Abstract

We present a practical method to determine femtosecond laser induced refractive index changes in transparent materials. Based on an iterative Fourier transform algorithm, this technique spatially resolves the refractive index of complex structures by combining the dimensions of the modified region with the corresponding phase change extracted from far-field intensity measurements. This approach is used to characterize optical waveguides written by a femtosecond laser in borosilicate glass.

© 2012 Optical Society of America

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References

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2011 (2)

I. Mingareev, R. Berlich, T. J. Eichelkraut, H. Herfurth, S. Heinemann, and M. C. Richardson, Opt. Express 19, 11397 (2011).
[CrossRef]

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

2010 (3)

T. Fernandez, S. Eaton, G. Della Valle, R. Vazquez, M. Irannejad, G. Jose, A. Jha, G. Cerullo, R. Osellame, and P. Laporta, Opt. Express 18, 20289 (2010).
[CrossRef]

T. Gerke and R. Piestun, Nat. Photon. 4, 188 (2010).
[CrossRef]

J. Choi, M. Ramme, T. Anderson, and M. C. Richardson, Proc. SPIE 7589, 75891A (2010).
[CrossRef]

2008 (2)

2004 (2)

A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, Opt. Lett. 29, 1840 (2004).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, J. Mod. Opt. 51, 2533 (2004).
[CrossRef]

2002 (1)

1999 (1)

1998 (1)

1996 (1)

I. Mansour and F. Caccavale, J. Lightwave Technol. 14, 423 (1996).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Anderson, A.

Anderson, T.

J. Choi, M. Ramme, T. Anderson, and M. C. Richardson, Proc. SPIE 7589, 75891A (2010).
[CrossRef]

Barrington, S.

Berlich, R.

Bonse, J.

Borrelli, N.

Brocklesby, W.

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, J. Mod. Opt. 51, 2533 (2004).
[CrossRef]

Caccavale, F.

I. Mansour and F. Caccavale, J. Lightwave Technol. 14, 423 (1996).
[CrossRef]

Cerullo, G.

Chen, W.

Choi, J.

J. Choi, M. Ramme, T. Anderson, and M. C. Richardson, Proc. SPIE 7589, 75891A (2010).
[CrossRef]

Della Valle, G.

Eason, R.

Eaton, S.

Eichelkraut, T. J.

Fernandez, T.

Gaeta, A.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Gerke, T.

T. Gerke and R. Piestun, Nat. Photon. 4, 188 (2010).
[CrossRef]

Glytsis, E.

Greef, R.

Grivas, C.

Heinemann, S.

Herfurth, H.

Herman, P.

Ho, S.

Homoelle, D.

Irannejad, M.

Jha, A.

Jose, G.

Laporta, P.

Li, J.

Lopez, C.

Mailis, S.

Mansour, I.

I. Mansour and F. Caccavale, J. Lightwave Technol. 14, 423 (1996).
[CrossRef]

Mermillod-Blondin, A.

Mingareev, I.

Ng, M.

Nolte, S.

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, J. Mod. Opt. 51, 2533 (2004).
[CrossRef]

Osellame, R.

Piestun, R.

T. Gerke and R. Piestun, Nat. Photon. 4, 188 (2010).
[CrossRef]

Ramme, M.

J. Choi, M. Ramme, T. Anderson, and M. C. Richardson, Proc. SPIE 7589, 75891A (2010).
[CrossRef]

Richardson, K.

Richardson, M.

Richardson, M. C.

Richter, D.

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

Rosenfeld, A.

Rutt, H.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Smith, C.

Thomas, J.

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

Tünnermann, A.

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, J. Mod. Opt. 51, 2533 (2004).
[CrossRef]

Vainos, N.

Vazquez, R.

Voigtländer, C.

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

Wielandy, S.

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, J. Mod. Opt. 51, 2533 (2004).
[CrossRef]

Zhang, H.

Zoubir, A.

Appl. Opt. (1)

Appl. Phys. A (1)

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, Appl. Phys. A 102, 35 (2011).
[CrossRef]

J. Lightwave Technol. (1)

I. Mansour and F. Caccavale, J. Lightwave Technol. 14, 423 (1996).
[CrossRef]

J. Mod. Opt. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, J. Mod. Opt. 51, 2533 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Photon. (1)

T. Gerke and R. Piestun, Nat. Photon. 4, 188 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Optik (1)

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Proc. SPIE (1)

J. Choi, M. Ramme, T. Anderson, and M. C. Richardson, Proc. SPIE 7589, 75891A (2010).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup to measure the far-field intensity pattern caused by an induced refractive index change distribution replicated in x direction.

Fig. 2.
Fig. 2.

950 PMMA A5 surface profile for one grating line measured with an AFM (solid curve) in comparison with the reconstructed phase change (dashed curve) using the Fourier reconstruction method.

Fig. 3.
Fig. 3.

Microscopic image of femtosecond-laser induced refractive index change. (a) Top view (x,y) of three grating lines and (b) cross section (x,y) of single grating line.

Fig. 4.
Fig. 4.

Refractive index change determination of a repeated waveguide written in borosilicate glass with a femtosecond-laser. (a) Far-field amplitude of resulting diffraction pattern using an He–Ne laser at 543 nm. (b) Determined effective refractive index change distribution, which represents an averaged induced waveguide.

Equations (3)

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

uout(x,y,z0)=uin(x,y,z0)·t(x,y)=uin(x,y,z0)·exp[iΔϕ(x,y)],
Δϕ(x,y)=2πλ0dΔn(x,y,z)dz=2πλ·Δneff(x,y)·d.
(Δxmin,Δymin)2(px,py)(N1,M1).

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