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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 12 — Jun. 13, 2005
  • pp: 4708–4716
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Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate

Shane M. Eaton, Haibin Zhang, Peter R. Herman, Fumiyo Yoshino, Lawrence Shah, James Bovatsek, and Alan Y. Arai  »View Author Affiliations


Optics Express, Vol. 13, Issue 12, pp. 4708-4716 (2005)
http://dx.doi.org/10.1364/OPEX.13.004708


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Abstract

High-repetition rate femtosecond lasers are shown to drive heat accumulation processes that are attractive for rapid writing of low-loss optical waveguides in transparent glasses. A novel femtosecond fiber laser system (IMRA America, FCPA µJewel) providing variable repetition rate between 0.1 and 5 MHz was used to study the relationship between heat accumulation and resulting waveguide properties in fused silica and various borosilicate glasses. Increasing repetition rate was seen to increase the waveguide diameter and decrease the waveguide loss, with waveguides written with 1-MHz repetition rate yielding ~0.2-dB/cm propagation loss in Schott AF45 glass. A finite-difference thermal diffusion model accurately tracks the waveguide diameter as cumulative heating expands the modification zone above 200-kHz repetition rate.

© 2005 Optical Society of America

1. Introduction

The most common laser system for optical waveguide writing has been amplified Ti:Sapphire lasers, which operate at low repetition rates (1 to 200 kHz). At such rates, high pulse energy (~1 mJ) is available for inducing strong nonlinear absorption in glass with weak focusing optics. Unfortunately, such focusing leads to waveguides with asymmetric refractive index profiles that exhibit significant coupling loss and birefringence. Recently, Osellame et al. [6

6. R. Osellame, N. Chiodo, G. Della 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]

] noted that thermal diffusion from a tight focusing volume can form symmetric waveguides written with a 166-kHz laser at 100-µm/s scan speed. However, femtosecond laser oscillators with high repetition rate (~10 MHz) have demonstrated fast (>1-mm/s) waveguide writing speeds in glass [2

2. C.B. Schaffer, J.F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition rate femtosecond laser,” Appl. Phys. A 76, 351–354 (2003). [CrossRef]

,3

3. K. Minoshima, A. W. 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]

]. These lasers yield a more symmetric guiding cross section due to cumulative heating arising when the interval between laser pulses is less than the time required for the absorbed laser energy to diffuse out of the focal volume [1

1. P.R. Herman, R.S Marjoribanks, and A. Oettl, “Burst-ultrafast laser machining method,” US Patent (6,552,301 B2)

3

3. K. Minoshima, A. W. 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]

]. The disadvantage of such high repetition rate laser systems is that because of their low pulse energy (~100 nJ), high numerical aperture (NA) focusing objectives are required, which limits the working distance and depth for full 3-D fabrication.

A femtosecond amplified fiber laser with a high repetition rate, recently introduced by IMRA America (FCPA µJewel), provides ideal operating conditions for optimizing the writing of optical waveguides in glasses. Variable repetition rate with pulse energies of 2.5 µJ at 100 kHz to 150 nJ at 5 MHz allows for greater control in optimizing waveguide properties. The 375-fs pulses were applied to fundamental studies of waveguide writing in borosilicate and pure fused silica glasses.

2. Experiments

The experimental arrangement for waveguide writing is shown in Fig. 1. An amplified Yb-fiber laser provided 375-fs pulses at 1045-nm wavelength with a M2<1.5 beam quality. A telescope was used to match the output beam diameter to the clear aperture of the 0.65-NA aspheric lens and provide diffraction-limited focusing of ~2-µm 1/e2 diameter. Waveguides were written transversely to the laser beam direction at scanning speeds of between 1 and 100 mm/s using computer-controlled Newport TS2000 3-axis motion stages. Laser polarization was parallel to the scanning direction. A CCD vision system accurately placed waveguides approximately 150 µm below the glass surface. Both static exposures and 5-cm long waveguides were written in Corning 1737F, Schott AF45, and Corning 7940 fused silica glasses. Table 1 provides material properties for each glass. For static exposures, a mechanical shutter was used to select the desired number of pulses.

Fig. 1. Ultrafast laser beam delivery system for transverse waveguide writing

The end facets of waveguides were ground and polished. The waveguide mode profile, insertion loss and propagation loss were characterized with a 1550-nm laser butt-coupled to the input waveguide facet using SMF28 fiber. The insertion loss was obtained from the power transmitted (Newport 818-IG photodetector) through the waveguide with butt-coupling SMF28 fiber at both the input and the output waveguide facet, and normalized to the power propagated by directly butt-coupled input and output fibers. Mode profiles were obtained by imaging the near-field intensity at the output facet of the waveguide sample with a 100X microscope objective and a phosphor-coated Spiricon SP-1550M CCD camera. Waveguide propagation losses were obtained with an infrared-sensitive InGaAs camera (Sensors Unlimited SU-320MX) by observing the exponential decay of the transversely scattered light from the waveguide sample.

Table 1. Glass properties Schott and Corning glasses [12]

table-icon
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3. Results

3.1 Microscope observation of cumulative heating

Amongst several factors influencing the cumulative heating process, we focus here on the effect of repetition rate and dwell time on the structure of both stationary and scanned waveguide exposures.

3.1.1 Static exposures

Figure 2 shows optical microscope images of AF45 glass modified by static laser exposure of 450-nJ pulse energy with varied repetition rate and number of pulses. Spherical laser-modified zones were observed for all static exposures tested, and arise from the three-dimensional symmetry of heat diffusion from a small laser absorption volume of ~2-µm diameter. These refractive index structures are the result of localized melting within a cumulative heating zone that is built up over many laser pulses, and then cools rapidly to resolidify after the laser exposure.

Evidence of cumulative heating is noted at repetition rates above 200 kHz, where the diameter of the modified volume significantly exceeds the ~2-µm laser spot size. Within each row (constant repetition rate) in Fig. 2, one notes a modest increase in the diameter of the heat affected zone despite a four order-of-magnitude increase in exposure. More dramatic is the ~10-fold increase in modified zone radius as noted when the repetition rate is increased from 0.1 to 1 MHz in each column. Since the total laser exposure is identical within any column, 200-kHz repetition rate defines the onset for cumulative heating effects above which thermal diffusion controls the properties of optical circuits formed by the femtosecond laser. One also notes that the size of the modification zone grows more quickly with the number of pulses when in the cumulative heat regime. The radial increase is highest at 1-MHz repetition rate here, and even larger increases are in evidence at 25 MHz as noted by Schaffer et al. [2

2. C.B. Schaffer, J.F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition rate femtosecond laser,” Appl. Phys. A 76, 351–354 (2003). [CrossRef]

] for Corning 0211, a zinc-doped borosilicate glass. In the same work, Schaffer et al. identified a larger 1-MHz onset for cumulative heating, a discrepancy explained by the lower pulse energy (~5 nJ) and smaller focal volume (1.4 NA objective) than used in the present experiment.

Fig. 2. Optical microscope images showing heat affected zones created in AF45 borosilicate glass with 450-nJ pulse energy from a 1045-nm femtosecond laser. Total pulse (top) and fluence accumulation (bottom) is shown for each column and the laser repetition rate is indicated for each row. Laser direction is normal to page.

The diameter of scanned waveguides in AF45 glass was found to be nearly identical to their static counterparts in Fig. 2 when applied at the same repetition rate and net fluence. The net fluence was based on the laser dwell time in a 2-µm spot diameter. Waveguides are further discussed in Section 3.3.

Static exposures of Corning 1737F borosilicate glass were also carried out at 450-nJ pulse energy and yielded observations very similar to those seen in Fig. 2 for AF45 glass. One noticeable difference was the diameter of the modified zone, which was ~46 microns at the maximum exposure of 4×107 pulses at 1 MHz, compared with 38 microns for AF45. This modest diameter increase is attributed to a 38% smaller thermal diffusivity of 1737F glass (Table 1) that enables a larger melted volume to form.

Corning 7940 fused silica showed no strong evidence of heat buildup over the same laser exposure conditions, yielding modified zones of approximately ~2-µm diameter that matched the laser focal spot size. This absence of heat accumulation is partly attributed to the 9.1-eV bandgap of fused silica, which is more than twice that of borosilicate (Table 1). Indeed, Streltsov and Borrelli [10

10. 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]

] have observed less absorbance in fused silica compared with borosilicate glass. Further, more laser energy is necessary to heat fused silica to its 1800°C working temperature, which is 1.4-fold higher than in borosilicate glass (Table 1). A combination of higher pulse energy, higher repetition rate, and shorter laser wavelength may provide the necessary conditions for driving cumulative heating effects in fused silica. Osellame et al. [5

5. 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]

] recently observed uncontrollable damage in fused silica using a 30-nJ, 26-MHz oscillator and a 1.4-NA oil-immersion objective. These refractive index structures showed evidence of thermal heating but were not suitable for waveguiding.

3.2 Numerical model of cumulative heating

To study the dynamics of the cumulative heating, a finite-difference thermal diffusion model [11

11. Y. Jaluria and K.E. Torrance, Computational Heat Transfer (Taylor & Francis, New York, 2003).

] was applied to laser conditions typically used in waveguide writing in Schott AF45 borosilicate glass. The heat source due to each laser pulse was assumed to be a delta function in time since the timescale for electron heating and electron-phonon coupling (<1 ps) is much shorter than the thermal diffusion time (>0.1 µs) under consideration here. The energy density of the heat source was approximated as a spherical Gaussian of the form:

E(r)=E0exp(r2w02)
(1)

where r is the radial distance and w 0 is the 1/e radius of the focused laser beam (~1 µm for NA=0.65). The normalization constant E 0 was determined by setting the volume integral of (1) equal to the measured absorbed energy (520-nJ incident laser energy multiplied by absorption). The governing equation for heat diffusion is:

r(r2Tr)=r2DTt
(2)

where T(r,t) is the temperature and D is the thermal diffusivity. The temperature profile is modified each time a new laser heating pulse arrives, by an instantaneous temperature rise, ΔT(r)=E(r)/cpρ, where cp and ρ are the specific heat capacity at constant pressure and density of the glass, respectively. Waveguide writing was theoretically treated as a static exposure, with the number of laser heating pulses specified by the product of repetition rate and laser dwell time. This approximation was validated by observation of nearly identical modification radii formed by static and scanning exposures when applied at the same net fluence. In the model, room-temperature values of specific heat, density and thermal diffusivity were used.

3.2.1 Effect of repetition rate

Fig. 3. Finite-difference model of glass temperature versus exposure, at a radial position of 2 µm from the center of the laser beam.

3.2.2 Melt radius versus net fluence

The finite-difference heating model was applied to waveguide writing conditions of 1-MHz repetition rate and 2 to 60-mm/s scan speed that yielded equivalent net fluence of 12.7 to 0.4 kJ/cm2. Following a similar approach by Schaffer et al. [2

2. C.B. Schaffer, J.F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition rate femtosecond laser,” Appl. Phys. A 76, 351–354 (2003). [CrossRef]

], we calculated the maximum radius out to where the temperature was maintained above the 1225°C working point of AF45 glass for varying net fluence. The results are shown in Fig. 4, and compared with experimental observations of the maximum radial dimension of the heat-modified waveguides, as viewed transversely with a differential interference contrast (DIC) microscope.

Figure 4 is significant in supporting a thermal model for ultrashort-pulse laser writing of refractive index structures at high repetition rate. The radius of the optical waveguides were found to correspond closely to the calculated melt radius. Further, the model predicts much reduced thermal cycling during the laser dwell times studied for this example of 1-MHz repetition rate than when outside the cumulative heating regime at lower repetition rate. For example, at 100 kHz, the sample temperature recovers fully to room temperature, driving a melt-fusion phase cycle every laser pulse, while the relative temperature modulation is much smaller at 1 MHz due to the higher average temperature.

Fig. 4. Melt radius versus net fluence: numerical simulation (solid line) assuming 40% absorption and observed waveguide diameter (solid circle).

3.3 Optical waveguide properties

At the fundamental laser wavelength of 1045 nm, the smoothest and lowest-loss waveguides were written in AF45 and 1737F glasses. In general, higher repetition rates (>200 kHz) resulted in lower insertion and propagation losses when probed with SMF28 fiber. However, waveguides were not observed above 2 MHz repetition rate due to the decrease in laser pulse energy below an absorption threshold of ~300 nJ for the present focusing arrangement. Low-loss waveguides could not be observed in fused silica at any repetition rate for the laser conditions tested here. However, it was possible to write low-loss (~0.8 dB/cm) waveguides in fused silica by frequency doubling the laser to 522 nm to increase the absorption [14

14. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1999 [CrossRef] [PubMed]

].

3.3.1 Waveguide mode profile and loss characterization

The lowest loss waveguides were written in Schott AF45 borosilicate glass at 1045-nm wavelength. At 1 MHz, an insertion loss of 2 dB was obtained at a scan speed of 15 mm/s and fluence of 16.5 J/cm2 per pulse (520-nJ pulse energy). The cross sectional microscope image in Fig. 5(a) indicates a near-circular guiding region of 4-µm diameter (bright white color), surrounded by a more complex geometry for the refractive index structure. Nolte et al. [4

4. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Modern Optics. 51, 2533–2542 (2004). [CrossRef]

] observed a similar waveguide structure in AF45 glass, formed with a 2-MHz repetition rate, 300-fs fiber laser. We did not have access to a refractive-index profiling tool, but Nolte et al. showed using refractive near-field (RNF) profilometry that the dark regions above and below the core corresponded to a small negative index change, while the bright central region corresponded to a positive index contrast [4

4. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Modern Optics. 51, 2533–2542 (2004). [CrossRef]

]. The laser modification zone in Fig. 5(a) extends to ~14-µm diameter, greatly exceeding the 2-µm beam diameter due to the heat accumulation effects presented in Section 3.2. Figure 5(b) shows a transverse microscope image of the waveguide. Figure 5(c) shows the near-field mode profile of the waveguide at 1550 nm. The mode profile is nearly circular with a mode-field diameter (MFD) of 10 µm.

Fig. 5. Left to right: cross sectional (a) and transverse (b) microscope images, and 1550-nm mode profile (c) of waveguide written in AF45 at 1 MHz, 520 nJ, 0.65-NA and 15 mm/s. The red arrows indicate the direction of the femtosecond laser.

After accounting for Fresnel loss of 4% per facet (0.36 dB), the 2-dB insertion loss for the 5-cm long waveguide gives an upper bound of 0.3 dB/cm for the propagation loss. A similar propagation loss of 0.2 dB/cm was inferred from the exponential decay of transversely scattered light along the length of the waveguide, as measured with an InGaAs IR-sensitive camera [15

15. Y. Okamura, S. Yoshinaka, and S. Yamamoto, “Measuring mode propagation losses of integrated optical waveguides: a simple method,” Appl. Opt. 22, 3892–3894 (1983). [CrossRef] [PubMed]

]. This propagation loss implies a coupling loss of 0.3 dB/facet. These small loss values are now approaching the attractive values provided by PECVD and etching technology (<0.1-dB/cm propagation loss), but with the added advantage of direct 3-D writing in bulk glasses in a single process step.

3.3.2 Refractive index change

For the lowest-loss AF45 waveguide shown in Fig. 5, the laser-induced refractive index change was estimated using a cylindrical waveguide mode solving routine (Rsoft BeamPROP 5) and assuming a step index profile of 4-µm diameter. An index contrast of Δn=0.007 best represents the observed MFD of 10 µm and is comparable to the 0.008-index contrast measured by Nolte et al. [4

4. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Modern Optics. 51, 2533–2542 (2004). [CrossRef]

] using RNF profilometry.

The large-diameter modification zones predicted in Fig. 4 and observed in Fig. 5(a) and 5(b) outside the 4-µm core guiding region for high repetition rate (~1 MHz) do not appear to contribute a large refractive index change. The MFD of 10-µm associated with these waveguides is fully supported by the 0.007 index change in the 4-µm core. However, the smaller cladding-like zone noted at low repetition rate was strongly associated with an increase in the propagation loss (>0.5 dB/cm), even when waveguides were scanned more slowly to provide the same net fluence exposure. The main benefit of heat accumulation during ultrashort laser waveguide writing are low propagation loss (~0.2 dB/cm) and high writing speeds (>10 mm/s). Further work to elucidate the refractive index changes extending from the core to this heat-accumulation zone may reveal additional benefits.

4. Conclusions

In summary, we have demonstrated cumulative heating in waveguides fabricated in glasses using the high-repetition rate IMRA FCPA µJewel femtosecond fiber laser. Laser repetition rate was seen to greatly influence the heat accumulation process. For typical exposure conditions, we found that cumulative heating was evident at repetition rates greater than 200 kHz in Schott AF45 and Corning 1737. In fused silica, there was no evidence of cumulative heating within our range of experimental conditions. Experimental observations were supported by a finite-difference heating simulation, which accurately determined the onset of heat accumulation and the modified zone diameter as a function of net fluence.

It was found that increasing repetition rate was the most significant factor in lowering waveguide loss. Through systematic optimization of exposure conditions, we were able to write ~0.2 dB/cm waveguides in Schott AF45 alkali-free borosilicate glass at 1-MHz repetition rate. To our knowledge, this is the lowest propagation loss reported for waveguides written in the cumulative heating regime. Future work will focus on studying higher repetition rates and higher laser energies at fundamental and second harmonic wavelengths to gain further knowledge of the laser heating process in pure fused silica and borosilicate glasses.

Acknowledgments

We would like to thank Jianzhao Li, Rajiv Iyer, Sjoerd Hoogland, and Amir Nejadmalayeri from the University of Toronto, Tadashi Yamamoto from IMRA America, Chris Schaffer from UCSD, and Michael Kania and Michelle deCastro from Schott glass for helpful input. Shane Eaton was supported by the Walter C. Sumner memorial and Ontario Graduate scholarships. Support from the Canadian Institute for Photonics Innovation and the Natural Sciences and Engineering Research Council are gratefully acknowledged.

References and links

1.

P.R. Herman, R.S Marjoribanks, and A. Oettl, “Burst-ultrafast laser machining method,” US Patent (6,552,301 B2)

2.

C.B. Schaffer, J.F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition rate femtosecond laser,” Appl. Phys. A 76, 351–354 (2003). [CrossRef]

3.

K. Minoshima, A. W. 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]

4.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Modern Optics. 51, 2533–2542 (2004). [CrossRef]

5.

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]

6.

R. Osellame, N. Chiodo, G. Della 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]

7.

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]

8.

Y. Sikorski, A.A. Said, P. Bado, R. Maynard, C. Florea, and K. Winick, “Optical waveguide amplifier in Nd-doped glass written with near-IR femtosecond laser pulses,” Electron. Lett. 36, 226–227 (2000). [CrossRef]

9.

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]

10.

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]

11.

Y. Jaluria and K.E. Torrance, Computational Heat Transfer (Taylor & Francis, New York, 2003).

12.

Thermal data for AF45 glass provided by M. deCastro, Schott glass.

13.

A.F. Van Zee and C.L. Babcock, “A method for the measurement of thermal diffusivity of molten glass,” J. Am. Ceram. Soc. , 34, 244–250 (1951). [CrossRef]

14.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1999 [CrossRef] [PubMed]

15.

Y. Okamura, S. Yoshinaka, and S. Yamamoto, “Measuring mode propagation losses of integrated optical waveguides: a simple method,” Appl. Opt. 22, 3892–3894 (1983). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(320.2250) Ultrafast optics : Femtosecond phenomena
(350.3390) Other areas of optics : Laser materials processing

ToC Category:
Research Papers

History
Original Manuscript: April 29, 2005
Revised Manuscript: June 4, 2005
Published: June 13, 2005

Citation
Shane Eaton, Haibin Zhang, Peter Herman, Fumiyo Yoshino, Lawrence Shah, James Bovatsek, and Alan Arai, "Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate," Opt. Express 13, 4708-4716 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-12-4708


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References

  1. P.R. Herman, R.S Marjoribanks, and A. Oettl, �??Burst-ultrafast laser machining method,�?? US Patent (6,552,301 B2)
  2. C.B. Schaffer, J.F. Garcia, and E. Mazur, �??Bulk heating of transparent materials using a high-repetition rate femtosecond laser,�?? Appl. Phys. A 76, 351-354 (2003). [CrossRef]
  3. K. Minoshima, A.W. 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]
  4. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, �??Ultrafast laser processing: new options for three-dimensional photonic structures,�?? J. Modern Optics. 51, 2533-2542 (2004) [CrossRef]
  5. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-612">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-612</a>. [CrossRef] [PubMed]
  6. R. Osellame, N. Chiodo, G. Della 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]
  7. 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]
  8. Y. Sikorski, A.A. Said, P. Bado, R. Maynard, C. Florea, and K. Winick, �??Optical waveguide amplifier in Nd-doped glass written with near-IR femtosecond laser pulses,�?? Electron. Lett. 36, 226-227 (2000). [CrossRef]
  9. 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]
  10. 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]
  11. Y. Jaluria and K.E. Torrance, Computational Heat Transfer (Taylor & Francis, New York, 2003).
  12. Thermal data for AF45 glass provided by M. deCastro, Schott glass.
  13. A.F. Van Zee and C.L. Babcock, �??A method for the measurement of thermal diffusivity of molten glass,�?? J. Am. Ceram. Soc., 34, 244-250 (1951). [CrossRef]
  14. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1999">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1999</a>. [CrossRef] [PubMed]
  15. Y. Okamura, S. Yoshinaka, and S. Yamamoto, �??Measuring mode propagation losses of integrated optical waveguides: a simple method,�?? Appl. Opt. 22, 3892-3894 (1983). [CrossRef] [PubMed]

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