Abstract

We select a chalcogenide core glass, AsSe, and cladding glass, GeAsSe, for their disparate refractive indices yet sufficient thermal-compatibility for fabricating step index fiber (SIF) for mid-infrared supercontinuum generation (MIR-SCG). The refractive index dispersion of both bulk glasses is measured over the 0.4 µm–33 µm wavelength-range, probing the electronic and vibrational behavior of these glasses. We verify that a two-term Sellmeier model is unique and sufficient to describe the refractive index dispersion over the wavelength range for which the experimentally determined extinction coefficient is insignificant. A SIF composed of the glasses is fabricated and calculated to exhibit an ultra-high numerical aperture >0.97 over the entire wavelength range 0.4-33 µm suggesting that the SIF glass pair is a promising candidate for MIR-SCG. Material dispersion characteristics and the zero dispersion wavelength, both critical design parameters for SIF for MIR-SCG, are derived.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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2014

2013

Y. Yu, X. Gai, T. Wang, P. Ma, R. Wang, Z. Yang, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Mid-infrared supercontinuum in chalcogenides,” Opt. Mater. Express3(8), 1075–1086 (2013).
[CrossRef]

W. Yuan, “2–10µm mid-infrared supercontinuum generation in As2Se3 photonic crystal fiber,” Laser Phys. Lett.10(9), 095107 (2013).
[CrossRef]

A. B. Seddon, “Mid-infrared (IR) – a hot topic, the potential for using mid-IR light for non-invasive, early detection of skin cancers in vivo,” Phys. Status Solidi B250(5), 1020–1027 (2013).
[CrossRef]

I. Shavrin, S. Novotny, and H. Ludvigsen, “Mode excitation and supercontinuum generation in a few-mode suspended-core fiber,” Opt. Express21(26), 32141–32150 (2013).
[CrossRef] [PubMed]

2012

2011

A. B. Seddon, “A prospective for new mid-infrared medical endoscopy using chalcogenide glasses,” Int. J. Appl. Glass Sci.2(3), 177–191 (2011).
[CrossRef]

2010

2009

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

2008

J. Orava, J. Šik, T. Wagner, and M. Frumar, “Optical properties of As33S 67−x Sex bulk glasses studied by spectroscopic ellipsometry,” J. Appl. Phys.103(8), 083512 (2008).
[CrossRef]

2006

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006).
[CrossRef]

2002

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett.27(2), 119–121 (2002).
[CrossRef] [PubMed]

1996

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interbandregion,” Appl. Phys. Lett.69(3), 371–373 (1996).
[CrossRef]

1995

A. B. Seddon, “Chalcogenide glasses: a review of their preparation, properties and applications,” J. Non-Cryst. Solids184, 44–50 (1995).
[CrossRef]

1974

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
[CrossRef]

Aggarwal, I. D.

Agger, C.

Bang, O.

Benson, T.

I. Kubat, C. R. Petersen, U. V. Møller, A. Seddon, T. Benson, L. Brilland, D. Méchin, P. M. Moselund, and O. Bang, “Thulium pumped mid-infrared 0.9-9μm supercontinuum generation in concatenated fluoride and chalcogenide glass fibers,” Opt. Express22(4), 3959–3967 (2014).
[CrossRef] [PubMed]

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Benson, T. M.

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

Brilland, L.

Choi, D.-Y.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006).
[CrossRef]

Collins, R. W.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Dantanarayana, H.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Deng, X.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Derkowska, B.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006).
[CrossRef]

Dupont, S.

Ferlauto, A. S.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Ferreira, G. M.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Frumar, M.

J. Orava, J. Šik, T. Wagner, and M. Frumar, “Optical properties of As33S 67−x Sex bulk glasses studied by spectroscopic ellipsometry,” J. Appl. Phys.103(8), 083512 (2008).
[CrossRef]

Furniss, D.

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Gai, X.

Ganguly, G.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006).
[CrossRef]

Harbold, J. M.

Howard, R. E.

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
[CrossRef]

Ilday, F. O.

Jellison, G.

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interbandregion,” Appl. Phys. Lett.69(3), 371–373 (1996).
[CrossRef]

Keiding, S. R.

Konyukhov, A.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Kubat, I.

Li, Q. Q.

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

Lian, Z.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Lian, Z. G.

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

Ludvigsen, H.

Luther-Davies, B.

Lyngsø, J. K.

Ma, P.

Macedo, P. B.

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
[CrossRef]

Madden, S.

Maklad, M. S.

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
[CrossRef]

Méchin, D.

Modine, F.

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interbandregion,” Appl. Phys. Lett.69(3), 371–373 (1996).
[CrossRef]

Mohr, R. K.

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
[CrossRef]

Møller, U. V.

Moselund, P. M.

Moynihan, C. T.

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
[CrossRef]

Nguyen, V. Q.

Novotny, S.

Orava, J.

J. Orava, J. Šik, T. Wagner, and M. Frumar, “Optical properties of As33S 67−x Sex bulk glasses studied by spectroscopic ellipsometry,” J. Appl. Phys.103(8), 083512 (2008).
[CrossRef]

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Pearce, J. M.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Pedersen, C.

Petersen, C. R.

Romanova, E.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Sanghera, J. S.

Seddon, A.

I. Kubat, C. R. Petersen, U. V. Møller, A. Seddon, T. Benson, L. Brilland, D. Méchin, P. M. Moselund, and O. Bang, “Thulium pumped mid-infrared 0.9-9μm supercontinuum generation in concatenated fluoride and chalcogenide glass fibers,” Opt. Express22(4), 3959–3967 (2014).
[CrossRef] [PubMed]

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Seddon, A. B.

A. B. Seddon, “Mid-infrared (IR) – a hot topic, the potential for using mid-IR light for non-invasive, early detection of skin cancers in vivo,” Phys. Status Solidi B250(5), 1020–1027 (2013).
[CrossRef]

A. B. Seddon, “A prospective for new mid-infrared medical endoscopy using chalcogenide glasses,” Int. J. Appl. Glass Sci.2(3), 177–191 (2011).
[CrossRef]

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

A. B. Seddon, “Chalcogenide glasses: a review of their preparation, properties and applications,” J. Non-Cryst. Solids184, 44–50 (1995).
[CrossRef]

Sewell, P.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Shavrin, I.

Shaw, L. B.

Šik, J.

J. Orava, J. Šik, T. Wagner, and M. Frumar, “Optical properties of As33S 67−x Sex bulk glasses studied by spectroscopic ellipsometry,” J. Appl. Phys.103(8), 083512 (2008).
[CrossRef]

Skorobogatiy, M.

Steffensen, H.

Thøgersen, J.

Thomsen, C. L.

Ung, B.

Vukovic, A.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Wagner, T.

J. Orava, J. Šik, T. Wagner, and M. Frumar, “Optical properties of As33S 67−x Sex bulk glasses studied by spectroscopic ellipsometry,” J. Appl. Phys.103(8), 083512 (2008).
[CrossRef]

Wãgner, T.

H. Dantanarayana, A. Vukovic, P. Sewell, Z. Lian, D. Furniss, A. Seddon, E. Romanova, A. Konyukhov, B. Derkowska, J. Orava, T. Wãgner, and T. Benson, “The optical properties of chalcogenide glasses: From measurement to electromagnetic simulation tools,” in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON) (2010), pp. 1–4.
[CrossRef]

Wang, R.

Wang, T.

Wise, F. W.

Wronski, C. R.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

Yang, Z.

Yu, Y.

Yuan, W.

W. Yuan, “2–10µm mid-infrared supercontinuum generation in As2Se3 photonic crystal fiber,” Laser Phys. Lett.10(9), 095107 (2013).
[CrossRef]

Appl. Phys. Lett.

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interbandregion,” Appl. Phys. Lett.69(3), 371–373 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

Z. G. Lian, Q. Q. Li, D. Furniss, T. M. Benson, and A. B. Seddon, “Solid microstructured chalcogenide glass optical fibers for the near-and mid-infrared spectral regions,” IEEE Photon. Technol. Lett.21(24), 1804–1806 (2009).
[CrossRef]

Int. J. Appl. Glass Sci.

A. B. Seddon, “A prospective for new mid-infrared medical endoscopy using chalcogenide glasses,” Int. J. Appl. Glass Sci.2(3), 177–191 (2011).
[CrossRef]

J. Appl. Phys.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92(5), 2424–2436 (2002).
[CrossRef]

J. Orava, J. Šik, T. Wagner, and M. Frumar, “Optical properties of As33S 67−x Sex bulk glasses studied by spectroscopic ellipsometry,” J. Appl. Phys.103(8), 083512 (2008).
[CrossRef]

J. Non-Cryst. Solids

A. B. Seddon, “Chalcogenide glasses: a review of their preparation, properties and applications,” J. Non-Cryst. Solids184, 44–50 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys. Lett.

W. Yuan, “2–10µm mid-infrared supercontinuum generation in As2Se3 photonic crystal fiber,” Laser Phys. Lett.10(9), 095107 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater. Express

Phys. Status Solidi B

A. B. Seddon, “Mid-infrared (IR) – a hot topic, the potential for using mid-IR light for non-invasive, early detection of skin cancers in vivo,” Phys. Status Solidi B250(5), 1020–1027 (2013).
[CrossRef]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006).
[CrossRef]

Solid State Commun.

M. S. Maklad, R. K. Mohr, R. E. Howard, P. B. Macedo, and C. T. Moynihan, “Multiphonon absorption in As2S3-As2Se3 glasses,” Solid State Commun.15(5), 855–858 (1974).
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Other

E. Palik, Handbook of optical constants of solids, vol. 3, (Academic Press, 1998).

A. Zakery and S. R. Elliott, Optical Nonlinearities in Chalcogenide Glasses and their Applications (Springer, 2007).

Amorphous Materials Inc, “AMTIR-2 Information” (consulted July 2013). http://www.amorphousmaterials.com/app/download/6552914504/Amtir-2+Information.pdf .

D. Furniss and A. B. Seddon, “Thermal analysis of inorganic compound glasses and glass-ceramics” in Principles and Applications of Thermal Analysis, Paul Gabbott, ed. (Wiley-Blackwell, 2007), Chap. 10.

G. E. Jellison, “Data analysis for spectroscopic ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, ed. (William Andrew, Inc., 2005), Chap. 3.

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[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (5th edition, Academic Press, 2013).

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Figures (5)

Fig. 1
Fig. 1

Refractive index (n) and extinction coefficient (κ) variation with wavelength calculated from the ellipsometry measurements of the AsSe core and GeAsSe cladding bulk glass samples.

Fig. 2
Fig. 2

Refractive index modeling error of < 0.1% for: (a) AsSe and (b) GeAsSe, using models: Sellmeier II (1VIS, 1FIR), Sellmeier III (2 VIS,1 FIR) and Sellmeier III (1 VIS,2 FIR).

Fig. 3
Fig. 3

SIF multimode fiber comprising an AsSe glass core and GeAsSe glass cladding: (a) scanning electron micrograph (SEM) of the cross-sectional view of the multimode fiber and (b) SEM energy dispersive X-ray analysis (EDX) Ge elemental mapping of the fiber cross-section where Ge was found only in the surrounding cladding (GeAsSe) and not in the core (AsSe), as expected.

Fig. 4
Fig. 4

NA variation with wavelength for an optical fibre comprised of the AsSe glass core and GeAsSe glass cladding.

Fig. 5
Fig. 5

Material dispersion D calculated from Eq. (7) and the fitted Sellmeier II (1,1) models of As-Se and Ge-As-Se. Inset: material dispersion close to the material ZDW.

Tables (1)

Tables Icon

Table 1 Sellmeier coefficients of As-Se and Ge-As-Se glasses. The numbers in parentheses correspond to the number of material resonances in the VIS and the FIR, respectively. AMTIR-2 data for As-Se, rearranged to see correspondence, is from reference [10].

Equations (7)

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r p r s =tanψ×exp(jΔ)
ε 2 (E)={ E 1 E exp( E E t E u ); ( E E g ) 2 ( E E g ) 2 + E p 2 A E 0 ΓE [ ( E 2 E 0 2 ) 2 + Γ 2 E 2 ] ; 0<E E t E> E t
ε 1 (E)= ε 1 ()+ 2 π 0 ξ ε 2 (ξ) ξ 2 E 2 dξ
n 2 1= A 0 + n=1 N A n λ 2 λ 2 a n 2
n 2 1=A+ B λ 2 + C λ 4
N A = n 1 2 n 2 2
D = λ c ( d 2 n d λ 2 )

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