Abstract

We report on structural modification in fused silica by a novel commercial femtosecond fiber laser with a fundamental wavelength of 1558 nm. The refractive-index change was induced by laser pulses at a repetition rate of 173 kHz and pulse duration of 870 fs. The refractive index change with a magnitude of 1.2 × 10-3 was estimated from the diffraction efficiencies of an internal grating.

©2006 Optical Society of America

1. Introduction

Nonlinear material processing using near-infrared femtosecond laser pulses has become an important area of research for the fabrication of photonic devices in transparent materials. This technique has been developing quickly for rapid prototyping to flexibly integrate photonic devices in three-dimensional space, including waveguides, couplers, and gratings by translating the focal spot of femtosecond laser pulses in a wide variety of glasses [1–26]. The fabrication of photonic devices is based on nonlinear absorption around the focal volume of femtosecond laser pulses. When near-infrared femtosecond laser pulses are focused inside the bulk of glass, the intensity in the focal volume becomes high enough to cause nonlinear absorption, which leads to a localized modification of the glass in the focal volume. Femtosecond laser pulses produce different types of structural modifications, such as voids, scattering damage, and refractive-index change in silica glass, depending on the focusing conditions and the materials, as well as the laser parameters (i.e. wavelength, pulse duration, energy, and repetition rate). Most studies on structural modification and device fabrication in fused silica have been performed with Ti: Sapphire lasers. It has been recently reported that optical waveguides were inscribed in fused silica by use of 70-fs, 1.5-μm femtosecond laser pulses from an optical parametric amplifier [15].

The fiber laser system is more attractive in photonic device fabrication in glass because of superior stability, reliability and robustness as compared with a femtosecond Ti: Sapphire lasers [22–24]. It has been reported that it was not possible to produce low-loss waveguides in fused silica when writing with the 1045-nm wavelength but that it was possible to fabricate good waveguides at the 522-nm second harmonic wavelength by use of a femtosecond amplified Yb-fiber laser with a high repetition rate and a pulse duration of 375 fs [23].

Despite the above-mentioned studies, the laser-processing window for photonic device fabrication in fused silica has not been fully investigated. To expand the laser-processing window for photonic device fabrication in fused silica, we report in this paper on the generation of refractive index change inside fused silica by use of a commercial amplified femtosecond Er-fiber laser system with a wavelength of 1558 nm. The laser parameters for structural modification in fused silica were investigated, including pulse energy, scan speed, and repetition rates. We demonstrate that filamentary refractive-index change can be induced with the amplified femtosecond Er-fiber laser system at a wavelength of 1558 nm, a repetition rate of 173 kHz and a pulse duration of 870 fs.

2. Experimental method

The optical setup for structural modification inside fused silica is shown in Fig. 1. An amplified femtosecond Er-fiber laser system generated 1558-nm laser pulses with variable repetition rate (IMRA America, FCPA μJewel B-Series). The system consists of three diode-pumped Er-fiber stages: an oscillator, pre-amplifier and large mode area Er-fiber power amplifier. The sample, fused silica (Tosoh S grade, size: 25 mm × 5 mm × 5 mm), was mounted on a two-dimensional translation stage with 100-nm resolution (Physik Instrumente V102.2L). The beam from the laser system was demagnified with a plano-convex lens (L1; focal length f of 100 mm) and a plano-convex lens (L2;f= 50 mm) to fill the back aperture of the objective lens. The laser pulses were focused at a depth of 200 μm beneath the surface by a 50× objective lens with a numerical aperture (NA) of 0.55 (OB1; Olympus LMPlan 50×IR). The pulse energy was controlled by the rotation of the half-wave plate in front of the Glan laser polarizer. In order to induce structural modification in fused silica, the sample was translated at scan speeds of between 2 and 5 μm/s for transverse writing, perpendicular to the optical axis. Transmission white-light microscope images of structural modification in fused silica were observed in the xy-plane and in the xz-plane by optical microscopes.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the experimental setup for inducing structural modification in fused silica. L1, plano-convex lens (focal length f = 100 mm); L2, plano-convex lens (f= 50 mm); L3, achromatic lens (f = 200 mm); HWP, λ/2 wavelength plate; P, Glan-laser polarizer; Shutter, electromagnetic shutter; DM, dichroic mirror; OB1 and OB2, objective lenses; M, mirror.

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3. Experimental results

3.1 Structural modification with different pulse energies

Among several factors influencing structural modification in fused silica, we focus here on the incident pulse energy and the scan speed in order to establish the optimal irradiation condition to induce refractive-index change. We used 870-fs laser pulses at a repetition rate of 173 kHz. The maximum output power of the laser system was 525 mW and the maximum energies were approximately 3 μJ/pulse at 173 kHz. First, structural modifications were produced at the pulse energy between 0.87 μJ/pulse (150 mW) and 2.02 μJ/pulse (350 mW) at a fixed scan speed of 2 μm/s. The sample was translated 200 μm along y-axis perpendicular to the laser propagation axis. Figures 2(a) and (b) show unpolarized transmission white-light microscope images of the induced structural modifications in fused silica as a function of the pulse energy observed from a direction perpendicular to the optical axis (in the xz-plane) and parallel to the optical axis (in the xy-plane), respectively. At a pulse energy of 0.87 μJ/pulse, no structural modification was induced. Whereas, at a pulse energy above 1.16 μJ/pulse (200 mW), scattering damage was produced. The scattering damage shapes were elongated along the optical axis. The length of the scattering damage along the optical axis varied from 24 μm to 38 μm at incident pulse energies between 1.16 μJ/pulse and 2.02 μJ/pulse.

 figure: Fig. 2.

Fig. 2. (a), (b), (d) and (e) are unpolarized transmission white-light microscope images of induced structural modifications in fused silica by 1558-nm laser pulses; (a) and (b) between 0.87 μJ/pulse (150 mW) and 2.02 μJ/pulse (350 mW) and (d) and (e) between 1.07 μJ/pulse (185 mW) and 1.1 μJ/pulse (190 mW). (c) and (f) are crossed-Nicols images of the structures indicated in (b) and (e), when the sample was set between two crossed polarizers.

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To investigate details of the structural modifications, we varied the pulse energies from 0.87 μJ/pulse to 1.16 μJ/pulse. Figures 2(d) and (e) show optical images of the structural modifications at pulse energies between 1.07 μJ/pulse (185 mW) and 1.10 μJ/pulse (190 mW). At a pulse energy between 1.07 μJ/pulse and 1.08 μJ/pulse (187 mW), a refractive-index change was induced. The shapes of refractive index change were elongated along the optical axis due to filamentation. The length of the refractive index change region was approximately 9 μm along the optical axis. At a pulse energy of 1.10 μJ/pulse, however, damage spots were produced in the refractive-index change region. Above 1.16 μJ/pulse, strong birefringence was observed. During writing process, we observed third harmonic generation of the fundamental at 522 nm when the damage occurred. Squier et al. reported third harmonic generation from scattering damage in optical glass by use of an optical parametric amplifier at the wavelength of 1.22 μm [27]. Third harmonic generation is a good indicator to discern scattering damage from refractive-index change. At a pulse energy below 1.04 μJ/pulse (180 mW), no structural modification was induced.

The birefringent properties of the structural modifications were investigated. Figures 2(c) and (f) show crossed-Nicols images of the structures indicated in Fig. 2(b) and (e), respectively, when the polarization angle of the first polarizer was set at 45 degree from the axis of the induced birefringence (y-axis). We evaluated a magnitude of laser-induced birefringence. The sample was illuminated by a light filtered from a halogen lamp. We used an interference filter whose central wavelength was 650 nm (band width (FWHM): 10 nm). The sample was placed between two polarizers. The transmitted light through the second polarizer was detected by a CCD (charge-coupled device) camera. The intensities of the transmitted light in the area of the laser-induced structural modification were averaged. When the second polarizer is set parallel to the first polarizer, the intensity of the transmitted light (I 45) is

I45=(I2)2(1+cosφ)2,

where, I is an intensity of the transmitted light through the first polarizer and φ is a phase retardation (φ = φy - φx). When the second polarizer is set at crossed-Nicols, the intensity of the transmitted light (I 135) is

I135=(I2)2(1cosφ)2,

By use of Eqs. (1) and (2), a phase retardation is represented by following equation:

ϕ=cos1(I45I135I).

From Eq. (3), finally, a magnitude of birefringence (Δn = ny - nx) is determined by following equation:

Δn=λcos1(I45I135I)(2πd),

where, λ is a wavelength of an incident light, d is the thickness of the birefringent region [28, 29]. Here, we assumed that the laser-induced birefringence is unity because the intensity of the light in the filament is constant.

 figure: Fig. 3.

Fig. 3. Magnitude of birefringence as a function of the incident pulse energy.

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Figure 3 shows the obtained magnitude of birefringence as a function of the incident pulse energy. The average magnitude of birefringence was approximately 1.3 × 10-3 below 1.10 μJ/pulse and that was approximately 2.6 × 10-3 above 1.16 μJ/pulse. At 1.10 μJ/pulse, the average magnitude of birefringence was approximately 1.3 × 10-3 and the maximum value was approximately 3.4 × 10-3 at damage spots. Therefore, the refractive-index change (type I), induced by the incident pulse energy between 1.07 μJ/pulse and 1.08 μJ/pulse, has only weak birefringent properties. On the other hand, the scattering damage (type II) induced by the incident pulse energy above 1.16 μJ/pulse, exhibited strong birefringent properties. Permanent birefringence produced by 1550-nm laser pulses is the same result found in the birefringent damage produced above a certain threshold of writing fluence at 800 nm using a Ti:Sapphire laser [30, 31].

3.2 Structural modification with different scan speed

We varied the scan speed from 2 to 5 μm/s at a fixed energy of 1.08 μJ/pulse (187 mW). Figures 4(a) and (b) show optical images of the induced structural modifications in fused silica as a function of the scan speed in the xz-plane and the xy-plane, respectively.

 figure: Fig. 4.

Fig. 4. Optical image of structural modifications in fused silica as a function of the scan speed at the pulse energy of 1.08 μJ/pulse (187 mW). (a) Transmission white-light microscope images of refractive-index change in fused silica observed in the xz-plane (b) and in the xy-plane by optical microscopes.

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The white area in the image observed in the xz-plane demonstrated that the refractive-index change increased due to guiding of light from the halogen lamp in the region with the refractive-index change. The diameter of the region with the refractive index change was approximately 1.3 μm. Attempts to obtain high index changes by exposure to higher energies led to waveguide damage, with scattering damage observed as the result of optical breakdown. With the laser parameters tests here, a refractive-index change can be obtained only with low scanning speeds on the order of micrometers per second.

3.3 Fabrication of grating

We determined the magnitude of the refractive-index change from the diffraction efficiencies of the fabricated internal grating. When a grating satisfies the condition for Raman-Nath diffraction, the Klein–Cook (Q) parameter meets the following equation [32]:

Q=2πλTn0Λ2<<1.

Here, λ is the wavelength of the incident light on the grating, T is the grating thickness, n 0 is refractive index in vacuum, and Λ is the grating period.

The distribution of refractive index is written by n 0 + Δn(x), where Δn(x) is the distribution of refractive-index change. x is the coordinate along the direction of the grating. We assume that the distribution of refractive-index change Δn(x) is represented by a superposition of a power series of sinusoidal phase modulation with refractive-index change of Δn(x) (m = 1,2,3, …) as follows [33]:

Δn(x)=m=1m=Δnmcos(m×2πxΛ)(m=1,2,3,)
=Δn1cos(2πxΛ)+Δn2cos(2*2πxΛ)+(m=1,2,3,).

Equation (6) assumes the fabricated grating consists of the gratings with the grating periods of Λ/m (m=1,2,3,…). In the case of normal incidence on the Raman-Nath grating, the l-th order diffraction efficiencies ηl are written with the following equation:

ηl=Jl2(2κlT)(l=1,2,3,).

Here, Jl(x) is a Bessel function, l is a diffraction order, and kl is l-th coupling coefficient, which is related to refractive-index change Δnl as follows:

κl=πΔnlλ(l=1,2,3,).

By Fourier analysis of Eq. (6), each diffraction efficiency ηl can be represented by first order diffraction with a grating period of Λ/m (m=1,2,3, …). From each diffraction efficiency ηm, we can calculate the maximum refractive-index change Δn(x) by

Δn(x)=m=1m=Δnm(m=1,2,3,).

We fabricated internal gratings in fused silica. In the experiment, the sample was displaced along the y-direction, perpendicular to the laser propagation axis, over a distance of 200 μm. To write a grating the procedure was repeated 20 times by steps of 10 μm in the x-axis. The incident power was 1.08 μJ/pulse (187 mW). The translation speed was 2 μm/sec. The condition was able to induce the strongest refractive-index change. Figure 5 shows an optical image of the fabricated grating in fused silica with a period of 10 μm. The grating thickness was measured to be 5 μm by an optical microscope. The calculated Q of the fabricated grating was 0.13 and satisfied the Eq. (5) for Raman-Nath grating.

We focused a He-Ne laser beam at 632.8-nm wavelength on a fabricated grating. We observed 8 diffraction patterns. The transmitted light through the grating was detected by an optical powermeter. From the diffraction efficiencies of the fabricated grating, we obtained that the induced refractive-index change, Δn, was 1.2 × 10-3, which is of the same order as previously reported in fused silica with 800-nm laser pulses from Ti:Sapphire lasers [4, 7].

 figure: Fig. 5

Fig. 5 Optical image of the fabricated grating with a period of 10 μm in fused silica.

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3.4 Processing window at variable repetition rate

We investigated the effect of repetition rate on structural modifications in fused silica. The laser pulses with pulse duration of 947 fs were applied in this experiment. The experiment was performed at repetition rates of 155 kHz, 250 kHz, 500 kHz, 650 kHz, 750 kHz, and 1 MHz. Figure 6 shows the thresholds of induced refractive-index change at different repetition rates. Scattering damage was produced above the threshold energy. No structural modification was induced below the threshold energy. The energy for induced refractive-index change decreased with higher repetition rates. The results indicate the slight thermal accumulation; however, fused silica showed no strong evidence of heat accumulation. At 750 kHz, refractive-index change was induced; however, we couldn’t observe the scattering damage because the maximum energy in front of the objective lens was 0.53 μJ/pulse (400 mW). At a repetition rate of 1 MHz, no structural modification was produced with full power applied.

 figure: Fig. 6.

Fig. 6. Thresholds of induced refractive-index change at different repetition rates.

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Previous studies show that ultrashort femtosecond laser pulses are used to induce a refractive-index change in silica glass. At 1-kHz Ti:Sapphire amplified lasers, longer pulse durations (> 200-fs) cause scattering damage [31, 32]. At higher repetition rates using a Yb:glass oscillator [21] and an amplified Yb-fiber laser [23], refractive-index change can be induced with ultrashort femtosecond laser pulses below 400 fs. In our experiments, a refractive-index change in fused silica was only evident in a narrow processing range of pulse energy and scanning speed, however it should noted that refractive-index change can be induced with laser pulses with a pulse duration of ~ 1 ps using the fiber laser at 1558 nm. Regarding the induction of a refractive-index change in fused silica for long pulse durations of 800–900 fs, the effects of avalanche ionization could be the dominant mechanism; however, the mechanism of the refractive-index change is still under investigation.

4. Conclusion

In conclusion, we have demonstrated structural modification in fused silica using the femtosecond fiber laser at 1558 nm. We found that filamentary refractive-index change can be induced with femtosecond laser pulses using 870-fs pulses. Fabricated gratings yielded an estimated refractive-index change of 1.2 × 10-3. Structural modification in fused silica with a compact and stable femtosecond fiber laser is an important step toward introducing this technique into an industrial environment.

Acknowledgment

The authors thank S. Onda, S. Sowa, and Y. Note from Osaka University, F. Yoshino, A. Arai, Y. Uehara, M. Stock, and L. Shah from IMRA America for helpful discussion.

References and links

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

4. 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]  

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

6. 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, 1559–1567 (2003). [CrossRef]  

7. 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]  

8. J. W. Chan, T. Huser, S. Risbud, and D. M. Krol, “Structural changes in fused silica after exposure to focused femtosecond laser pulses,” Opt. Lett. 26, 1726–1728 (2001). [CrossRef]  

9. Y. Cheng, K. Sugioka, and K. Midorikawa, “Microfluidic laser embedded in glass by three-dimensional femtosecond laser microprocessing,” Opt. Lett. 29, 2007–2009 (2004). [CrossRef]   [PubMed]  

10. T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. Part 2 44, L687–L689 (2005). [CrossRef]  

11. S. Sowa, W. Watanabe, T. Tamaki, J. Nishii, and K. Itoh, “Symmetric waveguides in poly(methyl methacrylate) fabricated by femtosecond laser pulses,” Opt. Express 14, 291–297 (2006). [CrossRef]   [PubMed]  

12. 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]  

13. W. Watanabe, Y. Note, and K. Itoh, “Fabrication of multimode interference couplers in glass using a femtosecond laser,” Opt. Lett. 30, 2888–2890 (2005). [CrossRef]   [PubMed]  

14. A. M. Streltsov and N. F. Borrelli, “Study of femtosecond-laser-written waveguides in glasses,” J. Opt. Soc. Am. B 19, 2496–2504 (2002). [CrossRef]  

15. A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005). [CrossRef]  

16. G. D. Valle, R. Osellame, N. Chiodo, S. Taccheo, G. Cerullo, P. Laporta, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “C-band waveguide amplifier produced by femtosecond laser writing,” Opt. Express 13, 5976–5982 (2005). [CrossRef]   [PubMed]  

17. 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]  

18. K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26, 1516–1518 (2001). [CrossRef]  

19. A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1061 (2005). [CrossRef]   [PubMed]  

20. 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, 612–620 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-612. [CrossRef]   [PubMed]  

21. R. Osellame, N. Chiodo, G. D. Valle, S. Taccheo, R. Ramponi, G. Cerullo, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Optical waveguide writing with a diode-pumped femtosecond oscillator,” Opt. Lett. 29, 1900–1902 (2004). [CrossRef]   [PubMed]  

22. S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005). [CrossRef]  

23. L Shah, A. Y. Arai, S. M. Eaton, and P. R. Herman, “Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate,” Opt. Express 13, 1999–2006 (2005). [CrossRef]   [PubMed]  

24. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005). [CrossRef]   [PubMed]  

25. M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004). [CrossRef]  

26. A. 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]  

27. J. A. Squier and M. Müller, “Third-harmonic generation imaging of laser-induced breakdown in glass,” Appl. Opt. 38, 5789–5794 (1999). [CrossRef]  

28. P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004). [CrossRef]  

29. N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002). [CrossRef]  

30. L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001). [CrossRef]  

31. S. Onda, W. Watanabe, K. Yamada, K. Itoh, and J. Nishii, “Study of filamentary damage in synthesized silica induced by chirped femtosecond laser pulses,” J. Opt. Soc. Am. B 22, 2437–2443 (2005). [CrossRef]  

32. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

33. K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, “Anisotropic refractive-index change in silica glass induced by self-trapped filament of linearly polarized femtosecond laser pulses,” J. Appl. Phys. 93, 1889–1892 (2003). [CrossRef]  

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. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999).
    [Crossref]
  4. 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]
  5. K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 26, 19–21 (2001).
    [Crossref]
  6. 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, 1559–1567 (2003).
    [Crossref]
  7. 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]
  8. J. W. Chan, T. Huser, S. Risbud, and D. M. Krol, “Structural changes in fused silica after exposure to focused femtosecond laser pulses,” Opt. Lett. 26, 1726–1728 (2001).
    [Crossref]
  9. Y. Cheng, K. Sugioka, and K. Midorikawa, “Microfluidic laser embedded in glass by three-dimensional femtosecond laser microprocessing,” Opt. Lett. 29, 2007–2009 (2004).
    [Crossref] [PubMed]
  10. T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. Part 2  44, L687–L689 (2005).
    [Crossref]
  11. S. Sowa, W. Watanabe, T. Tamaki, J. Nishii, and K. Itoh, “Symmetric waveguides in poly(methyl methacrylate) fabricated by femtosecond laser pulses,” Opt. Express 14, 291–297 (2006).
    [Crossref] [PubMed]
  12. 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]
  13. W. Watanabe, Y. Note, and K. Itoh, “Fabrication of multimode interference couplers in glass using a femtosecond laser,” Opt. Lett. 30, 2888–2890 (2005).
    [Crossref] [PubMed]
  14. A. M. Streltsov and N. F. Borrelli, “Study of femtosecond-laser-written waveguides in glasses,” J. Opt. Soc. Am. B 19, 2496–2504 (2002).
    [Crossref]
  15. A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005).
    [Crossref]
  16. G. D. Valle, R. Osellame, N. Chiodo, S. Taccheo, G. Cerullo, P. Laporta, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “C-band waveguide amplifier produced by femtosecond laser writing,” Opt. Express 13, 5976–5982 (2005).
    [Crossref] [PubMed]
  17. 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]
  18. K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26, 1516–1518 (2001).
    [Crossref]
  19. A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1061 (2005).
    [Crossref] [PubMed]
  20. 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, 612–620 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-612.
    [Crossref] [PubMed]
  21. R. Osellame, N. Chiodo, G. D. Valle, S. Taccheo, R. Ramponi, G. Cerullo, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Optical waveguide writing with a diode-pumped femtosecond oscillator,” Opt. Lett. 29, 1900–1902 (2004).
    [Crossref] [PubMed]
  22. S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
    [Crossref]
  23. L Shah, A. Y. Arai, S. M. Eaton, and P. R. Herman, “Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate,” Opt. Express 13, 1999–2006 (2005).
    [Crossref] [PubMed]
  24. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005).
    [Crossref] [PubMed]
  25. M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
    [Crossref]
  26. A. 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]
  27. J. A. Squier and M. Müller, “Third-harmonic generation imaging of laser-induced breakdown in glass,” Appl. Opt. 38, 5789–5794 (1999).
    [Crossref]
  28. P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
    [Crossref]
  29. N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002).
    [Crossref]
  30. L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001).
    [Crossref]
  31. S. Onda, W. Watanabe, K. Yamada, K. Itoh, and J. Nishii, “Study of filamentary damage in synthesized silica induced by chirped femtosecond laser pulses,” J. Opt. Soc. Am. B 22, 2437–2443 (2005).
    [Crossref]
  32. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  33. K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, “Anisotropic refractive-index change in silica glass induced by self-trapped filament of linearly polarized femtosecond laser pulses,” J. Appl. Phys. 93, 1889–1892 (2003).
    [Crossref]

2006 (1)

2005 (10)

W. Watanabe, Y. Note, and K. Itoh, “Fabrication of multimode interference couplers in glass using a femtosecond laser,” Opt. Lett. 30, 2888–2890 (2005).
[Crossref] [PubMed]

A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005).
[Crossref]

G. D. Valle, R. Osellame, N. Chiodo, S. Taccheo, G. Cerullo, P. Laporta, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “C-band waveguide amplifier produced by femtosecond laser writing,” Opt. Express 13, 5976–5982 (2005).
[Crossref] [PubMed]

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

L Shah, A. Y. Arai, S. M. Eaton, and P. R. Herman, “Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate,” Opt. Express 13, 1999–2006 (2005).
[Crossref] [PubMed]

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005).
[Crossref] [PubMed]

A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1061 (2005).
[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, 612–620 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-612.
[Crossref] [PubMed]

S. Onda, W. Watanabe, K. Yamada, K. Itoh, and J. Nishii, “Study of filamentary damage in synthesized silica induced by chirped femtosecond laser pulses,” J. Opt. Soc. Am. B 22, 2437–2443 (2005).
[Crossref]

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. Part 2  44, L687–L689 (2005).
[Crossref]

2004 (5)

2003 (4)

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, 1559–1567 (2003).
[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]

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]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, “Anisotropic refractive-index change in silica glass induced by self-trapped filament of linearly polarized femtosecond laser pulses,” J. Appl. Phys. 93, 1889–1892 (2003).
[Crossref]

2002 (2)

N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002).
[Crossref]

A. M. Streltsov and N. F. Borrelli, “Study of femtosecond-laser-written waveguides in glasses,” J. Opt. Soc. Am. B 19, 2496–2504 (2002).
[Crossref]

2001 (6)

1999 (2)

1997 (1)

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]

1996 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Aiello, L.

Allan, D. C.

N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002).
[Crossref]

Arai, A.

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

Arai, A. Y.

Asano, T.

Borrelli, N. F.

Bovatsek, J.

Brodeur, A.

Burghoff, J.

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[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]

Burns, G. R.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
[Crossref]

Cerullo, G.

Chan, J. W.

Cheng, Y.

Chin, S. L

A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005).
[Crossref]

Chiodo, N.

Davis, K. M.

De Nicola, S.

Eaton, S. M.

Ferraro, P.

Finizio, A.

Franco, M.

L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001).
[Crossref]

Fujimoto, J. G.

Gaeta, A. L.

García, J. F.

Guo, J.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
[Crossref]

Hartl, I.

Herman, P. R.

Hirao, K.

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]

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]

Ho, S.

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

Homoelle, D.

Huser, T.

Inouye, H.

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]

Ippen, E. P.

Itoh, K.

Killi, A.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kopf, D.

Kowalevicz, A. M.

Krol, D. M.

Laporta, P.

Lederer, M.

Limpert, J.

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[Crossref]

Lopez, C.

Luk, T. S.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
[Crossref]

Marangoni, M.

Maselli, V.

Mazur, E.

Midorikawa, K.

Minoshima, K.

Mitsuyu, T.

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]

Miura, K.

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]

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]

Morgner, U.

Müller, M.

Mysyrowicz, A.

L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001).
[Crossref]

Nishii, J.

Nolte, S.

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[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]

Note, Y.

Onda, S.

Osellame, R.

Pierattini, G.

Polli, D.

Prade, B.

L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001).
[Crossref]

Price, J. J.

N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002).
[Crossref]

Qiu, J.

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]

Ramponi, R.

Richardson, K.

Richardson, M.

Risbud, S.

Saliminia,, A.

A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005).
[Crossref]

Schaffer, C. B.

Schreiber, T.

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[Crossref]

Shah, L

Shah, L.

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

Sharma, V.

Silvestri, S. D.

Smith, C.

Smith, C. M.

N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002).
[Crossref]

Sowa, S.

Squier, J. A.

Streltsov, A. M.

Sudrie, L

L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001).
[Crossref]

Sugimoto, N.

Sugioka, K.

Taccheo, S.

Tamaki, T.

S. Sowa, W. Watanabe, T. Tamaki, J. Nishii, and K. Itoh, “Symmetric waveguides in poly(methyl methacrylate) fabricated by femtosecond laser pulses,” Opt. Express 14, 291–297 (2006).
[Crossref] [PubMed]

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. Part 2  44, L687–L689 (2005).
[Crossref]

Toma, T.

Tuennermann, A.

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]

Tünnermann, A.

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[Crossref]

Valle, G. D.

Vallée, R.

A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005).
[Crossref]

Vawter, G. A.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
[Crossref]

Watanabe, W.

Wielandy, S.

Will, M.

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[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]

Yamada, K.

Yang, P.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
[Crossref]

Yin, A.

Yoshino, F.

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005).
[Crossref] [PubMed]

Zavelani-Rossi, M.

Zhang, H.

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005).
[Crossref] [PubMed]

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

Zoubir, A.

Appl. Opt. (1)

Appl. Phys. A (1)

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]

Appl. Phys. Lett. (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]

N. F. Borrelli, C. M. Smith, J. J. Price, and D. C. Allan, “Polarized excimer laser-induced birefringence in silica,” Appl. Phys. Lett. 80, 219–221 (2002).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Appl. Phys. (2)

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, “Anisotropic refractive-index change in silica glass induced by self-trapped filament of linearly polarized femtosecond laser pulses,” J. Appl. Phys. 93, 1889–1892 (2003).
[Crossref]

P. Yang, G. R. Burns, J. Guo, T. S. Luk, and G. A. Vawter, “Femtosecond laser-pulse-induced birefringence in optically isotropic glass,” J. Appl. Phys. 95, 5280–5283 (2004).
[Crossref]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. Part 2  44, L687–L689 (2005).
[Crossref]

Opt. Commun. (2)

A. Saliminia,, R. Vallée, and S. L Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 μm,” Opt. Commun. 256, 422–427 (2005).
[Crossref]

L Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Study of damage in fused silica induced by ultra-short IR laser pulses,” Opt. Commun. 191, 333–339 (2001).
[Crossref]

Opt. Express (5)

Opt. Lett. (13)

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]

W. Watanabe, Y. Note, and K. Itoh, “Fabrication of multimode interference couplers in glass using a femtosecond laser,” Opt. Lett. 30, 2888–2890 (2005).
[Crossref] [PubMed]

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]

K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, “Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator,” Opt. Lett. 26, 1516–1518 (2001).
[Crossref]

A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, “Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator,” Opt. Lett. 30, 1060–1061 (2005).
[Crossref] [PubMed]

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]

J. W. Chan, T. Huser, S. Risbud, and D. M. Krol, “Structural changes in fused silica after exposure to focused femtosecond laser pulses,” Opt. Lett. 26, 1726–1728 (2001).
[Crossref]

Y. Cheng, K. Sugioka, and K. Midorikawa, “Microfluidic laser embedded in glass by three-dimensional femtosecond laser microprocessing,” Opt. Lett. 29, 2007–2009 (2004).
[Crossref] [PubMed]

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

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

R. Osellame, N. Chiodo, G. D. Valle, S. Taccheo, R. Ramponi, G. Cerullo, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Optical waveguide writing with a diode-pumped femtosecond oscillator,” Opt. Lett. 29, 1900–1902 (2004).
[Crossref] [PubMed]

A. 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]

Proc. SPIE (2)

S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, and P. R. Herman, “Thermal heating effects in writing optical waveguides with a 0.1 - 5 MHz rate ultrafast fiber laser,” Proc. SPIE 5713, 35–42 (2005).
[Crossref]

M. Will, J. Burghoff, J. Limpert, T. Schreiber, S. Nolte, and A. Tünnermann, “High speed fabrication of optical waveguides inside glasses using a high rep.-rate fiber CPA system,” Proc. SPIE 5339, 168–174 (2004).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of the experimental setup for inducing structural modification in fused silica. L1, plano-convex lens (focal length f = 100 mm); L2, plano-convex lens (f= 50 mm); L3, achromatic lens (f = 200 mm); HWP, λ/2 wavelength plate; P, Glan-laser polarizer; Shutter, electromagnetic shutter; DM, dichroic mirror; OB1 and OB2, objective lenses; M, mirror.
Fig. 2.
Fig. 2. (a), (b), (d) and (e) are unpolarized transmission white-light microscope images of induced structural modifications in fused silica by 1558-nm laser pulses; (a) and (b) between 0.87 μJ/pulse (150 mW) and 2.02 μJ/pulse (350 mW) and (d) and (e) between 1.07 μJ/pulse (185 mW) and 1.1 μJ/pulse (190 mW). (c) and (f) are crossed-Nicols images of the structures indicated in (b) and (e), when the sample was set between two crossed polarizers.
Fig. 3.
Fig. 3. Magnitude of birefringence as a function of the incident pulse energy.
Fig. 4.
Fig. 4. Optical image of structural modifications in fused silica as a function of the scan speed at the pulse energy of 1.08 μJ/pulse (187 mW). (a) Transmission white-light microscope images of refractive-index change in fused silica observed in the xz-plane (b) and in the xy-plane by optical microscopes.
Fig. 5
Fig. 5 Optical image of the fabricated grating with a period of 10 μm in fused silica.
Fig. 6.
Fig. 6. Thresholds of induced refractive-index change at different repetition rates.

Equations (10)

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I 45 = ( I 2 ) 2 ( 1 + cos φ ) 2 ,
I 135 = ( I 2 ) 2 ( 1 cos φ ) 2 ,
ϕ = cos 1 ( I 45 I 135 I ) .
Δn = λ cos 1 ( I 45 I 135 I ) ( 2 πd ) ,
Q = 2 πλT n 0 Λ 2 < < 1 .
Δn ( x ) = m = 1 m = Δ n m cos ( m × 2 πx Λ ) ( m = 1,2,3 , )
= Δ n 1 cos ( 2 πx Λ ) + Δ n 2 cos ( 2 * 2 πx Λ ) + ( m = 1,2,3 , ) .
η l = J l 2 ( 2 κ l T ) ( l = 1,2,3 , ) .
κ l = π Δ n l λ ( l = 1,2,3 , ) .
Δn ( x ) = m = 1 m = Δ n m ( m = 1,2,3 , ) .

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