Abstract

This analysis explores the theory and design of dielectric multilayer reflection-enhancing thin film stacks based on high and low refractive index alternating layers of cadmium sulfide (CdS) and lead sulfide (PbS) on silver (Ag)-coated hollow glass waveguides (HGWs) for low loss transmission at midinfrared wavelengths. The fundamentals for determining propagation losses in such multilayer thin-film-coated Ag hollow waveguides is thoroughly discussed, and forms the basis for further theoretical analysis presented in this study. The effects on propagation loss resulting from several key parameters of these multilayer thin film stacks is further explored in order to bridge the gap between results predicted through calculation under ideal conditions and deviations from such ideal models that often arise in practice. In particular, the effects on loss due to the number of dielectric thin film layers deposited, deviation from ideal individual layer thicknesses, and surface roughness related scattering losses are presented and thoroughly investigated. Through such extensive theoretical analysis the level of understanding of the underlying loss mechanisms of multilayer thin-film Ag-coated HGWs is greatly advanced, considerably increasing the potential practical development of next-generation ultralow-loss mid-IR Ag/multilayer dielectric-coated HGWs.

© 2013 Optical Society of America

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References

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  1. J. A. Harrington, Infrared Fiber Optics and Their Applications (SPIE, 2004).
  2. D. Rabii and J. A. Harrington, “Measurement and control of thin film uniformity in hollow glass waveguides,” Opt. Eng. 38, 2009–2015 (1999).
    [CrossRef]
  3. J. A. Harrington and V. Gopal, “Method, and article of the method, for fabricating a hollow waveguide,” U.S. Patent7,315,675 (January12008).
  4. M. Miyagi and S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
    [CrossRef]
  5. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2010).
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  7. E. Hecht, Optics, 3rd Ed. (Addison Wesley Longman, 1998).
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  10. R. J. George, “New dielectric thin film coatings for Ag and Cu coated hollow infrared waveguides,” Ph.D. dissertation (Rutgers University, 2004).
  11. V. Gopal and J. A. Harrington, “Deposition and characterization of metal sulfide dielectric coatings for hollow glass waveguides,” Opt. Express 11, 3182–3187 (2003).
    [CrossRef]
  12. C. M. Bledt, J. E. Melzer, and J. A. Harrington, “Investigation of metal sulfide optical thin film growth in low-loss IR hollow glass waveguides,” Opt. Mater. Express, 3, 1397–1407 (2013).
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    [CrossRef]

2013 (2)

2003 (1)

1999 (1)

D. Rabii and J. A. Harrington, “Measurement and control of thin film uniformity in hollow glass waveguides,” Opt. Eng. 38, 2009–2015 (1999).
[CrossRef]

1998 (1)

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

1997 (1)

1993 (1)

1989 (1)

1984 (1)

M. Miyagi and S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

1983 (1)

Bledt, C. M.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Fan, S.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

George, R. J.

R. J. George, “New dielectric thin film coatings for Ag and Cu coated hollow infrared waveguides,” Ph.D. dissertation (Rutgers University, 2004).

Ghosh, G.

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Gopal, V.

V. Gopal and J. A. Harrington, “Deposition and characterization of metal sulfide dielectric coatings for hollow glass waveguides,” Opt. Express 11, 3182–3187 (2003).
[CrossRef]

J. A. Harrington and V. Gopal, “Method, and article of the method, for fabricating a hollow waveguide,” U.S. Patent7,315,675 (January12008).

Harrington, J. A.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Film Solids, 1st ed. (Dover Publications, 1991).

Hecht, E.

E. Hecht, Optics, 3rd Ed. (Addison Wesley Longman, 1998).

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, R. D. Mead, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, R. D. Mead, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Kawakami, S.

M. Miyagi and S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

M. Miyagi and S. Kawakami, “Waveguide loss evaluation by the ray-optics method,” J. Opt. Soc. Am. 73, 486–489 (1983).
[CrossRef]

Matsuura, Y.

Mead, R. D.

J. D. Joannopoulos, S. G. Johnson, R. D. Mead, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Melzer, J. E.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Miyagi, M.

Orfanidis, S. J.

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2010).

Palik, E. D.

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Rabii, D.

D. Rabii and J. A. Harrington, “Measurement and control of thin film uniformity in hollow glass waveguides,” Opt. Eng. 38, 2009–2015 (1999).
[CrossRef]

Saito, M.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Sato, S.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, R. D. Mead, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

Appl. Opt. (1)

J. Lightwave Technol. (1)

M. Miyagi and S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

D. Rabii and J. A. Harrington, “Measurement and control of thin film uniformity in hollow glass waveguides,” Opt. Eng. 38, 2009–2015 (1999).
[CrossRef]

Opt. Express (1)

Opt. Mater. Express (1)

Science (1)

Y. Fink, J. N. Winn, S. Fan, J. Michel, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef]

Other (9)

J. A. Harrington, Infrared Fiber Optics and Their Applications (SPIE, 2004).

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

J. A. Harrington and V. Gopal, “Method, and article of the method, for fabricating a hollow waveguide,” U.S. Patent7,315,675 (January12008).

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2010).

J. D. Joannopoulos, S. G. Johnson, R. D. Mead, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Princeton University, 2008).

E. Hecht, Optics, 3rd Ed. (Addison Wesley Longman, 1998).

O. S. Heavens, Optical Properties of Thin Film Solids, 1st ed. (Dover Publications, 1991).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

R. J. George, “New dielectric thin film coatings for Ag and Cu coated hollow infrared waveguides,” Ph.D. dissertation (Rutgers University, 2004).

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Figures (11)

Fig. 1.
Fig. 1.

(a) Cross-sectional representation of Ag/multilayer dielectric stack-coated HGW and (b) representative refractive index profile of functional HGW thin films.

Fig. 2.
Fig. 2.

Geometrical representation of meridional ray propagating along a section of a HW (not to scale).

Fig. 3.
Fig. 3.

Theoretical waveguide propagation loss in the near and mid-IR for a total of (a) N=2, (b) N=5, (c) N=8, and (d) N=11 CdS/PbS alternating layers on an Ag-coated HGW of ID=700μm assuming an ideal film structure optimized for λ=2.94μm.

Fig. 4.
Fig. 4.

Theoretical waveguide propagation loss at λ=2.94μm as a function of total CdS/PbS alternating dielectric layers on an Ag-coated HGW of ID=700μm assuming an ideal film structure with each film thickness optimized for this wavelength.

Fig. 5.
Fig. 5.

Theoretical waveguide propagation loss at λ=2.94μm as a function of propagation angle on an Ag-coated HGW for N=2, 5, 8, and 11 total dielectric layers.

Fig. 6.
Fig. 6.

Theoretical waveguide propagation loss at λ=2.94μm as a function of total CdS/PbS alternating dielectric layers on an Ag-coated HGW for bore sizes of ID=2a=300, 500, 700, and 1,000 μm.

Fig. 7.
Fig. 7.

Theoretical waveguide propagation in the near and mid-IR for random individual film variation about optimal film thicknesses for λ=2.94μm with N=8 CdS/PbS alternating layers on an Ag-coated HGW of ID=700μm with film variation ranges of (a) CdS:±57%, PbS:±710%, (b) CdS:±810%, PbS:±1114%, (c) CdS:±1113%, PbS:±1518%, and (d) CdS:±1416%, PbS:±1922% with no film variation spectrum for comparison.

Fig. 8.
Fig. 8.

Theoretical waveguide propagation in the near and mid-IR with individual film thicknesses optimized for λ=2.94μm with optimized and nonoptimized innermost layer thicknesses for (a) N=7 and (b) N=8 total dielectric layers.

Fig. 9.
Fig. 9.

Theoretical waveguide propagation in the near and mid-IR with individual film thicknesses optimized for at λ=2.94μm with N=8 CdS/PbS alternating dielectric layers on an Ag-coated HGW of ID=700μm having individual film surface roughness contributions of (a) σRMS=10nm, (b) σRMS=20nm, (c) σRMS=30nm, and (d) σRMS=40nm with smooth film spectrum for comparison.

Fig. 10.
Fig. 10.

Theoretical waveguide propagation loss at λ=2.94μm as a function of total CdS/PbS alternating dielectric layers on an Ag-coated HGW for individual layer surface roughness contributions of σRMS=0, 10, 20, 30, and 40 nm.

Fig. 11.
Fig. 11.

(a) Calculated waveguide loss at λ=2.94μm as a function of total CdS/PbS alternating dielectric layers on an Ag-coated HGW according to the modified propagation loss model and (b) calculated spectral response of an Ag/multilayer-coated HGW with N=7 according to this modified model along with that for the ideal model for comparison.

Tables (1)

Tables Icon

Table 1. Variation Ranges for Simulated Losses

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

L=2atanφ=2acotφ.
2α=10·A2acotφα=10·1R(φ)4acotφ,
[Ti]=1τi1,i[1ρi1,iρi1,i1][ejkidi00ejkidi],
ρsi1,i=ηicos(θi)ηi1cos(θi1)ηicos(θi)+ηi1cos(θi1),
τsi1,i=2ηicos(θi)ηicos(θi)+ηi1cos(θi1),
ρpi1,i=ηicos(θi)ηi1cos(θi1)ηicos(θi)+ηi1cos(θi1),
τpi1,i=2ηicos(θi)ηicos(θi)+ηi1cos(θi1),
[TN]=i=1N[Ti],
[T]=[TN]1τN,Ag[1ρN,AgρN,Ag1].
[E0+E0]=[T][EAg+EAg][1E0]=[T11T12T21T22][EAg+0],
{1=EAg+T11E0=EAg+T21{EAg+=1T11E0=T21T11r=E0E0+=T21T11,
R=|rr*|=|(T21T11)·(T21T11)*|.
dF=λ04nF21,
δL=λ02πnL21tan1(nL(nL21)14(nLnH)(N12)(nL21nH21)(N14)),
δH=λ02πnH21tan1(nL21nL(nH21)14(nHnL)(N2)(nL21nH21)(N4)),
θnm=sin1(unmλ2πa),
ρσi1,i=ρi1,iexp(12(2k0·σi1,i·nisin(γi))2),
τσi1,i=τi1,iexp(12(k0·σi1,i·(nisin(γi)ni1sin(γi1)))2),

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