# Dynamic Ultrafast Laser-Induced Structural Changes and Extreme Nanostructuring in Hard Dielectric Materials

Rajeev Dwivedi, Huu Dat Nguyen, Sergio Sao Joao, Anne-Magali Seydoux-Guillaume, Thirunaukkarasu Kuppan, Ciro D'amico, Guillaume Kermouche, Razvan Stoian

► To cite this version:

Rajeev Dwivedi, Huu Dat Nguyen, Sergio Sao Joao, Anne-Magali Seydoux-Guillaume, Thirunaukkarasu Kuppan, et al.. Dynamic Ultrafast Laser-Induced Structural Changes and Extreme Nanostructuring in Hard Dielectric Materials. ACS photonics, 2025, 12 (7), pp.3644-3652. 10.1021/acsphotonics.5c00554. emse-05157075

HAL Id: emse-05157075

https://hal-emse.ccsd.cnrs.fr/emse-05157075v1

Submitted on 12 Jul 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Dynamic ultrafast laser-induced structural
changes and extreme nanostructuring in hard
dielectric materials

Rajeev Dwivedi,† Huu Dat Nguyen,† Sergio Sao Joao,‡ Anne-Magali Seydoux-Guillaume,¶ Thirunaukkarasu Kuppan,† Ciro D'Amico,† Guillaume Kermouche,‡ and Razvan Stoian*,†

†Laboratoire Hubert Curien UMR 5516 CNRS, Université Jean Monnet, 42000, Saint-Etienne, France

‡Laboratoire George Friedel, UMR 5307 CNRS, Ecole des Mines de Saint-Etienne, 42000, Saint-Etienne, France

¶LGL-TPE, UMR5276 CNRS, Université Jean Monnet, 42000, Saint-Etienne, France

E-mail: razvan.stoian@univ-st-etienne.fr

Abstract

Understanding matter transformation under light enables ultrafast 3D laser struc-
turing to attain precise control down to the nanoscale. This is challenging for hard
crystals given their mechanical resistance; nonetheless, it is key in structurally design-
ing matter, pendling between crystalline and amorphous phases. The particular time
evolution of structural and morphological changes can pinpoint either dynamics re-
lated to shock compaction or to thermal relaxation with phase transition. We report
quantified the time-resolved dynamics of laser modifications induced by non-diffractive
ultrafast laser beams in bulk sapphire using qualitative and quantitative phase-contrast
microscopy to link optical changes to thermodynamic and structural evolutions. The
final morphological changes of irradiated structures are revealed by high-resolution elec-
tron microscopy. Observations confirm that Bessel pulse irradiation transforms the
pristine crystalline structure into a homogeneous amorphous phase in tens of ns, via
the passage through a liquid phase nucleated at the early stages of the process. This
ns-lived liquid phase is subject to cavitation at higher energy concentrations on the
cooling phase (100 ns), facilitating nanoscale void fabrication with high aspect ratios.
The outcomes strongly support bulk modification without shock assistance, governed
instead by thermal relaxation. This determines a robust path for extreme laser struc-
turing down to the nanoscale.

KEYWORDS: ultrafast phenomenon, laser nanostructuring, phase-transition, light-matter
interaction, time-resolved imaging, bulk modification, structural changes, amorphisation

**Introduction**

Recent advances in ultrafast lasers and process development bring the resolution of laser
structuring from a few microns to tens of nanometers, achieving new functions associated
with both structural and morphological transformations of matter. ¹⁻⁵ An interest exists in
pushing the technique towards processing the hardest materials in volume, where confined
interaction puts forward specific challenges in understanding material behavior in extreme
conditions. Hard crystals with high strength, that include sapphire, have gained a lot of
interest due to their remarkable properties like high temperature, pressure and scratch resis-
tance, making them key elements in quantum optical, photonic and astronomical research
as well as industrial applications.⁶,⁷ However, mechanically processing hard crystals is an
effort-taking task and volume processing alternatives are scarce. Recent studies suggest
that ultrafast lasers can efficiently process hard crystals, such as sapphire and diamond,
on the surface as well as inside bulk, given that energy concentration can surpass the me-
chanical resistance. The laser-induced micro-blast in bulk dielectrics is usually achieved by
tightly confining ultrashort laser pulses to reach high energy concentrations exceeding thou-
sands of J/cm³, enough to create laser-induced nano plasmas that can generate extreme
non-equilibrium conditions via pressure, temperature gradients or via electronic effects on
molecular bonding. This interaction is the birthplace of a nanoscale morphological feature
in the form of a void. Such an interaction can be extended to larger volumes of particular
geometries in a single pulse irradiation using non-diffractive beams, for example, ultrafast
Bessel beams, which offer a more stable nonlinear excitation and result in high aspect ratio
volume modification. The value of the aspect ratio can exceed 100, with the nano-channels
having a diameter of less than 100 nm surrounded by amorphous or compressed phases. ⁸⁻¹⁰
Such scale outpacing the far-field optical resolution of the incoming beam is intrinsically
related to material transformation.

The pulse duration of the laser beams can have a determinant impact on these processes.
Controls the nonlinear behaviour of the pulse in interaction with matter, mitigating propaga-
tion, excitation, and adjusting the level of energy deposition. Usually, short pulse durations
favour self-regulated, intensity-clamped regimes that level out the energy density over a wide
range of input energies. Stronger energy deposition can be obtained by stretching the pulse
in time or by stronger focusing.¹¹ In glassy materials (such as silica), both positive and
negative refractive index modifications can be induced, suggesting respective variations in
density. This is intrinsically related to the amount of energy deposition in the presence of
nonlinear focusing and defocusing effects (Kerr self-focusing or charge defocusing) and the
related electronic, structural, and mechanical thermodynamic changes of a flexible glassy
matrix. In crystals, mostly crystalline to amorphous modifications, sometimes accompanied
by the generation of nano-channels, have been observed by tuning the pulse width of the
irradiating ultrafast Bessel pulse.¹²,¹³ Such transformation can be the origin of laser nano-
scribing technologies, and the formation of nanoscale morphological features poses questions
about the relevant transformation path of matter. Understanding light-matter interaction
in the regime of strong photon concentration and energy gradients will allow the design of
embedded structures that incorporate structural and morphological material changes, tuning material phases and void nanostructuring, and thus achieving extended functionalities. These may range from optical functions in guiding and sampling light down to metamaterial design capable of manipulating optical signals in three dimensions. The challenge is to associate process observation and extreme scale structuring, i.e. time and spatial scales, and to provide a clear transformation pathway. Following the temporal dynamics, one can determine the balance between mechanical effects, including pressure propagation and rarerfaction, and electronic excitation with carrier-phonon relaxation and thermodynamic phase transition, consuming the optical energy. A range of studies advocated the scenario of shock wave-assisted bulk modification, like in sapphire, where the post-effect of shock waves can be observed as the presence of a compressed Al-bcc phase in the surroundings of laser-fabricated nano-voids¹⁴ but also in the presence of amorphous zones. On the other hand, evidence of an early-stage plasma-to-intermediate liquid phase leading to cavitation or index modifications has been observed in fused silica and in quartz excited by a Bessel pulse.¹³ This suggests that bulk modification can be determined by the thermal relaxation of the excited matter that may undergo a nucleated phase transition to liquid phases, resulting in amorphisation and cavitation.

Investigating the intermediate stages of laser modifications can reveal the circumstances leading to structural changes, amorphisation, and cavitation in hard crystals when light is confined on very small scales. These modifications are responsible for obtaining feature sizes well beyond the diffraction limit of the processing light. In the present study, we performed time-resolved qualitative optical phase-contrast microscopy (PCM) and quantitative phase microscopy (QPM) to analyze the light-matter interaction in the case of ultrafast Bessel irradiation, its 3D confinement inside a bulk sapphire crystal and the relevant energy flow during transformation. The purpose is to explore the conditions for volume amorphisation and the manifestation of nano-channel production with a high-aspect ratio. Furthermore, we used high-resolution electron microscopy to perform both morphological and structural
analysis of single-shot ultrafast Bessel pulse modifications in bulk sapphire, where we target
changes of the crystalline matrix. Subsequently, we analysed the effect of tuning the pulse
width on the intermediate stages of laser modification and structure morphology, which is
equivalent to increasing the energy concentration in the confinement area. We observe that
this control is optimal for favouring stronger transitions and the generation of material failure
and cavitation. Extreme scales can thus be obtained. This study proposes an insightful
interspection into the light-matter interaction in ultrafast laser bulk modification in hard
crystals, which not only advances the field of laser volume processing but also opens up
opportunities to discover new material phases. Such a capability, combining structural design
with void-like morphological features, should enable extended flexibility in designing material
functions.

**Results and Discussion**

**Ultrafast 3D volume modifications**

A first perception of the laser-modified regions is given in Fig. 1 using optical PCM of the
traces along with cross-sections in scanning electron microscopy (SEM); the experimental
layout being given in Fig. 1(a) (see methods section for details). The laser impacts shown
in Fig. 1 (b) are fabricated with ultrafast Bessel pulse at increasing pulse widths, τ = 50 fs
, τ = 250 fs, and τ = 1.1 ps with pulse energy fixed at E ~ 4.5 µJ. These conditions il-
lustrate generically a range of structural changes that will be discussed below. The bright
regions in PCM images shown in Fig. 1 (b) depict negative refractive index modification,
(Δn< 0). We make here the hypothesis, based on the observation of laser changes in other
materials,¹¹,¹³ that the optical change in crystals like sapphire refers to either a structurally
changed, potentially amorphous region or a rarefaction process down to a cavity formation.
Such a hypothesis will be verified in the next sections. For a detailed morphological view,
SEM is performed after cross-polishing the sample, which reveals a transverse section of laser
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Conceptual schematic of the experiment, illustrating the sapphire sample excited by an ultrafast Bessel pulse at time t. Transient material changes depicted as phase images are recorded by illuminating the impacted region at different time delays, Δt. (b) Phase contrast microscopy (PCM) and scanning electron microscopy (SEM) images of permanent traces of laser-induced modifications at different pulse widths τ, of the Bessel pulse. Different structural and morphological domains are illustrated.</figcaption></figure>
modification featuring uniform laser modifications for ultrafast Bessel pulse irradiation at $\tau = 50$ fs and $\tau = 250$ fs (see Fig. 1 (b)).

<figure><img src="image_3.png" /><figcaption>Figure 2: (a) Transmission electron microscopy (TEM) images of lamellas prepared by FIB milling show the longitudinal view of the Bessel pulse-modified regions. (b) High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images showing crystalline and amorphous regions, along with crystal plane molecular structure. The spatial positioning of these regions is indicated by red squares and arrows.</figcaption></figure>

It is interesting to observe that the diameter of the laser structure increases with pulse width, from ~ 250 nm for $\tau = 50$ fs to ~ 350 nm for $\tau = 250$ fs, respectively, though the input energy stays constant. This marks an increase in the energy density in approximately the same ratio. The surroundings of these structures exhibit a couple of cracks torn out of the edge of these modified regions, leaving the amorphized interior region intact. This
could be the effect of mechanical orthogonal stress components due to the radial energy
transport geometry around the axis, stress developed beyond the interface, in the crystalline
non-irradiated solid. The increase of the pulse duration shows new features of interest. The
observed diameter of single τ = 1.1 ps Bessel pulse modifications is approximately 500 nm,
with a central void ~ 150 nm, (see Fig. 1 (b)). This clearly indicates a regime of higher
energy concentration with the opening of a nanoscale void within an amorphised region.
Before responding to the dynamics of the individual features, the question of the structural
change type is now of interest and first elements will be given in Fig. 2. TEM lamellas
of the modified region are prepared for τ = 250 fs and τ = 1.1 ps, respectively, using the
focused ion milling (FIB) technique and then imaged by TEM, showing a long uniform 3D
nano-volume modification for fs case, while opening of the void for ps Bessel pulse irradiation
(Fig. 2 (a)). The corresponding atomic arrangements are depicted in Fig. 2(b). This clearly
identifies a structurally disordered phase surrounding the void.

Homogeneous amorphisation

In Fig. 2 (b), the atomic structures revealed by high-angle annular dark-field scanning trans-
mission electron microscopy (HAADF-STEM) images of the crystalline regions are identified
by well-defined atomic structures, while the ultrafast Bessel pulse irradiated area is trans-
formed into random arrangements, evincing the amorphisation. However, the probe field in
HAADF-STEM can recrystallise the amorphous region; hence, unable to provide detailed
images of the modified region. For a more precise analysis and intelligible illustration, the
TEM image (see Fig. 3(a)) will be utilised in conjunction with selected area electron diffrac-
tion (SAED) patterns captured at three different locations of interest SAED₁, SAED₂ and
SAED₃ (see Fig. 3 (b)). The SAED patterns in Fig. 3 (b) are used to analyse the laser-
modified zone and confirm through their annular diffraction patterns the fabrication of a
homogeneous amorphous region irradiated with a fs Bessel pulse (region 1). The homogene-
ity and uniformity of the structural transformation without visible signs of rarefaction allow
<figure><img src="image_4.png" /><figcaption>Figure 3: (a)-(c) Ultrashort pulse induced changes ($\tau = 250$ fs). (a) Transmission electron microscopy (TEM) image of the Bessel pulse impact around the propagation axis, capturing the modified domains: amorphisation, structural distortions, and the pristine lattice. (b) Selected area electron diffraction (SAED) images showing diffraction patterns characteristic of the atomic arrangements in the selected regions. (c) Transmission Kikuchi diffraction (TKD) images indicating crystal plane orientation at each pixel grain. (d)-(f) Ps pulse induced changes ($\tau = 1.1$ ps), a cavitation process is present. (d), (e) and (f) represent the TEM, SAED and TKD images, respectively. For both cases, the locations mentioned as 1, 2 and 3 correspond to the amorphous (SAED₁), crystalline (SAED₂) and disordered crystalline (SAED₃) regions, respectively.</figcaption></figure>
us to advance the hypothesis of a phase transition intermediated by a liquid state and not
driven by compression mechanical waves. This suggests the crystal-to-liquid phase transition
at the early stages of light-matter interaction.

The crystalline-amorphous interface in region 3 reveals distorted crystalline planes, identified
as distortions observed in SAED<sub>3</sub> (see Fig. 3 (b)), which could be traces of local stress. For
a detailed analysis of this distorted region, we carried out TKD observations, showing the re-
gion of interest in blue colour with green as a crystalline background in Fig. 3 (c), indicating
a crystalline plane with disorientation close to (Δβ<sub>x</sub>, Δβ<sub>y</sub>, Δβ<sub>z</sub>) = (3.34°, 4.03°, 0.70°). Here
(Δβ<sub>x</sub>, Δβ<sub>y</sub>, Δβ<sub>z</sub>) = (0°, 0°, 0°) refers to the background crystalline plane. This confirms the
presence of stress on the interface. Such stress may result from internal pressure relaxation
or, most likely, from the structural relaxation of the amorphised region, which, due to a
lower reported density in the equilibrium, tends to occupy a higher volume, stressing the
interface. This process is characteristic of a range of energies and ultrashort pulse durations
where intensity clamping limits energy deposition to relatively moderate levels.

Cavitation

Increasing the τ to 1.1 ps facilitates the opening of a nano-void from the centre of the
amorphous region (see Fig. 3 (d)). Corroborated with the previous observation of uniform
amorphous region at lower energy concentration, the observation of the void in the ps pulse
case may be the effect of rarefaction in the liquid phase, as the concentration of energy aug-
ments<sup>11</sup>, a point which will be demonstrated by the dynamic behaviour. Such an increase in
the level of energy concentration has been reported in previous studies and in the discussion
below related to the bypass of nonlinear energy dissipation due to carrier focusing, which
makes the ps moderately-focused pulse more efficient in concentrating the energy compared
to the fs pulse. The contrast of the TEM images in both Fig. 3 (a) and (d), has been opti-
mized separately to visualize the regions of amorphisation and cavitation clearly; therefore,
the uniform amorphous region in Fig. 3 (a) is represented in bright contrast while the void
<figure><img src="image_5.png" /><figcaption>Figure 4: Time-resolved dynamics of ultrafast Bessel pulse interaction with bulk sapphire for pulse duration $\tau = 250$ fs, showing the time evolution of amorphisation. (a) Phase-contrast microscopy (PCM) images of the modified region at different values of $\Delta t$. The insert, a montage of the central regions of PCM images, depicts the variation of the transient index on a logarithmic time scale. (b) Line plot showing the quantitative information of $\Delta n$ and $\Delta\varphi$ obtained from time-resolved quantitative phase-contrast microscopy (QPM). $\Delta t_1$, $\Delta t_2$, $\Delta t_3$ and $\Delta t_4$ represent the duration of different transient phases. $\Delta n_{QPM}$ and $\Delta n_{SEM}$ are calculated using the size of the modified region measured from optical and electron microscopy, respectively. (c) Estimative deconvolution of the process via exponential fitting. The plasma phase (blue curve), hot thermal phase (red curve) and the onset of morphological changes (white) are represented. Y represents the spatial coordinate of PCM images perpendicular to the laser direction.</figcaption></figure>
in Fig. 3 (d) is shown in bright contrast with the amorphous region in grey. Intriguingly, the SAED₁ image in Fig. 3 (e) did not show any traces of crystalline structure in the amorphized region surrounding the void (region 1), confirming the presence of homogeneous amorphisation and supporting the existence of the liquid phase in transient stages of light-matter intersection.

In Fig. 3 (e), the SAED₃ diffraction pattern corresponding to region 3 shows increased distortion after increasing the pulse width of the irradiated Bessel pulse from $τ = 250$ fs to $τ = 1.1$ ps. Further, the TKD analysis indicated an enhancement in the disorientation of the crystalline plane ($Δβ_x, Δβ_y, Δβ_z$) = (104°, 61.24°, 35.78°), along with an extended area mainly stretched in the longitudinal direction of the trace (green area in Fig. 3 (f)). This refers to much stronger local stress in the case of ps Bessel illumination, which is discussed further in a later section.

## Temporal evolution of nano-volume modifications

We have so far observed structural and morphological changes, and the question of their mutual influence is relevant. The time evolution will offer insights with respect to the characteristic timescale of each process, establishing a causal connection. In this section, we study the time evolution of the process leading to permanent 3D volume modification inside the bulk sapphire using the pump and probe process. We will study specifically the cases of amorphisation for the fs pulse duration and cavitation for the ps pulse duration. We use a time-resolved phase contrast technique with qualitative and quantitative characteristics as indicated in the Experimental section. Estimation of refractive index changes from optical phase and dimensional corrections is described in the Methods section.

### fs Bessel pulse interaction

For the cases $τ = 250$ fs, varying the pulse energy, $E$, in the range of 1.3 µJ - 6 µJ, i.e. intensity clamping ranges, provides uniform amorphous phases. We will demonstrate that
they correspond to transient phase transitions to the liquid phase in time-resolved PCM images. In our study, we fixed the pulse energy to $E = 4$ µJ. The respective results are given in Fig. 4. The PCM images in Fig. 4 (a) are captured at different time delays between the pump and the probe, $\Delta t$, ranging from 0 ns to 1000 ns, where 0 ns signifies the time when the first change appeared in PCM images. Subsequently, QPM observations in Fig. 4 (b) represent quantitative evolutions in both $\Delta\varphi$ and $\Delta n$ (optical estimations $\Delta n_{QPM}$ and corrections $\Delta n_{SEM}$) along with qualitative PCM images obtained at different $\Delta t$ (Fig. 4 (a)) on a logarithmic time scale. These changes in PCM images with time indicate different transient domains of Bessel pulse interaction with bulk sapphire. Commonly, the temporal dynamics of light-matter interaction in transparent bulk materials can be described in four transient stages: plasma phase, $\Delta t_1$ (presence of free electrons and heating the system due to electron-phonon interaction), hot phase, $\Delta t_2$ (heat diffusion into surroundings) and cooling, the evolution of solid phase, $\Delta t_3$ and permanent modification, $\Delta t_4$ (see Fig. 4).

In Fig. 4 (a), the central region of PCM images during $\Delta t_1$ appears in bright contrast, referring to a reduced refractive index ($\Delta n < 0$); on this short time scale, it indicates the presence of free electron gas, reducing the refractive index locally in the laser-impacted area. The expected lifetime of free carriers in a cold solid sapphire is around 50 ps,¹⁵ accompanying the gradual heating of the sample. However, for $\tau = 250$ fs, the plasma phase in Fig. 4 is observed for a longer duration $\Delta t_1 \sim 5$ ns. Such an increase in lifetime can be the subject of carrier screening or vibrational activation, with a complete loss of matrix rigidity. A level of carrier excitation in the range of 1 % of the molecular density, seems to be too low to validate the first scenario. The measurement of the average $\Delta n_{SEM} \sim -0.067$ at 1 ns in Fig. 4 (b) corresponds to a plasma density of at least $N_e \sim 10^{20}cm^{-3}$ ($N_e \sim -2N_{cr}\Delta n_{SEM}$, $N_{cr}$ is the critical density of free electron gas in bulk sapphire). We should nonetheless keep in mind that, in the early stages, $\Delta n_{SEM}$ is the combination of both hot and plasma phases, hence undermining the peak value of $N_e$ (estimated more accurately in the discussion), indicating that the contribution of carrier screening can not be ruled out completely. However, the
most probable condition is the vibrational activation, where the energy transfer rate is given by a typical ps-long carrier-phonon coupling time, suggesting fast heating above the phase transition point. This hypothesis will be validated in further discussions. This increase in time could thus be explained by the passage to a liquid phase during the plasma phase (as the typical electron-phonon coupling is much shorter), as a liquid phase will modify the interaction of carriers with the matrix and their localization probability in deformation potentials. Similar behaviour was reported earlier in laser-irradiated silica above the softening point and in melted quartz.¹³,¹⁶ Recently, it has been reported that plasma lifetime in the liquid phase can reach more than tens of ns.¹⁷ This discussion supports our assumption that at the beginning, during $\Delta t_1$, electron-phonon interaction heats the system and creates a local region of reduced viscosity, reaching a liquid phase in the interaction area of the focused ultrashort Bessel pulse impact, allowing plasma to sustain for a longer duration. A hot liquid phase is formed that lasts for tens of ns. This can lead to a hypothesis that $\Delta t_1$ and $\Delta t_2$ are the combination of both plasma and hot phases in a confined environment, and $\Delta n$ in the transient range can be represented by,

$$ \Delta n = \Delta n(N_e) + \Delta n(\Delta T) \quad (1) $$

Here $\Delta T$ is the temperature of the system. We use this model to deconvolute electronic and thermal influences and to extrapolate the experimental data towards the early stages of light-matter interaction (experimentally inaccessible domains). Fig. 4 (c) represents the contribution of the plasma and hot phases separately by blue and red curves, respectively, obtained by exponential decay fitting of the variation of $\Delta n$ in the QPM curve (see Fig. 4 (b)), using $d_{SEM}$. Such a fit accounts for the decay in carrier population and in the decay of temperature by diffusion losses. With cooling of the hot phase, the refractive index decreases and then changes sign, indicating the onset of the structural phase. A passage from $\Delta t_2$ to a cold phase evolution $\Delta t_3$ and $\Delta t_4$ appears. For better visualisation, the white curve in Fig. 4 (c) refers to the manifestation of cooling towards the solid phase
$\Delta t_3$ and the permanent modification, $\Delta t_4$. Let us now attempt to quantify the conditions. For simplicity, the values of change in refractive index obtained for plasma and hot phases from the model after deconvolution and extrapolation are defined $\Delta n(N_e) = \Delta n_{SEM,plasma}$ and $\Delta n(\Delta T) = \Delta n_{SEM,heat}$, respectively. Using the extrapolated data in Fig. 4 (c), the deconvoluted curve of the plasma phase indicates that at the beginning $\Delta t_1$, the value of $\Delta n_{SEM,plasma} \sim -0.12$ measured for a fs Bessel pulse corresponds to an electron density close to $N_e \sim 10^{21} \text{cm}^{-3}$. At the same time, the hot phase curve with a maximum value of $\Delta n_{SEM,heat} \sim 0.9$ corresponds to a temperature change of $\Delta T_{SEM} \sim 4100$ K (calculated using $\Delta T = \Delta n/\xi$, where $\xi \sim 2.2 \times 10^{-5} \text{K}^{-1}$ is the thermo-optic coefficient of sapphire$^{18}$). It is evident from Fig. 4 (b) that in the transient domain $\Delta t_2$, the hot phase overtakes the contribution of the plasma phase and reaches a maximum value, $\Delta n_{SEM,heat} \sim 0.075$ followed by a rapid decay in matrix temperature and the manifestation of amorphised phase ($\Delta t_3$ and $\Delta t_4$), discussed later, where a density change will add to the index behavior.

## ps Bessel pulse interaction

Figure 5 demonstrates the intermediate temporal domains of light-matter interaction of a $\tau = 1.1$ ps Bessel pulse interaction with bulk sapphire, keeping $E = 4.5$ µJ fixed. We recall that a higher energy density is expected to occur. The bright region at the centre of PCM images (see Fig. 5 (a)) refers to a prolongation in the lifetime of the plasma phase, which is confirmed by the QPM analysis in Fig. 5 (b), indicating a duration of $\Delta t_1 \sim 20$ ns for the plasma phase followed by a hot phase with a maximum value of $\Delta n_{SEM} \sim 0.077$ during $\Delta t_2$. As discussed in the previous section, the QPM observations in $\Delta t_1$ and $\Delta t_2$ are the contributions of both plasma and hot phases. Therefore, using Eq. 1, we fitted the QPM data into two exponential decay functions showing the trend of free electron population density and matrix temperature separately in terms of $\Delta n(N_e)/\Delta n(\Delta T) = \Delta n_{SEM,plasma}/\Delta n_{SEM,heat}$ (see blue and red curves in Fig. 5 (c)). The maximum $\Delta n_{SEM,heat}$ obtained at the early stages of $\Delta t_1$ reaches close to 0.12 corresponding to $\Delta T_{SEM} \sim 5500$ K, at the same time, the plasma
phase curve estimated the minimum value of $\Delta n_{SEM_{plasma}} \sim -0.23$, refers to a plasma density increased by a factor of two compared to fs pulse irradiation. On the other hand, considering the optically measured dimension of the structure brings down the estimated temperature close to $\Delta T_{QPM} \sim 4300$ K, giving a lower limit of the observation. The transient domains $\Delta t_3$, $\Delta t_4$ show thermal relaxation followed by the evolution of permanent modification as discussed and compared with fs case in later sections.

## Effect of Tuning the Pulse width

Early stages of interaction: $\Delta t_1$ In general, a fs pulse offers a shorter excitation time and a swift carrier density increase at the centre of the focal region, which could lead to the phenomenon of plasma defocusing.¹⁹ This brings down the further focusing strength of the pulse, resulting in low-energy deposition near the centre of the ultrafast Bessel pulse-impacted region, hence dropping the temperature of the plasma surroundings in the case of 250 fs Bessel pulse in Fig. 4. On the other hand, increasing the pulse width close to $\tau = 1.1$ ps minimises the phenomenon of plasma defocusing, allowing high-energy deposition near the focal depth of ultrafast Bessel pulse and resulting in an extended plasma phase ($\Delta t_1 \sim 20$ ns), as shown in Fig. 5. The estimates show that $\Delta T$ is way above the boiling point of sapphire (3253 K) at normal pressure.²⁰ The fact that the solid does not boil in the heating phase in the first tens of ns with $\Delta T_{SEM} \sim 5500$ K implies an increase in the internal pressure in the irradiated domain. This will significantly increase the thermodynamic points of phase transition, including the melting point. The melting of sapphire at $\Delta T_{SEM} \sim 4100$ K indicates the internal pressure limited at $\sim 30$ GPa²¹ inferior to the bulk modulus.

Thermal relaxation: $\Delta t_2$ As seen in Fig. 4 (b), for $\tau = 250$ fs, the contribution of the hot phase overtakes the plasma phase and reaches a maximum $\Delta n_{SEM} \sim 0.075$ during $\Delta t_2$, corresponding to $\Delta T_{SEM} \sim 3500$K, while for $\tau = 1.1$ ps ultrafast Bessel pulse, this temperature remains in the same range, as the calculated maximum value of $\Delta n_{SEM}$ is $\sim 0.074$, (see Fig. 5 (b)), indicating an extremely hot phase. It is interesting to observe that at the point
<figure><img src="image_6.png" /><figcaption>Figure 5: Time-resolved dynamics of ultrafast Bessel pulse interaction with bulk sapphire for $\tau = 1.1$ ps, showing the time evolution of cavitation. (a) Phase-contrast microscopy (PCM) images of the modified region at different values of $\Delta t$. The insert, a montage of the central regions of PCM images, depicts the variation of the transient index on a logarithmic time scale. (b) Line plot showing the quantitative information of $\Delta n$ and $\Delta\varphi$ obtained from time-resolved quantitative phase-contrast microscopy (QPM). $\Delta t_1$, $\Delta t_2$, $\Delta t_3$ and $\Delta t_4$ represent the duration of different transient phases. $\Delta n_{QPM}$ and $\Delta n_{SEM}$ are calculated using the size of the modified region measured from optical and electron microscopy, respectively. (c) Estimative deconvolution of the process via exponential fitting. The plasma phase (blue curve), hot phase (red curve) and the onset of morphological changes (white) are represented. Y represents the spatial coordinate of PCM images perpendicular to the laser direction.</figcaption></figure>
where plasma decays entirely, for both $\tau = 250$ fs and $\tau = 1.1$ ps, the estimated temperature is close to the $\Delta T_{SEM} \sim 3500$ K, suggesting this temperature value is close to a threshold point required for sustaining the liquid phase. Also, this temperature is observed at longer times for ps Bessel pulse, suggesting enhancement of the liquid phase duration, allowing enough time for the process of cavitation in the interaction area. After plasma decay, fast diffusion of heat in the surroundings is observed, reducing the temperature of the excited region. Theoretically, the heat diffusion time for sapphire is $\Delta t_{diffusion} \sim 75$ ns (estimated by $\Delta t_{diffusion} = w/D$, $D = 12 \text{ mm}^2\text{s}^{-1}$ is the heat diffusion coefficient of sapphire and w is the width of the interaction area, i.e., the width of Bessel pulse), reduced by a factor of more than 10 compared to the process of heat diffusion in glasses like fused silica, comparable to the duration of heat diffusion discern in Fig. 4 and Fig. 5. The estimate takes into account the optical dimension of the beam as the size of the source. Nonetheless, if we account for the dimension of the thermal reservoir above the melting point in the case of $\tau = 250$ fs and $\tau = 1.1$ ps (i.e. $d_{SEM}$, respectively), a slightly faster cooling is to be expected for the fs case. Permanent modification: $\Delta t_3$ and $\Delta t_4$ Following the cooling dynamics of the hot phase, the phase-contrast images present a region where the contrast of the amorphous phase matches with the crystalline background, $\Delta n \sim 0$ for $\Delta t \sim 40$ ns and $\Delta t \sim 80$ ns, i.e., the interface of $\Delta t_2$ and $\Delta t_3$ in Fig. 4 and Fig. 5, respectively. We can then expect that, at this point, the density of the amorphous phase matches transiently that of the crystal, i.e. a densification of $\sim 15\%$. Then, upon cooling, a mechanical relaxation of the amorphous phase is to be expected, with an increase in the volume occupied by the amorphous phase. Similar behaviour has been reported recently, demonstrating the presence of disordered amorphous quartz with increased density at the interface of hot and cooling phases.¹³ The evolution of the solid phase, represented by $\Delta t_3$, shows the manifestation of a bright region ($\Delta n < 0$) at the centre of the laser-impacted region, leading to a permanent nano-structure in phase $\Delta t_4$, a permanent change of structure or morphology. The observed $\Delta n_{QPM}$ and $\Delta n_{SEM}$ for homogeneous amorphous traces fabricated from $\tau = 250$ fs Bessel pulse irradiation are $\sim -0.024$
and ~ -0.047, respectively, which can be used to calculate the density of amorphous traces using the Lorentz-Lorenz formula. The estimated density varies from ρ<sub>a-SEM</sub> = 3.79g/cm<sup>3</sup> to ρ<sub>a-QPM</sub> = 3.88g/cm<sup>3</sup>, which is an increment of ~ 10% to ~ 12% compared to the density of the relaxed amorphous alumina, ρ<sub>amorph</sub> = 3.47g/cm<sup>3</sup>.<sup>22</sup> This implies that the close confinement of the bulk sapphire does not allow the amorphous phase to relax completely, resulting in a denser amorphous phase. Hence, an additional density term Δn(ρ) should be considered in Eq. 1 to support this increase in the density of the final amorphous phase.

This confirms that the dynamics of fs Bessel pulse interaction with bulk-sapphire is gov-
erned by the ns-long thermal-relaxation, leading to a homogeneously amorphised 3D volume
through passage via a liquid phase. The alternative path to amorphisation, the shock-assisted
process, is not probable based on time characteristics. A shock-based compression occur-
ring in a 100 nm range with a supersonic mechanical wave above 10000 m/s would require
a process dynamics well below ns. A second scenario, based on defects amorphisation (at
N<sub>e</sub> ~ 10<sup>21</sup>cm<sup>-3</sup> the rate of defect production is expectably low) should lead to a heteroge-
neous mix of small crystalline and amorphous domains, which was not observed.<sup>23,24</sup>

Furthermore, on irradiating with a Bessel pulse of τ = 1.1 ps, a nano-void manifests at the
centre of the structure and increases the value of index modifications to Δn<sub>SEM</sub> ~ -0.077
(see Fig. 5 (b)). The opening of the void is facilitated by mechanical rarefaction, reaching a
stable cavitation regime. The slow expansion of the interface in a one-dimensional geometry
ensures the nm dimension of the void. Further increasing the pulse width, τ > 1.5 ps ,
leads to thermodynamic instability in the transient phases and results in the appearance of
fragmentation in the longitudinal profile of the Bessel pulse traces; similar behaviour has
been reported in fused silica.<sup>25</sup>

Thermal relaxation-assisted modifications

Let us review the potential modification mechanisms here. A shock-driven process is ex-
pected to end up with rarefaction regions in all cases and a gradual compaction at the edges.
It will also develop a faster dynamics as occurring at supersonic speeds (a few µm per ns being expected). We observe a different behaviour. First, the observed laser modifications from the fs Bessel pulse feature a region of homogeneous amorphisation with no cavitation, which strongly supports a shock-free process. This behaviour is confirmed at different energies and pulse durations, covering a large spectrum of experimental conditions regulated by intensity clamping. The previous section indicates that the temperature of the lattices after the electron-phonon interaction reached above the melting point of the sapphire, which supports attaining a liquid phase in the focal region; at the same time, electron microscopy images confirm a homogeneous amorphisation for a fs pulse. A further energy density increase will then trigger cavitation. Nonetheless, the cavitation process requires a mechanical drive, but its manifestation in a liquid phase does not imply strong pressure gradients.²⁵ Its characteristic time is of tens of ns (equivalent to a speed of m/s). Additionally, the temporal dynamics of thermal relaxation reveal the achievement of the transient amorphous phase, with $\Delta n \sim 0$, having a density equivalent to that of the surrounding crystal. Interestingly, the structure manifests after heat relaxation features a homogeneous amorphous phase with increased density for fs Bessel irradiation. Furthermore, the TKD analysis shows crystal grains with disoriented planes at the interface of the laser impact, which increases with pulse width and can be related to the density relaxation of the amorphous phase pressing on the interface while cooling. Another explanation could be faster mechanical compaction from pressure relaxation, which is a shock-driven process. However, the study outcomes strongly support the idea that thermal relaxation governs the ultrafast laser 3D bulk modification process inside hard crystals.

A relevant question is the nature of the chemical bonding in the amorphous phase, given the difficulty of $Al_2O_3$ in forming glasses from melt-quench, as it is not a network former.²⁶,²⁷ The elemental analysis performed here shows a quasi-conservation of stoichiometry, but the method is invasive and may produce oxidation artefacts. We therefore conclude with a potential conservation of amorphous glassy alumina due to the confinement.
## Conclusion

We performed time-resolved qualitative and quantitative phase-contrast microscopy to reveal the dynamics of ultrafast laser modifications in bulk sapphire. Phase-contrast images indicate that the transient temperature in the laser-irradiated zone increases beyond the melting point of sapphire, hence leading to the transient liquid phase at the time scale of tens of ns. Electron microscopy reveals that a Bessel pulse irradiation transforms crystalline media into a homogeneous amorphous phase, which, upon the energy density, may cavitate. This strongly supports the existence of the liquid phase at the early stages of the process. However, the presence of cracks and disoriented crystal planes at the boundary of the irradiated zone indicates that the crystal matrix locally experiences stress from the relaxation of the structural changes. Subsequently, increasing the pulse width facilitates the manifestation of a nano-channel of diameter 150 nm at the centre of the amorphous region. These observations strongly support the shock-free bulk modification governed by the process of thermal relaxation. This study will be beneficial in better understanding the process of laser structuring in hard crystals for exploring new phases and efficiently processing them for scientific and industrial applications.

## Methods

### Materials

The bulk of C-axis cut single crystal sapphire with a parallelepipedic shape having dimensions 20 × 10 × 3 mm³ is irradiated by an ultrafast laser pulse. The direction of laser radiation is perpendicular to the C-axis, 20 × 3 mm² face. Meanwhile, the polarization of the field is parallel to the C-axis.
Experimental setup

A pump and probe experimental assembly is used to perform time-resolved dynamics of
ultrafast laser-matter interaction (see Fig. 1).

Pump: ultrafast Bessel pulse

In order to generate an ultrafast Bessel pulse, an amplified vertically polarized Gaussian-
shaped ultrafast pulse, emitted by an ultrafast Ti: sapphire laser system (Coherent Legend
Elite), illuminates on an axicon of apex angle 179°. The pulse width is tunable in the range
of 50 fs to 5 ps by the compressor, while the assembly of a motorized tunable half-waveplate
and a thin-film polarizer controls the average power of the laser. The primary Bessel beam
is then projected into the sample. A 4-f setup comprises a 1000 mm lens and 20× infinity-
corrected Mityoto objective lens with an effective focal length of 10 mm and 0.42 NA, placed
after the axicon, tightly focusing the ultrafast Bessel beam on the sample plane, ensuring
an image of the Bessel beam demagnified by a factor of 100. The conical wavefronts after
the 4-f setup make a half-cone angle of 22° in free space and 12° inside the sapphire sample,
resulting in an ultrafast Bessel pulse with central spot width and depth of focus of 0.9 µm
and 60 µm, respectively, within the sample.

Probe: time-resolved phase-contrast microscopy

The probe system is arranged to observe the sample perpendicular to the direction of the pump, i.e. parallel to the c-axis, to avoid residual birefringence influences, displaying a longitudinal view of ultrafast Bessel pulse interaction within bulk sapphire. Zernike positive phase-contrast microscopy (PCM) assembled in an Olympus BX-51 microscope, attached with an electron multiplying charge-coupled device (EMCCD Andor iXon Ultra 897), is used to obtain high-quality images at different time delays between pump and probe. For illumination, a random lasing technique is used where the pulse is obtained by pumping a colloidal solution of Rhodamine B (2.5 g/l) and latex-nanobeads (0.32 µm) by a frequency-doubled
Nd: YAG ns-pulsed laser (7 ns, 532 nm, 10 Hz), synchronized with the pump laser.13 The Zernike positive PCM is restricted to qualitative phase information, as it converts the phase shift induced by the object into amplitude changes. Quantitative phase-contrast microscopy (QPM) is performed to obtain the quantitative phase changes by attaching a common-path diffraction-phase microscopy system (Phi Optics wDPM) in the same microscope. Which consists of a holographic arrangement that interferes the object observation with a self-reference filtered from the object, delivering absolute phase and amplitude information on the object.28 We used a 0.55 NA phase-contrast objective in an imaging system, followed by a spectral filter ($\lambda = 590$ nm, $\delta\lambda = 10$ nm) blocking the laser noise, allowing only the spatially low-coherent light of random lasing after interacting with the sample, delivering fringe and speckle-free images. However, phase-contrast images have inherent halo effects, which can restrict the capability of the technique in a few cases.

## Electron Microscopy

The scanning electron microscopy (SEM) uses a Zeiss Supra 55VP microscope to observe the ultrafast Bessel beam fabricated nanostructures. To expose the plane of structures, the bulk sapphire is polished using ion cross-polishing (Jeol IB-19530CP). Transmission electron microscope (TEM) JEOL NeoARM 200F facilitated crystalline structures and morphological analysis. The lamella for TEM analysis is prepared with a focused ion beam (FIB) milling, which induces a partial superficial amorphisation of the sample with respect to the pristine material, which is observed as a reduction of the contrast. The resolution, similar to the size of the structures, involves the acquisition of residual information about the crystalline surroundings. In addition to TEM observations, we also performed a transmission Kikuchi diffraction (TKD) analysis on the thin foil, carried out on a Zeiss SUPRA 55VP FEG-SEM system equipped with an Oxford Instrument Symmetry S2 electron backscatter diffraction (EBSD) detector, while mappings are acquired using AZTECHKL software. We measured $\Delta\beta_x$, $\Delta\beta_y$, and $\Delta\beta_z$ indicated the variation in the orientation of the crystalline plane in the
modified region with respect to the reference background measured in *x*, *y*, and *z* directions, respectively.

## Estimating change in refractive index

The quantitative phase changes $\Delta\varphi$, provided by the QPM observations, are used to calculate the variation in the refractive index. The detected phase change is the integral projection of the phase accumulated by light crossing the object, which has cylindrical symmetry. The evaluation of $\Delta n$ (the difference between the refractive index of the modified region and the crystalline background) will follow the inverse Abel transform method to determine the central peak change. Given an optical method and the sub-wavelength dimension of the object, nominally inferior to the optical resolution, a first evaluation is made using the optically detected size of the object ($d_{Opt} = 0.59 \ \mu m - 0.89 \ \mu m$), which is roughly the lateral optical resolution (the convolution between the object dimension and the microscope average response). This leads to a first underestimated value of $\Delta n$. This value is corrected by accounting for the real dimension of the object measured by SEM, giving the upper value of detection and setting, thus the confidence interval in $\Delta n$ measurement.

## Acknowledgements

The authors thank Javier Prada-Rodrigo for the discussions, Yaya Lefkir and Thomas Bilyk for helping with electron imaging, and Nicolas Faure for technical assistance in arranging the experimental setup.

## Funding Sources

This research was supported by the French National Research Agency (ANR) with the grants ANR-19-CE30-0036 and ANR-21-CE08-0005.

## Conflict of interest

The authors have no conflict of interest.
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For Table of Contents Use Only

Dynamic ultrafast laser-induced structural changes and
extreme nanostructuring in hard dielectric materials

Rajeev Dwivedi, Huu Dat Nguyen, Sergio Sao Joao, Anne-Magali

Seydoux-Guillaume, Thirunaukkarasu Kuppan, Ciro D'Amico, Guillaume

Kermouche, and Razvan Stoian*

razvan.stoian@univ-st-etienne.fr

<figure><img src="image_7.png" /><figcaption>Conceptual schematic of the pump-probe experiment, revealing temporal dynamics of crystalline to amorphous transition with time, Δt.</figcaption></figure>