1. Introduction

Ultrafast laser generation of volume subwavelength structures [1, 2] is a spectacular phenomenon, appearing as a succession of variable density layers in bulk glassy materials. They are typically spaced by λ/2n, n being the refractive index and λ the writing wavelength. This manifestation has recently acquired significant attention, particularly in the case of fused silica (a-SiO₂). Here the transformation is known as type II and requires more energetic irradiation conditions then usually needed for obtaining smooth refractive index changes. The ability to generate periodic nanoscale organization in the bulk has led to the development of a new set of optical functionalities related to polarization guiding, phase retardation, or multiscale information storage [1–7]. These remarkable functions are related specifically to the characteristics of the embedded nanoscale patterns; a large range of periodicities (Λ=150–500 nm), alignment perpendicular to the laser field, and a polarization dependent negative index variation associated to form birefringence. A typical example of nanostructured volume traces is given in Fig. 1, which depicts low index type II structures [3] [Fig. 1(a)], with the nanoscale arrangement visible in cross-section [Fig. 1(b)], as well as bulk nanogratings induced by radial and azimuthal laser polarization modes [Fig. 1(c,d)].

 

Fig. 1 Typical manifestation of type II traces in fused silica and the underlying nanogratings. (a) PCM trace of type II modifications. (b) Cross-section of the traces showing the nanoscale arrangement (electron microscopy). (c,d) Bulk nanograting patterns induced by radial and azimuthal polarization respectively.

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Although the intimate formation mechanism is still elusive, the nanoscale rearrangement triggered by the laser excitation seems to be determined by the properties of the generated carrier plasmas in terms of density and local temperatures [1,2]. These affect electron oscillations, light coupling in the excited region, and the local fields at the interaction region. All these properties are strongly dependent on the pulse duration, suggesting a control possibility via pulse envelopes. We therefore propose an open-loop method of in-situ real-time observation and control of the volume nanogratings induced by ultrashort pulses with varying forms in a-SiO₂ and discuss several direct effects on the interaction phenomenology. The photoinscription scheme is based on infrared ultrashort laser pulses with variable temporal envelopes via programmable design. The probing approach relies on the diffraction properties of the subwavelength pattern in UV (355 nm) accessing directly their periodicity, with the functional parameter being the writing pulse temporal envelope tailored on a picosecond scale. We note that optical diffraction is a sensitive and rapid method for evaluating periodic patterns [8], providing rapid monitoring of laser-matter interaction processes. We show that the period and the quality of the nanoscale arrangement could be influenced via pulse form, with a minimal periodicity around 0.7 ps. We relate this to the achievement of higher carrier densities triggering optical damage on extended domains, influencing the effective local dose and therefore the entire photoinscription process.

2. Experimental description

Polished fused silica parallelepipedic samples were irradiated with ultrashort infrared (λ=800 nm, spectral bandwidth 8 nm) light pulses with a nominal output pulse duration of 130 fs at a repetition rate of 100 kHz, delivered by an amplified Ti:sapphire laser system. A pulse control unit based on spectral phase modulation permits tailoring the time envelope of the output pulses [9]. The laser beam was focused inside the sample by a long working distance microscope objective (20× Mitutoyo M Plan, working distance 20 mm, nominal numerical aperture NA= 0.42). Beam truncation at the objective pupil imposes an effective numerical aperture of NA_eff = 0.29. The samples are mounted on a XYZ precision motion stage. A longitudinal writing configuration with sample translation antiparallel to the laser propagation axis was used, generating traces of 100 μm length, centered at a depth of 150 μm. An Olym-pus BX 41 positive optical phase-contrast microscope (PCM) images the interaction region in a side-view geometry. Positive index changes appear dark on a gray background, while white zones indicate negative index variations or scattering centers. A second pulse ps microchip laser operating at 355 nm was focused on the traces within a spot of 30 μm at the incidence angle α. The diffraction pattern, equivalent to a Fourier transform of the diffraction source, is recorded on a fluorescent paper screen backing the sample and, after IR filtering, further imaged on a charge-coupled CCD camera. The photoinscribed trace is probed in several locations and the results are averaged. The schematic description of the arrangement is given in Fig. 2, showing a glimpse of the recording setting. The incidence at the dielectric interface gives a value for α (inside material) of 34.4°, with a tolerance of 2° due to a dispersion of UV k vectors upon focusing. The typical nanogratings periods between 150 and 500 nm offer a large range of diffraction angles β (with respect to the IR axis) satisfying the grating equation, with a diffraction efficiency given by a thick grating. The upper limit β_max = 42.6° imposed by total reflection at the exit interface corresponds to a minimal period of 194 nm. In addition post-mortem birefringence measurements along the photowritten traces were made using cross-polarization microscopy (XPM).

 

Fig. 2 Schematic design of the experimental setup with the IR irradiation and the UV diffraction probing parts. α is the angle of incidence on the gratings with respect to the IR axis, β the diffraction angle (in the material). The inset indicates the typical UV Bragg reflectivity (diffraction efficiency) of the ordered layers with β_B being the Bragg angle.

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3. Results and discussion

3.1. Symmetric pulses

The results of the modification and the associated diffraction patterns subsequent to irradiation with different pulse durations are given in Fig. 3(a–c). The pulse elongation was obtained by upchirping the pulse using programmable second-order dispersion with variable GVD parameters. Typical traces achieved by photoinscription in static (stationary) and dynamic (longitudinally scanned) configurations are presented in Fig. 3(a), together with their axial birefringence properties. The static multipulse traces correspond to 10⁵ pulses per site (exposure time 1 ms). The scanned longitudinal traces are written at a scan velocity of 5 μm/s unless otherwise mentioned, which corresponds to accumulation doses of same magnitude (tens of thousands pulses per micrometer). In both cases the input power was 23 mW.

 

Fig. 3 (a) PCM images of static (10⁵ pulses) and scanned traces (5 μm/s, 100 kHz) for various pulse temporal envelopes, with axial XPM snapshots for the longitudinal traces indicating the on-axis birefringence levels. The arrival direction of the photowriting pulses is indicated by the narrow arrow. (b) UV diffraction patterns corresponding to the scanned traces with the periodicity scaling. The IR arrival is located on the left side. The dotted line is an eye guidance. Note the change in the color scale representing the relative luminosity. (c) Calculated maximal electron densities for Gaussian pulses with variable durations at two energy levels, 100 nJ (squares) and 300 nJ (circles). (d) Diffraction patterns from longitudinal traces photoinscribed by sequences of short and double pulses with 0.5 ps separation time at a scan velocity of 50 μm/s and constant average power.

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We shall first concentrate on the topological aspect of the static structures as they appear in PCM, as a function of the pulse duration. The short pulse (SP) static trace presents two main features [Fig. 3(a) top], a low index (white) head with birefringent properties and a filament type apex of isotropic positive index change. It was indicated before [4] that the nanogratings are formed preferentially in the head, subsequent to multiple microexplosions, as excitation is at its maximum, being thus responsible for the appearing form birefringence. A dependence of the energy dose for nanogratings creation as a function of pulse duration was already demonstrated [3, 10], showing a smaller efficiency for ultrashort pulses. This can be associated with the increased difficulty to generate hot bulk carrier densities by very short pulses due to plasma defocusing, filamentation and the absence of collisional heating processes. Upon scanning the exposure region, the main features of the longitudinal traces are fixed by the birefringent nanostructured (white) head, while the positive index apex erases the central part and imposes a shallow positive index core. With increasing pulse duration the birefringent nanostructured head increases in size, while the positive index apex becomes narrower and eventually vanishes for pulse durations above 2 ps. The corresponding longitudinal traces replicate the structure of the birefringent head. The XPM part in Fig. 3(a) indicates corresponding axial birefringence in the scanned traces, reflecting their internal anisotropies.

The resulting UV diffraction footprints taken from the scanned longitudinal traces are given in Fig. 3(b). We note a dependence of the position of the diffraction spot that departs towards larger angles (i.e. smaller nanogratings periodicities) as the pulse width increases. This shows an increase of the sub-micron order even though the macro-morphological aspect of the traces gets less uniform. The maximum diffraction probe deviation occurs around 0.65 ps IR pulse duration and a periodicity towards 210 nm is found at this pulse value. Fluctuations in the periodicities are visible in the broadening of the diffraction spot, and they become equally small at this pulse duration value. The angular deviation subsequently decreases and the angular dispersion increases above 2 ps. These diffraction patterns can be correlated with the aspect of the laser-induced traces in PCM. The SP result is the least performant, with a large scattering of diffraction angles and low periodicities (230–270 nm). At the same time we recall that the high-index filament-like apex has its strongest development for SP. During the scanning procedure in longitudinal configuration this may have a perturbative action on the nanogratings formation, erasing partially the existing structures and increasing the disorder degree. The filamentary apex reduces with increasing the pulse duration, its effect during photoinscription diminishes and the quality of the structures defined by the dispersion and the magnitude of the diffraction peak becomes higher. The intensity of the diffraction spot peaks for a pulse length of 0.65 ps and re-decreases for longer durations. The increase of the peak magnitude as the wavelength decreases may be partially attributed to approaching the Bragg condition (Bragg angle β_B=34.4°), however the Bragg response of such a structure is angularly rather large (few degrees). A pattern periodicity of 213 nm corresponds to the Bragg diffraction peak, close to the value obtained for 0.65 ps pulses. Nevertheless it appears from Fig. 3(b) that patterns of different intensities are obtained for similar periodicities, therefore a geometrical argument does not fully encompass the physical situation. Experiments with downchirped pulses indicate a similar situation, with even more reduced periodicities.

In addition to index contrast, the periodicity variation has a certain effect on the phase-retardation properties of the traces. Using standard formulas for form birefringence from periodic patterns [11], a variation of e.g. 35 nm in the periodicity leads to approximately 15% variation of the birefringence (value range 10⁻³), particularly via the change of the extraordinary index. In addition, a variation in the nanopatterning domains was previously observed in Ref. [4], with consequences in light transport in type II waveguides with birefringent nanostructured cladding.

3.2. Carrier densities

We discuss below the physical interaction scenario and possible factors that impact the periodicity and the arrangement quality. The periodicity follows approximately a λ/2n rule suggesting apriori an interference mediated light-matter coupling. This indicates a possible influence via the spectral content of the pulse or the transient material dielectric function. In the former case it is to be expected that a phase modulation and a blueshift of the pulse appears as electrons are generated [12]. However the spectral shift δλ ∼ dN_e/dt depends on the rate of carrier generation (N_e electronic density) and should be maximal for the shortest pulse.

As the spontaneous arrangement is intermediated by electronic excitation we have numerically evaluated the corresponding electronic densities. The single pulse excitation footprints were calculated using a pulse propagation code based on the nonlinear Schrödinger formalism in the slow varying envelope approximation [13]. A laser waist ω = 1.3 μm is assumed. Major nonlinear effects such as Kerr selfocusing, plasma defocusing, carrier generation via multiphoton (MPI) and collisional ionization (CI) were taken into account. The details and the parameters of the simulation approach are given in Ref. [13]. In view of the uncertainties of the excitation parameters we will concentrate on the qualitative aspects of these results. We stress that modeling is made for single pulses while multipulse data are collected experimentally. Within a multipulse exposure, the material resistance to damage goes down with the dose as a result of incubation [14], making excitation more effective. We therefore approximate the situation with an increase in the input energy for fixed material parameters. The characteristic behaviors are calculated for energy values that frame the experimental conditions (230 nJ/pulse) and the electron density results are presented in Fig. 3(c). For low input energies (e.g. 100 nJ) the peak electronic density decreases with increasing pulse duration, as it is expected for an MPI dominated interaction. However, as the input energy augments (e.g. 300 nJ), the situation changes drastically. As electrons are created already on the leading front of an SP, the strong defocusing character of the free carriers limits the achievable electron density to subcritical values of approximately 10²⁰ cm⁻³. This condition becomes less stringent when the pulse duration augments, as the electrons are created later in the pulse. The highest peak electron density, yet at subcritical values for single pulses, is achieved for 0.6 ps, where the defocusing effect is compensated by still a reasonable efficiency of the photoionization cross-section. This subsequently goes down with increasing pulse duration. We anticipate in the multipulse case a behavior that commences in the case of the low energy situation as the first pulses arrive, and ends in the high energy case. The fact is corroborated by the axial dimension of the birefringent part in the static traces assimilated to regions of high excitation. This has a maximum for input pulses around 0.65 ps. One important observation is to be made here. One of the current hypotheses concerning the nanograting formation is based on the material response to electronic plasma waves [15] in sub- to near-critical regimes. In this case the period of the nanogratings arrangement should increase with the electron density and temperature, as the plasma frequency rises and the real part of the dielectric function (ε_r) goes down due to the Drude response (Δε_r ∼ −N_e). The present results show an opposite behavior, however the actual level of electronic densities is still to be confirmed. Nevertheless, we would like to point out that electronic collisional damping in laser-triggered carrier plasmas in bulk dielectrics permits partial light propagation also in slightly supercritical regimes, reversing thus the trend expectable at lower densities.

A similar behavior was indicated by patterns induced at different energy levels, with lower periodicities as the energy increases [1, 10]. Equally, diffraction patterns from traces photoinscribed by another class of symmetric pulses show a decrease of periodicity and an increase in the alignment when sub-ps separated double pulses of same energy are used instead of short pulses [Fig. 3(d)]. Using double pulse sequences we have explored the region of 0.5 ps after the first impact for a scan velocity of 50 μm/s and otherwise similar exposure conditions as above. The result shows an increase of effectiveness of the energy deposition part leading to the formation of nanostructures, with a history of the first pulse excitation characterized by a residual electronic population.

3.3. Asymmetric pulses

To test the present findings we have employed asymmetric pulse shapes containing fast series of pulses with monotonously varying intensities based on third order dispersion (TOD) as they were shown to accurately master electronic densities on surfaces [16]. Positive and negative TOD pulses (φ⁽³⁾ = ±1 × 10⁷) with a statistical duration of approximately 2σ = 1300 fs generate the photoinscription and the diffraction results given in Fig. 4(a–f), putting together PCM images, angular diffraction patterns, and measured pulse envelopes. The trace induced by positive TOD sequences where the main pulse leads shows a stronger diffraction pattern and a slightly smaller period than the negative TOD counterpart. It is expectable for positive TOD pulses that MPI acts efficiently at the beginning, during the main pulse, supplying seed electrons for CI during the subsequent lower intensity pulses. Even in these conditions the bulk excitation limits the maximum achievable electron density by defocusing and restricts the full extent of CI. However, due to Bremsstrahlung absorption, the gain is reflected in electronic energy. The situation is more favorable for hot carrier generation than for negative TOD pulses where low intensity pulses lead the series and MPI is not particularly active before the end of the sequence. This is reflected in the size of the low index part in the static trace (as initially observed in the case of chirped pulses). We note here in addition without showing the corresponding results, that all these behaviors were confirmed at various writing speeds (5 and 50 μm/s) and input powers below or around the critical power for self-focusing (3 MW), with similar dependencies.

 

Fig. 4 PCM images of static (10⁵ pulses) and scanned (5 μm/s) traces (a,b) for negative and positive TOD pulses, with the corresponding UV diffraction patterns originating from longitudinal traces (c,d) and the periodicity scaling. The arrival direction of the laser pulse is indicated by the narrow arrow. The measured pulse forms are equally given (e,f), where the front of the pulse is represented for convenience towards the right side.

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3.4. Dimensional effects

The variable excitation has an implicit role in the level and the spatial distribution of energy. As a result, a dimensional effect was noticed when the pulse form varies, that will be discussed bellow based on the PCM static images. The increase in the axial size of the nanostructured head, a region of uniform topological transformation, has consequences in the effective accumulation dose at constant scan velocities. The size of the birefringent head will subsequently determine the number of effective pulses per micrometers (and capable of producing the observed structure) as N ∼ Lp/s, where L is the length of the birefringent region in the static trace, p the laser repetition rate, and s the scan velocity. We recall that at 100 kHz pulse repetition rates, the accumulation dose lies in the range of few tens of thousands pulses per micrometer at the chosen velocity. Due to the variation of L with the pulse form, the accumulation dose may vary within a factor of two. As nanogratings formation may be initiated by field enhancement at rugosities via a nanoplasmonic scenario [2], a higher accumulation dose will foster agglomeration of initiation centers and, via the increase in the range of Fourier vectors associated with nanor-oughness, facilitate more flexible coupling between light and electronic oscillations. Recent results are equally pointing out to an incubation-mediated nanoplasmonic scenario [17].

4. Conclusions

In conclusion we have shown an influence of the pulse form on the periodicity and the arrangement of nanogratings in longitudinally photowritten traces with a real-time in-situ probe. The time-engineered exposure allows controlling the effective dose leading to pattern formation via direct nonlinear propagation and excitation, carrier densities, and dimensional effects, impacting thus the period and its tunability. A minimum period is found for pulse durations around 0.7 ps for the energies employed, together with strong sensitivity to form symmetry. All these findings indicate a requirement for plasma development at maximal levels, influencing the spatial domains of material transformation. A scenario based on nanoplasma sheets followed then by hydrodynamic movement of the material in conditions of lower viscosity appears closer to the present results. The procedure can impact optimization schemes for laser-induced nanoscale patterning implying tunable birefringence and phase retardation properties.