Abstract

We show that a gradient-index element designed from a blend of three materials allows a designer to specify independently the element’s refractive index and its change in refractive index with respect to wavelength. We show further the effectiveness of this approach by comparing modeled chromatic performance of deflectors consisting of a single material, a binary blend of materials, and a ternary blend.

© 2016 Optical Society of America

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References

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  1. R. W. Wood, Physical Optics (Macmillan, New York, 1905).
  2. S. N. Houde-Walter and D. T. Moore, “Gradient-index profile control by field-assisted ion exchange in glass,” Appl. Opt. 24, 4326–4333 (1985).
    [Crossref] [PubMed]
  3. M. Ponting, A. Hiltner, and E. Baer, “Polymer Nanostructures by Forced Assembly: Process, Structure, and Properties,” Macromol. Symp. 294, 19–32 (2010).
    [Crossref]
  4. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).
  5. http://www.schott.com/advanced_optics/english/download/schott-optical-glass-pocket-catalog-january-2014-row.pdf . (Accessed March 5, 2015).
  6. R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21, 4970–4978 (2013).
    [Crossref] [PubMed]
  7. J. N. Mait, G. Beadie, P. Milojkovic, and R. A. Flynn, “Chromatic Analysis of a First-order Radial GRIN Lens,” Opt. Express 23, 22069–22086 (2015).
    [Crossref] [PubMed]
  8. G. Beadie, R. A. Flynn, J. N. Mait, and P. Milojkovic, “Materials figure of merit for achromatic gradient index (GRIN) optics,” in Advanced Optics for Defense Applications: UV through LWIR, J. N. Vizgaitis, B. F. Andresen, P. L. Marasco, J. S. Sanghera, and M. P. Snyder, eds., Proc. SPIE9822, 98220Q (2016).
  9. P. N. Robb, “Selection of optical glasses. 1: Two materials,” Appl. Opt. 24, 1864–1877 (1985).
    [Crossref] [PubMed]

2015 (1)

2013 (1)

2010 (1)

M. Ponting, A. Hiltner, and E. Baer, “Polymer Nanostructures by Forced Assembly: Process, Structure, and Properties,” Macromol. Symp. 294, 19–32 (2010).
[Crossref]

1985 (2)

Baer, E.

M. Ponting, A. Hiltner, and E. Baer, “Polymer Nanostructures by Forced Assembly: Process, Structure, and Properties,” Macromol. Symp. 294, 19–32 (2010).
[Crossref]

Beadie, G.

J. N. Mait, G. Beadie, P. Milojkovic, and R. A. Flynn, “Chromatic Analysis of a First-order Radial GRIN Lens,” Opt. Express 23, 22069–22086 (2015).
[Crossref] [PubMed]

R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21, 4970–4978 (2013).
[Crossref] [PubMed]

G. Beadie, R. A. Flynn, J. N. Mait, and P. Milojkovic, “Materials figure of merit for achromatic gradient index (GRIN) optics,” in Advanced Optics for Defense Applications: UV through LWIR, J. N. Vizgaitis, B. F. Andresen, P. L. Marasco, J. S. Sanghera, and M. P. Snyder, eds., Proc. SPIE9822, 98220Q (2016).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).

Fleet, E. F.

Flynn, R. A.

J. N. Mait, G. Beadie, P. Milojkovic, and R. A. Flynn, “Chromatic Analysis of a First-order Radial GRIN Lens,” Opt. Express 23, 22069–22086 (2015).
[Crossref] [PubMed]

R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21, 4970–4978 (2013).
[Crossref] [PubMed]

G. Beadie, R. A. Flynn, J. N. Mait, and P. Milojkovic, “Materials figure of merit for achromatic gradient index (GRIN) optics,” in Advanced Optics for Defense Applications: UV through LWIR, J. N. Vizgaitis, B. F. Andresen, P. L. Marasco, J. S. Sanghera, and M. P. Snyder, eds., Proc. SPIE9822, 98220Q (2016).

Hiltner, A.

M. Ponting, A. Hiltner, and E. Baer, “Polymer Nanostructures by Forced Assembly: Process, Structure, and Properties,” Macromol. Symp. 294, 19–32 (2010).
[Crossref]

Houde-Walter, S. N.

Mait, J. N.

J. N. Mait, G. Beadie, P. Milojkovic, and R. A. Flynn, “Chromatic Analysis of a First-order Radial GRIN Lens,” Opt. Express 23, 22069–22086 (2015).
[Crossref] [PubMed]

G. Beadie, R. A. Flynn, J. N. Mait, and P. Milojkovic, “Materials figure of merit for achromatic gradient index (GRIN) optics,” in Advanced Optics for Defense Applications: UV through LWIR, J. N. Vizgaitis, B. F. Andresen, P. L. Marasco, J. S. Sanghera, and M. P. Snyder, eds., Proc. SPIE9822, 98220Q (2016).

Milojkovic, P.

J. N. Mait, G. Beadie, P. Milojkovic, and R. A. Flynn, “Chromatic Analysis of a First-order Radial GRIN Lens,” Opt. Express 23, 22069–22086 (2015).
[Crossref] [PubMed]

G. Beadie, R. A. Flynn, J. N. Mait, and P. Milojkovic, “Materials figure of merit for achromatic gradient index (GRIN) optics,” in Advanced Optics for Defense Applications: UV through LWIR, J. N. Vizgaitis, B. F. Andresen, P. L. Marasco, J. S. Sanghera, and M. P. Snyder, eds., Proc. SPIE9822, 98220Q (2016).

Moore, D. T.

Ponting, M.

M. Ponting, A. Hiltner, and E. Baer, “Polymer Nanostructures by Forced Assembly: Process, Structure, and Properties,” Macromol. Symp. 294, 19–32 (2010).
[Crossref]

Robb, P. N.

Shirk, J. S.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, 1905).

Appl. Opt. (2)

Macromol. Symp. (1)

M. Ponting, A. Hiltner, and E. Baer, “Polymer Nanostructures by Forced Assembly: Process, Structure, and Properties,” Macromol. Symp. 294, 19–32 (2010).
[Crossref]

Opt. Express (2)

Other (4)

G. Beadie, R. A. Flynn, J. N. Mait, and P. Milojkovic, “Materials figure of merit for achromatic gradient index (GRIN) optics,” in Advanced Optics for Defense Applications: UV through LWIR, J. N. Vizgaitis, B. F. Andresen, P. L. Marasco, J. S. Sanghera, and M. P. Snyder, eds., Proc. SPIE9822, 98220Q (2016).

R. W. Wood, Physical Optics (Macmillan, New York, 1905).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).

http://www.schott.com/advanced_optics/english/download/schott-optical-glass-pocket-catalog-january-2014-row.pdf . (Accessed March 5, 2015).

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Figures (6)

Fig. 1
Fig. 1 Optical elements considered for deflection. (a) Triangular prism constructed from a single material. (b) Rectangular prism constructed from gradient index materials.
Fig. 2
Fig. 2 Index as a function of index slope for materials in Table 2 at λ0 = 0.55 µm. The circled numbers refer to the number of materials used to design the deflection elements in Table 1.
Fig. 3
Fig. 3 Deflector designs using GRIN materials. For the binary blend (a) the index, (b) index slope, and (c) volume ratios as a function of space at the design wavelength. (d)–(f) As in (a)–(c) but for the ternary blend. Note that the index slope in (b) is dependent upon the desired index in (a), whereas the index slope in (e) is specified independent of the index in (d).
Fig. 4
Fig. 4 Index as a function of index slope at three different wavelengths for a ternary blend of glasses. Blue represents 0.40 µm, green, 0.55 µm, and red, 0.70 µm.
Fig. 5
Fig. 5 Deflection angle as a function of wavelength for the elements in Table 1. Deflection angles for the prism are on the right and, for the GRIN elements, on the left. The scales are equal for both.
Fig. 6
Fig. 6 Deflection angle as a function of wavelength for ternary designs with different design wavelengths.

Tables (2)

Tables Icon

Table 1 Glass materials used to design deflectors in Table 1.

Tables Icon

Table 2 Deflection elements.

Equations (18)

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n 2 ( x , λ ) = γ a ( x ) n a 2 ( λ ) + γ b ( x ) n b 2 ( λ ) , = n a 2 ( λ ) + γ b ( x ) [ n b 2 ( λ ) n a 2 ( λ ) ] ,
γ a ( x ) + γ b ( x ) = 1 .
d n ( x , λ ) d λ = [ 1 n ( x , λ ) ] { n a ( λ ) d n a ( λ ) d λ + γ b ( x ) [ n b ( λ ) d n b ( λ ) d λ n a ( λ ) d n a ( λ ) d λ ] } .
γ b ( x ) = n ˜ 2 ( x ) n a 2 ( λ 0 ) n b 2 ( λ 0 ) n a 2 ( λ 0 ) .
n 2 ( x , λ ) = n a 2 ( λ ) + γ b ( x ) [ n b 2 ( λ ) n a 2 ( λ ) ] + γ c ( x ) [ n c 2 ( λ ) n a 2 ( λ ) ] ,
γ a ( x ) = 1 γ b ( x ) γ c ( x ) ,
d n ( x , λ ) d λ = [ 1 n ( x , λ ) ] { n a ( λ ) d n a ( λ ) d λ + γ b ( x ) [ n b ( λ ) d n b ( λ ) d λ n a ( λ ) d n a ( λ ) d λ ] + γ c ( x ) [ n c ( λ ) d n c ( λ ) d λ n a ( λ ) d n a ( λ ) d λ ] } .
[ n 2 ( x , λ ) n ( x , λ ) d n ( x , λ ) d λ ] = N ( λ ) [ γ b ( x ) γ c ( x ) ] + [ n a 2 ( λ ) n a ( λ ) d n a ( λ ) d λ ] ,
N ( λ ) = [ n b 2 ( λ ) n a 2 ( λ ) n b ( λ ) d n b ( λ ) d λ n a ( λ ) d n a ( λ ) d λ n c 2 ( λ ) n a 2 ( λ ) n c ( λ ) d n c ( λ ) d λ n a ( λ ) d n a ( λ ) d λ ] .
[ γ b ( x ) γ c ( x ) ] = N 1 ( λ 0 ) [ n ˜ 2 ( x ) n a 2 ( λ 0 ) n ˜ ( x ) d n ˜ ( x ) n a ( λ 0 ) d n a ( λ 0 ) d λ ] .
tan β R ( λ ) = [ n a ( λ ) 1 ] tan α .
θ G ( x , λ ) = ( 2 π d λ ) n ( x , λ ) .
n ( x , λ ) = n min ( λ ) + [ n max ( λ ) n min ( λ ) ] ( x W ) ,
tan β G ( λ ) = ( d W ) [ n max ( λ ) n min ( λ ) ] .
n ˜ max = n b ( λ 0 ) ,
n ˜ min = n a 2 ( λ 0 ) + γ a c [ n c 2 ( λ 0 ) n a 2 ( λ 0 ) ] ,
d n ˜ ( x ) = d n b ( λ 0 ) d λ .
γ a c = n b ( λ 0 ) d n b ( λ 0 ) / d λ n a ( λ 0 ) d n a ( λ 0 ) / d λ n c ( λ 0 ) d n c ( λ 0 ) / d λ n a ( λ 0 ) d n a ( λ 0 ) / d λ .

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