Abstract

Cut-off filters are usually operating at oblique incidence and exhibit polarization dependence properties. We propose a simple approach to design cut-off filters with low linear polarization sensitivity (LPS) based on dielectric-metal-dielectric (DMD) stacks. The designing method is derived from the theory of optical film characteristic matrix. The admittance loci of the film are adjusted to achieve similar spectral properties of s- and p-polarized light at oblique incidence. Different film structures are designed non-polarizing at different angles of incidence with the method. The results show that the designing method is efficient for designing non-polarizing cut-off filters, which are widely used in non-polarizing optical system.

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References

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  1. P. N. Slater, Remote Sensing: Optics and Optical Systems (Addison-Wesley, 1980).
  2. P. Ma, F. Lin, and J. A. Dobrowolski, “Design and manufacture of metal/dielectric long-wavelength cutoff filters,” Appl. Opt.50(9), C201–C209 (2011).
    [CrossRef] [PubMed]
  3. P. H. Berning and A. F. Turner, “Induced transmission in absorbing films applied to band pass filter design,” J. Opt. Soc. Am.47(3), 230–239 (1957).
    [CrossRef]
  4. L. G. Schulz, “The optical constants of silver, gold, copper, and aluminum. I. the absorption coefficient k,” J. Opt. Soc. Am.44(5), 357–362 (1954).
    [CrossRef]
  5. P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta (Lond.)8(2), 105–119 (1961).
    [CrossRef]
  6. W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the moderate resolution imaging spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Rem. Sens.36(4), 1088–1100 (1998).
    [CrossRef]
  7. G. Meister, E. J. Kwiatkowska, B. A. Franz, F. S. Patt, G. C. Feldman, and C. R. McClain, “Moderate-resolution imaging spectroradiometer ocean color polarization correction,” Appl. Opt.44(26), 5524–5535 (2005).
    [CrossRef] [PubMed]
  8. H. R. Gordon, T. Du, and T. Zhang, “Atmospheric correction of ocean color sensors: analysis of the effects of residual instrument polarization sensitivity,” Appl. Opt.36(27), 6938–6948 (1997).
    [CrossRef] [PubMed]
  9. V. R. Costich, “Reduction of polarization effects in interference coatings,” Appl. Opt.9(4), 866–870 (1970).
    [CrossRef] [PubMed]
  10. J. Ciosek, J. A. Dobrowolski, G. A. Clarke, and G. Laframboise, “Design and manufacture of all-dielectric nonpolarizing beam splitters,” Appl. Opt.38(7), 1244–1250 (1999).
    [CrossRef] [PubMed]
  11. A. Thelen, “Nonpolarizing interference films inside a glass cube,” Appl. Opt.15(12), 2983–2985 (1976).
    [CrossRef] [PubMed]
  12. A. Thelen, “Nonpolarizing edge filters,” J. Opt. Soc. Am.71(3), 309–314 (1981).
    [CrossRef]
  13. A. Thelen, “Nonpolarizing edge filters: Part 2,” Appl. Opt.23(20), 3541–3543 (1984).
    [CrossRef] [PubMed]
  14. H. Qi, R. Hong, K. Yi, J. Shao, and Z. Fan, “Nonpolarizing and polarizing filter design,” Appl. Opt.44(12), 2343–2348 (2005).
    [CrossRef] [PubMed]
  15. X. Ma, D. Liu, F. Zhang, and Y. Yan, “Non-polarizing broadband dichroic mirror,” J. Opt. A, Pure Appl. Opt.9(7), 573–576 (2007).
    [CrossRef]
  16. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, Bristol, UK, 2001).
  17. K. Wu, C. C. Lee, and T. L. Ni, “Advanced broadband monitoring for thin film deposition through equivalent optical admittance loci observation,” Opt. Express20(4), 3883–3889 (2012).
    [CrossRef] [PubMed]
  18. Q. Y. Cai, Y. X. Zheng, D. X. Zhang, W. J. Lu, R. J. Zhang, W. Lin, H. B. Zhao, and L. Y. Chen, “Application of image spectrometer to in situ infrared broadband optical monitoring for thin film deposition,” Opt. Express19(14), 12969–12977 (2011).
    [CrossRef] [PubMed]
  19. C. C. Lee and Y. J. Chen, “Multilayer coatings monitoring using admittance diagram,” Opt. Express16(9), 6119–6124 (2008).
    [CrossRef] [PubMed]
  20. C. C. Lee, K. Wu, S. H. Chen, and S. J. Ma, “Optical monitoring and real time admittance loci calculation through polarization interferometer,” Opt. Express15(26), 17536–17541 (2007).
    [CrossRef] [PubMed]
  21. T. W. Allen and R. G. DeCorby, “Conditions for admittance-matched tunneling through symmetric metal-dielectric stacks,” Opt. Express20(S5Suppl 5), A578–A588 (2012).
    [CrossRef] [PubMed]

2012

2011

2008

2007

2005

1999

1998

W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the moderate resolution imaging spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Rem. Sens.36(4), 1088–1100 (1998).
[CrossRef]

1997

1984

1981

1976

1970

1961

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta (Lond.)8(2), 105–119 (1961).
[CrossRef]

1957

1954

Allen, T. W.

Barnes, W. L.

W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the moderate resolution imaging spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Rem. Sens.36(4), 1088–1100 (1998).
[CrossRef]

Baumeister, P.

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta (Lond.)8(2), 105–119 (1961).
[CrossRef]

Berning, P. H.

Cai, Q. Y.

Chen, L. Y.

Chen, S. H.

Chen, Y. J.

Ciosek, J.

Clarke, G. A.

Costich, V. R.

DeCorby, R. G.

Dobrowolski, J. A.

Du, T.

Fan, Z.

Feldman, G. C.

Franz, B. A.

Gordon, H. R.

Hong, R.

Kwiatkowska, E. J.

Laframboise, G.

Lee, C. C.

Lin, F.

Lin, W.

Liu, D.

X. Ma, D. Liu, F. Zhang, and Y. Yan, “Non-polarizing broadband dichroic mirror,” J. Opt. A, Pure Appl. Opt.9(7), 573–576 (2007).
[CrossRef]

Lu, W. J.

Ma, P.

Ma, S. J.

Ma, X.

X. Ma, D. Liu, F. Zhang, and Y. Yan, “Non-polarizing broadband dichroic mirror,” J. Opt. A, Pure Appl. Opt.9(7), 573–576 (2007).
[CrossRef]

McClain, C. R.

Meister, G.

Ni, T. L.

Pagano, T. S.

W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the moderate resolution imaging spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Rem. Sens.36(4), 1088–1100 (1998).
[CrossRef]

Patt, F. S.

Qi, H.

Salomonson, V. V.

W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the moderate resolution imaging spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Rem. Sens.36(4), 1088–1100 (1998).
[CrossRef]

Schulz, L. G.

Shao, J.

Thelen, A.

Turner, A. F.

Wu, K.

Yan, Y.

X. Ma, D. Liu, F. Zhang, and Y. Yan, “Non-polarizing broadband dichroic mirror,” J. Opt. A, Pure Appl. Opt.9(7), 573–576 (2007).
[CrossRef]

Yi, K.

Zhang, D. X.

Zhang, F.

X. Ma, D. Liu, F. Zhang, and Y. Yan, “Non-polarizing broadband dichroic mirror,” J. Opt. A, Pure Appl. Opt.9(7), 573–576 (2007).
[CrossRef]

Zhang, R. J.

Zhang, T.

Zhao, H. B.

Zheng, Y. X.

Appl. Opt.

IEEE Trans. Geosci. Rem. Sens.

W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the moderate resolution imaging spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Rem. Sens.36(4), 1088–1100 (1998).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

X. Ma, D. Liu, F. Zhang, and Y. Yan, “Non-polarizing broadband dichroic mirror,” J. Opt. A, Pure Appl. Opt.9(7), 573–576 (2007).
[CrossRef]

J. Opt. Soc. Am.

Opt. Acta (Lond.)

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta (Lond.)8(2), 105–119 (1961).
[CrossRef]

Opt. Express

Other

P. N. Slater, Remote Sensing: Optics and Optical Systems (Addison-Wesley, 1980).

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, Bristol, UK, 2001).

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Figures (9)

Fig. 1
Fig. 1

Polarization spectra of 45° incident light on BK7 | 45nm ZnS/11nm Ag/45nm ZnS | Air.

Fig. 2
Fig. 2

The structure of non-polarizing cut-off filters based on DMD stacks.

Fig. 3
Fig. 3

The expected admittance loci of each layer of D1MD3 stack [16].

Fig. 4
Fig. 4

Admittance locus of BK7 | t1D1/t2M/t3D3 | Air at normal incidence.

Fig. 5
Fig. 5

Admittance locus of BK7 | t1D′1/t2M′/t1D″1 | Air at normal incidence.

Fig. 6
Fig. 6

Admittance locus of BK7 | (t1D′1/t2M′/t1D″1)x/t1D1/t2M/t3D3 | Air at normal incidence.

Fig. 7
Fig. 7

Polarization spectra at incident angle of 30° with x = 0, 1, 2.

Fig. 8
Fig. 8

Polarization spectra at incident angle of 45° with x = 2.

Fig. 9
Fig. 9

Polarization spectra at incident angle of 60° with x = 2.

Tables (2)

Tables Icon

Table 1 Designing Table for Ta2O5-Ag-SiO2 sStack

Tables Icon

Table 2 Designing Table for Ta2O5-Ag-Ta2O5 Stack

Equations (16)

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LPS= | T max T min | T max + T min = | T p T s | T p + T s .
Y=C/B,
[ B C ]={ j=1 K [ cos δ j isin δ j / η j i η j sin δ j cos δ j ] }[ 1 η sub ],
N 0 sin θ 0 = N j sin θ j ,
{ η rs = N r cos θ r fors-polarized light η rp = N r /cos θ r forp-polarized light .
[ cos δ j isin δ j / η j i η j sin δ j cos δ j ]
cos θ j = 1 sin 2 θ j = 1+ n 0 2 sin 2 θ 0 / k j 2 ,
{ η js = N j cos θ j =-i k j 1+ n 0 2 sin 2 θ 0 / k j 2 fors-polarized light η jp = N j /cos θ j =-i k j / 1+ n 0 2 sin 2 θ 0 / k j 2 forp-polarized light ,
δ j =2π N j d j cos θ j /λ=-i2π k j d j cos θ j /λ.
T=( 1R )ψ.
R=( η 0 Y η 0 +Y ) ( η 0 Y η 0 +Y ) * =( 1Y/ η 0 1+Y/ η 0 ) ( 1Y/ η 0 1+Y/ η 0 ) * .
Y/ η 0 =f( η sub , η 0 , η 1 ,, η j ,, η K , δ 1 ,, δ j ,, δ K ).
{ η rs N r ( 1 1 2 sin 2 θ r )= N r ( 1 1 2 N 0 2 N r 2 sin 2 θ 0 )fors-polarized light η rp N r ( 1+ 1 2 sin 2 θ r )= N r ( 1+ 1 2 N 0 2 N r 2 sin 2 θ 0 )forp-polarized light .
{ ( Y/ η 0 ) s f( N sub , N 0 , N 1 ,, N j ,, N K , δ 1 ,, δ j ,, δ K )Δ( Y/ η 0 )fors-polarized light ( Y/ η 0 ) p f( N sub , N 0 , N 1 ,, N j ,, N K , δ 1 ,, δ j ,, δ K )+Δ( Y/ η 0 )forp-polarized light .
{ R s | Δ( Y/ η 0 ) | 2 | 2-Δ( Y/ η 0 ) | 2 | Δ( Y/ η 0 ) | 2 4 fors-polarized light R p | Δ( Y/ η 0 ) | 2 | 2+Δ( Y/ η 0 ) | 2 | Δ( Y/ η 0 ) | 2 4 forp-polarized light .
d j = δ j λ 2π N j cos θ j = t j cos θ j .

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