Abstract

The Micro-Stripes program has been used to calculate resonance wavelengths and the bandwidth of inductive cross-shaped metal meshes in contact with dielectric layers. The shift of the resonance wavelength, depending on the thickness of the dielectric layers, has been studied for two refractive indices. The transmittance of two mesh filters with dielectric spacers or embedded in a dielectric has been calculated for specific alignment of the crosses of one mesh with respect to the other. Transmission line theory has been used to calculate the transmittance of two mesh filters with nonaligned crosses and dielectric layers. A coupled oscillator model has been used for interpretation of the interaction of resonance and Fabry–Perot modes.

© 2002 Optical Society of America

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References

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  1. R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry-Perot type,” IEEE Trans. MTT-11, 363–371 (1963).
  2. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
    [CrossRef]
  3. G. M. Ressler, K. D. Möller, “Far infrared bandpass filters and measurements on a reciprocal grid,” Appl. Opt. 6, 893–896 (1967).
    [CrossRef] [PubMed]
  4. R. Ulrich, “Interference filters for the far infrared,” Infrared Phys. 7, 1987–1996 (1967).
  5. S. T. Chase, R. D. Joseph, “Resonant array bandpass filters for the far infrared,” Appl. Opt. 22, 1775–1779 (1983).
    [CrossRef] [PubMed]
  6. L. B. Whitbourn, R. C. Compton, “Equivalent-circuit formulas for metal grid reflectors at dielectric boundary,” Appl. Opt. 24, 217–220 (1985).
    [CrossRef]
  7. T. Timusk, P. L. Richards, “Near millimeter wave bandpass filters,” Appl. Opt. 20, 1355–1360 (1981).
    [CrossRef] [PubMed]
  8. D. M. Kearns, R. W. Beatty, Basic Theory of Waveguide Functions and Introductory Microwave Network Analysis (Pergamon, Oxford, UK, 1967).
  9. K. D. Möller, O. Sternberg, H. Grebel, K. P. Stewart, “Near- field effect in multilayer inductive metal meshes,” Appl. Opt. 41, 1942–1948 (2002).
    [CrossRef] [PubMed]
  10. Micro-Stripes program, Flometrics, Inc., 275 Turnpike Road, Suite 100, Southborough, Mass. 01772.
  11. D. H. Dawes, R. C. McPhedran, L. B. Whitbourn, “Thin capacitive meshes on a dielectric boundary: theory and experiment,” Appl. Opt. 28, 3498–3510 (1989).
    [CrossRef] [PubMed]
  12. C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
    [CrossRef]
  13. D. W. Porterfield, J. L. Hesler, R. Densing, E. R. Mueller, T. W. Crowe, R. M. Weikle, “Resonant metal-mesh bandpass filters for the far infrared,” Appl. Opt. 33, 6046–6092 (1994).
    [CrossRef] [PubMed]
  14. R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).
  15. B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.
  16. K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
    [CrossRef]
  17. R. Ulrich, “Modes of propagation on an open periodic waveguide for the far infrared,” Proceedings of the Symposium of Optical and Acoustical Micro-Electronics, J. Fox, ed. (Polytechnic, New York, 1974), Vol. XXIII.

2002 (1)

1999 (1)

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

1994 (1)

1991 (1)

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

1989 (1)

1985 (1)

1983 (2)

C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

S. T. Chase, R. D. Joseph, “Resonant array bandpass filters for the far infrared,” Appl. Opt. 22, 1775–1779 (1983).
[CrossRef] [PubMed]

1981 (1)

1967 (3)

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

G. M. Ressler, K. D. Möller, “Far infrared bandpass filters and measurements on a reciprocal grid,” Appl. Opt. 6, 893–896 (1967).
[CrossRef] [PubMed]

R. Ulrich, “Interference filters for the far infrared,” Infrared Phys. 7, 1987–1996 (1967).

1963 (1)

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry-Perot type,” IEEE Trans. MTT-11, 363–371 (1963).

Ade, P.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Bacher, W.

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

Beatty, R. W.

D. M. Kearns, R. W. Beatty, Basic Theory of Waveguide Functions and Introductory Microwave Network Analysis (Pergamon, Oxford, UK, 1967).

Bley, P.

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

Botten, L. C.

C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Chase, S. T.

Compton, C.

C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Compton, R. C.

Crowe, T. W.

Dawes, D. H.

Densing, R.

Derrick, G. H.

C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Farmer, K. R.

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

Fischer, J.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Genzel, L.

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry-Perot type,” IEEE Trans. MTT-11, 363–371 (1963).

Grebel, H.

Greenhouse, M.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Harmening, M.

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

Hesler, J. L.

Hicks, B. C.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Isaacson, P.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Ivanov, D. V. P.

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

Joseph, R. D.

Kearns, D. M.

D. M. Kearns, R. W. Beatty, Basic Theory of Waveguide Functions and Introductory Microwave Network Analysis (Pergamon, Oxford, UK, 1967).

Lalanne, P.

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

Ma, D.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Marrian, C.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

McPhedran, R. C.

McPhedran, R. D.

C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

Möller, K. D.

Moseley, H.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Mueller, E. R.

Porterfield, D. W.

Rebbert, M.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Renk, K. F.

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry-Perot type,” IEEE Trans. MTT-11, 363–371 (1963).

Ressler, G. M.

Richards, P. L.

Ruprecht, R.

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

Schomburg, W. K.

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

Smith, H. A.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Sternberg, O.

K. D. Möller, O. Sternberg, H. Grebel, K. P. Stewart, “Near- field effect in multilayer inductive metal meshes,” Appl. Opt. 41, 1942–1948 (2002).
[CrossRef] [PubMed]

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

Stewart, K.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Stewart, K. P.

K. D. Möller, O. Sternberg, H. Grebel, K. P. Stewart, “Near- field effect in multilayer inductive metal meshes,” Appl. Opt. 41, 1942–1948 (2002).
[CrossRef] [PubMed]

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

Sudiwala, R.

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

Timusk, T.

Ulrich, R.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

R. Ulrich, “Interference filters for the far infrared,” Infrared Phys. 7, 1987–1996 (1967).

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry-Perot type,” IEEE Trans. MTT-11, 363–371 (1963).

R. Ulrich, “Modes of propagation on an open periodic waveguide for the far infrared,” Proceedings of the Symposium of Optical and Acoustical Micro-Electronics, J. Fox, ed. (Polytechnic, New York, 1974), Vol. XXIII.

Weikle, R. M.

Whitbourn, L. B.

Appl. Opt. (7)

IEEE Trans. (1)

R. Ulrich, K. F. Renk, L. Genzel, “Tunable submillimeter interferometers of the Fabry-Perot type,” IEEE Trans. MTT-11, 363–371 (1963).

Infrared Phys. (4)

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

R. Ulrich, “Interference filters for the far infrared,” Infrared Phys. 7, 1987–1996 (1967).

K. D. Möller, K. R. Farmer, D. V. P. Ivanov, O. Sternberg, K. P. Stewart, P. Lalanne, “Thin and thick cross shaped metal grids,” Infrared Phys. 40, 475–485 (1999).
[CrossRef]

C. Compton, R. D. McPhedran, G. H. Derrick, L. C. Botten, “Diffraction properties of a bandpass grid,” Infrared Phys. 23, 239–245 (1983).
[CrossRef]

KfK-Nachr. Jahrg. (1)

R. Ruprecht, W. Bacher, P. Bley, M. Harmening, W. K. Schomburg, “Investigation of bandpass filters for the far infrared and manufacturing using LIGA,” KfK-Nachr. Jahrg. 23, 2–91, 18–123 (1991).

Other (4)

B. C. Hicks, M. Rebbert, P. Isaacson, D. Ma, C. Marrian, J. Fischer, H. A. Smith, P. Ade, R. Sudiwala, M. Greenhouse, H. Moseley, K. Stewart, “Nanotechnology fabrication of polysilicon film/metal grid infrared filters,” presented at the NASA Laboratory Space Science Workshop, Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass., 1–3 April 1998.

R. Ulrich, “Modes of propagation on an open periodic waveguide for the far infrared,” Proceedings of the Symposium of Optical and Acoustical Micro-Electronics, J. Fox, ed. (Polytechnic, New York, 1974), Vol. XXIII.

Micro-Stripes program, Flometrics, Inc., 275 Turnpike Road, Suite 100, Southborough, Mass. 01772.

D. M. Kearns, R. W. Beatty, Basic Theory of Waveguide Functions and Introductory Microwave Network Analysis (Pergamon, Oxford, UK, 1967).

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Figures (15)

Fig. 1
Fig. 1

(a) Inductive cross-shaped mesh. Black is metal; white is the opening. (b) Geometric parameters g, a, and b of the crosses. (c) Cross in the shifted position. (d) Cross in the lined-up position.

Fig. 2
Fig. 2

Shunt impedance with incident and reflected waves with refractive index n 1 on the left side and with refractive index n 2 on the right side.

Fig. 3
Fig. 3

Shift of the resonance wavelength depending on refractive index and thickness of dielectric environment. The parameters of the mesh are g = 20 µm, 2a = 1.5 µm, 2b = 3 µm, and t = 0.2 µm. The horizontal lines indicate the results of TLT. The embedded mesh has dielectric layers of thickness of the substrate on each side. Micro-Stripes calculations: for n = 3.4, the upper squares are the embedded case and the lower triangles are for the substrate. For n = 1.5, the upper squares are the embedded case and the lower triangles are for the substrate.

Fig. 4
Fig. 4

Schamatic of the spacer configuration (SP) with thickness d and embedded configuration (EM) with spacer thickness d and thickness d* of layers outside of the meshes. Black is metal, gray is the dielectric. In filter configuration (A), the openings of both metal meshes are lined up; in configuration (B), the openings of one mesh is between the openings of the other mesh.

Fig. 5
Fig. 5

Transmission line calculations of peak wavelengths of resonance and Fabry–Perot peaks of two meshes with dielectrics of n = 1.5 depending on the thickness of spacer d = 2–16 µm. Squares (SP), spacer only; circles (EM), embedded. Transmission line parameters are λ0 = 32.4 µm, A1 = 0.1, a1 = 0.001 corresponding to g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. The thickness of the outside layer for the embedded case is d* = 10 µm.

Fig. 6
Fig. 6

Two metal meshes with a spacer of refractive index n = 1.5 and thickness d = 4 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT calculations with parameters λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 7
Fig. 7

Two metal meshes with a spacer of refractive index n = 1.5 and thickness d = 8 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT calculations with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 8
Fig. 8

Two metal meshes embedded in a dielectric of refractive index n = 1.5, spacer thickness d = 4 µm, and outside layer of thickness d* = 10 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 9
Fig. 9

Two metal meshes embedded in a dielectric of refractive index n = 1.5, spacer thickness of d = 8 µm, and outside layer of thickness d* = 10 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 10
Fig. 10

Transmission line calculations of peak wavelengths of resonance and Fabry–Perot peaks of two meshes with dielectrics of refractive index n = 3.4 depending on the thickness of spacer d = 2–16 µm. Squares (SP), spacer only; circles (EM), embedded. Transmission line parameters are λ0 = 32.4 µm, A1 = 0.1 and a1 = 0.001 corresponding to g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. The thickness of the outside layer for the embedded case is d* = 5 µm.

Fig. 11
Fig. 11

Two metal meshes embedded in a dielectric of refractive index n = 3.4 and spacer thickness of d = 4 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 12
Fig. 12

Two metal meshes with a spacer of refractive index n = 3.4 and thickness d = 8 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 13
Fig. 13

Two metal meshes embedded in a dielectric of refractive index n = 3.4, spacer thickness d = 4 µm, and an outside layer of thickness d* = 5 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 14
Fig. 14

Two metal meshes embedded in a dielectric of refractive index n = 3.4, spacer thickness d = 8 µm, and outside layer of thickness d* = 5 µm. Geometric parameters are g = 24 µm, 2a = 9.6 µm, 2b = 3.6 µm, and a thickness of 0.2 µm. Thick solid curve, Micro-Stripes calculation of filter (A); thin solid curve, Micro-Stripes calculation of filter (B); dashed curve, TLT with parameters of λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001.

Fig. 15
Fig. 15

Transmittance of two meshes with a spacer of thickness 8 µm. Transmission line parameters are λ0 = 32.4 µm, A1 = 0.1, and a1 = 0.001. Free-standing meshes (F), spacer of refractive index n = 1.5 (SP), and embedded (EM) in dielectrics of refractive index n = 1.5 with d* = 10 µm. The ratio of the bandwidth at half-height to the peak wavelength bandwidth for (F) is equal to 10%, for (SP) is equal to 10%, and for (EM) is equal to 12%.

Equations (9)

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Yλ=1/a1-iωA1/Ωλ,
ω=ω02/n12+n221/2,
Ωλ=g/λω-λω/g.
b1=m11a2+m12b2, a1=m21a2+m22b2.
b1/a1=m12/m22.
b2/a1=1/m22.
m111=-Y+n1+n2/2n1m112=-Y+n1-n2/2n1m121=Y+n1-n2/2n1m122=Y+n1+n2/2n1.
m211=n1+n2/2n1m212=n1-n2/2n1m221=n1-n2/2n1m222=n1+n2/2n1.
m311=exp-i2πdn/λm312=0m321=0m322=expi2πdn/λ.

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