Abstract

Rectangular apertures have been used as a simple means to approximate elliptical Gaussian beams in femtosecond direct writing systems to correct for the elongated focus inherent in low numerical aperture (NA) systems. In this work it is recognized that the rectangular aperture, more accurately functions as a diffractive element and hence redistributes the intensity gradient around the focus in accordance to the physical effects of diffraction. A diffractive model for the technique was proposed and confirmed experimentally to investigate the effects of diffraction and the extent of its influence on the focus shape over different conditions. It was found that because of diffraction, the radius of curvature for the leading edge of the focal spot is dissimilar from its trailing edge. However this effect is mitigated when lower processing energy is used and circular waveguides can be obtained.

© 2005 Optical Society of America

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References

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  1. K.M. Davis, K. Miura, N. Sugimoto, and K. Hirao, �??Writing waveguides in glass with a femtosecond laser,�?? Opt. Lett. 21, 1729-1731 (1996).
    [CrossRef] [PubMed]
  2. K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, �??Photowritten optical waveguides in various glasses with ultrashort pulse laser,�?? Appl. Phys. Lett. 71, 3329-3331 (1997).
    [CrossRef]
  3. K. Minoshima, A.M. Kowalevicz, I. Hartl, E.P. Ippen, and J.G. Fujimoto, �??Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing,�?? Opt. Express 10, 645-652 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-645.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-645.</a>
    [PubMed]
  4. C. Florea and K.A. Winick, �??Fabrication and Characterization of Photonic Devices Directly Written in Glass Using Femtosecond Laser Pulses,�?? J. Lightwave Technol. 21, 246-253 (2003).
    [CrossRef]
  5. K. Sugioka, Y. Cheng, and K. Midorikawa, �??Three-dimensional micromachining of glass using femtosecond laser for lab-on-a-chip device manufacture,�?? Appl. Phys. A 81, 1-10 (2005).
    [CrossRef]
  6. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, �??Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,�?? Appl. Phys. A 77, 109-111 (2003).
    [CrossRef]
  7. J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and WaterWaves (Adam Hilger Series in Optics and Optoelectronics, Bristol and Boston: Institute of Physics Publishing, 1986).
  8. C.B. Schaffer, A. Brodeur, J.F. García, and E. Mazur, �??Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,�?? Opt. Lett. 26, 93-95 (2001).
    [CrossRef]
  9. Z. Bor, �??Distortion of femtosecond laser pulses in lenses,�?? Opt. Lett. 14, 119-121 (1989).
    [CrossRef] [PubMed]
  10. R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S.D. Silvestri, and G. Cerullo, �??Femtosecond writing of active optical waveguides with astigmatically shaped beams,�?? J. Opt. Soc. Am. B 20, 15591567 (2003)
    [CrossRef]
  11. Y. Cheng, K. Sugioka, K. Midorikawa, M. Masuda, K. Toyoda, M. Kawachi, and 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).
    [CrossRef] [PubMed]
  12. M. Ams, G.D. Marshall, D.J. Spence, and M.J. Withford, �??Slit beam shaping method forfemtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,�?? Opt. Express 13, 5676-5681 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5676.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5676.</a>
    [CrossRef] [PubMed]
  13. J.W. Goodman, Introduction to Fourier optics (McGraw-Hill Book Co., New York, 1996).
  14. M. Masuda, K. Sugioka, Y. Cheng, N. Aoki, M. Kawachi, K. Shihoyama, K. Toyoda, H. Helvajian, and K. Midorikawa, �??3-D microstructuring inside photosensitive glass by femtosecond laser excitation,�?? Appl. Phys. A 76, 857-860 (2003).
    [CrossRef] [PubMed]

Appl. Phys. A

K. Sugioka, Y. Cheng, and K. Midorikawa, �??Three-dimensional micromachining of glass using femtosecond laser for lab-on-a-chip device manufacture,�?? Appl. Phys. A 81, 1-10 (2005).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, �??Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,�?? Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

M. Masuda, K. Sugioka, Y. Cheng, N. Aoki, M. Kawachi, K. Shihoyama, K. Toyoda, H. Helvajian, and K. Midorikawa, �??3-D microstructuring inside photosensitive glass by femtosecond laser excitation,�?? Appl. Phys. A 76, 857-860 (2003).
[CrossRef] [PubMed]

Appl. Phys. Lett.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, �??Photowritten optical waveguides in various glasses with ultrashort pulse laser,�?? Appl. Phys. Lett. 71, 3329-3331 (1997).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S.D. Silvestri, and G. Cerullo, �??Femtosecond writing of active optical waveguides with astigmatically shaped beams,�?? J. Opt. Soc. Am. B 20, 15591567 (2003)
[CrossRef]

Opt. Express

Opt. Lett.

Other

J.W. Goodman, Introduction to Fourier optics (McGraw-Hill Book Co., New York, 1996).

J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and WaterWaves (Adam Hilger Series in Optics and Optoelectronics, Bristol and Boston: Institute of Physics Publishing, 1986).

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Figures (11)

Fig. 1.
Fig. 1.

Elongated transverse profile obtained from a 150-fs pulse (at 400 mw) focused into fused silica using a 50x objective.

Fig. 2.
Fig. 2.

Diffractive aperture placed immediately in front of lens results in improved AR around the focus in the horizontal plane. Writing motion is in the vertical direction along the V axis.

Fig. 3.
Fig. 3.

Longitudinal intensity distribution at focal region viewed from axis V of Fig. 2. Aperture width wx of (a) 4 units, (b) 6 units, (c) 8 units, (d) 10 units, (e) 12 units and (f) 14 units. AR stands for the aspect ratio of the focus. Beam enters from left.

Fig. 4.
Fig. 4.

Contour plots of the intensity distributions shown in Fig. 3. Parameter r is a ratio of l1/l2 describing the beam asymmetry about the vertical axis. Aperture width wx are (a) 4 units, (b) 6 units, (c) 8 units, (d) 10 units, (e) 12 units and (f) 14 units.

Fig. 5.
Fig. 5.

Longitudinal intensity distribution at focal region obtained from elliptical Gaussian beam model. Input beam ellipticity Ry/Rx of (a) 24, (b) 16, (c) 12. Beam direction is from the left to right.

Fig. 6.
Fig. 6.

Typical optical microscope images of the written profiles using a) 120 μm, b) 130 μm, c) 140 μm, d) 150 μm, e) 170 μm, f) 190 μm, g) 240 μm and h) 300μm aperture widths. Processing conditions of 140 to 460 mW (estimate ~3 to 30 μJ), 50x 0.55 NA at writing speed of 0.1 mm/s. Beam enters from left.

Fig. 7.
Fig. 7.

Plot of waveguide AR against increasing aperture width.

Fig. 8.
Fig. 8.

Structural morphologies obtained using 50x Na 0.55 objective and translation speed of 0.1 mm/s. Aperture width used a) 130 μm, b) 170 μm, c) 190 μm and d) 240 μm. Beam enters from left.

Fig. 9.
Fig. 9.

Simulated plot of beam AR against increasing aperture width.

Fig. 10.
Fig. 10.

Influence of beam power and energy on focal shape for aperture width a) 4 units b) 6 units c) 8 units and d) 10 units. Beam decreases in power from left to right.

Fig. 11.
Fig. 11.

Near field profile at exit surface of waveguide in FOTURAN glass. Inset: 3D profile of near field image.

Equations (7)

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U f x y = f x y l A x y
= FT 1 { F ( f x , f y ) * L A ( f x , f y ) } .
F ( f x , f y ) = e j 2 π z λ 1 ( λf x ) 2 ( λf y ) 2 .
rect ( x w x ) = { 1 w x 2 ξ w x 2 . 0 otherwise
L A ( f x , f y ) = FT { A x y rect ( x w x ) rect ( y w y ) e j k 2 f ( x 2 + y 2 ) } .
I = 1 [ 1 + ( z 2 z x 0 2 ) 1 2 ] 1 [ 1 + ( z 2 z y 0 2 ) 1 2 ] X
exp { 2 x 2 w x 0 2 [ 1 + ( z 2 z x 0 2 ) ] } exp { 2 y 2 w y 0 2 [ 1 + ( z 2 z y 0 2 ) ] } .

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