Abstract

We present a detailed examination of the design and expected operation of an artificially birefringent material based around the nanostructured stack-and-draw fabrication technique developed recently. The expected degree of birefringence is estimated using a Finite Difference Time Domain simulation of the physical system and is shown to be in agreement with that predicted by a second order effective medium theory treatment of the nanostructured material. The effects of finite device dimensions are studied and an estimate of the required device thickness for a half-wave retardation is made.

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References

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  1. F. Hudelist, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, “Design and fabrication of nano-structured gradient index microlenses,” Opt. Express17(5), 3255–3263 (2009).
    [CrossRef] [PubMed]
  2. N. Lu, D. Kuang, and G. Mu, “Design of transmission blazed binary gratings for optical limiting with the form-birefringence theory,” Appl. Opt.47(21), 3743–3750 (2008).
    [CrossRef] [PubMed]
  3. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A14(10), 2758–2767 (1997).
    [CrossRef]
  4. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A14(7), 1592–1598 (1997).
    [CrossRef]
  5. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
    [CrossRef]
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  7. F. Hudelist, J. M. Nowosielski, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured elliptical gradient-index microlenses,” Opt. Lett.35(2), 130–132 (2010).
    [CrossRef] [PubMed]
  8. J. M. Nowosielski, R. Buczynski, F. Hudelist, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured GRIN microlenses for Gaussian beam focusing,” Opt. Commun.283(9), 1938–1944 (2010).
    [CrossRef]
  9. A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
    [CrossRef]
  10. I. Richter, P.-C. Sun, F. Xu, and Y. Fainman, “Design considerations of form birefringent microstructures,” Appl. Opt.34(14), 2421–2429 (1995).
    [CrossRef] [PubMed]
  11. S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag.44, 1630–1639 (1996).
    [CrossRef]

2010 (2)

F. Hudelist, J. M. Nowosielski, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured elliptical gradient-index microlenses,” Opt. Lett.35(2), 130–132 (2010).
[CrossRef] [PubMed]

J. M. Nowosielski, R. Buczynski, F. Hudelist, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured GRIN microlenses for Gaussian beam focusing,” Opt. Commun.283(9), 1938–1944 (2010).
[CrossRef]

2009 (1)

2008 (1)

1997 (2)

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag.44, 1630–1639 (1996).
[CrossRef]

1995 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

Buczynski, R.

Fainman, Y.

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag.44, 1630–1639 (1996).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Hudelist, F.

Kuang, D.

Lalanne, P.

Li, L.

Lu, N.

Mu, G.

Nowosielski, J. M.

F. Hudelist, J. M. Nowosielski, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured elliptical gradient-index microlenses,” Opt. Lett.35(2), 130–132 (2010).
[CrossRef] [PubMed]

J. M. Nowosielski, R. Buczynski, F. Hudelist, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured GRIN microlenses for Gaussian beam focusing,” Opt. Commun.283(9), 1938–1944 (2010).
[CrossRef]

Richter, I.

Sihvola, A.

A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
[CrossRef]

Sun, P.-C.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Taghizadeh, M. R.

Waddie, A. J.

Xu, F.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (2)

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag.44, 1630–1639 (1996).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J. M. Nowosielski, R. Buczynski, F. Hudelist, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured GRIN microlenses for Gaussian beam focusing,” Opt. Commun.283(9), 1938–1944 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (2)

A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (10)

Fig. 1
Fig. 1

Preforms and final device of nanostructured microlens. (a) Initial preform (ϕ = 60mm) (b) Intermediate preform (ϕ = 30mm) (c) Final microlens (ϕ = 100μm).

Fig. 2
Fig. 2

One dimensional effective medium nanostructures. Each row of the figure is a separate nanostructure with the light incident from the bottom to the top of the structure. The incident light is polarised with the Ez (Hz) component out of the page for TE (TM) polarisation respectively.

Fig. 3
Fig. 3

(a) Variation of phase for TM polarised light through effective medium with thickness (b) Effective refractive index of material for TE (red) and TM (blue) polarisations.

Fig. 4
Fig. 4

Basic nanostructured birefringent device design composed of two soft glasses. The incident light propagation direction is shown by the large red arrow with the Ez (Hz) component coming out of the page for TE (TM) polarised light.

Fig. 5
Fig. 5

Variation of birefringence as a function of wavelength of light for a 250nm period low-index contrast material. The second order effective medium theory (solid blue) shows good agreement with the fully vectorial results (blue dots). The general trend matches that of the refractive index difference between the two constituent glasses (red). An inverse wavelength fit (green) to the simulated dn shows constant birefringence over 300nm wavelength bands.

Fig. 6
Fig. 6

Variation of refractive index difference in a low-index contrast nanostructure as a function of period for four wavelengths of light - 500nm (blue), 1000nm (red), 1500nm (green) and 2000nm (yellow). The dn values are normalised to the peak dn for each wavelength of operation. The inset figures show the electric field structure at the indicated points for an incident wavelength of light of 1000nm.

Fig. 7
Fig. 7

Fourier Modal Method simulation of low (red) and high (blue) index contrast structure.

Fig. 8
Fig. 8

Finite Difference Time Domain simulation of finite (red) and infinite (blue) low index contrast structure.

Fig. 9
Fig. 9

Transmission through finite slab of low index contrast nanostructured material.

Fig. 10
Fig. 10

(a) Effective medium fit to oscillatory trend and comparison to FDTD simulations. (b) Extension of Eq. (8) to greater thicknesses.

Tables (2)

Tables Icon

Table 1 Low (LIC) and High (HIC) Index Contrast Soft Glass Families

Tables Icon

Table 2 Sellmeier Coefficients for Low Index Contrast Glass Family

Equations (11)

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ɛ e = ɛ m ɛ i ( 1 + 2 δ ) ɛ m ( 2 δ 2 ) ɛ m ( 2 δ ) + ɛ i ( 1 δ )
n e TE = δ ɛ i + ( 1 δ ) ɛ m + 1 3 ( δ ( 1 δ ) Λ π λ ) 2 ( ɛ i ɛ m ) 2
n e TM = ɛ ¯ + 1 3 ( δ ( 1 δ ) Λ π λ ) 2 ( 1 ɛ i 1 ɛ m ) 2 ( ɛ ¯ ) 3 ( δ ɛ i + ( 1 δ ) ɛ m )
ɛ ¯ = ɛ i ɛ m δ ɛ m + ( 1 δ ) ɛ i
d n scaled = 1 1 Δ Λ 1 + exp [ 10 ( Λ λ T Λ ) ]
Δ Λ = 0.38 0.07 Λ λ
T Λ 1.57 0.4 Λ λ
I = 1 1 + F sin 2 ( ϕ 2 )
ϕ = 2.0 π λ 2 t n ¯ F = 4 R ( 1 R ) 2 R = ( n ¯ 1 ) 2 ( n ¯ + 1 ) 2
ψ = atan ( R sin ϕ 1 R cos ϕ )
t π λ = 1 2 ( n TE ¯ n TM ¯ )

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