Abstract

Laser-written waveguides in glass have many potential applications as photonic devices. However, there is little knowledge of the actual profile of the usually asymmetric refractive index (RI) change across the femtosecond (fs) laser–written waveguides. We show, here, a new nondestructive method to measure any symmetric or asymmetric two-dimensional RI profile of fs laser–written waveguides in transparent materials. The method is also suitable for the measurement of the RI profile of any other type of waveguide. A Mach-Zehnder interferometer is used to obtain the phase shift of light propagating transversely through the RI-modified region. A genetic algorithm is then used to determine the matching cross-sectional RI profile based on the known waveguide shape and dimensions. A validation of the method with the comparison to a RNF measurement of the industry-standard SMF-28 is presented, as well as a demonstration of its versatility with measurements on fs laser–written waveguides.

© 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] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (2)

2014 (1)

2013 (2)

2010 (1)

2009 (4)

V. Maselli, J. R. Grenier, S. Ho, and P. R. Herman, “Femtosecond laser written optofluidic sensor: Bragg Grating Waveguide evanescent probing of microfluidic channel,” Opt. Express 17(14), 11719–11729 (2009).
[Crossref] [PubMed]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref] [PubMed]

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47(2), 259–263 (2009).
[Crossref]

2008 (1)

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (5)

2004 (1)

2002 (1)

2001 (1)

1986 (1)

R. Göring and M. Rothhardt, “Application of the refracted near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7(3), 82–85 (1986).
[Crossref]

1981 (1)

1979 (1)

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11(2), 185–196 (1979).
[Crossref]

1977 (1)

1975 (1)

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurement of clad optical fibers,” Appl. Phys. Lett. 26(10), 574–575 (1975).
[Crossref]

1965 (1)

Aiello, L.

Ampem-Lassen, E.

Ams, M.

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref] [PubMed]

Bachim, B. L.

Barty, A.

Baxter, G. W.

Bélanger, E.

Bérubé, J.-P.

Bharadwaj, V.

Booth, M. J.

Cerullo, G.

Chen, Q.

Chiodo, N.

de Dorlodot, B.

De Nicola, S.

Dekker, P.

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref] [PubMed]

Della Valle, G.

Dong, X.

Dragomir, N. M.

Eaton, S. M.

Epstein, M.

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurement of clad optical fibers,” Appl. Phys. Lett. 26(10), 574–575 (1975).
[Crossref]

Fernandez, T. T.

Ferraro, P.

Finizio, A.

Fujimoto, J. G.

Gagné, M.

Gardner, W. B.

Gaylord, T. K.

Geerinck, P.

Goh, X. M.

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[Crossref] [PubMed]

Göring, R.

R. Göring and M. Rothhardt, “Application of the refracted near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7(3), 82–85 (1986).
[Crossref]

Gorski, W.

Grenier, J. R.

Haque, M.

Hartl, I.

Herman, P. R.

Ho, P. S.

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurement of clad optical fibers,” Appl. Phys. Lett. 26(10), 574–575 (1975).
[Crossref]

Ho, S.

Huntington, S. T.

Ippen, E. P.

Irannejad, M.

Jesacher, A.

Jha, A.

Jose, G.

Kashyap, R.

Kniazewski, P.

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47(2), 259–263 (2009).
[Crossref]

Kowalevicz, A. M.

Kozacki, T.

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47(2), 259–263 (2009).
[Crossref]

Kujawinska, M.

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47(2), 259–263 (2009).
[Crossref]

Lanzani, G.

Lapointe, J.

Laporta, P.

Lee, K. K. C.

Li, M.-J.

Liu, Z.

Lo, S. A.

Malitson, I. H.

Marhic, M. E.

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurement of clad optical fibers,” Appl. Phys. Lett. 26(10), 574–575 (1975).
[Crossref]

Mariampillai, A.

Marquet, P.

Marshall, G. D.

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref] [PubMed]

Maselli, V.

Matthews, J. C.

Mettler, S. C.

Minoshima, K.

Nugent, K. A.

O’Brien, J. L.

Osellame, R.

Osten, W.

Ottevaere, H.

Pierattini, G.

Piper, J. A.

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

Politi, A.

Ramponi, R.

Roberts, A.

Rothhardt, M.

R. Göring and M. Rothhardt, “Application of the refracted near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7(3), 82–85 (1986).
[Crossref]

Salter, P. S.

Saunders, M. J.

Soci, C.

Sotillo, B.

Standish, B. A.

Thienpont, H.

Vallée, R.

Van Daele, P.

Van Put, S.

Van Steenberge, G.

Vazquez, R. M.

Vázquez, M. R.

Watté, J.

White, K. I.

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11(2), 185–196 (1979).
[Crossref]

Withford, M. J.

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref] [PubMed]

Xu, Y.

Yang, V. X. D.

Yin, A.

Yin, C.

Young, M.

Zavelani-Rossi, M.

Zheludev, N. I.

Zheng, Y.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurement of clad optical fibers,” Appl. Phys. Lett. 26(10), 574–575 (1975).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Commun. (1)

R. Göring and M. Rothhardt, “Application of the refracted near-field technique to multimode planar and channel waveguides in glass,” J. Opt. Commun. 7(3), 82–85 (1986).
[Crossref]

J. Opt. Soc. Am. (1)

Laser Photonics Rev. (1)

M. Ams, G. D. Marshall, P. Dekker, J. A. Piper, and M. J. Withford, “Ultrafast laswer written active devices,” Laser Photonics Rev. 3(6), 535–544 (2009).
[Crossref]

Microsc. Res. Tech. (1)

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[Crossref] [PubMed]

Opt. Express (9)

E. Bélanger, J.-P. Bérubé, B. de Dorlodot, P. Marquet, and R. Vallée, “Comparative study of quantitative phase imaging techniques for refractometry of optical waveguides,” Opt. Express 26(13), 17498–17510 (2018).
[Crossref] [PubMed]

M. R. Vázquez, V. Bharadwaj, B. Sotillo, S. A. Lo, R. Ramponi, N. I. Zheludev, G. Lanzani, S. M. Eaton, and C. Soci, “Optical NP problem solver on laser-written waveguide platform,” Opt. Express 26(2), 702–710 (2018).
[Crossref] [PubMed]

T. T. Fernandez, S. M. Eaton, G. Della Valle, R. M. Vazquez, M. Irannejad, G. Jose, A. Jha, G. Cerullo, R. Osellame, and P. Laporta, “Femtosecond laser written optical waveguide amplifier in phospho-tellurite glass,” Opt. Express 18(19), 20289–20297 (2010).
[Crossref] [PubMed]

V. Maselli, J. R. Grenier, S. Ho, and P. R. Herman, “Femtosecond laser written optofluidic sensor: Bragg Grating Waveguide evanescent probing of microfluidic channel,” Opt. Express 17(14), 11719–11729 (2009).
[Crossref] [PubMed]

K. K. C. Lee, A. Mariampillai, M. Haque, B. A. Standish, V. X. D. Yang, and P. R. Herman, “Temperature-compensated fiber-optic 3D shape sensor based on femtosecond laser direct-written Bragg grating waveguides,” Opt. Express 21(20), 24076–24086 (2013).
[Crossref] [PubMed]

J. Lapointe, M. Gagné, M.-J. Li, and R. Kashyap, “Making smart phones smarter with photonics,” Opt. Express 22(13), 15473–15483 (2014).
[Crossref] [PubMed]

G. D. Marshall, A. Politi, J. C. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref] [PubMed]

R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator,” Opt. Express 13(2), 612–620 (2005).
[Crossref] [PubMed]

E. Ampem-Lassen, S. T. Huntington, N. M. Dragomir, K. A. Nugent, and A. Roberts, “Refractive index profiling of axially symmetric optical fibers: a new technique,” Opt. Express 13(9), 3277–3282 (2005).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

P. Kniazewski, T. Kozacki, and M. Kujawinska, “Inspection of axial stress and refractive index distribution in polarization-maintaining fiber with tomographic methods,” Opt. Lasers Eng. 47(2), 259–263 (2009).
[Crossref]

Opt. Lett. (4)

Opt. Mater. Express (1)

Opt. Quantum Electron. (1)

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11(2), 185–196 (1979).
[Crossref]

Other (2)

Corning, “Corning single-mode optical fiber,” PI1036 datasheet (2002).

Corning, “Corning Gorilla Glass 3 with NDR,” F_090315 datasheet (2015).

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Figures (8)

Fig. 1
Fig. 1 (a) Mach-Zehnder interferometer setup used to measure the phase shift produced by the waveguide. A piezoelectric actuator is used to induce a phase delay in one arm. The polarizers and wave plates are adjusted to maximize the fringe visibility. An image of the sample is formed at the camera by the objective and lens. (b) Setup used to obtain an image of the waveguide's cross-section. The polished end-facet of the sample is illuminated by a white light source coming from an angle.
Fig. 2
Fig. 2 (a) Schematic cross-section of the sample used for the validation of the method and (b) the expected phase shift of light propagating downwards through the sample from the top. The fiber is immersed in index-matching liquid and placed between glass plates. Secondary fibers are used for support. The phase shifts more or less, depending on the optical path length for light at a given x position.
Fig. 3
Fig. 3 (a) Phase image after reconstruction for an SMF-28 fiber. (b) Measured light intensities at camera pixels A and B versus phase delay. (c) Result of the FFT at pixel A. The measured phase for the given pixel is the phase of the dominant frequency.
Fig. 4
Fig. 4 (a) Evolution of some of the parameters used to model the SMF-28 fiber using the genetic algorithm and the corresponding error. Parameters dictating the geometry converge very fast while fine-tuning of the RI levels takes more iterations. (b) Evolution of the RI profile calculated by the genetic algorithm.
Fig. 5
Fig. 5 (a) Cross-section of the SMF-28 fiber obtained with the setup of Fig. 1(b). (b) RI change profile reconstructed by the genetic algorithm for the SMF-28 fiber based on the measured phase shift and the known shape and dimensions from Fig. 5(a). (c) Measured and modeled phase shifts along cross-section B of Fig. 5(a). (d) Reconstructed RI change profile and result of the RNF measurement along cross-section A of Fig. 5(b).
Fig. 6
Fig. 6 (a) Cross-section of the weakly asymmetric laser written waveguide obtained with the setup of Fig. 1(b). (b) RI change profile reconstructed by the genetic algorithm for the weakly asymmetric laser written waveguide based on the measured phase image and the known shape and dimensions from Fig. 6(a). (c) Measured and modeled phase shifts along cross-section B of Fig. 6(b). (d) Reconstructed RI change along cross-section A of Fig. 6(b).
Fig. 7
Fig. 7 (a) Cross-section of the strongly asymmetric laser written waveguide obtained with the setup of Fig. 1(b). (b) RI change profile reconstructed by the genetic algorithm for the strongly asymmetric laser written waveguide based on the measured phase image and the known shape and dimensions from Fig. 7(a). (c) Measured and modeled phase shifts along cross-section C of Fig. 7(b). (d) Reconstructed RI change along cross-sections A and B of Fig. 7(b).
Fig. 8
Fig. 8 Resulting image of the 1 µm resolution target for (a) transmitted light amplitude without interference and (b) the calculated phase shift. The pattern is clearly resolved, indicating a sub-micron spatial resolution.

Equations (4)

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φ( x,z )= 2π λ Δn( x,y,z )dy .
F{ cos( ω 0 tφ) }=δ(ω ω 0 ) e iφ
Δn( r )= Δ n core 2 erfc( r r core w core )+Δ n liq H( r r clad )+Δ n dip e r 2 / w dip 2
Δn( r,θ )= Δ n out 2 erfc( r r out w out )+ i=1 4 Δ n i e ( r r i ( θ ) ) 2 / w i 2 ( θ ) .

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