Ultrashort pulsed laser irradiation of bulk fused silica may result under specific energetic conditions in the self-organization of subwavelength material redistribution regions within the laser trace. The modulated structures have birefringent properties and show unusual anisotropic light scattering and reflection characteristics. We report here on the formation of waveguiding structures with remarkable polarization effects for infrared light. The photoinscription process using 800 nm femtosecond laser pulses is accompanied by third harmonic generation and polarization dependent anisotropic scattering of UV photons. The photowritten structures can be arranged in three-dimensional patterns generating complex propagation and polarization effects due to the anisotropic optical properties.
©2009 Optical Society of America
Laser-induced birefringence is not an uncommon phenomenon when linearly polarized radiation is used to irradiate bulk isotropic glass materials. Depending on the pulse duration and on the geometry of the energy deposition region, local anisotropies with birefringent properties may appear due to residual effects of electrostriction or stress related artifacts appearing from expansion or compression cycles [1–4] during irradiation and propagation. For ultrashort laser pulses however, a novel phenomenon leading to form birefringence was observed [5, 6], which is based on the self-formation of organized volume nano-sheet arrays inside the laser traces [7–9]. The resulting layered structures show different refractive indices with respect to the surrounding and are oriented perpendicular to the electric field vector, leading to birefringence values in the range of δoe=5×10-3 for 633 nm wavelength. Two factors need to be observed in this case. First, the ultrashort duration triggers essentially electronic polarization effects while keeping the molecular reorientation low. Second, the accumulation dose supports a positive feedback response for stimulating the growth of the organized subwavelength structures. Both aspects indicate a driving electronic mechanism of self-organization, with modulated energy transfer to the glass matrix and supporting particular propagation modes in localized underdense nanoscaled plasma sheets, which favors the preferential growth locked on the specific modulation. The proposed models [7, 8] involve collective electronic oscillations and local changes in polarizabilities which, due to a modulation of energy deposition and hydrodynamic matter redistribution, lead to the formation of a rippled structure in volume. The resulting gratings consist in narrow layers of lower index, oriented perpendicular to the laser electric field (i.e. spatial vector q aligned parallel to the master field), with an interlayer period of approximately λ/2n, n being the refractive index and λ the writing wavelength. The modulated structures also show noteworthy structural and optical properties; among these, a preferential concentration of oxygen-deficiency centers (ODC) in the layers , and peculiar optical scattering [10, 11] or reflection properties .
The formation of birefringent regions based on nanoscale self-organization in fused silica (a-SiO2) is highly dependent on the irradiation regime [5, 13, 14], as often observed in experiments conceptually designed for inducing waveguiding modifications in bulk transparent materials. With respect to structures resulting from scanning the laser beam either parallel or perpendicular to the propagation axis, it is practical to divide the achieved structures in various classes as follows. Low irradiation levels usually induce isotropic positive changes of the refraction index denoted type I structures, while higher energy doses are able to initiate the type II birefringent material modifications . The formation of self-organized nanoscaled arrays was associated with type II structures [13, 14]. The nanograting formation was consequently exploited for the fabrication of phase plates, birefringent filters and reflectors, or nanofluidic devices, as well as potential alternative for damage resistant optical recording [13–16].
The laser-induced photosensitivity and the subsequent refractive index change [17–20] are equally important in photonic applications based on waveguiding [21–24]. In this respect, besides the formation of ordered structures, polarization control may also influence the excitation cross-sections in multiphoton or collisional processes , thus regulating the magnitude of the index variations [26, 27]. Observing both waveguiding and birefringent properties, we exploit here some of the characteristics of complex 3D design and anisotropic optical properties for fabricating polarization-sensitive devices in bulk fused silica.
The paper is organized as follows. The experimental section provides the fabrication recipe of light guiding structures and indicates process investigation details. The discussion part concentrates on three major issues. We firstly describe the properties of the different structure types, emphasizing the conditions for the observed optical anisotropies, namely the geometric characteristics of the injected light in scattering, reflection, or transmission properties. Secondly, we note the angular-dependent emission properties for the accompanying third harmonic generated during the writing procedure. Thirdly, we demonstrate the fabrication of polarizing and polarization-sensitive devices based on the preferential scattering and indicate the possibility to confine light in three-dimensional (3D) regular structures.
2. Experimental description
The exposure was made with ultrashort infrared (800 nm) light pulses from a regeneratively amplified Ti:sapphire ultrafast laser system delivering 300 mW of usable power at a repetition rate of 100 kHz and a nominal pulse duration of 150 fs. Polished fused silica (Corning 7980-5F) parallelepipedic samples (10×20×3 mm) were employed, mounted on XYZ motion controller that allows translation parallel or perpendicular to the laser propagation axis. The laser beam was focused inside the target by a long working distance 20× Mitutoyo microscope objective (working distance 20 mm, nominal numerical aperture NA=0.42). Due to the beam truncation at the objective pupil (approximately 0.56 relative ratio between the transverse dimension of the beam and that of the pupil) we estimate an effective numerical aperture of NA=0.29. A longitudinal writing configuration, with translation parallel to the laser propagation axis, was used throughout the text unless otherwise mentioned. A positive phase contrast microscope (PCM) was employed to image the interaction region in a side-view geometry. In this arrangement, the relative positive index changes are appearing dark on a gray background, while white zones indicate negative index variations or scattering centers. The image was recorded with a charge-coupled (CCD) camera. Further characterization was performed by axial transillumination microscopy using additional incoherent white light (WL) sources or by probing the modification properties with unpolarized HeNe laser radiation at 633 nm. Additionally, to a great extent, the optical properties were verified upon injection with 800 nm light. A schematic view of the experimental arrangement is given in Fig. 1(a).
3. Results and discussion
3.1. Laser photoinscription
In relatively gentle exposure conditions, two intensity dependent regimes of positive refractive index modifications, hereafter referred to as type I and type II, were observed upon irradiation with 800 nm femtosecond laser pulses. Apart from this, very energetic regimes favor also void production and subsequent negative index changes. A schematic description of the processing window for each resulting waveguide type in a longitudinal writing configuration is given in Fig. 1(b), emphasizing a large range of usable parameters systematically determined for the same focusing geometry. These values are reported for a working depth of 500 µm, but they are qualitatively indicative for a larger range of depths in our focusing conditions. However, the two regimes are very sensitive to the duration of the pulse. A narrow intermediary transition region may appear, caused by small deviations from the nominal pulse length; the shortest duration leading to a larger processing window for type I traces, while slightly increasing the pulse duration (e.g. via positive dispersion or wavefront variations through the objective) favors the apparition of type II structures. The reported results were obtained for input pulse durations in the range of 150–200 fs. In these irradiation conditions, the threshold for observing a static structure for 1 s irradiation is approximately 17mW. As a rule of thumb derived from experimental observations, type II traces are favored by tighter focusing, higher energies (mainly in supercritical range with respect to self-focusing), and lower scan velocities, permitting a stronger accumulation dose of thousand pulses per micrometer. For tighter focusing, as a function of the scan velocity, soft but negative index buffer regions may intermediate the type I to type II transition. The regime of higher energy deposition suggests as well that hydrodynamic and thermomechanical effects  start to play an increasing role in determining the type II trace. Type I waveguiding is induced by lower laser energy densities, showing a smooth positive refractive index change at the center of the laser focus relative to the unprocessed material. Different writing beam polarizations were used to photoinscribe guiding traces and, in the presented cases, we obtained a positive axial index change upon the scanning procedures as shown in Fig. 2. It is of interest to note that birefringent zones were also reported to result in negative refractive index changes [13, 29].
Figure 2 depicts examples of type I (upper part) and type II (bottom part) laser-induced longitudinal traces for different polarization orientations together with near-field modes of guided 800 nm light. Type I traces show normally a smooth type of modification as noticeable in the PCM traces, with weak index changes in the range of 10−4–10−3 (depending on the scan velocity), indicated by the shallow dark color in the left upper panel of Fig. 2. The tracks were subsequently injected with polarized 800 nm light. No noticeable polarization sensitivity was observed (Fig. 2 top right), both vertical (V) and horizontal (H) orthogonal polarizations being guided (see figure). The type II traces show as well an overall axial positive refractive index change (dark colors in PCM), bordered by narrow rougher edges of negative index change or scattering zones (white colors in PCM). The index increase is significantly higher as for the type I guide, reaching up to a factor of ten in magnitude depending on the writing conditions. Upon injection with 800 nm light we have observed a notable behavior. Type II traces indicate light guiding properties only for injected light with the electric vector perpendicular to the initial writing beam vector; a different polarization being scattered away. This observation holds essentially for injected 800 nm; the polarization sensitivity being visibly reduced for injected 633 nm. Considering that nanoarrays are formed in the trace as previously reported [7, 8], they allow light transport for polarizations aligned along the planes (TE with respect to the structure), orthogonal to the polarization of the writing beam. Note also the strong confinement of the field mode as a result of the higher index contrast, however the optical losses are significantly increased by the rugous borders to several dB/cm. No guiding modes were observed for circular writing polarization due to the reported presence of less ordered scattering nanostructures within the trace .
The polarization efficiency depends on the length of the tracks and can determine behaviors that change from a birefringent zone for short lengths [13, 14] to a high contrast polarizer at more significant lengths, a situation depicted in Fig. 3(a) which indicates the polarization extinction ratio (PER) as a function of the propagation length. The PER can augment to around 30 dB for input light at 800 nm, however it strongly diminishes at 633 nm. The polarization behaviors, namely the polarization dependent transmission (PDT) and the polarization dependent scattering (PDS), were tested by employing axial and off-axis detectors while rotating the input injection electric vector by a half-wave plate. The full PDT pattern is indicated in Fig. 3(b) together with the PDS pattern [Fig. 3(c)], showing antagonist behaviors: maximal transmission for injected light electric vector along the nanoplane (TE) and maximum scattering or mode leaking for light vectors perpendicular to the nanoplanes (TM). The directional scattering attenuates rapidly along the propagation direction. We note that similar polarization behaviors were reported for tilted fiber Bragg gratings configurations [31, 32]. However, in our case it appears that the specific polarization effect is related to different confinement of TE and TM modes along the periodic nanometric slab structure and a more leaky characteristics of the TM mode. We believe that the preferential leak can lead to the observed anisotropic scattering, indicated in Fig. 3. Nonetheless, in the absence of data concerning the index contrast in the present conditions, it is difficult to indicate quantitative evaluations for this effect.
Noteworthy, in case of type II traces, the writing procedure was accompanied by the generation of an intense and readily observable ultraviolet (UV) emission along the infrared beam, deflected in a plane parallel to the writing laser electric vector. The UV emission was identified as the third harmonic (267 nm). Anisotropic scattering of radiation was reported before in case of fluorescence of ODC centers in Ge-doped silica or photoluminescence of Eu2+ ions in Eu-doped fluoroaluminate glass, in a spectral domain around 400 nm, observed as an elongated fluorescence spot in the vicinity of the excitation zone [10, 11]. In the present case, though ODC or other type of defects  as well as free-free transition luminescence  should result following irradiation as typical irradiation products, the major part of the observed directionally scattered light (Fig. 4) was provided by the third harmonic. Third harmonic generation (THG) process is normally dipole allowed in isotropic media and plasmas [35–38] resulting from time-dependent polarizabilities and having patterns related to the symmetry and isotropy of the propagation environment.
The involvement of UV photons was previously presumed when explaining the experimentally-observed anisotropic blue luminescence [10,11]. It was suggested that UV scattering by the photoelectronic current may assist in exciting fluorescent defect states along the laser polarization in regions that exceed the spatial extension of the infrared spot. Axially-modulated shear stress was also indicated as providing phase-matching conditions  in collinear emission. The observed UV pattern deflected in the plane of the laser polarization depicted in Fig. 4(a,b,c) consists of two lobs distributed symmetrically with respect to the fundamental beam. This specific distribution can be associated with a diffraction phenomenon, suggesting the presence of subwavelength arrays. The preferential scattering takes place on the nanoarrays in a plane perpendicular to the grating and for incidence angles given by the spread of wavevectors in the excitation zone, delivering an additional proof for the existence of subwavelength matter organization. Figure 4(a,b,c) shows the polarization dependence of the scattered UV pattern for various polarizations of the fundamental beam, horizontal, rotated with 45°, and, respectively, vertically polarized. Due to image acquisition reasons, the distribution was recorded for transverse writing, however a similar picture emerges for longitudinal writing in the conditions discussed in the text. The corresponding spectral information is given in Fig. 4(d). The diffraction angles, after correction for refraction and eventual total reflection at the glass interface, are situated around a value of 30° inside the material and correspond to a diffraction pattern given by incidence angles imposed by the input cone of the infrared writing beam. The diffraction pattern is superimposed by a peaked background given by off-axis phase matching [37–40] (not shown) at smaller deflection angles. To verify the grating assumption we have also employed borosilicate crown BK7, known for its resistance to the formation of ordered nanoscale structures . No anisotropic scattering was detected, consistent with previous statements on the absence of nanogratings in this material . The presence of sub-wavelength gratings indicated in earlier works [7–9] and presumed in the discussion above was directly confirmed at a later stage by scanning electron microscopy (SEM) images of transverse profiles of fused silica type II traces written in the conditions of Fig. 2, using the cleaving, polishing, etching, and imaging techniques reported in . Examples of subwavelength organization for type II traces written by vertically polarized ultrafast laser radiation are given in Fig. 4(f), showing also an apparent agglomeration of intact nano-sheets towards the boards of the structure, in a region corresponding to the index switch from the central positive changes to the negative variations at the diffusing edges. While suggesting combined interface and modulation effects, further investigations are needed to elucidate these aspects. Moreover, in that concern both the edges and the circularity of the profile, an additional influence determined by eventual asymmetries of the laser beam (e.g. residual astigmatism and non-reciprocal effects due tilted fronts ) cannot be totaly ruled out.
3.2. Fabrication of components
3D design of complex structures based on refractive index changes show particularly interesting properties for controlling the propagation of light in confined and discrete spaces [41–43]. Observing the anisotropic reflection and scattering properties indicated above, as well as previous reports on preferential scattering of light interacting with subwavelength structured traces when the incident electric vector is parallel to the writing vector , we have designed 3D structures assembled from type II longitudinal waveguides in fused silica. A first hexagonal array was fabricated, schematically indicated in Fig. 5(a). The structure was subsequently injected in the central region with low intensity 800 nm ultrafast radiation through a NA=0.29 objective. The angularly selective scattering properties confine the laser radiation through periodic reflections upon propagation and only support the guiding of specific polarized modes [Fig. 5(b,c)]. Propagation occurs for this geometric arrangement when the injected light polarization is parallel to the writing beam electric vector, as indicated also by the PDT pattern in Fig. 5(c). No guiding mode was observed for structures written by circularly polarized light or for orthogonal writing-injection polarization configurations. The reason for the observed guiding properties can be either related to the anisotropic reflecting properties of the edges or to the onset of densified matter along the central axis due to cumulated stress. It should be noted that, in particular conditions, stress accumulation between laser tracks may provide the required refractive index change for light guiding. The effect is present  when the separation distance stays within the shock propagation distance, that is in the range of few microns [3, 28]. Tests on BK7 glass, which has a high thermal expansion coefficient and facilitates stress accumulation, did not confirm the hypothesis. This suggests that the guiding in our case is related to the anisotropic reflection on the supporting structures when the injected field vector (TM) is parallel to the nanoarray spatial vector which is present in each individual trace forming the hexagonal array and not to stress accumulation along the central axis. We have also verified that the guiding properties rest visible for separation distances between the waveguides amounting up to 85 µm, thus excluding the stress contribution to the guiding properties and relying on the enhanced reflectivity at the proper polarization . Complex polarization dependent propagation effects were obtained for parallelepipedic designs as well. This behavior can be connected with different effective refractive indices seen by the light in the traces , creating a propagation mode or superposition of modes that, due to boundary conditions, keeps the memory of the structure. However, this implies that the superposition of modes may drastically change as a function of the geometry of the structure. It should be noted as well that a hexagonal structure of similar geometry fabricated exclusively from type I waveguides allows light coupling and isotropic propagation in the individual traces [Fig. 5(d)].
The polarization selectivity indicates also other concepts of optical design. Consequently, based on the polarization dependent transmission of type II waveguides and the isotropic properties of the type I trace, a hybrid structure acting as an optical router was designed. The structure is based on a central type I waveguide with a length chosen to allow complete evanescent coupling of light into the adjacent type II waveguides separated by approximately 15µm. The two type II traces are written with orthogonal polarizations respectively. The result is shown in Fig. 6(a) together with the polarization dependent guided modes [Fig. 6(b,c)] at 800 nm. This shows the possibility to selectively transport light through each trace. The switching efficiency described by the relative transported intensity contrast is superior to 50 in this configuration. The high extinction ratios of the type II traces indicate the prospect of obtaining a high contrast polarization dependent optical router.
In conclusion we have observed the conditions for fabricating type I and type II guiding traces, showing peculiar polarization properties upon transporting light. The diffraction pattern of the observed THG was related to the reported presence of nanoscale material organization in regular gratings inside the trace, perpendicular to the laser polarization. This was further confirmed by electron microscopy inspection. Based on the observed anisotropic scattering and reflection characteristics, the guiding elements were assembled in complex structures with polarization and switching functions when injected with the same radiation wavelength as the writing laser.
Support of ANR and PICS programs is gratefully acknowledged. We would also like to thank O. Parriaux, A. Tishchenko, Y. Ouerdane and A. Boukenter for illuminating discussions.
References and links
1. 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]
2. 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]
4. 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]
5. L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171, 279–284 (1999). [CrossRef]
6. E. Bricchi, B. G. Klappauf, and P. G. Kazansky, “Form birefringence and negative index change created by femtosecond direct writing in transparent materials,” Opt. Lett. 29, 119–121 (2004). [CrossRef] [PubMed]
7. Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91, 247405/1–4 (2003). [CrossRef]
8. V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404/1–4 (2006). [CrossRef]
9. D. Wortmann, J. Gottmann, N. Brandt, and H. Horn-Solle, “Micro- and nanostructures inside sapphire by fs-laser irradiation and selective etching,” Opt. Express 16, 1517–1522 (2008). [CrossRef] [PubMed]
10. P. G. Kazansky, H. Inouye, T. Mitsuyu, K. Miura, J. Qiu, K. Hirao, and F. Starrost, “Anomalous anisotropic light scattering in Ge-doped silica glass,” Phys. Rev. Lett. 82, 2199–2202 (1999). [CrossRef]
11. J. Qiu, P. G. Kazansky, J. Si, K. Miura, T. Mitsuyu, K. Hirao, and A. L. Gaeta, “Memorized polarization-dependent light scattering in rare-earth-ion-doped glass,” Appl. Phys. Lett. 77, 1940–1942 (2000). [CrossRef]
12. J. D. Mills, P. G. Kazansky, E. Bricchi, and J. J. Baumberg “Embedded anisotropic microreflectors by femtosecond-laser nanomachining,” Appl. Phys. Lett. 81, 196–198 (2002). [CrossRef]
13. P. G. Kazansky and Y. Shimotsuma, “Self-assembled sub-wavelength structures and form birefrigence created by femtosecond laser writing in glass: properties and applications,” J. Ceram. Soc. Japan. 116, 1052–1062 (2008). [CrossRef]
14. R. Taylor, C. Hnatovsky, and E. Simova, “Applications of femtosecond laser induced self-organized planar nanocracks inside fused silica glass,” Laser and Photon. Rev. 2, 26–46 (2008). [CrossRef]
15. E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, “Birefringent Fresnel zone plates in silica fabricated by femtosecond laser machining,” Opt. Lett. 27, 2200–2202 (2002). [CrossRef]
16. W. Cai, A. R. Libertun, and R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14, 3785–3791 (2006). [CrossRef] [PubMed]
18. 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]
19. V. R. Bhardwaj, E. Simova, P. B. Corkum, D. M. Rayner, C. Hnatovsky, R. S. Taylor, B. Schreder, M. Kluge, and J. Zimmer, “Femtosecond laser-induced refractive index modification in multicomponent glasses,” J. Appl. Phys. 97, 083102/1–9 (2005). [CrossRef]
20. K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31, 620–625 (2006). [CrossRef]
21. 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]
22. A. Szameit, D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Discrete nonlinear localization in femtosecond laser written waveguides in fused silica,” Opt. Express 13, 10552–10557 (2005). [CrossRef] [PubMed]
23. G. Della Valle, S. Taccheo, R. Osellame, A. Festa, G. Cerullo, and P. Laporta, “1.5 µm single longitudinal mode waveguide laser fabricated by femtosecond laser writing,” Opt. Express 15, 3190–3194 (2006). [CrossRef]
24. H. Zhang, S. M. Eaton, J. Li, A. H. Nejadmalayeri, and P. R. Herman, “Type II high-strength Bragg grating waveguides photowritten with ultrashort laser pulses,” Opt. Express 15, 4182–4191 (2007). [CrossRef] [PubMed]
25. V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, A. El-Khamhawy, and D. von der Linde, “Multiphoton ionization in dielectrics: comparison of circular and linear polarization,” Phys. Rev. Lett. 97, 237403/1–3 (2006). [CrossRef]
26. D. J. Little, M. Ams, P. Dekker, G. D. 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, 20029–20037 (2008). [CrossRef] [PubMed]
27. W. Gawelda, D. Puerto, J. Siegel, A. Ferrer, A. Ruiz de la Cruz, H. Fernández, and J. Solis, “Ultrafast imaging of transient electronic plasmas produced in conditions of femtosecond waveguide writing in dielectrics,” Appl. Phys. Lett. 93, 121109/1–3 (2008). [CrossRef]
28. A. Mermillod-Blondin, I. M. Burakov, Yu. P. Meshcheryakov, N. M. Bulgakova, E. Audouard, A. Rosenfeld, A. Husakou, I. V. Hertel, and R. Stoian, “Flipping the sign of refractive index changes in ultrafast and temporally shaped laser-irradiated borosilicate crown optical glass at high repetition rates,” Phys. Rev. B 77, 104205/1–8 (2008). [CrossRef]
29. D. Grojo, M. Gertsvolf, H. Jean-Ruel, S. Lei, L. Ramunno, D. M. Rayner, and P. B. Corkum, “Self-controlled formation of microlenses by optical breakdown inside wide-band-gap materials,” Appl. Phys. Lett. 93, 243118/1–3 (2008). [CrossRef]
32. S. Lu, O. Xu, S. Feng, and S. Jian, “Analysis of radiation-mode coupling in reflective and transmissive tilted fiber Bragg gratings,” J. Opt. Soc. Am. A 26, 91–98 (2009). [CrossRef]
33. N. Fukata, Y. Yamamoto, K. Murakami, M. Hase, and M. Kitajima, “In situ spectroscopic measurement of transmitted light related to defect formation in SiO2 during femtosecond laser irradiation,” Appl. Phys. Lett. 83, 3495–3497 (2003). [CrossRef]
34. C. W. Carr, M. D. Feit, A. M. Rubenchik, P. De Mange, S. O. Kucheyev, M. D. Shirk, H. B. Radousky, and S. G. Demos, “Radiation produced by femtosecond laser-plasma interaction during dielectric breakdown,” Opt. Lett. 30, 661–663 (2005). [CrossRef] [PubMed]
35. C. S. Liu and V. K. Tripathi, “Third harmonic generation of a short pulse laser in a plasma density ripple created by a machining beam,” Phys. Plasmas 15, 023106/1–4 (2008).
36. P. N. Saeta and N. A. Miller “Distinguishing surface and bulk contributions to third-harmonic generation in silicon,” Appl. Phys. Lett. 79, 2704–2706 (2001). [CrossRef]
37. F. Théberge, N. Aközbek, W. Liu, J.-F. Gravel, and S. L. Chin, “Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses,” Opt. Commun. 245, 399–405 (2005). [CrossRef]
38. S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Efficient third-harmonic generation through tailored IR femtosecond laser pulse filamentation in air,” Opt. Express 17, 3190–3195 (2009). [CrossRef] [PubMed]
39. S. Juodkazis, E. Gaižauskas, V. Jarutis, J. Reif, S. Matsuo, and H. Misawa, “Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating,” J. Phys. D 39, 50–53 (2006). [CrossRef]
40. L. A. Siiman, J. Lumeau, L. Canioni, and L. B. Glebov, “Non-collinear generation of third harmonic of IR ultrashort laser pulses by PTR glass volume Bragg gratings,” Opt. Express 17, 3564–3573 (2009). [CrossRef] [PubMed]
41. V. Diez-Blanco, J. Siegel, and J. Solis, “Femtosecond laser writing of optical waveguides with controllable core size in high refractive index glass,” Appl. Phys. A: Mater. Sci. Process. 88, 239–242 (2007). [CrossRef]
42. A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B: Laser Opt. 82, 507–512 (2006). [CrossRef]
43. C. Mauclair, G. Cheng, N. Huot, E. Audouard, A. Rosenfeld, I. V. Hertel, and R. Stoian, “Dynamic ultrafast laser spatial tailoring for parallel micromachining of photonic devices in transparent materials,” Opt. Express 17, 3531–3542 (2009). [CrossRef] [PubMed]
44. V. Diez-Blanco, J. Siegel, and J. Solis, “Waveguide structures written in SF57 glass with fs-laser pulses above the critical self-focusing thresholds,” Appl. Surf. Sci. 252, 4523–4526 (2006). [CrossRef]
45. A. B. Buckman, “Polarization-selective lateral waveguiding in layered dielectric structures,” J. Opt. Soc. Am. 72, 688–691 (1982). [CrossRef]