Abstract

Nanostructured GRIN components are optical elements which can have an arbitrary refractive index profile while retaining flat-parallel entry and exit facets. A method of their fabrication requires assembly of large quantities of glass rods in order to satisfy subwavelength requirement of the effective medium theory. In this paper, we present a development of gradient index microlenses using a combination of methods: nanostructurization of the preform and controlled diffusion process during lens drawing on a fiber drawing tower. Adding a diffusion process allows us to overcome limits of the effective medium theory related to maximum size of nanorods in the lens structure. We show that nanorods are dissolved during the fiber drawing process in high temperature and glass components are locally quasi-uniformly distributed. To demonstrate feasibility of the proposed approach, we have developed and experimentally verified the performance of a nGRIN microlens with a diameter of 115 µm composed of 115 rods on the diagonal, and length of 200 µm devoted to work for the wavelength over 658 nm.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

2018 (2)

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
[Crossref]

2017 (1)

H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
[Crossref]

2015 (1)

2014 (1)

2013 (1)

2012 (4)

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express 3(5), 1077–1085 (2012).
[Crossref]

K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
[Crossref]

M. R. Taghizadeh, A. J. Waddie, R. Buczynski, J. Nowosielski, A. Filipkowski, and D. Pysz, “Nanostructured micro-optics based on a modified stack-and-draw fabrication technique,” Adv. Opt. Technol. 1(3), 171–180 (2012).
[Crossref]

J. Nowosielski, R. Buczynski, A. J. Waddie, A. Filipkowski, D. Pysz, A. McCarthy, R. Stepien, and M. R. Taghizadeh, “Large diameter nanostructured gradient index lens,” Opt. Express 20(11), 11767–11777 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (1)

2008 (2)

C. Gomez-Reino, M. Perez, C. Bao, and M. Flores-Arias, “Design of grin optical components for coupling and interconnects,” Laser Photonics Rev. 2(3), 203–215 (2008).
[Crossref]

M. Wang and N. Pan, “Predictions of effective physical properties of complex multiphase materials,” Mater. Sci. Eng., R 63(1), 1–30 (2008).
[Crossref]

2007 (1)

S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
[Crossref]

2005 (1)

1999 (2)

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Design of binary subwavelength diffractive lenses by use of zeroth-order effective-medium theory,” J. Opt. Soc. Am. A 16(5), 1157–1167 (1999).
[Crossref]

1995 (1)

W. Ceelen, J. P. Jacobs, H. H. Brongersma, E. G. F. Sengers, and F. Janssen, “Cesium diffusion in sodium borosilicate glass studied by low-energy ion-scattering,” Surf. Interface Anal. 23(10), 712–716 (1995).
[Crossref]

1992 (1)

O. Vankessel, H. H. Brongersma, J. G. A. Holscher, R. G. Vanwelzenis, E. G. F. Sengers, and F. Janssen, “Diffusion of Cesium in Sodium Borosilicate Glasses for Nuclear Waste Immobilization, Studied by Low-Energy Ion Scattering,” Nucl. Instrum. Methods Phys. Res., Sect. B 64(1-4), 593–595 (1992).
[Crossref]

1989 (1)

M. P. Thomas and H. Matzke, “Sodium diffusion in the nuclear waste glass GP98/12,” J. Am. Ceram. Soc. 72(1), 146–147 (1989).
[Crossref]

1971 (1)

1949 (1)

L. S. Darken, “Diffusion of carbon in austenite with a discontinuity in composition,” Trans. AIME 180, 430 (1949).

1945 (1)

L. Onsager, “Theories and problems of liquid diffusion,” Ann. N. Y. Acad. Sci. 46(5 The Diffusion), 241–265 (1945).
[Crossref]

1942 (1)

L. S. Darken, “Diffusion in metal accompanied by phase change,” Trans. AIME 150, 157–169 (1942).

Aiken, S.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

Anuszkiewicz, A.

R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
[Crossref]

Bao, C.

C. Gomez-Reino, M. Perez, C. Bao, and M. Flores-Arias, “Design of grin optical components for coupling and interconnects,” Laser Photonics Rev. 2(3), 203–215 (2008).
[Crossref]

C. Gomez-Reino, M. Perez, and C. Bao, Gradient-index Optics: Fundamentals and Applications (Springer Verlag, 2002).

Baukens, V.

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

Brongersma, H. H.

W. Ceelen, J. P. Jacobs, H. H. Brongersma, E. G. F. Sengers, and F. Janssen, “Cesium diffusion in sodium borosilicate glass studied by low-energy ion-scattering,” Surf. Interface Anal. 23(10), 712–716 (1995).
[Crossref]

O. Vankessel, H. H. Brongersma, J. G. A. Holscher, R. G. Vanwelzenis, E. G. F. Sengers, and F. Janssen, “Diffusion of Cesium in Sodium Borosilicate Glasses for Nuclear Waste Immobilization, Studied by Low-Energy Ion Scattering,” Nucl. Instrum. Methods Phys. Res., Sect. B 64(1-4), 593–595 (1992).
[Crossref]

Brown, C. M.

Buczynski, R.

R. Buczynski, A. Filipkowski, B. Piechal, H. T. Nguyen, D. Pysz, R. Stepien, A. Waddie, M. R. Taghizadeh, M. Klimczak, and R. Kasztelanic, “Achromatic nanostructured gradient index microlenses,” Opt. Express 27(7), 9588–9600 (2019).
[Crossref]

R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
[Crossref]

J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

M. R. Taghizadeh, A. J. Waddie, R. Buczynski, J. Nowosielski, A. Filipkowski, and D. Pysz, “Nanostructured micro-optics based on a modified stack-and-draw fabrication technique,” Adv. Opt. Technol. 1(3), 171–180 (2012).
[Crossref]

J. Nowosielski, R. Buczynski, A. J. Waddie, A. Filipkowski, D. Pysz, A. McCarthy, R. Stepien, and M. R. Taghizadeh, “Large diameter nanostructured gradient index lens,” Opt. Express 20(11), 11767–11777 (2012).
[Crossref]

F. Hudelist, J. M. Nowosielski, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, “Nanostructured elliptical gradient-index microlenses,” Opt. Lett. 35(2), 130–132 (2010).
[Crossref]

F. Hudelist, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, “Design and fabrication of nano-structured gradient index microlenses,” Opt. Express 17(5), 3255–3263 (2009).
[Crossref]

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

Ceelen, W.

W. Ceelen, J. P. Jacobs, H. H. Brongersma, E. G. F. Sengers, and F. Janssen, “Cesium diffusion in sodium borosilicate glass studied by low-energy ion-scattering,” Surf. Interface Anal. 23(10), 712–716 (1995).
[Crossref]

Charan, K.

Charpentier, T.

H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
[Crossref]

Chen, W.

Cook, J.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

Darken, L. S.

L. S. Darken, “Diffusion of carbon in austenite with a discontinuity in composition,” Trans. AIME 180, 430 (1949).

L. S. Darken, “Diffusion in metal accompanied by phase change,” Trans. AIME 150, 157–169 (1942).

Debaes, N.

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

Ding, Y.

Divliansky, I.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

Filipkowski, A.

R. Buczynski, A. Filipkowski, B. Piechal, H. T. Nguyen, D. Pysz, R. Stepien, A. Waddie, M. R. Taghizadeh, M. Klimczak, and R. Kasztelanic, “Achromatic nanostructured gradient index microlenses,” Opt. Express 27(7), 9588–9600 (2019).
[Crossref]

R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
[Crossref]

M. R. Taghizadeh, A. J. Waddie, R. Buczynski, J. Nowosielski, A. Filipkowski, and D. Pysz, “Nanostructured micro-optics based on a modified stack-and-draw fabrication technique,” Adv. Opt. Technol. 1(3), 171–180 (2012).
[Crossref]

J. Nowosielski, R. Buczynski, A. J. Waddie, A. Filipkowski, D. Pysz, A. McCarthy, R. Stepien, and M. R. Taghizadeh, “Large diameter nanostructured gradient index lens,” Opt. Express 20(11), 11767–11777 (2012).
[Crossref]

Flores-Arias, M.

C. Gomez-Reino, M. Perez, C. Bao, and M. Flores-Arias, “Design of grin optical components for coupling and interconnects,” Laser Photonics Rev. 2(3), 203–215 (2008).
[Crossref]

Glebov, L. B.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

Gomez-Reino, C.

C. Gomez-Reino, M. Perez, C. Bao, and M. Flores-Arias, “Design of grin optical components for coupling and interconnects,” Laser Photonics Rev. 2(3), 203–215 (2008).
[Crossref]

C. Gomez-Reino, M. Perez, and C. Bao, Gradient-index Optics: Fundamentals and Applications (Springer Verlag, 2002).

Gouillart, E.

H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
[Crossref]

Goulet, A.

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

Heremans, P.

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

Ho, S.-T.

Holscher, J. G. A.

O. Vankessel, H. H. Brongersma, J. G. A. Holscher, R. G. Vanwelzenis, E. G. F. Sengers, and F. Janssen, “Diffusion of Cesium in Sodium Borosilicate Glasses for Nuclear Waste Immobilization, Studied by Low-Energy Ion Scattering,” Nucl. Instrum. Methods Phys. Res., Sect. B 64(1-4), 593–595 (1992).
[Crossref]

Howard, S. S.

Huang, Y.

Hudelist, F.

Huland, D. M.

Jacobs, J. P.

W. Ceelen, J. P. Jacobs, H. H. Brongersma, E. G. F. Sengers, and F. Janssen, “Cesium diffusion in sodium borosilicate glass studied by low-energy ion-scattering,” Surf. Interface Anal. 23(10), 712–716 (1995).
[Crossref]

Jahns, J.

S. Sinzinger and J. Jahns, Microoptics (Wiley-VCH, 2003).

Janssen, F.

W. Ceelen, J. P. Jacobs, H. H. Brongersma, E. G. F. Sengers, and F. Janssen, “Cesium diffusion in sodium borosilicate glass studied by low-energy ion-scattering,” Surf. Interface Anal. 23(10), 712–716 (1995).
[Crossref]

O. Vankessel, H. H. Brongersma, J. G. A. Holscher, R. G. Vanwelzenis, E. G. F. Sengers, and F. Janssen, “Diffusion of Cesium in Sodium Borosilicate Glasses for Nuclear Waste Immobilization, Studied by Low-Energy Ion Scattering,” Nucl. Instrum. Methods Phys. Res., Sect. B 64(1-4), 593–595 (1992).
[Crossref]

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Jun Ki, K.

K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
[Crossref]

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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

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R. Buczynski, A. Filipkowski, B. Piechal, H. T. Nguyen, D. Pysz, R. Stepien, A. Waddie, M. R. Taghizadeh, M. Klimczak, and R. Kasztelanic, “Achromatic nanostructured gradient index microlenses,” Opt. Express 27(7), 9588–9600 (2019).
[Crossref]

R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
[Crossref]

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K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
[Crossref]

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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
[Crossref]

R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
[Crossref]

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R. Buczynski, A. Filipkowski, B. Piechal, H. T. Nguyen, D. Pysz, R. Stepien, A. Waddie, M. R. Taghizadeh, M. Klimczak, and R. Kasztelanic, “Achromatic nanostructured gradient index microlenses,” Opt. Express 27(7), 9588–9600 (2019).
[Crossref]

R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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Lonergan, C.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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Mait, J. N.

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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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Matzke, H.

M. P. Thomas and H. Matzke, “Sodium diffusion in the nuclear waste glass GP98/12,” J. Am. Ceram. Soc. 72(1), 146–147 (1989).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
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K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
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Pogrebnyakov, A. V.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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Pysz, D.

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R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
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J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

M. R. Taghizadeh, A. J. Waddie, R. Buczynski, J. Nowosielski, A. Filipkowski, and D. Pysz, “Nanostructured micro-optics based on a modified stack-and-draw fabrication technique,” Adv. Opt. Technol. 1(3), 171–180 (2012).
[Crossref]

J. Nowosielski, R. Buczynski, A. J. Waddie, A. Filipkowski, D. Pysz, A. McCarthy, R. Stepien, and M. R. Taghizadeh, “Large diameter nanostructured gradient index lens,” Opt. Express 20(11), 11767–11777 (2012).
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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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Rivero Baleine, C.

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
[Crossref]

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H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
[Crossref]

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W. Ceelen, J. P. Jacobs, H. H. Brongersma, E. G. F. Sengers, and F. Janssen, “Cesium diffusion in sodium borosilicate glass studied by low-energy ion-scattering,” Surf. Interface Anal. 23(10), 712–716 (1995).
[Crossref]

O. Vankessel, H. H. Brongersma, J. G. A. Holscher, R. G. Vanwelzenis, E. G. F. Sengers, and F. Janssen, “Diffusion of Cesium in Sodium Borosilicate Glasses for Nuclear Waste Immobilization, Studied by Low-Energy Ion Scattering,” Nucl. Instrum. Methods Phys. Res., Sect. B 64(1-4), 593–595 (1992).
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K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
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K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
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R. Kasztelanic, A. Filipkowski, A. Anuszkiewicz, P. Stafiej, G. Stepniewski, D. Pysz, K. Krzyżak, R. Stepien, M. Klimczak, and R. Buczynski, “Integrating Free-Form Nanostructured GRIN Microlenses with Single-Mode Fibers for Optofluidic Systems,” Sci. Rep. 8(1), 5072 (2018).
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J. Pniewski, T. Stefaniuk, G. Stepniewski, D. Pysz, T. Martynkien, R. Stepien, and R. Buczynski, “Limits in development of photonic crystal fibers with a subwavelength inclusion in the core,” Opt. Mater. Express 5(10), 2366–2376 (2015).
[Crossref]

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M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
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Tang, X.

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R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
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M. P. Thomas and H. Matzke, “Sodium diffusion in the nuclear waste glass GP98/12,” J. Am. Ceram. Soc. 72(1), 146–147 (1989).
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S. Kumar, N. Rawat, A. S. Kanekar, B. S. Tomar, V. K. Manchanda, M. S. Sonavane, N. L. Sonar, and K. Raj, “Sodium diffusion in sodium borosilicate glass used for immobilization of high level liquid waste,” J. Radioanal. Nucl. Chem. 274(2), 225–228 (2007).
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H. Pablo, S. Schuller, M. J. Toplis, E. Gouillart, S. Mostefaoui, T. Charpentier, and M. Roskosz, “Multicomponent diffusion in sodium borosilicate glasses,” J. Non-Cryst. Solids 478, 29–40 (2017).
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O. Vankessel, H. H. Brongersma, J. G. A. Holscher, R. G. Vanwelzenis, E. G. F. Sengers, and F. Janssen, “Diffusion of Cesium in Sodium Borosilicate Glasses for Nuclear Waste Immobilization, Studied by Low-Energy Ion Scattering,” Nucl. Instrum. Methods Phys. Res., Sect. B 64(1-4), 593–595 (1992).
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R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
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R. Buczynski, V. Baukens, T. Szoplik, A. Goulet, N. Debaes, A. Kirk, P. Heremans, R. Vounckx, I. Veretennicoff, and H. Thienpont, “Fast optical thresholding with an array of optoelectronic transceiver elements,” IEEE Photonics Technol. Lett. 11(3), 367–369 (1999).
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K. Jun Ki, L. Woei Ming, K. Pilhan, C. Myunghwan, J. Keehoon, K. Seonghoon, and Y. Seok Hyun, “Fabrication and operation of GRIN probes for in vivo fluorescence cellular imaging of internal organs in small animals,” Nat. Protoc. 7(8), 1456–1469 (2012).
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Adv. Mater. (1)

M. Kang, A. M. Swisher, A. V. Pogrebnyakov, L. Liu, A. Kirk, S. Aiken, L. Sisken, C. Lonergan, J. Cook, T. Malendevych, F. Kompan, I. Divliansky, L. B. Glebov, M. C. Richardson, C. Rivero Baleine, C. G. Pantano, T. S. Mayer, and K. Richardson, “Ultralow Dispersion Multicomponent Thin Film Chalcogenide Glass for Broadband Gradient Index Optics,” Adv. Mater. 30(39), 1803628 (2018).
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GRINTECH GmbH website: < www.grintech.de >.

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Figures (11)

Fig. 1.
Fig. 1. a) Effective refractive index distribution in the nanostructured GRIN lens and b) the corresponding profile, c) refractive index distribution of the ideal, continuous GRIN lens, d) schematic of rods arrangement in nGRIN lens. Color bar denotes refractive index difference in the GRIN lens with respect to the background glass NC34
Fig. 2.
Fig. 2. SEM image of the fabricated nGRIN lens, which design was based on a schematic from Fig. 1(d). The lens has 32 µm diameter on the diagonal. Dark and bright areas correspond to nanorods made of low and high index glasses with different oxide composition in the structure.
Fig. 3.
Fig. 3. The schematics of the influence of the diffusion process on the elemental composition and refractive index profile for the case of two closely located rods.
Fig. 4.
Fig. 4. SEM image of the diffused structure fabricated at various temperatures of the drawing process, (a) at 750°C, (b) at 790°C, (c) at 830°C. Inner circles denote non-diffused areas of high refractive index glass NC42. The outer circles denote area of diffusion between high index and low index component glasses (NC42 and NC34, respectively) in the lens structure. (d) Diffusion range as a function of temperature.
Fig. 5.
Fig. 5. EDS image of the concentration of the Pb, K and Ba oxides in the measured sample. (a) 20 µm lens, (b) 40 µm lens, 115 µm lens.
Fig. 6.
Fig. 6. nGRIN lens structures used in the BPM simulations. (a) – lens without diffusion, (b) – lens with diffusion pattern similar to the EDS images, (c) – ideal GRIN lens. Top row shows refractive index distributions, while the bottom row shows cross-sections along diagonal of the hexagon, drawn with the same resolution as the EDS image – 0.2 µm.
Fig. 7.
Fig. 7. BPM modelling of light propagation through 200 µm long and 115 µm wide lenses, corresponding to structures presented in Fig. 6 respectively. In the left column we show intensity distributions along the propagation axis in free space after end facet of the nGRIN lens. In the right column there are intensity cross-sections at the focal plane.
Fig. 8.
Fig. 8. Schematic of the setup used for characterization of nGRIN lens focusing properties.
Fig. 9.
Fig. 9. The cross-sections of laser beams measured along the propagation axis for the 658 nm wavelength, behind the nGRIN microlens.
Fig. 10.
Fig. 10. Schematic of the setup used to verify the imaging properties of nGRIN microlenses.
Fig. 11.
Fig. 11. Verification of imaging properties of nGRIN microlenses: (a) test pattern, (b) image of the test pattern obtained with nGRIN microlens with magnification 1.3.

Tables (3)

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Table 1. Thermal and optical properties of the glasses used in the lens fabrication

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Table 2. Chemical composition of the glasses used in lens fabrication

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Table 3. Comparison between simulation and experimental results for the tested nGRIN lens.

Equations (4)

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g = 2 ( n 0 n ) n 0 r 2 ,
f = 1 n 0 g sin ( l g ) ,
w d = f c o s ( l g ) .
P = 2 π g ,