Abstract
In this work, we report a model for accurately calculating the focal volumes corresponding to astigmatic elliptical beams used in fs-laser waveguide writing. The model is based on the use of the ABCD matrix formalism for the propagation of a Gaussian beam. The code includes the effects of propagation on the astigmatic elliptical beam, and the effects of beam truncation and diffraction at the entrance pupil of the focusing objective due to beam clipping when overfilling the pupil. The results predict that for a given astigmatism value and propagation distance it is possible to efficiently suppress the astigmatic focus closer to the surface. This explains previous experimental results where single structure waveguides with controllable aspect-ratio were fabricated using astigmatic-elliptical beams. Furthermore, we investigate the respective roles of astigmatism and beam propagation, as well as the strong impact of truncation and diffraction effects caused by clipping the beam at the pupil of the focusing optics. Finally, based on the results from our model, we present some practical considerations in terms of beam propagation and phase wrapping constraints.
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H. Misawa, S. Juodkazis (eds.), 3D Laser Microfabrication. Principles and Applications (Wiley-VCH, New York, 2006)
N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, B. Loiseaux, Programmable focal spot shaping of amplified femtosecond laser pulses. Opt. Lett. 30(12), 1479–1481 (2005)
V. Diez-Blanco, J. Siegel, A. Ferrer, A. Ruiz De La Cruz, J. Solis, Deep subsurface waveguides with circular cross section produced by femtosecond laser writing. Appl. Phys. Lett. 91, 1104 (2007)
C. Hnatovsky, R. Taylor, E. Simova, V. Bhardwaj, D.M. Rayner, P.B. Corkum, High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations. J. Appl. Phys. (2005)
Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, Q. Gong, Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica. J. Opt. A, Pure Appl. Opt. (2005)
C.B. Schaffer, J.F. García, E. Mazur, Bulk heating of transparent materials using a high-repetition-rate femtosecond laser. Appl. Phys. A, Mater. Sci. Process. 76, 351 (2003)
G.D. Love, Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator. Appl. Opt. 36, 1517 (1997)
C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, R. Stoian, Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction. Opt. Express 16(8), 5481 (2008)
G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, S. de Silvestri, Femtosecond micromachining of symmetric waveguides at 1.5 m by astigmatic beam focusing. Opt. Lett. 27, 2002 (1938)
Y. Cheng, K. Sugioka, K. Midorikawa, M. Masuda, K. Toyoda, M. Kawachi, K. Shihoyama, Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser. Opt. Lett. 28, 55–57 (2003)
Y. Hayasaki, T. Sugimoto, A. Takita, N. Nishida, Variable holographic femtosecond laser processing by use of a spatial light modulator. Appl. Phys. Lett. 87(3), 1–3 (2005)
M. Pospiech, M. Emons, A. Steinmann, G. Palmer, R. Osellame, N. Bellini, G. Cerullo, U. Morgner, Double waveguide couplers produced by simultaneous femtosecond writing. Opt. Express 17(5), 3555–3563 (2009)
F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, K. Midorikawa, Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses. Opt. Lett. 35(7), 1106 (2010)
M. Ams, G.D. Marshall, D.J. Spence, M.J. Withford, Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses. Opt. Express 13, 5676 (2005)
A. Ruiz De La Cruz, A. Ferrer, W. Gawelda, D. Puerto, M. Galván Sosa, J. Siegel, J. Solis, Independent control of beam astigmatism and ellipticity using a SLM for fs-laser waveguide writing. Opt. Express 17(23), 20853–20859 (2009)
S.A. Collins, Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. A 60(9), 1168–1177 (1970)
G. Zhao, X. Ji, B. Lu, Approximate analytical propagation equations of gaussian beams through hard-aperture optics. Optik 114(6), 241–245 (2003)
Y. Zhang, Nonparaxial propagation analysis of elliptical gaussian beams diffracted by a circular aperture. Opt. Commun. 248, 317 (2005)
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Ruiz De la Cruz, A., Ferrer, A., del Hoyo, J. et al. Modeling of astigmatic-elliptical beam shaping during fs-laser waveguide writing including beam truncation and diffraction effects. Appl. Phys. A 104, 687–693 (2011). https://doi.org/10.1007/s00339-011-6316-1
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DOI: https://doi.org/10.1007/s00339-011-6316-1