Abstract

We report on the fabrication of symmetric waveguides in bulk poly(methyl methacrylate) (PMMA) by femtosecond laser pulses. A waveguide with a circular transverse profile can be obtained by using a slit beam shaping method. The refractive index in the core increases by up to 4.6 × 10-4 and the waveguide works as single-mode waveguide at a wavelength of 632.8 nm. This writing technique is applied to the fabrication of a directional coupler to split a coupled beam with a 1:1 splitting ratio at 632.8 nm.

© 2006 Optical Society of America

1. Introduction

Polymer materials are widely used for fabricating photonic components due to their numerous advantages, such as their low cost, ease of manufacture, and ease with which they can be doped with various materials. In particular, poly(methyl methacrylate) (PMMA) is one of the most widely used polymer materials for optical components. PMMA has high transmission in the visible and near-infrared regions and is often used for plastic optical fibers and planar waveguide devices [1].

To meet the increasing data capacity requirements in communication systems, there is a growing demand for materials and techniques for fabricating three-dimensionally integrated photonic devices. Femtosecond laser fabrication allows the integration of photonic devices in three dimensions. Focused femtosecond laser pulses can induce localized structural changes inside transparent materials due to nonlinear absorption. There have been many reports using this technique to fabricate waveguide devices in a wide variety of glasses [2–8]. Moreover, in recent years, femtosecond laser fabrication in PMMA has also been demonstrated [9–14]. For example, tubular waveguides, in which guiding occurs within an annular core, were fabricated using a femtosecond oscillator with a repetition rate of 25 MHz [14]; however, tubular waveguides embedded in PMMA are not suitable for connection to conventional waveguide devices because the refractive index in the core is usually positive.

In this paper, we report, to the best of our knowledge, the first fabrication of a symmetric waveguide in bulk PMMA by femtosecond laser pulses. The symmetric waveguide allowed single-mode propagation at a wavelength of 632.8 nm. As an application, we demonstrate a directional coupler that splits a coupled beam with a 1:1 splitting ratio.

2. Experiments

Our sample was commercially available bulk PMMA (Shinkolite A L-#000, supplied by Mitsubishi Rayon Co., Ltd.). The dimensions were 30 mm × 6 mm × 3 mm. Laser pulses with a pulse width of 85 fs were generated by a Ti:sapphire laser system with a wavelength of 800 nm and a repetition rate of 1 kHz. The pulse energy was attenuated by rotating a half-wave plate in front of a polarizer. The beam diameter was 4 mm. The laser pulses were focused by a 50× microscope objective with a numerical aperture (NA) of 0.55, and the focal point was located 200 μm below the sample surface. The sample was mounted on a computer-controlled translation stage, and the waveguide writing was carried out in a transverse geometry in which the sample was translated perpendicular to the laser beam propagation direction. After irradiation with the femtosecond laser pulses, the sample was polished until the waveguide ends were exposed at the sample surface. The fabricated waveguide length was 5.5 mm.

 

Fig. 1. Schematic of the optical setup for waveguide writing in bulk PMMA.

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The optical setup for waveguide writing is shown in Fig. 1. First, we describe an experiment without a slit. The sample was moved at 0.2 mm/s perpendicular to the optical axis (-x direction). The energy per pulse was 27 nJ before the objective lens. Above 27 nJ/pulse, void-like scattering damage structures, which impede light guiding, were observed. Figure 2(a) shows an optical microscope image of the exit surface of the waveguide in the yz-plane when illuminated with a halogen lamp. The bright region, where guiding of halogen light occurred, appeared asymmetrical in shape.

The waveguide asymmetry in the transverse geometry can be eliminated using a pair of cylindrical lenses [15] or a slit [16,17]. The use of a slit allows a simple optical setup and free adjustment to the required beam shape. Therefore, we placed a slit before the objective lens and demonstrated its effectiveness for fabricating waveguides in PMMA. By reducing the beam diameter in the y-direction (Ry) to be shorter than that in the x-direction (Rx), we can achieve a symmetric intensity profile at the focus on the yz-plane. Figures 2(b) and 2(c) show optical images of the exit surface of the waveguide fabricated using slits of different dimensions. The dimensions of the slit along the y-axis were 0.8 mm in Fig. 2(b) and 0.4 mm in Fig. 2(c), respectively. The length of Rx was 4 mm, which was the same as the beam diameter. The aspect ratio of laser beam diameters Rx/Ry was 5 and 10 in Figs. 2(b) and 2(c), and the energy per pulse was 97 nJ and 185 nJ, respectively. When the aspect ratio Rx/Ry was 10, the optical microscope image revealed that the cross section of the waveguide was almost symmetric.

 

Fig. 2. Optical image of the fabricated waveguides (a) without a slit and using a slit with aspect ratios Rx/Ry of (b) 5 and (c) 10.

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We compared the cross section of the waveguide of the experimental results with that calculated by numerical simulation. For an elliptical Gaussian beam, the intensity distribution in yz-plane (x = 0) near the focal spot can be expressed as [16],

I(y,z)=1[1+(z2z02)]121[1+(z2z'02)]12exp{2y2ω'02[1+(z2z'02)]}.

where ω´0 = (Rx/Ry0=λ/(NA ∙;π) is the beam waist containing the slit effect, z´0 = kω´2 0/2 is the corresponding Rayleigh length, and λ and k are the wavelength and the wave vector, respectively. We defined the aspect ratio of the cross section of the intensity profile αcal as the full-width at half-maximum of the calculated intensity. The aspect ratio of the cross section of fabricated waveguides using various slit widths αexp was defined as the full-width at half-maximum of the bright region in the optical image. Figure 3 shows the aspect ratio of the cross section of waveguides as a function of the aspect ratio of laser beam diameter Rx/Ry. When Rx/Ry was 5, the aspect ratio αcal was nearly symmetry in simulation; however, the experimental result αexp was 0.14. The difference between numerical simulation and experimental result is attributed to spherical aberration, and nonlinear processes, such as self-focusing and filamentation. The experiments in Fig. 3 demonstrated that beam shaping using the slit is effective in fabricating symmetric waveguides in PMMA, and subsequent experiments were performed using the slit with the aspect ratio Rx/Ry of 10.

 

Fig. 3. The aspect ratio of the cross-section of waveguides as a function of the aspect ratio of laser beam diameter Rx/Ry.

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We investigated the near-field pattern (NFP) at the output of the symmetric waveguide. We coupled a He-Ne laser beam of wavelength 632.8 nm to the symmetric waveguide in Fig. 2(c) with a 0.55-NA objective lens. Figure 4 shows the near-field output image using a 50× objective lens and a CCD camera and its cross-sectional intensity profiles in the yz-plane. The full-width at half-maxima of the intensity profiles were approximately 4.3 μm in the y-direction and 6.7 μm in the z-direction. These intensity profiles demonstrated that the waveguide works essentially as a single-mode waveguide at 632.8 nm.

 

Fig. 4. Near-field pattern at symmetric waveguide output. The intensity profiles in the horizontal and vertical directions are shown.

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The magnitude of the refractive index change (Δn) was estimated by measuring the numerical aperture (NA) of the waveguide output [18]. We fabricated 5.5-mm-long waveguides at different pulse energies by scanning at a velocity of 0.2 mm/s. We coupled the He-Ne laser light into the waveguides and measured the NA of the cone of the guided light that exited the waveguides in the far field. By assuming step-index profile of the waveguide cross section, the NA is related to Δn by NA = (2n 0 Δn)1/2, where n 0 = 1.49, the refractive index of the bulk PMMA. Figure 5 shows the relation between incident pulse energy and estimated refractive index change. When the incident laser pulse energy was increased, the magnitude of the refractive index change increased; however, scattering damage was induced at energies over 185 nJ/pulse. In addition, overwriting by femtosecond laser pulses induced scattering damage. As a result, the maximum refractive index change was 4.6 × 10-4 at 185 nJ/pulse. The propagation loss of the waveguide was found to be 4.2 dB/cm at 632.8 nm by measuring the propagated light intensities from waveguides of different lengths.

 

Fig. 5. The magnitude of the refractive index change as a function of incident pulse energy.

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As an application, we fabricated directional couplers in PMMA. Figure 6(a) shows an illustration of a directional coupler containing a 5.5-mm-long straight waveguide and a waveguide with two bends of 0.6°. The coupler has an interaction region of length L where the two waveguides are parallel and separated by a center-to-center distance of 10-μm. The gap between the two waveguides at the end plane was 30 μm. Figures 6(b) and 6(c) show the NFPs and cross sections of the coupler outputs with L = 1.0 mm and L = 2.0 mm, respectively. The splitting ratios of the directional couplers with L = 1.0 mm and L = 2.0 mm were approximately 3:2 and 1:1, respectively.

 

Fig. 6. (a) Schematic diagram of a directional coupler. Near-field patterns and cross sections of the coupler output at 632.8 nm for (b) L = 1.0 mm and (c) L = 2.0 mm.

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3. Discussion

We attributed the mechanism of the increased refractive index to a volume contraction, by analogy with the refractive index change caused by ultraviolet (UV) laser irradiation. When UV light is irradiated at the surface of a PMMA sample, a volume contraction as a result of partial separation of the PMMA chains leads to an increased refractive index [19]. Although the physical mechanisms involved have not been studied in detail, bond breaking occurs around the focus through multiphoton, tunnel, and avalanche ionization by irradiating the PMMA sample with femtosecond laser pulses. This bond breaking causes contraction of the volume and resultant increase in refractive index. In Ref. 11, the void formation produced by picosecond laser pulses in PMMA was attributed to the defects created by breaking the PMMA chains. In our experiments, we observed broadband fluorescence around 550-800 nm from scattering damage by excitation with an argon laser at a wavelength of 488 nm. The fluorescence from scattering damage is in agreement with that from the voids formation [11] and the filamentary cavity formation [13]. Therefore, scattering damage is produced due to the formation of a high-density plasma. The free electrons generated by tunnel ionization and multiphoton ionization act as seeds for avalanche ionization, which exponentially increases the free carrier density. The free electrons absorb the energy from the electromagnetic field of the laser pulse, leading to laser-induced optical breakdown, the generation of a high-density plasma, and production of scattering damage. In contrast, focusing femtosecond laser pulses with lower energies, refractive index change is induced due to the formation of a low-density plasma. The low-density plasma leads to partial bond breaking in PMMA. This partial bond-breaking causes contraction of the volume and resultant increase in refractive index. However, the physical mechanism responsible for the induction of refractive index change is still under investigation and will be the subject of a future study.

In a high-repetition-rate femtosecond laser system (MHz order), focusing femtosecond laser pulses results in an increase in temperature for a localized region surrounding the focal spot. The large diameter of the modified region with respect to the focal spot size is explained by heating of the PMMA through heat accumulation [14,20]. In a low-repetition-rate system (kHz order), however, the heat accumulation is comparatively small, and the modified region is directly related to the intensity distribution of the focused beam or the subsequent plasma density. Thus, the slit beam shaping method is effective for fabricating symmetric waveguides in PMMA by kilohertz-repetition-rate amplified femtosecond lasers.

4. Conclusion

We have demonstrated the fabrication of symmetric waveguides in PMMA by using femtosecond laser pulses. The refractive index change in the core was as large as 4.6 × 10-4. The waveguides work as single-mode waveguides at 632.8 nm. A directional coupler to split the coupled beam with a 1:1 splitting ratio has been demonstrated using this technique. The results obtained using our proposed technique to fabricate symmetric waveguides in bulk PMMA indicate the potential for three-dimensional polymer integrated optics.

Acknowledgments

This work was supported by a research grant from The Mazda Foundation.

References and links

1. L. Eldada and L. W. Shachlette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6, 54–68 (2000). [CrossRef]  

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. Yamada, W. Watanabe, T. Toma, J. Nishii, and K. Itoh, “In situ observation of photoinduced refractive index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 26, 19–21 (2001). [CrossRef]  

4. C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, “Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy,” Opt. Lett. 26, 93–95 (2001). [CrossRef]  

5. M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, “Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses,” Appl. Opt. 41, 4360–4364 (2002). [CrossRef]   [PubMed]  

6. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. 26, 42–43 (2001). [CrossRef]  

7. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt. Lett. 28, 2491–2493 (2003). [CrossRef]   [PubMed]  

8. Y. Nasu, M. Kohtoku, and Y. Hibino, “Low-loss waveguides written with a femtosecond laser for flexible interconnection in a planar light-wave circuit,” Opt. Lett. 30, 723–725 (2005). [CrossRef]   [PubMed]  

9. Y. Li, K. Yamada, T. Ishizuka, W. Watanabe, K. Itoh, and Z. Zhou, “Single femtosecond pulse holography using polymethyl methacrylate,” Opt. Express 10, 1173–1178 (2002). [PubMed]  

10. P. J. Scully, D. Jones, and D. A. Jaroszynski, “Femtosecond laser irradiation of polymethylmethacrylate for refractive index gratings,” J. Opt. A 5, S92–S96 (2003). [CrossRef]  

11. K. Yamasaki, S. Juodkazis, M. Watanabe, H.-B. Sun, S. Matsuo, and H. Misawa, “Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films,” Appl. Phys. Lett. 76, 1000–1002 (2000). [CrossRef]  

12. K. Ohta, M. Kamata, and M. Obara, “Optical waveguide fabrication in new glasses and PMMA with temporally tailored ultrashort laser,” Proc. SPIE 5340, 172–178 (2004). [CrossRef]  

13. S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly(methyl methacrylate) induced by single femtosecond pulse,” Appl. Phys. A 81, 1587–1590 (2005). [CrossRef]  

14. A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, “Femtosecond laser fabrication of tubular waveguides in poly(methyl methacrylate),” Opt. Lett. 29, 1840–1842 (2004). [CrossRef]   [PubMed]  

15. G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Femtosecond micromachining of symmetric waveguides at 1.5 μm by astigmatic beam focusing,” Opt. Lett. 27, 1938–1940 (2002). [CrossRef]  

16. 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]  

17. M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express 13, 5676–5681 (2005). [CrossRef]   [PubMed]  

18. D. Homoelle, W. Wielandy, A. L. Gaeta, E. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999). [CrossRef]  

19. C. Wochnowski, S. Metev, and G. Sepold, “UV-laser-assisted modification of the optical properties of polymethylmethacrylate,” Appl. Surf. Sci. 154–155, 706–711 (2000). [CrossRef]  

20. D. Day and M. Gu, “Microchannel fabrication in PMMA based on localized heating by nanojoule high repetition rate femtosecond pulses,” Opt. Express 13, 5939–5946 (2005). [CrossRef]   [PubMed]  

References

  • View by:
  • |

  1. L. Eldada and L. W. Shachlette, "Advances in polymer integrated optics," IEEE J. Sel. Top. Quantum Electron. 6, 54-68 (2000).
    [CrossRef]
  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. Yamada, W. Watanabe, T. Toma, J. Nishii, and K. Itoh, "In situ observation of photoinduced refractive index changes in filaments formed in glasses by femtosecond laser pulses," Opt. Lett. 26, 19-21 (2001).
    [CrossRef]
  4. C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett. 26, 93-95 (2001).
    [CrossRef]
  5. M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 41, 4360-4364 (2002).
    [CrossRef] [PubMed]
  6. M. Streltsov and N. F. Borrelli, "Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses," Opt. Lett. 26, 42-43 (2001).
    [CrossRef]
  7. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Opt. Lett. 28, 2491-2493 (2003).
    [CrossRef] [PubMed]
  8. Y. Nasu, M. Kohtoku, and Y. Hibino, "Low-loss waveguides written with a femtosecond laser for flexible interconnection in a planar light-wave circuit," Opt. Lett. 30, 723-725 (2005).
    [CrossRef] [PubMed]
  9. Y. Li, K. Yamada, T. Ishizuka, W. Watanabe, K. Itoh, and Z. Zhou, "Single femtosecond pulse holography using polymethyl methacrylate," Opt. Express 10, 1173-1178 (2002).
    [PubMed]
  10. P. J. Scully, D. Jones, and D. A. Jaroszynski, "Femtosecond laser irradiation of polymethylmethacrylate for refractive index gratings," J. Opt. A 5, S92-S96 (2003).
    [CrossRef]
  11. K. Yamasaki, S. Juodkazis, M. Watanabe, H.-B. Sun, S. Matsuo, and H. Misawa, "Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films," Appl. Phys. Lett. 76, 1000-1002 (2000).
    [CrossRef]
  12. K. Ohta, M. Kamata, and M. Obara, "Optical waveguide fabrication in new glasses and PMMA with temporally tailored ultrashort laser," Proc. SPIE 5340, 172-178 (2004).
    [CrossRef]
  13. S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, "Filamentary cavity formation in poly(methyl methacrylate) induced by single femtosecond pulse," Appl. Phys. A 81, 1587-1590 (2005).
    [CrossRef]
  14. A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, "Femtosecond laser fabrication of tubular waveguides in poly(methyl methacrylate)," Opt. Lett. 29, 1840-1842 (2004).
    [CrossRef] [PubMed]
  15. G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, "Femtosecond micromachining of symmetric waveguides at 1.5 µm by astigmatic beam focusing," Opt. Lett. 27, 1938-1940 (2002).
    [CrossRef]
  16. 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]
  17. M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, "Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses," Opt. Express 13, 5676-5681 (2005).
    [CrossRef] [PubMed]
  18. D. Homoelle, W. Wielandy, A. L. Gaeta, E. F. Borrelli, and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Opt. Lett. 24, 1311-1313 (1999).
    [CrossRef]
  19. C. Wochnowski, S. Metev, and G. Sepold, "UV-laser-assisted modification of the optical properties of polymethylmethacrylate," Appl. Surf. Sci. 154-155, 706-711 (2000).
    [CrossRef]
  20. D. Day and M. Gu, "Microchannel fabrication in PMMA based on localized heating by nanojoule high repetition rate femtosecond pulses," Opt. Express 13, 5939-5946 (2005).
    [CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. A (1)

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, "Filamentary cavity formation in poly(methyl methacrylate) induced by single femtosecond pulse," Appl. Phys. A 81, 1587-1590 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

K. Yamasaki, S. Juodkazis, M. Watanabe, H.-B. Sun, S. Matsuo, and H. Misawa, "Recording by microexplosion and two-photon reading of three-dimensional optical memory in polymethylmethacrylate films," Appl. Phys. Lett. 76, 1000-1002 (2000).
[CrossRef]

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]

Appl. Surf. Sci. (1)

C. Wochnowski, S. Metev, and G. Sepold, "UV-laser-assisted modification of the optical properties of polymethylmethacrylate," Appl. Surf. Sci. 154-155, 706-711 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron (1)

L. Eldada and L. W. Shachlette, "Advances in polymer integrated optics," IEEE J. Sel. Top. Quantum Electron. 6, 54-68 (2000).
[CrossRef]

J. Opt. A (1)

P. J. Scully, D. Jones, and D. A. Jaroszynski, "Femtosecond laser irradiation of polymethylmethacrylate for refractive index gratings," J. Opt. A 5, S92-S96 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (9)

D. Homoelle, W. Wielandy, A. L. Gaeta, E. F. Borrelli, and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Opt. Lett. 24, 1311-1313 (1999).
[CrossRef]

A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, "Femtosecond laser fabrication of tubular waveguides in poly(methyl methacrylate)," Opt. Lett. 29, 1840-1842 (2004).
[CrossRef] [PubMed]

G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, "Femtosecond micromachining of symmetric waveguides at 1.5 µm by astigmatic beam focusing," Opt. Lett. 27, 1938-1940 (2002).
[CrossRef]

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]

K. Yamada, W. Watanabe, T. Toma, J. Nishii, and K. Itoh, "In situ observation of photoinduced refractive index changes in filaments formed in glasses by femtosecond laser pulses," Opt. Lett. 26, 19-21 (2001).
[CrossRef]

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett. 26, 93-95 (2001).
[CrossRef]

M. Streltsov and N. F. Borrelli, "Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses," Opt. Lett. 26, 42-43 (2001).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Opt. Lett. 28, 2491-2493 (2003).
[CrossRef] [PubMed]

Y. Nasu, M. Kohtoku, and Y. Hibino, "Low-loss waveguides written with a femtosecond laser for flexible interconnection in a planar light-wave circuit," Opt. Lett. 30, 723-725 (2005).
[CrossRef] [PubMed]

Proc. SPIE (1)

K. Ohta, M. Kamata, and M. Obara, "Optical waveguide fabrication in new glasses and PMMA with temporally tailored ultrashort laser," Proc. SPIE 5340, 172-178 (2004).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the optical setup for waveguide writing in bulk PMMA.

Fig. 2.
Fig. 2.

Optical image of the fabricated waveguides (a) without a slit and using a slit with aspect ratios Rx/Ry of (b) 5 and (c) 10.

Fig. 3.
Fig. 3.

The aspect ratio of the cross-section of waveguides as a function of the aspect ratio of laser beam diameter Rx /Ry .

Fig. 4.
Fig. 4.

Near-field pattern at symmetric waveguide output. The intensity profiles in the horizontal and vertical directions are shown.

Fig. 5.
Fig. 5.

The magnitude of the refractive index change as a function of incident pulse energy.

Fig. 6.
Fig. 6.

(a) Schematic diagram of a directional coupler. Near-field patterns and cross sections of the coupler output at 632.8 nm for (b) L = 1.0 mm and (c) L = 2.0 mm.

Equations (1)

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I ( y , z ) = 1 [ 1 + ( z 2 z 0 2 ) ] 1 2 1 [ 1 + ( z 2 z ' 0 2 ) ] 1 2 exp { 2 y 2 ω ' 0 2 [ 1 + ( z 2 z ' 0 2 ) ] } .

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