

Other user: mie_approximation(), mie_bh(), mie_ml(), mie()

---

average_Mloc

Description

Average Mloc

Usage

average_Mloc(wavelength, epsilon, radius, medium = 1, n_max = 10)

Arguments

wavelength	real vector
epsilon	complex vector
radius	scalar
medium	scalar, refractive index of surrounding medium
n_max	truncation order

Details

Enhancement factor averaged over the surface

Value

data.frame with wavelength and Mloc

Author(s)

Baptiste Auguie

---

efficiencies

Description

Efficiencies

Usage

efficiencies(x, GD, mode = c("EM", "Magnetic", "Electric"), order = NULL)

Arguments

x	real vector, size parameter
GD	list with Gamma, Delta, A, B
mode	type of mode
order	order of multipoles

Details

Calculates the far-field efficiencies for plane-wave illumination

Value

matrix of Qext, Qsca, Qabs

Author(s)

Baptiste Auguie

---

mie

Description

Far-field cross-sections

Usage

mie(
  wavelength,
  epsilon,
  radius,
  medium = 1,
  n_max = ceiling(2 + max(x) + 4 * max(x)^(1/3)),
  efficiency = FALSE,
  mode = c("EM", "Magnetic", "Electric"),
  order = Inf
)

Arguments

wavelength	real vector
epsilon	complex vector
radius	scalar
medium	scalar, refractive index of surrounding medium
n_max	truncation order
efficiency	logical, scale by geometrical cross-sections
mode	type of mode
order	order of multipoles

Details

Homogeneous sphere illuminated by a plane wave

Value

data.frame

Author(s)

Baptiste Auguie

See Also

Other user: mie-package, mie_approximation(), mie_bh(), mie_ml()

Examples

gold <- epsAu(seq(400, 800))
cross_sections <- with(gold, mie(wavelength, epsilon, radius=50, medium=1.33, efficiency=FALSE))
matplot(cross_sections$wavelength, cross_sections[, -1], type="l", lty=1,
        xlab=expression(lambda/mu*m), ylab=expression(sigma/mu*m^2))
legend("topright", names(cross_sections)[-1], col=1:3, lty=1)

---

mie_approximation

Description

Analytical approximation

Usage

mie_approximation(
  radius,
  wavelength,
  epsilon,
  medium = 1.33,
  order = Inf,
  efficiency = FALSE,
  ...
)

Arguments

radius	scalar
wavelength	real vector
epsilon	complex vector
medium	scalar, refractive index of surrounding medium
order	truncation order
efficiency	logical, scale by geometrical cross-sections (unused)
...	unused

Details

Sphere illuminated by a plane wave

Value

data.frame

Author(s)

Baptiste Auguie

See Also

Other user: mie-package, mie_bh(), mie_ml(), mie()

---

mie_bh

Description

Far-field cross-sections

Usage

mie_bh(
  wavelength,
  epsilon.core,
  epsilon.coating = medium^2,
  radius,
  thickness = 0,
  medium = 1,
  lmax = ceiling(2 + max(y) + 4 * max(y)^(1/3)),
  efficiency = TRUE
)

Arguments

wavelength	real vector
epsilon.core	complex vector
epsilon.coating	complex vector
radius	scalar
thickness	scalar
medium	scalar, refractive index of surrounding medium
lmax	truncation order (unused)
efficiency	logical, scale by geometrical cross-sections

Details

Coated sphere illuminated by a plane wave

Value

data.frame

Author(s)

Baptiste Auguie

See Also

Other user: mie-package, mie_approximation(), mie_ml(), mie()

Examples

gold <- epsAu(seq(400, 800))
coated <- with(gold, mie_bh(wavelength, epsilon, radius=50, medium=1.33, 
efficiency=FALSE))
bare <- with(gold, mie(wavelength, epsilon, radius=50, medium=1.33, 
efficiency=FALSE))
matplot(coated$wavelength, coated[, -1], type="l", lty=1,
        xlab=expression(lambda/nm), ylab=expression(sigma/nm^2))
matlines(bare$wavelength, bare[, -1], type="l", lty=2)
legend("topright", c(names(coated)[-1], "bare"), col=1:3, lty=c(1,1,1,2))

---

mie_ml

Description

Far-field cross-sections

Usage

mie_ml(
  wavelength,
  epsilon,
  radii,
  n_max = 10,
  efficiency = FALSE,
  mode = c("EM", "Magnetic", "Electric"),
  order = Inf
)

Arguments

wavelength	real vector
epsilon	list of dielectric functions, from inner to outer medium
radii	concentric radii of each interface, from smaller to larger
n_max	truncation order
efficiency	logical, scale by geometrical cross-sections
mode	type of mode
order	order of multipoles

Details

Multilayered sphere illuminated by a plane wave

Value

data.frame

Author(s)

Baptiste Auguie

See Also

Other user: mie-package, mie_approximation(), mie_bh(), mie()

Examples

library(dielectric)
library(mie)
gold <- epsAg(seq(300, 800))
a <- 30
b <- 34
c <- 35

bare <- mie(gold$wavelength, gold$epsilon, radius=a, medium=1.33, efficiency=FALSE)

leps <- list(gold$epsilon, 1.33^2, 1.5^2, 1.33^2)
# leps <- list(1.5^2, gold$epsilon,  1.33^2)
la <- list(a,b,c)
coated <- mie_ml(gold$wavelength, leps, radii=la, efficiency=FALSE)

matplot(bare$wavelength, bare[, -1], type="l", lty=1,
        xlab=expression(lambda/mu*m), ylab=expression(sigma/mu*m^2))
matlines(coated$wavelength, coated[, -1],  type="l",  lty=2)

legend("topright", c(names(bare)[-1], "coated"), col=1:3, lty=c(1,1,1,2))

---

psi

Description

Riccati-Bessel function psi and its derivative

Usage

psi(rho, n_max)

Arguments

rho	complex vector, argument
n_max	integer, maximum order

Details

Obtained from BesselJ, converted to spherical Bessel, and scaled

Value

a list with psi_n and psi'_n

Author(s)

Baptiste Auguie

---

susceptibilities

Description

Generalised susceptibility for multilayer Mie theory

Usage

susceptibilities(ls, lx, n_max)

Arguments

ls	list of relative refractive index
lx	list of size parameters
n_max	integer, maximum order

Details

Corresponds to the usual coefficients a_n, b_n, c_n, d_n

Value

list with Gamma, Delta, A, B

Author(s)

Baptiste Auguie

---

susceptibility

Description

Generalised susceptibility for the Mie theory

Usage

susceptibility(s, x, n_max)

Arguments

s	complex vector, relative refractive index
x	real vector, size parameter
n_max	integer, maximum order

Details

Corresponds to the usual coefficients a_n, b_n, c_n, d_n

Value

list with Gamma, Delta, A, B

Author(s)

Baptiste Auguie

---

xi

Description

Riccati-Bessel function xi and its derivative

Usage

xi(rho, n_max)

Arguments

rho	complex vector, argument
n_max	integer, maximum order

Details

Obtained from BesselH (Hankel function), converted to spherical Hankel, and scaled

Value

a list with psi_n and psi'_n

Author(s)

Baptiste Auguie

---