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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19542–19550
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Femtosecond laser direct-writing of waveguide Bragg gratings in a quasi cumulative heating regime

Christopher Miese, Michael J. Withford, and Alexander Fuerbach  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19542-19550 (2011)
http://dx.doi.org/10.1364/OE.19.019542


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Abstract

Waveguide Bragg gratings (WBGs) were directly inscribed into Alkaline Earth Boro-Aluminosilicate glass samples in a single process step at high fabrication speeds. We utilized a 5.1 MHz femtosecond oscillator to exploit high repetition rate heat accumulation effects. The pulse energy was modulated using a Pockels cell in order to fabricate waveguides that contain a periodic array of nano-structures inside their core. We have demonstrated, for the first time, that the transient build-up of heat accumulation within the sample can lead to the formation of a permanent nano-void. This effect can be exploited to fabricate WBGs at high speeds.

© 2011 OSA

1. Introduction

The highly flexible femtosecond (fs) laser direct-write technique allows the fabrication of arbitrary 3-dimensional optical circuits in a wide range of dielectric media [1

1. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996). [CrossRef] [PubMed]

]. The fabricated devices typically feature very low propagation losses, are inherently stable and can easily be interfaced with standard optical fibers [2

2. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008). [CrossRef]

]. The technique is based on a localized refractive index modification that is induced via nonlinear absorption of tightly focused fs-laser pulses inside a transparent medium. By moving the sample with respect to the focus, complex waveguiding structures can be inscribed. Furthermore, the incorporation of Bragg gratings into these waveguides has been demonstrated utilizing the point-by-point inscription [3

3. G. D. Marshall, M. Ams, and M. J. Withford, “Direct laser written waveguide-Bragg gratings in bulk fused silica,” Opt. Lett. 31(18), 2690–2691 (2006). [CrossRef] [PubMed]

] and the burst-mode writing methods [4

4. H. Zhang, S. M. Eaton, and P. R. Herman, “Single-step writing of Bragg grating waveguides in fused silica with an externally modulated femtosecond fiber laser,” Opt. Lett. 32(17), 2559–2561 (2007). [CrossRef] [PubMed]

]. These methods enable the fabrication of narrowband Waveguide Bragg gratings (WBGs) that find applications as wavelength selective passive filters. Furthermore, optical feedback can be realized by inscribing WBGs into actively doped glasses, allowing the fabrication of integrated and monolithic miniature chip-lasers [5

5. G. D. Marshall, P. Dekker, M. Ams, J. A. Piper, and M. J. Withford, “Directly written monolithic waveguide laser incorporating a distributed feedback waveguide-Bragg grating,” Opt. Lett. 33(9), 956–958 (2008). [CrossRef] [PubMed]

].

The inscription of smooth waveguiding structures relies on a substantial spatial overlap between successive focused laser pulses and fabrication times are therefore directly proportional to the repetition rate of the laser source. Consequently, low writing speeds are necessary when kHz laser systems are used, which limits the achievable throughput. In addition, the low process speed (fabrication times can be of the order of many hours) can potentially lead to higher propagation losses due to unavoidable fluctuations in the fabrication parameters (temperature, laser power, vibrations...) that occur during the writing process.

In order to increase fabrication speeds, high repetition rate laser sources in the MHz regime have been considered. The use of a high repetition rate laser system directly reduces the required fabrication times and thus typically improves waveguide quality as one becomes less exposed to fluctuations during the writing process. Most importantly, the switch to a repetition rate above about 1 MHz is also marked by the onset of an entirely new writing regime [6

6. S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16), 2533–2542 (2004). [CrossRef]

8

8. S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005). [CrossRef] [PubMed]

]. In this regime inherently symmetric waveguides with high index contrast are obtained due to isotropic heat diffusion, in contrast to the kHz writing regime where the final waveguide diameter is purely defined by the focusing geometry [9

9. 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(15), 5676–5681 (2005). [CrossRef] [PubMed]

, 10

10. R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20(7), 1559–1567 (2003). [CrossRef]

]. Moreover, the actual physical mechanism that leads to a local change in the index of refraction differs for laser repetition rates in the kHz and in the MHz regime, respectively. It has been reported that melting and subsequent re-solidification, leading to a change in the fictive temperature of the glass, is the dominant index modification process in the MHz regime [11

11. H. Kakiuchida, K. Saito, and A. J. Ikushima, “Refractive index, density and polarizability of silica glass with various fictive temperatures,” Jpn. J. Appl. Phys. 43(6A), L743–L745 (2004). [CrossRef]

]. By comparison the formation of non-bridging oxygen atoms is believed to dominate index modification in the kHz regime [12

12. D. J. Little, M. Ams, P. Dekker, G. D. Marshall, J. M. Dawes, and M. J. Withford, “Femtosecond laser modification of fused silica: the effect of writing polarization on Si-O ring structure,” Opt. Express 16(24), 20029–20037 (2008). [CrossRef] [PubMed]

, 13

13. D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011). [CrossRef]

]. However, the detailed processes that result in a permanent index change are more complex and difficult to isolate in both writing regimes. It has been clearly shown that both, the actual glass composition as well as the initial glass fictive temperature play an important role but the exact details are not fully understood and subject to ongoing research.

In the case of MHz laser writing, the process of heat diffusion decouples the final waveguide dimensions from the associated laser focal spot size. This brings a much higher flexibility about as the diameter of the fabricated structures can now be controlled by the process parameters, i.e. laser power and writing speed. In addition, heat diffusion also smoothes out small fluctuations that can occur during the writing process. The trade-off is, the resolution of the fabricated devices becomes limited because the final waveguide dimensions are no longer confined to the (potentially very small) focal volume of the laser beam but are smeared out due to isotropic heat diffusion to the surrounding volume. However, for the inscription of narrowband first order waveguide Bragg gratings, periodic structures with a pitch of about half the Bragg-wavelength in the medium (corresponding to approximately 500 nm for C-band devices) have to be inscribed into the sample. For higher order WBGs the modulation period is a multiple of the fundamental pitch and can thus become larger than the heat diffusion zone but the strength of the Bragg resonance is reduced for higher order gratings. In order to compensate for those weak Bragg resonances, either the index contrast has to be very high and/or the gratings have to be very long which can be challenging with regard to the required positioning precision.

2. Experiment

The laser source that was used in our experiments was a stretched cavity Ti:Sapphire chirped pulse oscillator (CPO) operating at a 5.1 MHz repetition rate, emitting sub-50 fs laser pulses at a center wavelength of 800 nm (FEMTOSOURCE scientific XL 500, Femtolasers GmbH). The laser beam was focused 170 µm below the sample surface by a 100x 1.25NA oil immersion objective. The writing beam polarization was chosen to be circular in order to eliminate any potential directional effects. We used Eagle 2000 (Alkaline Earth Boro-Aluminosilicate glass from Corning) as our substrate material. A fast RTP Pockels cell enabled us to not only lower the repetition rate of the laser down to 1 MHz if required but also to generate a series of bursts of pulses at the full repetition rate of 5.1 MHz. The sample itself was mounted on a set of 3D high precision air-bearing translation stages (Aerotech).

For the fabrication of WBGs, the stages were moved at a constant speed of 200 mm/min, resulting in a fabrication time of ~3 seconds for a single, 10 mm long WBG. The signals that were used to trigger the Pockels cell switches were in that case synchronized with the translation of the stages. Figure 1
Fig. 1 Schematic of the writing setup. The pulse energy of the Chirped Pulse Oscillator (CPO) is adjusted via a half-wave plate and a polarizing beam splitter (PBS). Pulse-bursts are generated by the Pockels cell that is synchronized with the motion of the stages. The quarter-wave plate in front of the microscope objective (MO) generates circular polarized light for the waveguide-inscription.
shows a schematic of the writing setup.

3. Results and discussion

When laser sources that deliver femtosecond pulses with a combination of high repetition rates and high pulse energies are used for the fabrication of optical waveguides, the complex interplay of heat accumulation, heat diffusion and thermal wavefront distortion leads to peculiar and interesting effects. We have investigated how the extent of the heat diffusion zone, i.e. the final waveguide diameter changes as a function of writing speed and pulse energy for a repetition rate of 5.1 MHz and for a reduced repetition rate of 1 MHz. For this purpose we have fabricated an array of individual waveguides that were written at different pulse energies and writing speeds and have measured the resulting waveguide diameter using Differential Interference Contrast (DIC) microscopy. Figure 2
Fig. 2 Final waveguide diameter as a function of pulse energy and translation speed for a laser repetition rate of 5.1 MHz (left) and 1 MHz (right), from experimental results. The black area represents a parameter regime where voids are produced inside the material. The blue area represents a pulse energy regime below the material specific threshold for heat diffusion induced material modification. Additional notes: The white corner in the left figure does not indicate the formation of voids. In this regime the average power becomes too high, leading to the formation of bubbles in the oil film between the writing objective and the sample. Further, the boundary from damage to the cumulative heating regime is a transition, i.e. the measurement of the heat modified zone in the presence of damage, causing uncertainty in the interpretation of heat diffusion radius.
summarizes our experimental results. The left graph shows the extent of the heat modified zone at 5.1 MHz repetition rate, where heat accumulation dominates the modification process, in contrast to 1 MHz repetition rate, where heat accumulation is less pronounced, as shown in the right graph. At both repetition rates heat diffuses out of the focal spot and a much larger volume eventually becomes modified. The full parameter range can be divided in three distinctive regimes: The first regime consist of heat accumulation (colored area in the graph: cyan, green, red), where the heat modified zone clearly exceeds the dimensions of the focal spot. The second region consists of material modification that is limited to the focal volume, marked by the blue area. Finally a third regime indicated by the black area represents a parameter regime that is characterised by the presence of void structures.

The behavior shown in Fig. 2 can be explained as follows. For a small range of pulse energies (that depend on the actual focusing conditions and on the translation speed) the damage threshold of the material is reached before cumulative heating effects affect the writing dynamics noticeably. However, at even higher writing pulse energies, heat diffuses out of the focal volume and into the substrate, which results in the melting of a larger volume of material surrounding the focal spot. This effect eventually distorts the propagation of the subsequent laser pulses and therefore lowers the effective writing fluence below the damage threshold [15

15. C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 351–354 (2003). [CrossRef]

]. Thus, no void structures can be observed in the core of the waveguide. Note that by comparing the two figures for the two different repetition rates of 5 MHz and 1 MHz, respectively, it can be clearly seen that the parameter range that leads to damage inside the material is much wider for lower repetition rates, providing further evidence that it is indeed a thermal effect that prevents material damage: The hot material that stems from heat accumulation and diffusion at high repetition rates induces a change in refractive index of the sample around the focal spot via the temperature coefficient of refractive index. Boro-Aluminosilicate glass compositions, similar to Eagle 2000, are reported to have a temperature coefficient in the order of 10−5 per Kelvin [16

16. G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, San Diego, Calif., 1998.

]. It is this that eventually leads to a distortion of the wavefront of the femtosecond laser pulses that are subsequently focused into the material. This also implies that a longer pulse separation time of 1 µs (for 1 MHz) is sufficient to reduce this heat-induced beam distortion and enable micro structuring of the material in a wider parameter range. Furthermore, from Fig. 2 it can also be seen that, in the parameter range that has been investigated, damage is induced by multiple pulses. This hypothesis is based on the fact that at fast translation speeds where the pulse overlap is reduced, void formation is not observed.

Strictly speaking, the three distinct regimes that have been identified in Fig. 2 only exist when long sections of waveguides are inscribed into the glass. However, as the characteristic heat diffusion time in most transparent dielectrics is in the order of ~1µs [8

8. S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005). [CrossRef] [PubMed]

], this is also the timescale for the onset of the wavefront distortion effect that has been described above. This means that material damage can also be induced with combinations of pulse energy and/translation speed that lie outside the black area in Fig. 2, i.e. whenever high-energy pulse bursts are focused into a substrate that is still cold. This effect is explained in more detail in Fig. 3
Fig. 3 (a) Schematic representation of pulse-by-pulse heat accumulation within the sample. The red spikes represent the incident laser pulses, the orange area represents the resultant instantaneous temperature response. After 1µs diffusion time the temperature dropped below the modifying threshold (b) Qualitative average temperature profile within the focal volume during burst inscription, (c) Corresponding Differential Interference Contrast (DIC) microscope image of the resulting waveguide segments. The nano-voids (shown by the arrow) that are produced at the beginning of each burst can be clearly seen. Also note the distinct heat diffusion taper that can be seen at the end of each segment.
.

The microscope image in Fig. 3 (c) shows waveguide segments that have been inscribed into bulk glass utilizing femtosecond laser pulses at the full repetition rate of 5.1 MHz. In order to fabricate individual, short segments, the pulse train that was emitted by the laser was repeatedly switched on and off by the Pockels cell (33 µs on-time, 33 µs off-time, respectively). Figures 3 (a) and (b) schematically illustrate that it takes a series of laser pulses to reach an equilibrium between heat supply via the laser pulses and heat removal via diffusion, i.e. until the steady-state temperature distribution is reached inside the material. It can be seen clearly that at the beginning of each segment, when heat accumulation is still building up, nano-voids are formed. These are eventually surrounded by index modified material due to the isotropic nature of heat diffusion. This happens without an erasure of the nano-structure in the core itself, indicating that this structure is a permanent feature and moreover, resistant to the heat diffusion process. In this work we exploit this transient effect and the resulting nano-structures for the inscription of low order waveguide Bragg gratings at high fabrication speeds.

In order to fabricate WBGs, the sample was moved at a constant speed of 200 mm/min while bursts of femtosecond laser pulses (at 5.1 MHz repetition rate) with a 50:50 duty cycle were fired every 0.52 µm of sample translation. This corresponds to 390 laser pulses that were repeatedly transmitted and blocked by the Pockels cell, respectively. This extremely small pitch of Λ = 0.52 µm is necessary if one wants to inscribe a first order Bragg grating at a wavelength in air of 1.5 µm as the Bragg wavelength is given by λBragg = Λ × 2neff with neff being the effective index of the propagating mode. The individual laser pulses that were focused into the sample had an energy of 38 nJ each. Post-fabrication, the sample was ground back to a total length of 9 mm and subsequently polished to remove any residual taper. The wavelength-selective properties of the written structures were probed using a C-band swept wavelength system (SWS). Single mode fibers and index matching gel were used to couple light in and out of the WBGs.

Figure 4
Fig. 4 Reflection and transmission spectrum of a first order WBG of 9 mm length.
shows the transmission and reflection spectrum of a WBG that has been fabricated as described above. The actual waveguide has a diameter of about 8 µm (due to isotropic heat diffusion) as shown in Fig. 5
Fig. 5 Microscope image of the WBG. The small pitch of 0.52 µm can clearly be seen. The white bars mark the full width of the waveguide.
. The first order Bragg grating shows a transmission notch of −6.75 dB and a total insertion loss of ~6.5 dB, including all coupling losses. The Bragg resonance at 1551.8 nm has a FWMH-width of only 90 pm. This implies that permanent structures that are substantially smaller than the heat diffusion zone have been successfully inscribed into the sample.

As mentioned above, these results show that heat diffusion is associated with this parameter regime (the focus of the laser pulse is in the order of <1 µm while the waveguide diameter is about an order of magnitude larger). The presence of heat diffusion does not erase the periodic nano-structures. The individual grating periods can also clearly be seen in Fig. 5. Note that because the nano-structures are much smaller than the diameter of the waveguide (full waveguide cross-section is marked with white bars as a visual aid), the nano-structures in the core only fill a fraction of the full waveguide cross-section. This results in a relatively weak overlap between the index modulation and the waveguide mode field and leads to the trade-off between large damage structures resulting in a strong Bragg resonance with high associated scattering losses or small structures with a weak Bragg resonance but low scattering losses.

Our experiments indicate that the nano-structures are induced by the first few tightly focused laser pulses of each burst, before heat accumulation causes thermal defocusing and distorting effects that distribute the pulse energy over a larger volume, thus lowering the effective peak intensity below the damage threshold. The inter-burst period interrupts the cumulative heating process, allows the material to cool and therefore enables the formation of a new nano-void induced by the subsequent burst. We describe this blend of processes as quasi cumulative heating. While the quasi cumulative heating regime can indeed be exploited to inscribe a first order WBG, it is important to mention that the technique is very sensitive and depends on the exact right balance of pulse energy, writing speed and the inter-burst period. The nano-voids are only induced when the onset of cumulative damage is fast enough and the void is generated before cumulative heating of the sample substantially distorts the wavefront of the writing beam and thus results in a lower intensity within the focal volume. As a consequence, the parameter window for WBG inscription in the quasi cumulative heating regime is extremely narrow.

To investigate the morphology of the induced nano-structures we ground a typical sample down to the center of the waveguide, i.e. to the plane were the nano-structures are located. We then exposed the sample for 4 minutes to Hydrofluoric acid (HF, 16% concentration) in order to etch the glass and enhance the visibility of the written structures. The scanning-electron microscope (SEM) image in Fig. 6
Fig. 6 SEM image showing a typical nano-void array within the core of a WBG. The inset shows that the dimension of the nano-voids is much smaller than the diffraction limited writing spot
shows the periodic nano-void structure that is characterized by a feature size of ~300 nm. A larger fishbone-like structure that surrounds the voids can also be seen. It is not fully understood if this structure is induced by the HF etching process or byproduct of the writing process, (i.e. local variations in the fictive temperature which influences HF etching rates) [17

17. A. Agarwal and M. Tomozawa, “Correlation of silica glass properties with the infrared spectra,” J. Non-Cryst. Solids 209(1-2), 166–174 (1997). [CrossRef]

]. However, the fishbone structure is not strictly periodic and also not visible in DIC microscope images (see Fig. 5), indicating that these structures have no significant index contrast. Further a strong index fluctuation would alter the shape of Bragg peak [18

18. C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008). [CrossRef]

]. The fluctuations may have an impact on the spectral shape, but as no strong spectral broadening or side peaks are visible in transmission or reflection spectra (Fig. 4) we estimate the index fluctuation to be low.

As shown in the inset, the induced periodic nano-structures are indeed much smaller than the diameter of the laser focus (~1 µm), which can be explained by the nonlinear nature of the light- matter interaction process whereby only the peak of the Gaussian intensity profile of the writing beam exceeds the damage threshold of the material. This effect relies on the fact that for the very short pulse durations that are used in our experiments, the electrons absorb the laser energy almost entirely via multi photon and tunnel ionization. This results in a highly deterministic damage threshold in contrast to the stochastic behavior that can be observed for longer pulse durations [19

19. M. Lenzner, “Femtosecond laser-induced damage of dielectrics,” Int. J. Mod. Phys. B 13(13), 1559–1578 (1999). [CrossRef]

]. The subsequent transfer of energy from the highly energetic electrons to the lattice results in a micro-explosion: A strong shock wave compresses the surrounding material to the yield point and the shock wave eventually loses its energy due to material dissipation. Once the energy has dropped below a certain threshold, it continues to propagate as an acoustic wave through the material without inducing any additional structural changes [20

20. B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters [Invited],” Opt. Mater. Express 1(4), 766–782 (2011). [CrossRef]

23

23. E. G. Gamaly, S. Juodkazis, H. Misawa, B. Luther-Davies, A. V. Rode, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Formation of nano-voids in transparent dielectrics by femtosecond lasers,” Curr. Appl. Phys. 8(3-4), 412–415 (2008). [CrossRef]

]. It is important to mention that the nano voids are not induced by a single laser pulse alone, but by a series of laser pulses, as discussed above. Thus, a cumulative but non-thermal effect must play a role in this process. It has been shown previously that mid-gap states can accumulate electrons after excitation by sub-threshold pulses and lower the threshold for subsequent pulses [24

24. L. A. Emmert, M. Mero, and W. Rudolph, “Modeling the effect of native and laser-induced states on the dielectric breakdown of wide band gap optical materials by multiple subpicosecond laser pulses,” J. Appl. Phys. 108(4), 043523 (2010). [CrossRef]

]. We believe a similar mechanism is responsible for these results.

5. Conclusion

In conclusion, high speed single step direct inscription of WBGs in the high repetition quasi-cumulative heating regime was demonstrated for the first time. We have shown that a narrow process window exists where the onset of cumulative heating is marked by the formation of a single nano-sized void structure. By periodically interrupting the waveguide writing process in the cumulative heating regime, this transitional nano-damage effect can be exploited to fabricate highly periodic void structures. We describe this as quasi cumulative heating regime. We have demonstrated that this regime enables the inscription of a first-order Bragg structure with a pitch of as small as 520 nm that is embedded within a waveguide that has a diameter that is determined by the extent of the heat diffusion zone and that can thus be as large as 8 micron, perfectly matched to standard single-mode fiber technology. Fabrication speeds of up to 200 mm/min have been realized.

Acknowledgments

This research was conducted by the Australian Research Council Centre of Excellence for Ultrahigh Bandwidth Devices for Optical Systems (project number CE110001018) and LIEF program.

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(21), 1729–1731 (1996). [CrossRef] [PubMed]

2.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008). [CrossRef]

3.

G. D. Marshall, M. Ams, and M. J. Withford, “Direct laser written waveguide-Bragg gratings in bulk fused silica,” Opt. Lett. 31(18), 2690–2691 (2006). [CrossRef] [PubMed]

4.

H. Zhang, S. M. Eaton, and P. R. Herman, “Single-step writing of Bragg grating waveguides in fused silica with an externally modulated femtosecond fiber laser,” Opt. Lett. 32(17), 2559–2561 (2007). [CrossRef] [PubMed]

5.

G. D. Marshall, P. Dekker, M. Ams, J. A. Piper, and M. J. Withford, “Directly written monolithic waveguide laser incorporating a distributed feedback waveguide-Bragg grating,” Opt. Lett. 33(9), 956–958 (2008). [CrossRef] [PubMed]

6.

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16), 2533–2542 (2004). [CrossRef]

7.

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(2), 612–620 (2005). [CrossRef] [PubMed]

8.

S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005). [CrossRef] [PubMed]

9.

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(15), 5676–5681 (2005). [CrossRef] [PubMed]

10.

R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20(7), 1559–1567 (2003). [CrossRef]

11.

H. Kakiuchida, K. Saito, and A. J. Ikushima, “Refractive index, density and polarizability of silica glass with various fictive temperatures,” Jpn. J. Appl. Phys. 43(6A), L743–L745 (2004). [CrossRef]

12.

D. J. Little, M. Ams, P. Dekker, G. D. Marshall, J. M. Dawes, and M. J. Withford, “Femtosecond laser modification of fused silica: the effect of writing polarization on Si-O ring structure,” Opt. Express 16(24), 20029–20037 (2008). [CrossRef] [PubMed]

13.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011). [CrossRef]

14.

C. Miese, A. Fuerbach, and M. Withford, “Dynamics of waveguide writing using a high pulse energy (600 nJ) MHz femtosecond oscillator,” in CLEO/Europe and EQEC 2009 Conference Digest (Optical Society of America, 2009), paper CM_P12.

15.

C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 351–354 (2003). [CrossRef]

16.

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, San Diego, Calif., 1998.

17.

A. Agarwal and M. Tomozawa, “Correlation of silica glass properties with the infrared spectra,” J. Non-Cryst. Solids 209(1-2), 166–174 (1997). [CrossRef]

18.

C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008). [CrossRef]

19.

M. Lenzner, “Femtosecond laser-induced damage of dielectrics,” Int. J. Mod. Phys. B 13(13), 1559–1578 (1999). [CrossRef]

20.

B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters [Invited],” Opt. Mater. Express 1(4), 766–782 (2011). [CrossRef]

21.

S. Juodkazis, H. Misawa, E. G. Gamaly, B. Luther-Davies, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Is the nano-explosion really microscopic?” J. Non-Cryst. Solids 355(18-21), 1160–1162 (2009). [CrossRef]

22.

L. Hallo, C. Mézel, A. Bourgeade, D. Hébert, E. G. Gamaly, and S. Juodkazis, “Laser-matter interaction in transparent materials: confined micro-explosion and jet formation,” in Extreme Photonics Applications (Springer, 2010), pp. 121–146.

23.

E. G. Gamaly, S. Juodkazis, H. Misawa, B. Luther-Davies, A. V. Rode, L. Hallo, P. Nicolai, and V. T. Tikhonchuk, “Formation of nano-voids in transparent dielectrics by femtosecond lasers,” Curr. Appl. Phys. 8(3-4), 412–415 (2008). [CrossRef]

24.

L. A. Emmert, M. Mero, and W. Rudolph, “Modeling the effect of native and laser-induced states on the dielectric breakdown of wide band gap optical materials by multiple subpicosecond laser pulses,” J. Appl. Phys. 108(4), 043523 (2010). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.1480) Optical devices : Bragg reflectors

ToC Category:
Integrated Optics

History
Original Manuscript: July 19, 2011
Revised Manuscript: September 8, 2011
Manuscript Accepted: September 8, 2011
Published: September 22, 2011

Citation
Christopher Miese, Michael J. Withford, and Alexander Fuerbach, "Femtosecond laser direct-writing of waveguide Bragg gratings in a quasi cumulative heating regime," Opt. Express 19, 19542-19550 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19542


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References

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