Laser-induced self-organization of regular nanoscale layered patterns in fused silica is investigated using spectroscopy and microscopy methods, revealing a high presence of stable broken oxygen bonds. Longitudinal traces are then generated by replicating static irradiation structures where the nanoscale modulation can cover partially or completely the photoinscribed traces. The resulting birefringence, the observed anisotropic light scattering properties, and the capacity to write and erase modulated patterns can be used in designing bulk polarization sensitive devices. Various laser-induced structures with optical properties combining guiding, scattering, and polarization sensitivity are reported. The attached polarization functions were evaluated as a function of the fill factor of the nanostructured domains. The polarization sensitivity allows particular light propagation and confinement properties in three dimensional structures.
© 2010 Optical Society of America
The formation of regular self-organized nanoscale structures under energetic beam exposure of materials is an intriguing physical phenomenon of quasi-universal nature. The three-dimensional (3D) volume extension of the observed self-patterning events relies particularly on prior laser-driven electronic oscillations confining the energy in nanoscale domains. The resulting transformations indicate remarkable anisotropies in the optical properties that involve selective reflection and form birefringence [1–3]. The laser electric field direction is the main factor in controlling both excitation efficiency and subsequent polarization of the dielectric matrix [4, 5] that assists the formation of ordered nano-sheet arrays [1–3]. These are usually oriented perpendicular to the driving field with an interlayer period of approximately λ/2n, n being the refractive index and λ the writing laser wavelength in vacuum. Typical parameters are reported in [1,2], namely an alternance of λ/2n regions with a slightly higher index (Δn = 10−3) separated by narrow (10–30 nm) quasi-hollow low index regions. This arrangement gives negative form birefringence values in the range of δoe = 5 × 10−3 for 633 nm wavelength. Several possible applications were already proposed that include the fabrication of phase plates, birefringent filters and reflectors, computer holograms, optofluidic devices, polarization-sensitive waveguides, or new environments for optical recording [1, 2, 6–8].
Continuing exploring the mechanisms and the properties of 3D self-organized patterns is important for further developing the concept of volume functionalization of optical materials [ [9–13] and references therein] using ultrafast laser radiation, acquiring in addition particular polarization functions. If usually at low photon doses quasi-isotropic refractive index changes are induced via soft electronic alterations that may involve defects, densification, or increased matrix polarization [5, 14, 15], in more energetic regimes, corresponding to thermo-mechanical photoinscription effects, ultrafast laser radiation generates the above mentioned nanoscale spontaneous arrangement, leading to form birefringence and modulated index patterns . This regime is characterized here by spatially-resolved spectroscopic means, revealing an increased presence of stable oxygen broken bonds, consequence of strong nonlinear energy confinement. Taking advantage of the laser capacity of writing and erasing these domains, the amount on nanoscale modulated regions in the photoinscribed traces can be varied. Using the resulting birefringence properties and the associated anisotropic light scattering features characteristic to the ordered nanostructures, polarization functions were evaluated as a function of the fill factor of the nanostructured domains within the generated trace. The polarization sensitivity allows particular light propagation and tailored confinement properties in 3D structures.
The paper is organized as follows. The experimental section provides the fabrication conditions and indicates the investigation details. The discussion part concentrates on two major issues. We firstly describe the observed optical anisotropies, correlating the nonlinear energy deposition with the particular types of morphological material alterations. Spectroscopic investigations give further insights into the nature of the relevant structural changes. Secondly, we fabricate polarization-sensitive guiding structures and we indicate the potential control of light transport in 3D regular structures based on designed birefringence of the system boundaries.
2. Experimental description
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 output pulse duration of 130 fs were used to expose bulk glassy targets. Polished wet fused silica (Corning 7980-5F) parallelepipedic samples (10×20×3 mm) were employed, mounted on a XYZ motion controller that allows translation parallel or perpendicular to the laser propagation axis. The laser beam was focused inside the target by various focusing optics including a long working distance 50× microscope objective OB1 (Nikon L Plan, working distance 17 mm, nominal numerical aperture NA= 0.45) and a long working distance 20× microscope objective OB2 (Mitutoyo M Plan, working distance 20 mm, nominal numerical aperture NA= 0.42). Due to the beam truncation at the objective pupil (relative ratio between the transverse dimension of the beam and that of the pupil), we estimate an effective numerical aperture of NAeff = 0.42 for the OB1 objective and a lower value of NAeff = 0.29 for the OB2 objective. A longitudinal writing configuration with translation parallel to the laser propagation axis and in the direction of the laser source was used throughout the text unless otherwise mentioned, with the purpose of replicating the symmetry of the laser beam. An Olympus BX 41 positive optical phase-contrast microscope 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. The phase contrast microscopy (PCM) was accompanied by optical transmission (OTM), cross-polarization microscopy (CPM), and imaging techniques of the plasma fluorescence generated during the photoinscription process. Further characterization was performed by axial transillumination microscopy using additional incoherent white light (WL) sources or by probing the modification properties with polarized and unpolarized HeNe laser radiation at 633 nm. Additionally, to a great extent, the optical properties were verified upon injection with polarized 800 nm light.
The laser-induced traces were further analyzed using photoluminescence (PLM) and Raman microscopy (RM). RM and PLM spectra were measured in backscattering configuration with a confocal microscope. The measurements focused on spectral signatures of defect centers involving oxygen bond breakage, with emphasis on non-bridging oxygen hole centers (NBOHC), and, equally, on spectral features of additional compaction/polarizability in the glass matrix (D2 Raman ring modes at 606 cm−1). For excitation, 488 nm Ar+ laser light was focused and collected by a 100× objective with micrometer spatial resolution. Subsequent to irradiation, the written traces were also exposed in cross-section after polishing and etching following the technique presented in  and imaged using Scanning Electron Microscopy (SEM).
3. Results and discussion
3.1. Laser photoinscription
We have indicated above that the resulting laser modification depends essentially on the energetic dose  and the photoinscription regimes can be divided into several categories . We consequently explore the effects of laser multipulse irradiation in static and dynamic (scanned) conditions. As these regimes are mainly characterized by the irradiation result in terms of the refractive index change, we employ PCM to directly indicate positive or negative refractive index changes as they can be linked to particular structural and thermo-mechanical transformations. Additionally, the birefringence properties are monitored. A summary of possible ultrafast photoinscription regimes is shown in Fig. 1 which indicates static multipulse (N = 5 ×104) exposure at OB1 focusing conditions [Fig. 1(a–c)] and longitudinally scanned traces in similar circumstances [Fig. 1(d–f)], as a function of the incident power. We recall that positive index changes are denoted by dark colors and negative index variations by white colors. By observing the figure, several key factors are outlined below.
As a function of the incident laser power density, two main regimes can be noted. At low input powers a soft material transformation type (denoted type I) can be defined [Fig. 1(a,d)]. The transformation indicates a visible but low positive index change (10−4) surrounded by an extremely weak (barely observable on the figure) negative index change (note however that usually small objects in PCM are accompanied by hallo patterns with similar appearance). The longitudinal guiding trace probed by HeNe light at 633 nm shows isotropic light transport properties with respect to the field vector (discarding some stress and trace symmetry issues) and is basically a replication of the static trace. A weak emission (400–700 nm) accompanies the photoinscription process, showing a symmetric axial spatial distribution [Fig. 1(g)]. Activated by HeNe radiation, a reddish luminescence characteristic to NBOHC persists several minutes after irradiation (not shown). Increasing the energy, the situation changes. As observed in the static traces, a highly scattering region of negative index change becomes visible [white color in Fig. 1(b,c)], resembling catastrophic optical damage. It accompanies positive index changes bearing a conical form with the apex in the direction of light propagation. These regions of negative index show birefringence and are located in the static structure head as previously observed [17, 18]. Upon longitudinal scan, this regime, denoted type II, can be further divided into two subranges. At moderate fluences, the resulting longitudinal traces show quasi complete negative refractive index changes and do not support guiding [Fig. 1(e)]. This indicates that the dominant transformation upon scanning derives from the low index head. The corresponding traces will be called type II-NG. The plasma emission starts to show an asymmetric distribution upshifted towards the laser beam, accompanied by scattered light [Fig. 1(h)]. At high input powers and low scan velocities the central positive index change reappears into the longitudinal traces [Fig. 1(f)], leading to structures that support guiding of particular polarization  (type II-WG). In this photoinscription regime, plasma emission is significantly increased and has a higher emissivity in the direction of the laser input. Further non-uniformities and secondary emission regions develop with increasing energy dose [Fig. 1(i)]. A summary of plasma luminescence as a function of the input power is given in Fig. 1(g–i). Concerning the spectral distribution, a red-shifted deviation of the emission pattern was previously noticed as the photoinscription transits from type I to disordered traces  at 1 kHz repetition rate. As noted in PCM, the positive index increase in the type II-WG core is higher than for type I modifications.
A first conclusion can be drawn by analyzing the transition between different regimes. As it is firstly controlled by the incident power (note the type I to type II transition at few tens of mW), it appears that self-focusing accelerates the capability of creating depressions and low index regions. This was previously related to the possibility of triggering mechanical expansion inducing local rarefaction [20, 21]. We recall that the critical power of self-focusing in fused silica is PSF = 2.8 MW , which translates into an average power in our experimental conditions of 45 mW. Smaller values for the critical self-focusing power were also reported . Consequently, average powers well below this level should not lead to self-focusing, showing a quasi-symmetric axial deposition profile distributed around the geometrical focus, in conditions where the beam is not strongly depleted. The result is typically a type I trace [Fig. 1(a,d)]. However, considering the type II requirements, the capacity to self-focus is not the only criterion, a certain energy density level appears necessary to establish type II conditions. It has been recently observed that the threshold for the formation of type II structures increases dramatically with decreasing pulse duration  even though the energy required to achieve the critical PSF decreases. In the present conditions (NAeff = 0.42), a factor two between the observed thresholds for type I and type II formation is found for pulses around 150 fs, factor that increases with lower numerical apertures. This indicates that the early low-density plasma formation favored in case of short pulses leads to efficient defocusing, largely compensating the self-focusing effect. As the right energy balance is achieved, the multipulse exposure gradually increases the birefringence characteristics in the type II domain via the formation of regular nanogratings.
The input power is not the sole factor leading to the formation of various structure types, the degree of accumulation plays also a significant role. As a critical amount of incubation is required to support the positive feedback leading to the structural periodic arrangements, the scan velocity V can be linked to a critical density of pulses as V = ν/ρN where ν is the laser repetition rate and ρN is the required density of pulses per micrometer. For type II structures ρN is in the range of 102–103 pulses/μm. We have subsequently used SEM to inspect in detail the transverse cross-section of the dynamic traces, similar to the structures in Fig. 1, particularly in the high energy range (OB2 focusing). A summary of these images is given in Fig. 2(a–i) indicating the presence of nanolayers within the modification region as a function of scan velocity and the writing polarization. As indicated in , the transition from smooth to modulated structures can lead to a change in the guiding properties that can be further influenced by the cover range of nanogratings in the laser-induced trace [Fig. 2(j)]. The form birefringence associated to these structures can have interesting consequences that will be discussed in the next sections.
Two aspects require specific attention at this point for type II. As visible in Fig. 2, at low writing speeds a quasi-circular uniform core appears inside the structure cross section. Corroborated with the information in Fig. 1, this represents a high index core surrounded by a birefringent structured cladding where the layer spacing is approximately 250 nm (in particular conditions it can vary between 200 nm and 270 nm), the structures being oriented perpendicular to the driving field. This is particularly seen for linear polarization, while dot-like structures are visible for circular polarization [Figure 2(g–i)]. Considering the direction of translation in the longitudinal traces, the formation of birefringent regions (the head) leads in the scanning procedure as these are first generated, being followed by the high index trail visible in Fig. 1(b,c). This indicates that the previously structured central regions are erased and re-modified by the high index trail, suggesting the achievement of high temperatures in the multipulse domain. Reversibility, movability, and erasure of laser photoinscription effects even at high energies leading to void formation have been observed in various conditions [25, 26] that involve soften, viscous material. In particular materials this can lead to the complete disappearance of the laser-induced structures. Due to different transverse dimensions associated with the birefringent head and the high index cone in the static structure, the result is the establishment of the high index region in the center, surrounded by unerased nanolayered shells [Fig. 2(a,d)]. This particular geometry supports more efficient guiding (tested with 800 nm light) as long as the injected electric field is parallel to the nanolayers alignment (type II WG). This was previously connected to increased losses at the polarization-sensitive frontier for TM polarized injection as compared to the TE component and field confinement . Efficient guiding was not observed for structures of circular polarization. A second striking observation is that at higher scan velocities (i.e. lower incubation rates) the nanolayers spacing is double (500 nm), suggesting that the gratings develop in steps of λ/n harmonics. Note that in this case the area is fully covered by these layers [Fig. 2(c,f)]. The guiding efficiency of the longitudinal traces as a function of the scan velocity is indicated in Fig. 2(j), in the conditions where the structure transverse morphology varies from a shell-like appearance [Fig. 2(a,d)] to a disk-like form [Fig. 2(c,f)]. The drop in the guiding efficiency as we follow the transition from type II-WG to type II-NG is evident.
3.2. Nonlinear energy deposition and multipulse effects
As the effect of pulse accumulation is critical to nanograting formation due to the underlying positive feedback involved in the growth, the sequential (low-rate) effect of increasing the pulse number (N) is analyzed below. Figure 3(a) shows static traces induced with a variable number of ultrashort pulses at a constant energy of 1.2 μJ. A single pulse produces a conical region of dominant positive but weak index increase around and ahead the geometrical focus, and a restricted region of negative index change before the focus. In these OB1 focusing conditions, the nonlinear propagation affects the energy redistribution via self-focusing and filamentation. At this specific energy, the self-focusing effect is already visible in the onset of a void-like form  [white dot in Fig. 3(a)] before focus. Increasing the number of pulses leads to a replication of the void at regular positions [27, 28] along the trace, before stabilizing the structure in the trace head position at higher accumulation rate. Though spherical aberration was proposed as a reason for the intensity modulation , in the present experimental conditions, at the depth of 200 μm, this influence is minimal. During this process, before achieving the saturation level, we note the appearance and disappearance of the voids which indicate the possibility to erase laser-induced structures by subsequent irradiation [25, 26]. In the vicinity of the voids or in between (see inset), regions of compacted material with higher positive index contrast are noticed. It is conceivable that, though triggered by a filamentary propagation, in the high N regime additional effects contribute to the positive index contrast. With significant number of pulses per site, birefringent structures form where the initial void serves apparently as a seed event, developing in a region previously affected by weak fluence exposures. Figure 3(b) shows a comparison of transmission, phase contrast and polarizing microscopy of multipulse structures, where a slight birefringence is to be noted in the pre-void area before a large modulated zone develops.
Further information can be gathered by monitoring the preferential regions of energy distribution [Fig. 3(c,d)]. The nonlinear energy transport in the case of a single laser pulse in the irradiated sample was evaluated using a pulse propagation code based on the nonlinear Schrödinger formalism in the slow varying envelope approximation . The formalism described in detail in  analyzes the nonlinear pulse propagation in transparent materials and studies in a time- and space-resolved manner the excitation footprints [Fig. 3(c,d)]. The approach takes into consideration key features of pulse propagation such as self-focusing, phase modulation, and defocusing on carrier plasmas. The laser pulse parameters involved in the simulation are: 170 fs pulse duration (and the corresponding spectral bandwidth), 1 μJ pulse energy, and a theoretical waist at the focus of 0.9 μm.
By comparing the single pulse simulation results with the experimental single pulse effects, several observations can be drawn. Part of them were already exposed in , but we consider useful that some of the conclusions are reminded in the present discussion. According to the scenario in  where the time-resolved exposure is investigated, the focused beam illuminates the geometrical focus only in the first moments of irradiation. There, due to the emergence of a low density plasma but also due to amplification of self-focusing as the momentary intensity increases, a screening effect develops. The energy starts to be scattered away and agglomerates at later times in regions preceding the geometrical point of focusing. The following facts are considered important for the typical appearance of the standard structures.
Firstly, the void formation is due to a maximization of the energy exposure by self focusing [Fig. 3(c)]. A value of a couple of J/cm2 was calculated at the peak located before the geometrical focus at z = 75 μm. Apart of being continuously fed by the incoming light, the exposure in this region seems also prolonged due to the associated moving focus effect, accompanied all along by additional quantities of energy scattered away by the emerging plasma. The deposited energy, allowing temperatures in the vicinity of the softening point , is sufficient to trigger thermal expansion in this restricted zone. The subsequent rarefaction leads to a negative density change . As further pulses are coming on, it appears that it is particularly here where, upon subsequent exposure, nanoscale rearrangements are seeded and evolve. A slight deviation towards the laser beam of the low index region is noticed as an effect of incubation [Fig. 3(a)]. In the saturation region, the multiple microexplosions lead to increased roughness that may initiate field enhancement in the pre-void regions .
However, at and ahead the geometrical focus (z = 75 μm), perhaps less because of nonlinear spectral broadening, but merely due to the fact that this region is illuminated mainly at the beginning of the irradiation due to incipient plasma defocusing, the exposure is less effective and shorter as compared to other regions (though comparable to the initial duration). The intensity is at its peak, clamped at a level below 1014 W/cm2 in the plasma filament [Fig. 3(d)]. It is in this region that the refractive index increase occurs and the nanograting formation is not efficiently supported by the shorter duration of light exposure. This is consistent with previous observations concerning the increasing type II threshold when the pulse duration diminishes .
The spatial decoupling of the high deposited energy zone that corresponds to nanograting formation at increased photon doses from the high intensity region suggests different mechanisms of electronic excitation. The occurrence of collisional electronic multiplication mechanisms as the exposure is prolonged in the birefringent head of the structure was already proposed in . Though usually subcritical densities are reported upon waveguide photoinscription, it is conceivable that, due to the formation of additional seed centers (not necessarily color centers but nano-rugosity and field enhancement effects) in this particular region, the electronic density increases upon multipulse exposure. This way, significant energy can be locally deposited in nano-domains, leading to local phase transitions and material redistribution via viscoelastic flow as indicated in . As a side observation, a similar phenomenon visible on surfaces (ripples) is usually associated with an intermediate fluence regime, in between melting/modification onset and macroscopic ablation. We note however that these single-shot based conclusions should be taken with precautions when multishot regimes are involved. Incubation effects and modification of absorption cross-sections, but, as well, perturbative effects of the already established index structures on the incoming light increase the difficulty of the discussion. We note for example the onset of higher index regions superposed on the initial filament zone, the various emission regions (Fig. 1), or the slight birefringence already visible in Fig. 3(b) before the dominant low index area is formed. Not all void regions acquire birefringent properties [Fig. 3(b)]. These observations could involve different dynamics between thermal and mechanical contributions to index changes and may lead to different spatial energy redistribution that requires quantification. This puts forward the challenge of defining the energetic and structural differences between the birefringent and the isotropic regions.
3.3. Spectroscopic investigation of laser-induced structures
As different types of index changes were observed, one of the important questions refers to the nature of the corresponding structural or electronic modifications and the scale of the physical transformation (i.e. localized defects or a macroscopic transition to the liquid phase and beyond). To that scope, laser spectroscopy [30–33] is a powerful method to investigate the electronic and structural modifications in the different refractive index regions discussed above. The investigations we have performed here concern the probability to permanently break Si-O bonds with consequences in forming NBOHC and floating bonds.
The spectroscopy results are given in Fig. 4 were the photoluminescence (PL) features around 650 nm were observed. They usually imply O link breakage involving NBOHC. First, Fig. 4(a) shows the structure transverse cross-section luminescence map for type II-WG traces (after prior polishing) corresponding to a distribution deriving mainly from NBOHC [500–800 nm spectral domain], obtained using a confocal arrangement. Typical PL spectra in the 500–800 nm range (488 nm excitation wavelength) are given in Fig. 4(b). The used 488 nm excitation light does not resonantly excite the 1.9 eV NBOHC band and may slightly involve the low energy wing of the 4.8 eV band or prior stages of excitation transfer via oxygen deficiency centers. Furthermore, the subsequently observed photoluminescence centered at 650 nm is affected by local density modifications as indicated below, which modify the inhomogeneous broadening of optically active centers. The spatially modulated region shows a distorted luminescence band that can be interpreted as deriving from strained broken bonds , without ruling out surface effects and eventual water/hydrogen influences. The NBOHC yield is several times higher than in the central core, showing an agglomeration of broken oxygen bonds in the nanostructured areas. Indication of oxygen deficiency in the narrow planes was given before [  and references therein], suggesting also possible Si agglomeration [35, 36], but also concentration of oxygen vacancies in damaged regions . It is hence presumable that the preferential energy deposition and possible field enhancement in the birefringent regions lead to noticeable bond breaking. We note nevertheless that the spectroscopy results reflect stable permanent changes, being acquired several weeks after exposure. Reddish luminescence can be observed also in the guiding parts for several minutes after irradiation, readily excitable by HeNe 633 nm laser radiation. This implies that a transformation mechanism occurs for NBOHC in the high index region, facilitated by an electronic background that requires further investigations. A detailed spectroscopic report will be given in a future publication focusing of defect precursors, generated oxygen deficiency centers and multiple Si-Si bonds [36, 38, 39].
At the same time, the degree of disorder in the various regions was monitored by Raman spectroscopy as well as the onset of atomic-scale ordered structures. For example, the D2 vibrational ring mode at 606 cm−1 is indicative in certain conditions of a variation of the three-member rings concentration [31,37,40] that may affect as well the matrix polarizability . A strong D2 increase is observed, accompanied by a shift in the ω4 TO band (1063 cm−1) in the homogeneous central zone [Fig. 4(c)]; sign of material compaction via a thermodynamic path.
3.4. Optical properties
Summarizing the observations above related principally to the morphological appearance of the various traces and their optical properties as a function of the photoinscription conditions, the main conclusions can be grouped in the following categories.
Low photon dose corresponds to a homogeneous weak refractive index increase (Δn = 10−4 – 10−3, depending on the accumulation rate) with isotropic properties. In the traces formed under these conditions, different injected polarization components (verified at 800 nm and 633 nm for vertical and horizontal directions with respect to the photoinscription geometry) are guided, provided that no deviations from the circular symmetry of the processing spot are present.
Higher energy doses lead to the formation of nanostructured domains with subwavelength spacing and rich in broken bonds that, upon scanning, can cover partially or fully the irradiated areas. In the case where the covering is partial, the anisotropic guiding traces at high photon doses consist of a homogeneous core and a birefringent cladding. If the core acts as a waveguide for all polarization components, the birefringent cladding ring changes the effective index. As the birefringence is negative, for maximum transmission the guided polarized radiation (e.g. at 800 nm) has to have the electric field aligned parallel to the nanoplanes, sensing thus a higher effective index as compared to the polarization perpendicular to the planes. A polarization sensitive guiding function emerges . The guiding properties of the laser-induced type II-WG structures are not particularly efficient (propagation losses in the range of 10 dB/cm, scan velocity dependent) as compared to type I case (below 0.5 dB/cm), but this is conceivable in view of the smoothness of the boundaries. The propagation losses vary with the pulse duration as the morphological material changes may be affected. The trace morphologies and their performances as a function of the pulse duration are given in Fig. 5. The lower propagation losses (6 dB/cm) were found for pulse durations between 130 fs and 400 fs in this high power regime [Fig. 5(a)], where, in the trace morphology [Fig. 5(b)], the core appears to be well delimited. We note however that, due to dispersion, the value of the pulse at the interaction region may be shorter than the one measured before the interface (the given pulse values are corrected for objective dispersion), closer to the expectation that the shortest pulses will deliver the lowest losses, but still with a residual negative chirp. This also appears to be linked to a dimensional effect in the structure symmetry [Fig. 5(b)] due to perhaps initial asymmetries in the laser pulse. The third type of structure presents a full covering with nanolayers with periods of multiple of λ/2n, leading to birefringent properties (see higher speed traces in Fig. 2). The subwavelength modulation in type II-NG determines an optically anisotropic nature of the structure  with strong polarization sensitivities in transmission for specific orientations of the electric vector.
These types of polarization sensitivity can further develop the field of applications. In spite of the propagation losses which depend on the trace dimensions and the corresponding cross-sections, interesting effects can be obtained when the two types of guiding structures are combined, putting together isotropic and anisotropic functions. A first example of an optical router was given in . The combination of type I and type II-WG traces can be used to fabricate polarized or polarization maintaining waveguides, showing equally the potential to induce controlled phase retardation with low losses. An example of this is given in Fig. 6(a–c) which indicates the possibility of rotating the polarization. The length of the type II structure was designed to perform a quarter-phase operation at 633 nm, ensuring an efficient transmission of light. Despite the different propagation efficiencies along the fast and slow axes corresponding to the birefringent cladding, we do not expect severe selective attenuations for the lengths involved (170 μm), resulting in a waveguide quarter wave plate (QWP) function.
In case of type II-NG however, in spite of their transmissivity at full coverage, these traces are not guiding. Nevertheless they can perform the function of an index wall for external waves incident at grazing incidence. The form birefringence associated to this morphology depends on the dimensions of the structures and on the period of the nano-pattern. Using illustrative values of the modulated structures (maximum index 1.45, minimum index 1.0, a period of 500 nm, and a layer width of 30 nm, where the index contrast is taken from [1, 2] to be at the extremes of the given domains) the index changes are δne = −0.03, δno = −0.015. Higher values are obtained when spacing increases. This indicates that stronger reflective properties are obtained for polarizations perpendicular to the nanolayers for external radiation at quasi grazing incidence. Particularly important in these cases, a difference of several degrees between the angles for total reflection can be noted for different polarizations (s, p), indicating domains where only one polarization is reflected with maximum efficiency. A calculus of the optical properties showing this effect can be seen in Fig. 7(a). In addition, directional scattering effects may take place according to the polarization-dependent distribution of incident wave vectors with respect to the grating vector, as in the case of tilted Bragg gratings .
As the optical properties are polarization-selective especially at grazing incidence, optical systems can be imagined taking advantage of these characteristics. Consequences are visible when 3D structures are fabricated. It was already indicated  that light can be confined in 3D structures even when the spacing significantly exceeds the radiation wavelength, though with losses. Here we further explore the light transport and confinement properties in structures of predefined geometries; octagonal and square, as a function of the fill factor and the orientation of the self-arranged nanolayered domains. A first example is constituted by a 3D octagonal arrangement of type II traces as seen in Fig. 7, with its conceptual design depicted in Fig. 7(b). Using different scan speeds, a smooth transition from type II-WG to type II-NG is generated in the forming traces and different 3D structures were built with various relative coverings of nanolayers [Fig. 7(c)]. As here the writing polarization is vertical, the nanogratings are oriented horizontally, maintaining a direction perpendicular to the driving field. The excitation is made on axis with focused laser radiation at 800 nm using a numerical aperture of NA=0.29. Observing the guiding properties of the array, the following statement can be put forward. Light is confined in the array in particular conditions. In case of 3D arrangements constructed of type II-NG (high scan velocities) the light stays within the array when the injection polarization is perpendicular to the nanogratings. Due to the birefringent properties as discussed above, the polarization of the electric field normal to the nanogratings is better reflected by the segmented wall as a consequence of a higher effective index under grazing incidence.
In case of a similar structure made of type II-WG a different pattern is noticed. If, due to the longitudinal non-uniformities of the traces, light couples into the guides, the horizontal polarization propagates in the individual traces due to a higher effective index. The vertical polarization leaks out from the individual traces. Concerning the collective transport in the array, as in the previous case, the light injected at the center of the array with a vertical polarization sees a higher index wall than the horizontal polarization. A weak transverse resonance appears within the array which mimics the symmetry of the polarization-selective wall, but not in the traces themselves. However, a non-zero reflection persists for the horizontal polarization. In conclusion, the polarization selectivity as well as the mode spatial distribution can be determined by the fill factor of the nanogratings in the structures, i.e. in this case by the scan velocity.
A question may be raised on how this selectivity evolves if the nanogratings in the various traces composing the array are oriented in different directions. An example is given in Fig. 8 showing a 3D octagonal structure where the orientation of nanogratings is mixed and reciprocally perpendicular, forming crossing rectangles of similar orientation of the nanolayers. The scan speed employed in this case, 50 μm/s, ensures a dominant covering with nanogratings, however a small homogeneous core may persist. Particularly, due to the writing procedure that translates structures similar to Figs. 1(a–c), the traces present at the output a small positive index region of few tens of microns. That implies also, that similarly to above, light is slightly coupled into the waveguides and the two particular modes are at work, nevertheless with different efficiencies. The polarization oriented perpendicular to the corresponding structures remains trapped (i.e. only the polarization normal to the lines experience high reflection), the other component leaks out. If only the structures with similar orientation (2x2 traces) would be preserved in the same geometry, the light would still be trapped in the array, but the confinement in one direction would be accompanied by a leak in the other direction due to the asymmetry.
A last example concerns a 3D trace arrangement with a square section form. As a function of the orientation of the injection field, the mode spatial distribution changes, mapping the reflective properties of the structure. As reflection components for both polarizations may persist, though with different efficiencies, particular “resonance” patterns can be transmitted as seen in Fig. 9(a–c). A rotation of the structure with π/4 performs as well a rotation of the mode. Concerning the transport properties, we note a certain length dependence according to which the mode changes along the axis, before stabilizing at a symmetry-matching form [Fig. 9(d–h)].
In conclusion we have demonstrated that the energy deposition largely determines the structural transitions leading to refractive index changes and optical anisotropies. High energy doses and prolonged exposure lead to the self-arrangement of the material in nanolayers where stable molecular broken links are present in excess. Polarized guiding and phase retardation were shown. 3D arrangements of birefringent structures lead also to polarization dependent light transport properties. The properties can be tailored using different coverings of nanostructured domains. Examples involved octagonal and quadrilateral forms of light confining patterns.
Authors K. Mishchik and G. Cheng, contributed equally to this work.
References and links
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