1. Introduction

Femtosecond laser processing of transparent glasses offers selective material modification to induce refractive index changes with (Type II or Regime 2) or without (Type I or Regime 1) the presence of nanograting structures [1,2]. Refractive index changes have also been associated with the formation of anisotropic nanopores [3]. These laser interactions underpin widespread applications today in three-dimensional (3D) structuring of integrated photonic and optofluidic devices [4,5]. The self-organized assembly of nanograting structures under multiple pulse exposure [6] imposes a polarization and stress anisotropy [1], facilitating polarization control [7] either by intrinsic [8] or stress birefringence [9–11]. Nanogratings thus enable denser optical data storage [12] and fabrication of polarization elements in photonic circuits [8–11,13–17] with quantum optic applications [9,13–15]. Moreover, Hnatovsky et al. introduced selective chemical etching, guided by the geometry of the nanogratings [18], to enable 3D structuring of micro/nano-fluidic and micro-mechanical devices [19,20].

Fundamental studies on the laser formation of nanograting structures has shed light on practical means for tailoring of the phase retardance to improve optical properties, for example, by tuning laser parameters [21–24] such as pulse energy [13], repetition rate [25], pulse front tilt [26] or multi-scanning [21]. However, the above nanograting studies have been based only on traditional Gaussian beam shapes. Cheng et al. have recently reported on the formation of nanogratings inside of fused silica that followed the shape of a Bessel beam as generated by an axicon [27]. Recently, spatial light modulators (SLM) have emerged as a powerful tool to manipulate the laser interaction volume inside of transparent materials by shaping the incoming beam into various forms [28,29]. Nevertheless, the influence of the focused beam shape on the size and form of the nanograting volume and the resulting birefringence and stress field is an unexplored opportunity to manipulate the macroscopic optical properties of glasses in new directions. Moreover, a larger and shaped focal volume facilitates a flexible 3D shaping of polarization-based optical devices inside of bulk glasses while also enabling higher speed and parallel processing.

In this paper, the possibility of 3D shaping of the nanograting volume has been explored in fused silica glass by scanning exposure of Gaussian beams shaped with diverging (positive) and converging (negative) conical phase front. When focused into the glass, such beams had been transformed into a doughnut shape profile at the Fourier plane. However, higher intensity interaction had been identified at the position of Gaussian-Bessel like filaments that stretch above or below the focal plane to permit tuning of filament length by the conical phase front angle [30]. The further influence of multi-pulse scanning exposure in [31] had demonstrated a control over waveguide mode profile and loss, but without examining the underlying assembly of nanogratings and associated birefringence properties. In the present work, ion-milling and scanning electron microscopy confirmed the assembly of nanogratings over the full length of the laser filament, thus verifying large volume parallel writing. The influence of the conical phase front on the optical and mesoscopic properties of the structure, such as birefringence, optical path difference, dichroism, and nano-grating orientation was evaluated. An unexpected asymmetric response of the structural shape and resulting birefringence for positive and negative conical phase fronts had been assessed by nonlinear optical simulations to arise from differences in intensity clamping effects according to pre- or post-focusing of the filament relative to the doughnut beam position. The results confirm that the nanograting volume will assemble to the spatial shape of the laser beam focus, providing another degree of freedom in manipulating the induced birefringence effect in the volume of transparent glasses. Moreover, an anomalous rotation of the nanograting plane orientation outside of the normal to the polarization axis of the laser is reported for the first time.

2. Experimental methodology

Nanograting modification tracks were formed inside of fused silica glass (Nikon; NIFS-S) with a frequency-doubled, ytterbium-doped fiber laser (Amplitude Systems; Satsuma). The system generated pulses of 250 fs duration at 515 nm wavelength. The Gaussian beam quality was $\textrm{M}_x^2\; $ = 1.14 and $\textrm{M}_y^2\; $ = 1.01. The laser tracks were written at 0.4 mm/s scan speed and 500 kHz repetition rate, using parameters optimized previously for offering high contrast chemical etching [32]. The laser pulse energy was varied in the range of 78 to 434 nJ. Beams with conical phase fronts were generated by an SLM (Hamamatsu; X10468-04) and relayed through a 4f optical arrangement (Fig. 1(a)) onto the back focal plane of an aspherical lens (0.55 NA, Newport; 5722-A-H) as described previously [30]. A beam diameter (1/e²) of 1.86 mm was selected for the SLM image plane (Fig. 1(a)) to underfill the lens (0.20 NA) and to minimize the influence of the surface aberration effect. The laser beam waist and depth of focus (DOF) were calculated to be ∼1 µm (1/e²) and 11 µm, respectively, in the fused silica.

 

Fig. 1. Simplified schematic (a) for inscription of nanograting tracks inside of fused silica with femtosecond laser beams shaped by an SLM into a conical phase front. Cartoon drawing of modification volume (b) assembled by parallel scanning of the laser tracks (+x direction) and the anticipated orientation of nanograting planes (c) when the writing laser polarization is parallel with the writing direction (+x direction). Simplified schematic (d) for polarization probing of birefringence induced by the laser modification in the sample.

Download Full Size | PDF

A systematic study of the concave ($\theta $ < 0) and convex ($\theta $ > 0) conical phase front and their influence on nanograting structures was carried out by imposing complementary conical angles in the range of – 0.69 mrad $\le \theta \le + 0.69{\; }$ mrad on the incoming Gaussian beam at the SLM surface (Fig. 1(a)). These conical angles were magnified 2.43-fold by relaying through the 4f imaging system to the back focal plane of the fabrication lens (i.e., SLM image plane, Fig. 1(a)). All angles reported below have been defined with respect to the SLM plane. Large volume modification zones were assembled at 100 µm focusing depth by scanning parallel modification tracks, each of 60 µm length (x-direction in Fig. 1(b)) and offset by 1 µm spacing (y-direction in Fig. 1(b)). The linear array of tracks defined a modification zone of 60 µm by 60 µm area (x-y plane), with thickness defined by the elongated filament interaction length (z-direction in Fig. 1(b)). The potential for directional dependence on laser modification [33] was evaluated by reproducing modification volumes with opposing scanning directions (i.e., +x and -x, Fig. 1(b)). Manipulation of the nanograting orientation by laser polarization orientation was also studied by forming modification zones with linear laser polarization aligned parallel (x axis) and perpendicular (y axis) with respect to the writing direction, yielding nanograting planes with orientation expected in the y and x directions, respectively (Fig. 1(c)).

The optical and mesoscopic properties of the laser-formed structures were characterized by optical microscopy, by polarimetry and by scanning electron microscopy.

A cursory evaluation of the birefringence induced by the laser modification volume was provided with a commercial polarimeter (ilis Strainmatic, Model M4). The polarimeter measured the locally resolved optical path difference of horizontally or vertically linear polarized light at 587 nm wavelength with 5 µm resolution without accounting for diattenuation. In the sample, this optical path difference arose from the cumulated anisotropic response of the nanograting along the transmission direction. Since the measurement precision was limited due to the neglection of diattenuation in the measurement algorithm, the alternative arrangement in Fig. 1(d) was used to obtain more precise birefringence values.

In Fig. 1(d), a Helium Neon laser of 633 nm wavelength was followed with a linear polarizer and a half-waveplate to continuously vary the input polarization orientation as defined by angle, $\alpha $. The laser light was focused with a 4 ${\times} $ plan achromat objective lens (Olympus, 0.10 NA) to ∼16 µm spot size (1/e² radius) to probe the region of interest in the sample, and then imaged with 20 ${\times} $ plan achromat objective lens (Olympus) onto an iris diaphragm, used to crop the probing zone in the central modification area. The beam was then filtered with a rotatable linear polarizer before entering the powermeter. For each input polarization angle, $\alpha $, two values of transmission, ${T_{uncrossed}}(\alpha )$ (when the polarizer after the sample is parallel to the input polarization) and ${T_{crossed}}(\alpha )$ (when the polarizer after the sample is perpendicular to the input polarization) are measured. The sum of the transmittance through the polarizer in both directions yielded the total transmission, $T(\alpha )= {T_{uncrossed}}(\alpha )+ {T_{crossed}}(\alpha ),{\; }$ that depended on the input polarization through the polarization dependent losses. The maximum and minimum values over the measured data range, $T({\alpha = 0{\; \textrm{to}\; }360^\circ } )$ defined the maximum polarization dependent transmission, ${T_{max}},$ and the minimum polarization dependent transmission, ${T_{min}}$, respectively.

The dichroism was calculated from the maximum and the minimum polarization dependent transmission values as: $D = \frac{{{T_{max}} - {T_{min}}}}{{{T_{max}} + {T_{min}}}} = \frac{{\Delta T}}{{{T_{max}} + {T_{min}}}}\; $. To retrieve the retardance, $\delta$, and the orientation of the fast axis, ${\alpha _0},$ from each modification volume, the crossed transmission, ${T_{crossed}}(\alpha ),$ was fitted to the equation:

Prior to scanning electron microscopy (SEM), the samples were polished to bring the modification zones to the surface. The samples were etched with 1% HF acid for 90 s to open the nanograting planes, and then coated with carbon to reduce charge accumulation during SEM imaging. End facet SEM images were directly recorded from the polished surface (z-x plane) while focused ion beam milling (FIB) into the underlying volumetric structure was used to facilitate SEM imaging of the y-z plane.

The analysis of the structure formation was further supported by simulations of the focal beam shape of laser as well as by the laser propagation dynamics. An optical Fourier propagation simulation of the Gaussian beam having a conical phase front was first carried out without the nonlinear light-matter interaction by following [31,35]. This simulation included surface aberration, which was found negligible for 100 µm focusing depth and 0.20 NA. The dynamics of the electromagnetic field in the sample was then generalized to the nonlinear case [36] by building on the results of the linear simulations as initial conditions. Briefly, the model accounted for propagation and dissipation of a single pulse exposure of femtosecond light in glass, where different nonlinear mechanisms were simultaneously at work. The mechanisms included focusing by the Kerr effect, nonlinear absorption by multiphoton ionization, and defocusing by plasma [37], but neglected temporal dispersion, avalanche photoionization and accumulation effects of multiple pulses at any temporal scale. Whereas for Gaussian beams the optical propagation in the nonlinear perturbative regime can be theoretically described for example using variational theory [36], a numerical simulation of the scalar model from Ref. [36] was required here to account for the transformation between doughnut and Gaussian-Bessel like beams in the focal interaction zone and to interpret the shape of permanent modifications [38]. The surface aberration was found to be insignificant and was neglected in the nonlinear modelling. Details of both simulation models can be found in the Supplement 1.

3. Results and discussion

3.1 Optical microscopy

An optical microscope image (z-x plane) of a representative sample of laser modification zones is shown in Fig. 2(a) for the progression of conical phase front angles varying from −0.60 to +0.60 mrad and applied with a fixed pulse energy of 332 nJ. For the case of the unmodified beam shape ($\theta = 0$ mrad), a nearly uniform modification has been formed across the 60 µm wide zone of overlapping tracks (y-direction Fig. 1(b)), without resolving any line-by-line features on the 1 µm track offset. The vertical modification was also relatively uniform, seen centered near the focal plane at 100 µm depth with a vertical thickness of 35 µm. This modification height was 3.2 ${\times} $ larger than the DOF (11 µm) as expected by linear optical simulation (Fig. 2(c)). The height and contrast of the modification zone both increased with increasing pulse energy from a modification threshold (<43 nJ), as confirmed with morphological observation of an isolated scanning track [32]. A thin dark zone of modification was also formed along the top surface layer but without revealing line-by-line features in Fig. 2(a). Evidence of micro-cracks, surface ablation or other forms of damage were not observed up to the maximum 434 nJ pulse energy applied here.

 

Fig. 2. A representative optical microscopy image of laser modification zones (a) in fused silica with nanograting structures inscribed with 332 nJ pulse energy and 0.4 mm/s scanning speed for various conical phase front angles (values on the horizontal axis). Simulated longitudinal intensity profiles for complementary conical phase front angles of $\theta $ = –0.51 (b), 0 (c), and +0.51 (d) mrad. Simulated transverse intensity profile of the doughnut profile (e), enhanced by 16 ${\times} $ with respect to the longitudinal profiles. The white dashed line indicates the 100 µm paraxial focus. The black line marks the glass surface. Laser propagates in + z direction. The 20 µm scale bar applies to (b) to (d).

Download Full Size | PDF

The influence of concave (negative angle) or convex (positive angle) conical phase fronts were associated (Fig. 2(a)) with upward or downward shifts, respectively, of the modification zones with respect to the position (100 µm depth) of the unmodified beam ($\theta = 0$ mrad). The center positions had shifted monotonically, moving nearly symmetrically upward by 52 µm or downward by 48 µm for the respective conical angles of –0.60 mrad and +0.60 mrad. However, the thickness of the modification zones increased asymmetrically, rising to 73 µm and 41 µm for symmetrical changes of the conical phase front angle to – 0.60 mrad and +0.60 mrad, respectively. This asymmetry may be more pronounced for the case of –0.60 mrad where the modification zone had reached the surface to induced ablation.

A comparison with Fourier propagation modelling showed a good correspondence between the shifts and stretching, for example, for – 0.51 mrad angle, where an upward shift of 47 µm and a modification thicknesses of 73 µm can be directly compared with respective values of 52 µm and 56 µm (DOF) as extracted from the simulated profile in Fig. 2(b). The largest discrepancies were noted for the positive conical phase front angles which predicted a near-symmetric and inverted intensity profile (Fig. 2(b) versus Fig. 2(d)). For +0.51 angle, the observed 44 µm downward shift and elongation to 38 µm thickness deviated from an intensity profile (Fig. 2(d)) predicted to shift downward by 47 µm and stretch to a DOF of 52 µm. A deeper investigation of the nonlinear optical interactions was necessary to account for the nonsymmetrical responses observed here for positive and negative angles. The nonlinear interactions hidden in the low-intensity doughnut profile (i.e., Fig. 2(e)) forming at the focal plane of the lens will be shown to significantly degrade the nonlinear interaction of the filaments forming at a lower depth for the positive signs of conical phase front angle.

3.2 Nonlinear simulation

The asymmetry of the modification length as observed between the positive and negative angles of conical phase front in Fig. 2(a) were evaluated according to differing nonlinear effects arising on the light propagation according to positioning of the Gaussian-Bessel like filament before (negative conical angle) or after (positive conical angle) the doughnut-shaped focus (Fig. 2(e)). Accounting for the laser wavelength and bandgap of fused silica, the nonlinear absorption, $\mathrm{\alpha }(\textrm{I} )= {\mathrm{\beta }_4}{\; }{\textrm{I}^3},\; $ in the propagation model was tuned to 4-photon ionization, with the coefficient ${\beta _4} = 2 \times {10^{ - 50}}{({{m^2}/W} )^3}{m^{ - 1}}$ calculated from the Keldysh formula (see Supplement 1 for details) [39]. The resulting fluence profiles for single pulse exposure are plotted in Fig. 3.

 

Fig. 3. Numerical simulations for nonlinear propagation of single pulse excitation in fused silica. False color distribution of laser fluence on the longitudinal cross section of the sample for three different conical angles (as labelled in each panel) for a pulse energy of (a) 5 fJ and (b) 300 nJ to represent propagation in the linear and nonlinear domains, respectively. The beam propagates downward through the input interface at z = 0 µm and the paraxial focal plane at 100 µm. (c) The longitudinal fluence plotted along the symmetry axis of laser propagation coordinate (r = 0 line in a and b), z, for pulse energy increasing from the linear domain (left panel) to 700 nJ (right panel). Each frame presents profiles varying with conical phase front angles of $\theta $ = −0.7 (blue), −0.35 (orange), 0 (green), +0.35 (red) and +0.7 (magenta) mrad.

Download Full Size | PDF

Figure 3(a) presents fluence distributions expected in axial views of the focal volume at exposure below the onset of nonlinear optical interaction (i.e., 5 fJ pulse energy) and for conical phase front angles of $\theta $ = – 0.7, 0, and +0.7 mrad. The fluence distribution closely aligns with the Fourier propagation simulation, for example, shown in Fig. 2(b)-(d) for a slightly smaller angle range. The axial fluence profile appears to shift similarly by −42 µm and +40 µm from the focal plane or to stretch symmetrically to 50 µm and 50 µm filament length, respectively, with either positive ($\theta $ = +0.7 mrad) or negative sign ($\theta $ = −0.7 mrad) changes in the conical beam angle, respectively, in contrast with a 7 µm length for the unmodified beam ($\theta $ = 0 mrad).

Figure 3(b) unveils the strong influence of nonlinear interactions for the same sequence of conical phase front angles applied at a pulse energy of 300 nJ. For the unmodified Gaussian beam profile ($\theta $ = 0 mrad), the upward skewing and angular distortions in the fluence profile (Fig. 3(b) relative to 3(a)) depict an interplay between Kerr lensing, plasma defocusing, and multiphoton ionization but without significantly influencing the peak exposure zone. The high fluence zone had expanded only marginally from the diffraction limited beam waist by plasma defocusing, but otherwise remained contained in a narrow vertical interaction zone (z = 90 to 115 µm, FWHM) positioned within several microns of the paraxial focal plane (z = 100 µm).

In the case of a negative conical phase front ($\theta $ = – 0.7 mrad), the high field zone in the nonlinear domain (Fig. 3(b), left panel) had been largely confined into a narrow filament shape of 1 µm diameter (FWHM) and z = 0 to 75 µm length as predicted for the case of linear propagation in Fig. 3(a) (left panel). A somewhat stronger and modulated fluence profile is noted (Fig. 3(b), left panel) near the input interface (z = 0 µm) relative to the linear case (Fig. 3(a), left panel). The simulation thus supports an elongation of the laser modification zone into high aspect ratio filaments when inducing negative angles on the conical phase fronts.

The 75 µm filament length in Fig. 3(b) (left panel) corresponds well with the observed 73 µm thicknesses for the morphology zone (Fig. 2(a)) formed with similar laser parameters (i.e., $\theta ={-} 0.60{\; \textrm{mrad}}$ 332 nJ pulse energy). The simulation further showed an insignificant fluence arriving inside of the doughnut focal zone (Fig. 3(b), left panel) as otherwise observed at the ∼8 µm radius position of the focal plane (z = 100 µm) in the linear simulation plot of Fig. 3(a) (left panel). Intensity clamping and other nonlinear dissipation and propagation effects arising by focusing first into the higher positioned filament zone (z = 0 to 100 µm) has precluded appreciable laser energy from converging into the doughnut. The resulting modification was thus restricted only to the filament zone (z = 0 to 75 µm) justifying the absence of laser induced structures forming at the paraxial focus as observed in Fig. 2(a) for all negative values of conical angle. The further influence of multi-pulse accumulation effects and the assembly mechanisms of the nanograting or other structures cannot be anticipated by the present model.

In sharp contrast, the opposite symmetric case of a positive conical angle with +0.7 mrad (Fig. 3(b), right panel) had predicted a notably stronger interaction fluence arising in the doughnut (∼8 µm radius, z = 100 µm). Consequently, the nonlinear phase modulation and nonlinear absorption due to the doughnut had distorted the further beam propagation and clamped the maximum intensity available to the filament forming below the ring. However, the highest exposure remained inside of the filament zone, with the position of peak fluence now shifted slightly upward and concentrated into a narrower depth of high fluence relative to the linear case (Fig. 3(a), right panel). The modeling thus supports the formation of morphological zones in the filament zone and not the doughnut, but with filament elongation curtailed by a strong doughnut interaction that remains below the threshold for permanent material modification. The 23 µm thickness of modification observed in Fig. 2(a) for exposure by a similar conical angle (θ = +0.7 mrad) and pulse energy (260 nJ) aligns well with the high exposure zone stretching over z = 140 to 170 µm for fluence at 75% of the peak value in Fig. 3(b) (right panel).

The asymmetric beam distortions arising differently along the symmetry axis (r = 0) are better exemplified for the varying conical phase front angles (θ = −0.7 to + 0.7 mrad) as plotted in Fig. 3(c). The fluence profiles first rise up with symmetric distributions as plotted for the linear case (left panel) and give way to the distorted distributions shown for the highest exposure case of 700 nJ (right panel). Up to 5 nJ exposure, the longitudinal fluence envelope is observed intensifying, elongating, and shifting away from the focal plane (z = 100 µm) in symmetric profiles for increasing of both negative and positive angles. The onset of appreciable multi-photon ionization and other nonlinear effects is noted at a pulse energy of 50 nJ as manifested in a strong clamping of the maximum fluence exposure beginning at ∼0.95 J/cm² regardless of the position along the symmetry axis or a further 14-fold rise in the exposure to 700 nJ. This 50 nJ exposure coincides closely with the pulse energy threshold of 43 nJ observed for the permanent modification of fused silica. For negative conical angles, the nonlinear propagation model increases the portion of inward light bending compared to the linear case due to the self-phase modulation, the nonlinear absorption, and their interplay along a conical phase front. The result is a moderate intensification of the filament zone ahead of the focal plane, lengthening and flattening the filament profile over the low-energy case (e.g., 500 nJ versus linear for $\theta ={-} 0.7 \textrm{mrad}$).

For positive conical angle, the filament zone forming below the focus is influenced differently. Above 50 nJ, the nonlinear interactions arising first in the doughnut zone (i.e., Fig. 3(b), right panel) results in a reduced exposure in the filament, leading to a ∼ 20% reduction of the maximum fluence exposure to ∼0.75 J/cm² (Fig. 3(c), positive θ) in contrast with the negative angle cases. The phase modulation had further skewed the high exposure zone to concentrate into the front portion of the filament, and possibly result in a narrowing in the depth of the modification zone relative to the profile of the linear case as noted in Fig. 2.

The beam propagation modelling (Fig. 3) has thus followed the nonlinear effects of Kerr lensing, plasma defocusing, and multiphoton absorption to identify the underlying mechanisms distorting the symmetry in filament modification structures (Fig. 2(a)), when generated with symmetric conical phase fronts of positive and negative angle. With analogy to a saturable absorber, fluence clamping [37,40] limited the maximum level of fluence exposure available with increasing pulse energy regardless of the conical angle applied to form a filament-shaped interaction zone. Moreover, the self-phase modulation and clamping gave rise to a further elongation of the filament when the conical angle was negative (Fig. 3(c)). For positive angles, the pre-focusing through the doughnut resulted in a stronger influence of fluence saturation and phase modulation effects, leading to a relative weakening and narrowing of the fluence profile to that provided in the linear or negative angle cases (Fig. 3(c)). Additional results showing the behavior in time of light can be found in Section 5 of the Supplement 1.

3.3 Nanograting morphology

Selected samples of laser modification zones were processed and evaluated on facet views (z-x plane) by SEM, yielding images as shown in Fig. 4. Nanograting formation was confirmed to align perpendicular to the laser polarization and fall inside of the modification boundaries as observed optically (i.e., Fig. 2(a)). Using Fourier transformation, the predominant grating periods were found to lie in the range of 120 to 240 nm, depending on the inscription parameters used. This range encompasses the predicted value of $\frac{\lambda }{{2n}} = 176\; nm$ for fused silica (refractive index n = 1.46) as based on the nanoplasmonic model for nanograting formation [20] . Generally, a wide variance of the period has been reported that further depends on the inscription parameters [25,41,42].

 

Fig. 4. Representative SEM images of nanograting structures on moderate (a-c) and high (d-f) magnification scales, recorded from laser modification zones formed with pulse energy of E = 332 nJ, scanning speed of 0.4 mm/s along the x axis, polarization along the x axis, and varying conical phase front angles (as marked above image). The viewing face is the x-z plane with the laser directed along the z axis. The vertical nanograting thickness (a-c) conform with the modification zones observed optically in Fig. 2(a) (note the nanograting structure extends beyond the image size for $\theta $ = −0.51 mrad). The images were tuned to highlight visual contrast. The brightest zones are artefacts of charge accumulation during SEM recording.

Download Full Size | PDF

A thick layer of nanograting modification created with a negative conical phase front angle of $\theta $ = –0.515 mrad is shown in Fig. 4(a), with a zoom into the structure given in Fig. 4(d). Highly contrasting gratings of 210 to 270 nm period are noted for a moderate 332 nJ pulse exposure, aligning perpendicularly to the laser polarization axis along x. The nanograting cross-section shows a highly uniform morphology from top to bottom, following the elongation of the focused laser by the conical phase front. The reference case of unmodified beam exposure (Fig. 4(b)) at $\theta $ = 0 mrad conical angle presents a disordered grating structure with shorter grating planes that is typically observed in the head of nanograting modifications created with Gaussian beams (see Ref. [42]). Hence, the axial stretching of the beam for the $\theta $ = −0.51 mrad case may be understood to spread the same laser energy over larger areal exposure, resulting in the formation of pristine nanogratings (Fig. 4(a), with a closeup given in Fig. 4(d)) without overexposure. For positive conical phase front angles, the nanograting volumes did not expand vertically as expected by the linear optics simulations (Fig. 2(d)). For $\theta $ = +0.51 mrad angle, the nanograting structure (Fig. 4(c)) was mostly confined within the shortened interaction zone as observed by optical microscopy for the same positive conical angle (Fig. 2(a), $\theta $ = +0.51 mrad). Without the full stretching, the 332 nJ pulse energy was compressed into a smaller modification volume, causing formation of the non-uniform grating structure visible in Fig. 4(b) and (c), with closeups of the structures given in Fig. 4(e) and (f). Hence, the nonlinear optical simulations (Fig. 3(b)) provided an accurate insight into where energy dissipation arises, and nanograting formation would potentially take place. A balance of laser pulse energy and conical beam stretching was required to generate an optimal intensity for assembling nanogratings uniformly over a larger volume than was possible with traditional focusing of the Gaussian shaped beam.

For linear polarization along the x axis (Fig. 1(a) and (b)), the nanograting planes in Fig. 4 have aligned as expected, parallel with the z axis. However, tilted nanograting planes of 0.3 µm period have also been unveiled on the y-z plane as shown in Fig. 5 for the case of an unmodified beam ($\theta $ = 0 mrad) applied at 168 nJ pulse energy. This anomalous alignment, tilted at 45 $^\circ $ angle from the laser polarization (x axis) has not previously been reported to the best of our knowledge and may represent a new assembly mechanism that we speculate is associated with the cumulative effects of the line-by-line writing. This new grating alignment was not investigated for the conically shaped beams.

 

Fig. 5. SEM image of a laser modification zone showing tilted nano-gratings after opening the z-y plane by FIB. An unmodified Gaussian beam ($\theta $ = 0 mrad) of 168 µJ pulse energy was scanned at 0.4 mm/s speed along the x axis in parallel scans offset on the y direction. The laser propagated along the z direction. A grating spacing of 304 nm is marked by the arrow between the red lines.

Download Full Size | PDF

3.4 Polarimetry

A cursory polarimetry assessment of the laser modification zones with the StrainMatic polarimeter verified a birefringence alignment that faithfully followed the orientation of nanograting planes and laser polarization for all modes of testing. No significant influence on the optical path difference was observed on reversing the writing direction (i.e., +x to –x). The quantitative assessment of birefringence and dichroism by the HeNe laser analyzer (Fig. 1(d) and Eq. (1)) provided the grid of false color images as plotted in Fig. 6 over varying laser pulse energy (78 nJ to 434 nJ) and conical phase front angle ($\theta ={-} $ 0.69 mrad to $+ $ 0.69 mrad). The scanning direction and polarization of the fabrication laser were aligned with the + x direction. The false color graphs present the experimentally determined responses of (a) the optical path difference (OPD), (b) the total transmission loss ($1 - {T_{min}}$), (c) the thickness, and (d) the dichroism, $D$, observed through the full zone of laser modification. A second scale of axial focal elongation (i.e., DOF) was also provided along the top horizontal axis using values calculated in the linear optical domain of Fourier propagation (Section 3.1) for varying conical phase front angle.

 

Fig. 6. False color plots (scaling on right) of optical parameters measured in laser-modified volumes of fused silica: (a) the optical path difference in nm, (b) the total transmission loss (fraction) scaled logarithmically, (c) the thickness of the modification zone in µm, and (d) the dichroism (fraction).

Download Full Size | PDF

In Fig. 6(a), the OPD is generally observed to rise with increasing pulse energy for both positive and negative conical phase front angles up to the maximum investigated exposure of 434 nJ. The overall response was weakest for the case of the unmodified beams ($\theta $ = 0 mrad), yielding OPD values increasing from 45 nm to 74 nm for pulse energy increasing from 167 nJ to 434 nJ. The OPD climbed most strongly for negative conical phase front angles, rising in value from 77 nm to 175 nm over the same energy range for $\theta =-0.51\; \textrm{mrad}$ angle. The highest OPD values were observed when applying the maximum investigated exposure of 434 nJ in narrow angular zones centered at conical angles of $\theta = -0.51\; \textrm{mrad}$ and $+ 0.6$ mrad (positive case) angles. The OPD response was asymmetric on sign of the angle, with converging conical beams ($\theta = -0.51\; \textrm{mrad}$), providing approximately 25% higher OPD. With decreasing pulse energy, the maximum OPD was generated at a decrease value of conical beam angle, for example, yielding an OPD of 147 nm for a pulse energy of 256 nJ applied at $\theta ={-} 0.43\; \textrm{mrad}$.

The polarization independent losses of the modification volumes (Fig. 6(b)) were found to rise with increasing pulse energy and were most pronounced for the traditional Gaussian beam ($\theta = {\; }$ 0 mrad), peaking at 39% for 434 nJ pulse energy. For the maximum pulse energy exposure (434 nJ), modifications created with negative conical phase front angle yielded higher losses than the positive conical phase front angles. The losses improved with increasing elongation to a minimum 17% at $\theta = {\; }$–0.6 mrad.

Figure 6(c) presents the vertical thickness of the modified volumes as determined by optical microscopy, viewed along the z direction (i.e., Fig. 2(a)). For positive conical phase front angles, no clear dependence of the modification thickness on the pulse energy was evident, whilst for negative conical phase front angles, a thickening of the modification was observed. The elongation for positive angles was inhibited by the pre-focusing interaction in the doughnut beam shape (Fig. 3(b), right panel). There is a stark asymmetry in the elongation which only fully develops with negative conical phase front angle. A maximum thickness of 86 µm was measured for $\theta = -0.51\; \textrm{mrad}$ conical phase front angle and 434 nJ pulse energy.

The dichroism data in Fig. 6(d) roughly follow the same trend lines as for OPD data (Fig. 6(a)), rising in value for each angle with increasing pulse energy. The maximum measured dichroism of 35% was obtained with a conical phase front angle of 0.6 mrad and a pulse energy of 434 nJ. The maximal dichroism for positive conical phase front angles was 20% and observed at $\theta = + $0.69 mrad and 434 nJ pulse energy.

Figure 6 clearly leans to a selection of high pulse energy and negative angles of conical phase front to create the thickest modification zones and provide maximum values of OPD and dichroism with minimum loss per inscription layer. An alternate view is presented in Fig. 7 which scales the data in Fig. 6 against the modification thickness (given in Fig. 6(c)) or transmission loss (given in Fig. 6(b)). The normalized data highlight the laser exposure conditions providing the largest volumetric birefringent or dichroic responses regardless of the physical size of modification zones.

 

Fig. 7. False color plots (scaling on right) presenting a normalization of optical parameters of the laser modification data from Fig. 6: (a) the birefringence (b) the transmission loss (fraction) normalized to the modification thickness in µm^-1 scaled logarithmically, (c) the optical path difference normalized by transmission loss in nm/% scaled logarithmically, and d) the dichroism normalized to the nanograting thickness in %/mm^-1.

Download Full Size | PDF

The average birefringence of the modification zones in Fig. 7(a), obtained by dividing the optical path difference (Fig. 6(a)) by the modification thickness (Fig. 6(c)), is more homogeneous over the same range of laser exposures. The rising OPD values for negative conical phase angles in Fig. 6(a) rest more on the elongation of the modification zone than on a fundamental enhancement of the structural birefringence. A modest enhancement of the medium birefringence is noted only for the highest pulse energy exposures at positive conical phase front angles in Fig. 7(a).

Similarly, the normalized loss data as displayed in Fig. 7(b) have flattened relative to the data in Fig. 6(a) to again show that the modification thickness is the major driving factor for strengthening the optical responses. An exception of high loss is noted for high pulse energies (i.e., ≥332 nJ) when applied in a narrow range of small positive angles observed at $\theta$ = 0.0 to 0.1 mrad. The high intensity exposure here attests to a higher scale of material damage and density of scattering defects.

Figure 7(c) shows the OPD data in Fig. 6(a) normalized to the losses of Fig. 6(b), providing a measure of retardation per loss scaled to units of nm/%. A maximum value of this normalized OPD is desirable in optical waveplates to provide the highest amount of retardation with the least amount of loss. The OPD to loss ratio was lowest for cases near the unmodified beam condition of $\theta = {\; }$ 0 ${\pm} $ 0.1 mrad, peaking at 1.8 nm retardation per 1% loss at 0.43 µJ pulse energy. Both diverging and converging conical phase fronts were thus beneficial for scaling up the OPD without inducing losses that are not desired in such femtosecond laser inscribed retardation elements. The highest values OPD to loss ratio of >11 nm/% was found for negative conical phase front angles of $\theta = {\; }$–0.34 mrad.

A normalization of the dichroism data (Fig. 6(d)) to the modification thickness (Fig. 6(c)) is shown in Fig. 7(d) to switch the strong-to-weak asymmetry of dichroic response with respective to the negative-to-positive angles of conical phase front. The highest dichroic densities (∼1.6%/µm) occurred for positive conical angles of $\theta = $ +0.35 to +0.69 mrad and pulse energies of 332 nJ and higher. The graphical data thus indicates that the dichroism of the microstructure of nanogratings created with negative conical phase front angles is intrinsically lower than for the unmodified beam. The larger negative conical angles enable the dichroism (Fig. 6(d)) to accumulate appreciably over the increasing thickness of modification zone.

4. Discussion and summary

This paper presents a facile means of extending nanograting volumes over large micro-optic scale by augmenting the traditional means of overlapping laser scanning tracks with beam shaping control. Conical phase fronts were induced into Gaussian beams to elongate the interaction volume in fused silica. Values of negative conical phase front angle were found to offer the most significant elongation effect and generate net increases to the optical path difference (Fig. 6(a)) and dichroism (Fig. 6(d)) properties by scaling up both the pulse energy and the conical phase front angle. The SEM assessment of laser modification volumes (Fig. 4) verified that the assembly of ordered nanogratings extended through the elongated laser modification zones. Such a volumetric scaling up of the laser writing process with shaped beams permits one to improve processing speed and gain further geometric control over the modification shape.

The linear optical simulations (Fig. 2(b)-(d)) suggested the axial beam elongation should rise symmetrically with increases in either of the positive and negative values of conical phase front angle. However, only the negative conical phase front angles provided an appreciable scaling up of the laser filament length (Fig. 2(a)), enabling a modification over larger volumes of material by a single irradiation scan. In contrast, there was significantly less elongation provided with positive conical phase front angle, even with an increasing pulse energy (Fig. 6(c)). The nonlinear propagation simulation (Fig. 3(b) and (c)) unveiled a significant laser interaction at the beam doughnut, which disturbed the downstream beam propagation and prevented full development into a filament beam shape as was otherwise anticipated from the linear optical simulation.

The negative conical phase front angles were found most attractive for elongating the modification zones (Fig. 6(c)) and boosting the OPD response (Fig. 6(a)). However, the thicker zones also lead to higher dichroism (Fig. 6(d)) and increase in overall transmission loss (Fig. 6(b)). In different view, the beam shaping offered a net gain of the OPD over the loss (Fig. 7(c)) with negative conical phase front angle yielding the largest benefits over the positive ones. When normalizing the data to the thickness of the modification zone, positive conical phase front angles were found more beneficial in generating higher birefringence (Fig. 7(a)) and higher normalized dichroism (Fig. 7(d)) compared to the modifications induced with negative conical phase front angles. The data shows that the present single-layered nanograting volumes can serve directly as retardation elements with only modest losses, when inscribing beams shaped with conical phase front angles. For example, quarter-wave retarders with losses of ∼ 8% are provided at 633nm wavelength for structures formed with 345 nJ energy and θ = −0.5 mrad angle (Fig. 6(a) and (b)).

The reported 45° rotation of the nanograting planes, as noted in the y-z plane of Fig. 5, broke from the firm expectation of orthogonal alignment to the polarization axis (x direction). Such anomalous grating alignment opens opportunities for rotating the birefringence axis or directing chemical etching into directions not readily accessible by the traditional laser writing and polarization control techniques.

The observations clearly point to several benefits of harnessing conical beams to improve control of the shape and size of modification lines, while tailoring the optical properties per volume for a variety of micro-optic application directions. The higher birefringence and lower loss available from positive conical phase front angles are beneficial for meeting the tight packaging requirements in integrated photonics. The large volume modification provided with negative conical phase front angles is otherwise beneficial in speeding processing times. Furthermore, the results show the possibility to independently specify birefringence and thickness values for nanograting volume by a purely electro optical modulation, without changing the beam delivery apparatus. Such decoupling of phase retardation from structural thickness affords polarization and dispersion control in photonic devices, for example, as based upon the Pancharatnam-Berry phase [3]. The groundwork here indicates many more promising opportunities to be expected from future studies that explore other beam shapes or beam deliver options and consider different geometric focusing shapes for creating and integrating discrete and distributed macroscopic birefringent or dichroic volume elements.