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# Dynamic spatial beam shaping for ultrafast laser processing: a review

Cyril Mauclair, Bahia Najih, Vincent Comte, Florent Bourquard, Martin Delaigue

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Cyril Mauclair, Bahia Najih, Vincent Comte, Florent Bourquard, Martin Delaigue. Dynamic spatial beam shaping for ultrafast laser processing: a review. Opto-Electronic Science, 2025, pp.250002 - 250002. 10.29026/oes.2025.250002. hal-05104555

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Dynamic spatial beam shaping for ultrafast laser processing: a review

Cyril Mauclair, Bahia Najih, Vincent Comte, Florent Bourquard and Martin Delaigue

**Citation:** Mauclair C, Najih B, Comte V, et al. Dynamic spatial beam shaping for ultrafast laser processing: a review. *Opto-Electron Sci* **4**, 250002 (2025).

https://doi.org/10.29026/oes.2025.250002

Received: 15 January 2025; Accepted: 24 March 2025; Published online: 6 June 2025

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DOI: 10.29026/oes.2025.250002

CSTR: 32246.14.oes.2025.250002

# Dynamic spatial beam shaping for ultrafast laser processing: a review

Cyril Mauclair<fnref n="1" />*, Bahia Najih²,³, Vincent Comte⁴,⁵, Florent Bourguard² and Martin Delaigue³

This review examines the state-of-the-art in spatial manipulation of ultrafast laser processing using dynamic light modulators, with a particular focus on liquid crystal-based systems. We discuss phase modulation strategies and highlight the current limitations and challenges in surface and bulk processing. Specifically, we emphasize the delicate balance between high-fidelity beam shaping and energy efficiency, both critical for surface and bulk processing applications. Given the inherent physical limitations of spatial light modulators such as spatial resolution, fill factor, and phase modulation range. We explore techniques developed to bridge the gap between desired intensity distributions and actual experimental beam profiles. We present various laser light modulation technologies and the main algorithmic strategies for obtaining modulation patterns. The paper includes application examples across a wide range of fields, from surgery to surface structuring, cutting, bulk photo-inscription of optical functions, and additive manufacturing, highlighting the significant enhancements in processing speed and precision due to spatial beam shaping. The diverse applications and the technological limitations underscore the need for adapted modulation pattern calculation methods. We discuss several advancements addressing these challenges, involving both experimental and algorithmic developments, including the recent incorporation of artificial intelligence. Additionally, we cover recent progress in phase and pulse front control based on spatial modulators, which introduces an extra control parameter for light excitation with high potential for achieving more controlled processing outcomes.

**Keywords:** spatial light modulator; ultrafast laser processing; spatial beam shaping; laser surface structuring; laser bulk structuring

Mauclair C, Najih B, Comte V et al. Dynamic spatial beam shaping for ultrafast laser processing: a review. *Opto-Electron Sci x*, 250002 (2025).

## Introduction

The use of ultrafast laser pulses for surface and bulk processing is a technique that has now several applications due to the high degree of structuring precision because of its particular light-matter interaction with low thermal side-effects<fnref n="1" />,². The field has known a recent change of paradigm with the development of Ytterbium-based

laser sources and amplifiers with scalable architectures³,⁴ that allowed for high power and high pulse repetition rates with a much higher degree of stability than the historical Ti:Sa based platform⁵⁻⁶⁷.

This technological breakthrough has opened many doors for biomedical and industrial applications as power and speed (i.e repetition rate) of the laser sources are not anymore the main limitations to most of the processing

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<footnote n="1">¹Université d'Angers, LPHIA, SFR MATRIX, 49000 Angers, France; ²Laboratoire Hubert Curien, UMR 5516 CNRS, Université Jean Monnet, 42000 Saint-Étienne, France; ³Amplitude, 33600 Pessac, France; ⁴Laboratoire BiiO, Université Jean Monnet, 42000 Saint-Étienne, France; ⁵Keranova, 42000 Saint-Étienne, France.</footnote>

<footnote>*Correspondence: C Mauclair, E-mail: cyril.mauclair@univ-angers.fr</footnote>

<footnote>Received: 15 January 2025; Accepted: 24 March 2025; Published online: 6 June 2025</footnote>
applications. Indeed, the current main question is how to
handle so many and so intense pulses in an effective
way? Most of the time, micro processing applications do
not require more than a few µJ per pulse (eye surgery<sup>8,9</sup>,
surface or bulk nano or microstructuring<sup>10,11</sup>,
ablation<sup>12,13</sup>, glass sculpting<sup>14</sup>, bulk photoinscription<sup>15</sup>,
photopolymerisation<sup>16</sup> etc.). Higher pulse energy often
lead to unwanted side effects either within the processed
area or along the beam propagation path before reach-
ing the target. In the first case, too large pulse energies
decrease the material removal efficiency (the ratio of the
ablated mass with respect to the number of photons)<sup>17</sup>
and may add chaotic surface structuring<sup>18,19</sup>. Similar
problems are encountered in bulk processing where un-
controlled cracking can occur<sup>20</sup>. In the second case, beam
deformation may take place in air when a focused region
is necessary before reaching the target or within the bulk
when focusing inside transparent materials<sup>21,22</sup>.

High repetition rates also constitute a challenge by
themselves. The high degree of processing precision as-
sociated with ultrafast pulses is mainly related to a light-
matter interaction with a much lower onset of thermal
effects than in the case of longer laser pulses<sup>12,23</sup>. When
sending pulses at MHz repetition rates or more, thermal
relaxation between pulses is no longer ensured even on
metals leading to uncontrolled structuring on surfaces
and inside transparent materials<sup>24,25</sup>. We note here that
sometimes, melted and re-solidified structures can be of
interest to confer specific properties to the surface, like
hydrophobicity<sup>26</sup> but also to accelerate the process of
percussion drilling<sup>27</sup>. However, high repetition rate man-
agement usually consists in very high speed scanning of
the laser spot to reduce the pulse spatial overlap on the
target. This is now a bottleneck of femtosecond surface
processing, leading to the developments of high deflec-
tion speed polygonal scanners<sup>28,29</sup>, or electro/acousto-op-
tic scanners<sup>30</sup>. Let us mention here that even higher repe-
tition rates (of a few GHz and above) lead to phenomena
where enhanced ablation is achieved with low onset of
side thermal effects, refereed to as the ablation-cooled
regime<sup>31,32</sup>. In this regime however, the most efficient ab-
lation and milling regimes are usually accompanied with
lower surface quality, requiring additional low pulse en-
ergy processing<sup>33</sup>.

Apart from high speed scanning, the alternate and
complimentary strategy to maintain proper processing
conditions with high energetic and high repetition rate
laser sources is to adapt the beam intensity distribution

to the adequate fluence level. Most of the time, the laser
beam is quite strongly attenuated with half waveplate
and polarizer and filters<sup>2</sup>. If the technique is simple and
efficient for experimental research, it is obvious that such
an additional waste of energy is simply not acceptable for
industrial application; especially considering the very low
energy efficiency of high power lasers<sup>4,34</sup>.

Let us recall that laser spot enlarging to decrease the
peak intensity towards the adequate fluence can be per-
formed using lenses or parabolic mirrors. However this
techniques obviously augments the laser spot size and
thus the interaction area. As a consequence, it cannot by
applied to many ultrafast laser processing applications
where a typical micrometric spatial structuring resolu-
tion is required. This is where dynamic spatial beam
shaping comes to play<sup>35-37</sup>. By sculpting the laser intensi-
ty distribution in a quasi-arbitrary manner (with some
limitations that will by addressed later), both precision
and proper fluence levels can be combined. In the fol-
lowing, we strive to give a rather complete picture of the
technique of dynamic spatial beam shaping in ultrafast
processing. An emphasis on liquid crystal based spatial
phase modulators is given due to their intrinsic advan-
tage of dynamic reconfigurability and high laser energy
efficiency.

After describing the current state of the art of the
commercially available light modulators with their devel-
opment trends and limitations, we present the main
strategies currently used for light modulation pattern
calculation and discuss their shortcomings when it
comes to the experimental implementation. An overview
of applications in a wide variety of fields is then given
with a particular effort to confront some results with the
technological and algorithmic limitations. After that, we
review some applications of spatial beam shaping involv-
ing precision surface structuring and bulk structuring.
The generation and use of non-diffractive beams for
drilling and cutting is then addressed followed by vortex
beam shaping and spatial polarization shaping. We then
discuss additive manufacturing applications taking ad-
vantage of spatial beam shaping. The latest algorithmic
and experimental improvements are also revised with an
emphasis on feedback assisted optimization loops and
artificial intelligence computation strategies. In some
cases, these progresses are not directly related to laser
processing applications, but the attained level of perfor-
mance triggers a strong interest for the topic of this re-
view. Finally, recent results concerning spatiotemporal
effects involving pulse front control are described due to their strong potential of excitation localization control in ultrafast laser processing.

## Basics of dynamic spatial beam shaping

An historical example of spatial beam control can be found in the report of the siege of Syracuse 212 BC. Following Archimedes instructions, numerous parabolic reflective surfaces (probably polished shields of Cu or bronze) were positioned to redirect and focus the light rays from the sun onto the Roman fleet boats. Interestingly, the experience was repeated by a group of students of the MIT in October 2005. Fire ignition was obtained on wood³⁸. The city was eventually invaded by the Romans, as a very early proof of the fact that spatial beam control requires careful developments and optimizations to reach its target.

Much more recently, it is interesting to note that the keywords 'beam shaping' and 'laser beam shaping' have known a continuous gain of utilization in scientific articles over the last twenty years, with a doubling occurrence factor between 1990 and 2020 (extraction from Google Scholar database using the Python script in ref.³⁹). When handling a light beam emitted from a stable laser cavity, the spatial intensity repartition of the fundamental mode detected in a given plane $I(x, y)$ is most of the time represented by a Gaussian distribution. In the frame of the paraxial approximation (i.e the transverse beam dimensions remain small enough compared to propagating distances), a quite famous solution to the scalar wave equation designed to represent laser emission is the Gaussian beam⁴⁰. Thus, $\tilde{u}(x, y, z)$ takes then the form:

$$ \tilde{u}(x, y, z) = \frac{u_0}{q(z)} \exp \left( -ik \frac{x^2 + y^2}{2q(z)} \right), \quad (1) $$

where

$$ \frac{1}{q(z)} = \frac{1}{R(z)} - \frac{i\lambda}{\pi w^2(z)} = \frac{1}{q_0 + z}, \quad (2) $$

$R(z)$ is the wavefront radius of curvature. It is worth noting the $z$ dependency, meaning that any beam modulation in amplitude or in phase has a consequence in the transverse plane and along the propagation axis. $w(z)$ is the beam radius at $\frac{1}{e^2}$ of the intensity profile $I(x, y, z) = \tilde{u}(x, y, z) \times \tilde{u}(x, y, z)^*$ which follows a Gaussian distribution. $q(z)$ is the complex beam parameter.

This quantity allows for a complete spatial definition of the Gaussian beam with the relation $q(z) = q_0 + z$. Taking the origin of the $z$-axis at $z = 0$ at the waist position $w(z) = w_0$ we have $R(z) = \infty$ meaning that at this point the wavefront is a plane orthogonal to the propagation axis (although not to be confused with a plane wave⁴¹).

From these equations, it can be seen that any modulation of amplitude and/or wavefront in a given $x-y$ plane has an impact on the subsequent laser intensity distribution in further $x-y$ planes and along the $z$ axis. For example, if a laser beam goes through a converging lens of focal length $f$, the corresponding parabolic wavefront modulation can be taken into account by adding the phase term $\phi_f = -i\pi \frac{x^2 + y^2}{\lambda f}$ in the exponential of Eq. (1). This modulation enters in competition with the intrinsic divergence of the Gaussian beam wavefront represented by the term $-ik \frac{x^2 + y^2}{2q(z)}$. Thus, the lens alters the beam size, ultimately leading to a focal spot at the position $z = f$. More generally, if the laser beam encounters any spatial phase modulation $\phi_M$ or any amplitude modulation, those can be mathematically applied by a factor to Eq. (1) with consequences on the propagated laser beam profile.

Following ref.⁴², within the paraxial approximation and neglecting spectral effects, the transverse intensity profile $I(x', y')$ after propagation over the distance $D$ of a Gaussian laser field of amplitude $\tilde{A}(x, y)$ focused by a lens of focal distance $f$ is defined by:

$$ I(x', y') \propto |\mathcal{F}_{f_{x'}, f_{y'}}[\tilde{A}(x, y)e^{-\phi_D + \phi_f + \phi_{Ab} + \phi_M}]|^2, \quad (3) $$

where $\mathcal{F}_{f_{x'}, f_{y'}}$ is the two-dimensional (2D) Fourier transform with respect to the spatial frequencies in the $(x', y')$ plane, $\lambda$ is the laser wavelength, $\phi_D = i\pi \frac{x^2 + y^2}{\lambda D}$ is the phase term corresponding to the beam propagation over $D$, $\phi_{Ab}$ comprehends the optical aberrations and $\phi_M$ stands for the phase modulation purposely added on the beam path to control $I(x', y')$. Usually, this plane of interest is the focal plane of a lens or a focusing element, where both the maximum of intensity and ultimate resolution can be reached. This focal intensity distribution in and around the focal plane can be computed from Eq. (2) using the fast Fourier transforms (FFT) readily available in many computing languages⁴². The concept of ultrafast laser beam shaping is illustrated by Fig. 1. By tuning the amplitude and/or the wavefront of the laser before the focusing element, it is possible to control the focal intensity distribution. Amplitude modulation techniques
have shown interesting results for ultrafast laser processing with relatively simple experimental apparatus like slit shaping for bulk transverse waveguide photoinscription$^{43}$, iris imaging for surface structuring$^{21}$ or more advanced set-up involving dynamic reconfigurability$^{44}$. However, the amplitude modulation inevitably implies a significant loss of laser energy in the blocked parts of the beam. Thus, we focus in the following on wavefront modulation, a technique that potentially preserves all the laser energy which is required for efficient surface or bulk processing. Phase modulation masks are placed on the ultrafast laser beam path and permit to shape the focal intensity distribution by generating arrays of spots, changing the spot shape or controlling the beam diffraction around the focal plane as illustrated in Fig. 1. The light modulator device allows for dynamic changes of the wavefront modulation $\phi_M$ that can be operated during laser processing giving a higher degree of efficiency and flexibility to the process.

Let us briefly precise that this report considers light pulses whose spectral bandwidth can be assumed thin enough so that any chromatic aberration can be disre-

garded in a first approximation (the situation will be different in Section Perspectives offered by spatio-temporal where spatiotemporal effects will be considered). When dealing with ultrafast laser pulses from Ti:Sa lasers at 800 nm, the spectral bandwidth can be as large as 100 nm for a Fourier-limited 10 fs pulse (i.e a pulse whose spectral components are not temporally spread$^{41}$). In the other way around, 100 fs pulses carry a 10 nm spectral bandwidth. Let us consider a simple converging lens. The chromatic aberrations implies that rays associated with the redder part of the spectrum are focused further than the bluer one. Given the focal length $f$ of a lens of refractive index $n$, the axial spreading $\Delta f$ around $F$ along the propagation axis writes:

$$ \frac{\Delta f}{f} = \frac{\Delta \lambda}{\lambda} \frac{\Delta n}{n-1}, \qquad (4) $$

with $\Delta \lambda \approx 10$ nm being the laser source relatively narrow spectral bandwidth centered on 800 nm and $\Delta n$ the refractive index difference for the boundary wavelength of the laser spectrum obtained from the Sellmeier relations$^{45}$. For a fused silica lens, $\frac{\Delta f}{f} = 4.8 \times 10^{-6}$,

<figure><img src="image_9.png" /><figcaption>Fig. 1 | Principle of spatial beam shaping of ultrafast laser. A light modulator (transmittive or reflective) is placed on the laser beam path. It imprints a wavefront modulation (modulation mask) that rearranges the laser intensity distribution in a further plane of propagation, usually the focal plane of a converging element. There, a variety of beam distributions can be obtained in the three dimensions, from multi-spot arrangement to continuous beam shapes, as well as non-diffracting beams.</figcaption></figure>
corresponding to a few nanometers in the case of a focal length of $f=1$ cm which is clearly negligible compared to the micrometric dimensions of the focal intensity distribution. In this latter case and for even thinner spectral bandwidth (e.g Ytterbium-based ultrafast laser with $\Delta\lambda$ below 7 nm and $\approx 300$ fs pulse duration), it is thus quite reasonable to neglect the effect of chromatic aberration. This being said, research efforts have focused on adapting spatial beam shaping techniques to accommodate large spectral bandwidth ultrafast pulses. The strategy involves using consecutive diffractive optical elements for successive beam shaping planes, followed by dispersion-related compensation$^{46,47}$. Additionally, it is noteworthy that wavefront shaping with intensity feedback can mitigate these types of non-uniformities, requiring only a single reconfigurable wavefront shaper$^{48}$.

## Dynamic spatial beam shaping apparatus

Dynamic wavefront modulation for spatial beam shaping can be performed through several techniques, we

have retained 5 of them that present interesting performances and are well-known to the community.

Spatial light modulators (SLM) based on a liquid crystal layer are widespread components in photonics with a large variety of applications including laser processing, imaging, communications (refer to an interesting review here$^{49}$). They have triggered much attention in the field of laser processing$^{50}$ and significantly enhanced the capabilities of ultrafast laser processing$^{51}$. As illustrated in Fig. 2(a)), the LC layer can act as a dynamic phase retardation map thanks to the possibility to orientate the LC molecules with a local electric field. The principle is applicable in reflection or in transmission with a photoconductive material$^{52}$. The SLM technology has known remarkable advances in terms of resolution and fill factor$^{49}$ allowing for more controlled beam shapes. Their typical pixel size is now below 5 µm with 4k definition and a refresh rate of 50–100 Hz commercially available. The phase range is usually $2\pi$. Power handling and response time are the two main directions of developments$^{53,54}$,

<figure><img src="image_10.png" /></figure>

**Fig. 2** | Main experimental systems for dynamic wavefront modulation. (a) Spatial light modulators (SLM) are based on a liquid crystal (LC) layer whose molecules can be orientated under an electric field *E*, permitting to dynamically control the spatial optical retardation of an impinging laser beam. (b) Deformable mirrors (DM) rely on a similar principle with actuators whose controllable height defines the optical retardation on the beam wavefront. They can be membrane-based or segmented. (c) The acousto-optic deflectors (AOD) are based on the generation of sound waves inside a crystal (e.g. TeO₂ or PbMoO₄). The related periodical variation of refractive index also permits wavefront modulation. (d) The multi-plane light conversion (MPLC) set-up is based on spatial mode conversion through successive passages on specifically designed phase retardation maps. (e) The general phase contrast method (GPC) relies on the principle of phase contrast microscopy where the transparent pure-phase sample corresponds to a controlled phase modulation (applied with an SLM for example) and the phase contrast filter (PCF) is the optical element turning this modulation into an intensity contrast in an imaging plane. See text for more details.
noteworthy following the advances of ultrafast laser systems in terms of average power and repetition rates.

Deformable mirrors (DM) are very well-known devices used in adaptive optics to correct for geometrical aberrations. As illustrated in Fig. 2(b)), controlling the height of a series of actuators permits to modulate the laser wavefront reflected on the device. The DMs can be membrane-based or segmented. The reflection principle gives an advantage other SLM in terms of power handling potential<sup>55</sup>, however DMs generally offer only a few tens of actuators across the modulation pupil and their response time is larger. As a consequence, the variety of phase modulation that DMs can reproduce is limited compared to SLMs and phase mask calculation are usually based on the first Zernike coefficients or on each actuator successive adjustment using iterative optimization algorithms<sup>56</sup>. An interesting study uses an SLMs to simulate the effect of changing the DM actuators size on the beam shaping quality<sup>57</sup>. Let us include in this family the DMD (digital micromirror device), mostly used for display application. DMD show a much thinner surface element resolution (a few micrometers) with short response time (≈ ms). However only 2 surface states available (mirror tilt angle), reducing the applications to light amplitude masking, or very particular wavefront shaping based on binary amplitude holograms (a complete review of DMD performances and applications can be found here<sup>58</sup>.

Deformable mirrors (DM) are very well-known devices used in adaptive optics to correct for geometrical aberrations. As illustrated in Fig. 2(b)), controlling the height of a series of actuators permits to modulate the laser wavefront reflected on the device. The DMs can be membrane-based or segmented. The reflection principle gives an advantage other SLM in terms of power handling potential<sup>55</sup>, however DMs generally offer only a few tens of actuators across the modulation pupil and their response time is larger. As a consequence, the variety of phase modulation that DMs can reproduce is limited compared to SLMs and phase mask calculation are usually based on the first Zernike coefficients or on each actuator successive adjustment using iterative optimization algorithms<sup>56</sup>. An interesting study uses an SLMs to simulate the effect of changing the DM actuators size on the beam shaping quality<sup>57</sup>. Let us include in this family the DMD (digital micromirror device), mostly used for display application. DMD show a much thinner surface element resolution (a few micrometers) with short response time (≈ ms). However only 2 surface states available (mirror tilt angle), reducing the applications to light amplitude masking, or very particular wavefront shaping based on binary amplitude holograms (a complete review of DMD performances and applications can be found here<sup>58</sup>.

Acousto-optic deflectors (AOD) are devices whose primary goal was not related to beam shaping but to high speed deflection for multiplexing and demultiplexing optical signals and beam scanning<sup>30</sup>. By generating sound waves inside a crystal (e.g. TeO<sub>2</sub> or PbMoO<sub>4</sub>) with a transducer, a periodic pattern of varying refractive index is generated and diffracts the laser beam. Thus, the phase modulation relies on the sum of periodic signals that are sent to the transducers (in x and y) where each diffraction angle contribute to the desired beam shape<sup>59</sup> as shown in Fig. 2(c)). Even though this technique doesn't offer the large flexibility and precision of SLMs, AODs have the advantage of much quicker response time and an inherent intensity smoothing effect due to the chromatic aberration associated with the diffraction angles, even though this also degrades the ultimate beam spot size<sup>60</sup>.

The multi-plane light conversion (MPLC) set-up is based on the principle of spatial mode conversion through successive phase retardation masks that can be displayed with an SLM or with fabricated phase plates<sup>61</sup>. In the reflection scheme as depicted in Fig. 2(d)), several beam reflections on a modulation plate permit the mode conversion<sup>62</sup>. This technique was initially developed for the field of optical telecommunication for optical signal multiplexing and demultiplexing and is now gaining a strong interest for laser surface processing with high power lasers and ultrafast lasers<sup>63,64</sup>. With the advantage of high power handling thanks to the reflection scheme, the MPLC lacks dynamic straightforward reconfigurability, unless a SLM is incorporated as the modulation plate or if the modulation plate is designed to perform different shaping for different angles of the incident beam<sup>63</sup>.

We also have to mention here the technique of general phase contrast (GPC) at the frontier of amplitude and phase modulation<sup>65,66</sup>. This elegant technique relies on the principle of phase contrast microscopy (PCM). There, the portion of the light beam that is diffracted by the observed phase sample is purposely put in interference with the non diffracted beam (the background light in PCM). That way, the phase contrast is turned to an intensity contrast on the microscope camera<sup>67</sup>. In the case
of laser beam shaping, the plane of wavefront regulation corresponds to the sample plane of the phase contrast microscope. In order to turn this phase modulation to an intensity modulation, the GPC method employs a phase contrast filter (PCF) positioned at the focal plane of a lens (Fig. 2(e))). The wavefront modulation plane is conjugated on the PCF through a lens and then the PCF is conjugated to the imaging plane. GPC achieve much lower laser intensity losses as compared to amplitude modulation⁶⁸. This technique gives remarkable beam shaping qualities and is successfully employed in the field of optical tweezers⁶⁹. The challenge with this technique for laser processing is related to the small disk in the focal plane of the lens. In the case of femtosecond laser with high intensity, this element can be damaged because of the laser focusing on the disk, or detrimental nonlinear propagation effect can occur and deteriorate the desired beam distribution.

Another technique that has to be discussed here is the direct laser interference patterning (DLIP) that is based on the interference of two or more coherent laser beams usually coming from the same laser source. The interference pattern constitutes a tunable intensity distribution

that depends on the number of beams and their phase and angle relationship⁷⁰. Those parameters can be tuned with diffractive optical elements (DOE) or SLMs for a higher degree of reconfigurability⁷¹⁻⁷³. Recent efforts have been conducted towards higher processing rates including coupling with scanners and roll to roll processes⁷⁴,⁷⁵.

Let us also mention the tunable acoustic gradient index of refraction lens or TAG-lens which is a liquid z-scanning lens operating at 0.1–1 MHz⁷⁶ permitting a very quick axial displacement of the focused laser spot enabling enhanced depth of field laser processing⁷⁷ and that has recently been used for simultaneous laser surface processing and monitoring at high speed⁷⁸. The Table 1 summarizes the main characteristics of these phase modulation devices.

We now briefly consider the capacity of these apparatus in terms of laser power and fluence handling. From a general point of view, all the methods based on reflection can benefit from the possibility to have very high laser induced damage threshold (LIDT) reflective layer, well-adapted to the laser wavelength. This includes the DMs, DMDs, MPLC and the DLIP (unless the beam

<table><caption>**Table 1** | Comparison of dynamic wavefront modulation techniques for ultrafast laser spatial beam shaping. See text for more details and relevant references.</caption><thead><tr><td>Technique</td><td>Principle</td><td>Advantages</td><td>Disadvantages</td><td>Common applications</td></tr></thead><tbody><tr><td>Spatial light modulators (SLM)</td><td>Liquid crystal layer controlled by electric field</td><td>High resolution (pixel size &lt; 5 µm), 2π phase range, flexible modulation</td><td>Limited power handling, slow response time (50–100 Hz)</td><td>Ultrafast laser processing, holography, optical trapping, imaging, communications</td></tr><tr><td>Deformable mirrors (DM)</td><td>Actuator-driven mirror surface modulation</td><td>High power handling, non-pixelated</td><td>Limited spatial resolution (tens of actuators), slower than SLMs</td><td>Adaptive optics, aberration correction, laser beam shaping</td></tr><tr><td>Digital micromirror devices (DMD)</td><td>Binary tilting micromirrors</td><td>Fast response time (≈ ms), high resolution</td><td>Binary phase modulation or amplitude control (energy losses)</td><td>High-speed imaging, beam steering, structured illumination</td></tr><tr><td>Acousto-optic deflectors (AOD)</td><td>Sound waves generating a refractive index modulation in a crystal</td><td>Fast modulation, inherent smoothing effect</td><td>Dispersion degrades focus, limited shaping flexibility</td><td>Beam scanning, multiplexing, ultrafast switching</td></tr><tr><td>Multi-plane light conversion (MPLC)</td><td>Successive phase masks for spatial mode conversion</td><td>High power handling, mode conversion flexibility</td><td>Limited dynamic reconfigurability unless SLM-based</td><td>Optical telecommunications, ultrafast laser processing, structured beam generation</td></tr><tr><td>General phase contrast (GPC)</td><td>Phase modulation converted to intensity contrast using phase contrast filtering</td><td>Low energy losses, high contrast beam shaping</td><td>Sensitive to high intensity femtosecond lasers (potential nonlinear effects)</td><td>Optical tweezers, phase imaging, structured light applications</td></tr><tr><td>Direct laser interference patterning (DLIP)</td><td>Interference of multiple laser beams to create structured intensity distributions</td><td>Large beam patterning</td><td>Requires phase control, limited to periodic structures</td><td>Surface structuring, micro/nanopatterning, high-rate laser processing</td></tr><tr><td>Tunable acoustic gradient (TAG) lens</td><td>Liquid lens modulated by acoustic waves for fast axial focus control</td><td>MHz-scale modulation, fast depth scanning</td><td>Limited lateral shaping capability</td><td>High-speed laser processing, real-time depth control, imaging</td></tr></tbody></table>
duplication is achieved with a DOE). Examples of con-
tinuous kW lasers used with such coated devices can al-
ready be found<sup>63,79</sup>. Considering the current efforts to op-
timize the interplay between the electric field distribu-
tion, refractive index and intrinsic LIDT of the dielectric
layers, there is little doubt that this can be extended to
high power ultrafast sources as recent developments have
shown optimized multi-layer schemes with a LIDT pos-
sibly surpassing 2 J/cm<sup>2</sup> for ultrafast pulses<sup>80</sup>. LIDT ap-
pears to be more problematic for devices requiring trans-
mission through a modulating medium as for SLMs,
GPC, AOD and TAG lenses. Interestingly, the liquid
crystal LIDT has been recently studied for ultrafast pul-
es at various repetition rates, with values ranging from
1.1 to 0.07 J/cm<sup>2</sup> for single shot and 1 MHz regime, re-
spectively, showing the problematic decrease of LIDT at
high repetition rates<sup>81</sup>. The relatively high damage
threshold at single shots has triggered efforts to use galli-
um nitride for the transparent electrodes in the case of
all-optical SLMs<sup>82</sup>. However, the LIDT decrease with the
repetition rate has motivated SLM fabricants to propose
cooled systems with sapphire cover glass for enhanced
heat dissipation, allowing the use 183 W picosecond
pulses at 1 MHz<sup>83,84</sup>. Lower LIDT should be expected for
TAG lenses, AOD and GPC. Indeed, TAG lenses require
a liquid (usually a silicon oil<sup>76</sup>), AOD are based on a crys-
tal (TeO<sub>2</sub>) and GPC relies on a phase filtering element at
the focal plane. Thus, a reduced capacity in terms of
LIDT and power handling at high repetition rates can be
expected. Moreover; nonlinear propagation effects can
also intervene in these media before damage, degrading
the beam propagation conditions and ultimately the
beam shaping quality at lower laser power. Indeed, the
nonlinear refractive index of common liquid crystals like
MLC2132 has been recently measured at ≈ 40 × that of
fused silica for ultrafast pulses<sup>85</sup>, similar values were ob-
tained for TeO<sub>2</sub> crystals<sup>86</sup> meaning that nonlinear beam
degradation before LIDT can also be envisaged at high
laser powers.

Now that the main wavefront modulation techniques
were accounted for, and especially the ones that have al-
ready been used for ultrafast laser processing, we focus
on the calculation strategies of the modulation masks.

Calculation of the phase modulation

There are many solutions to calculate the proper spatial
phase modulation, called phase mask of computer gener-
ated hologram (CGH). Usually, the phase modulation

plane corresponds to the object focal plane of the focus-
ing lens. In this case, a Fourier transform permits to
mathematically relate the complex laser amplitude of this
plane to the focal plane under the paraxial approxima-
tion⁴² (If the phase modulation is performed in another
plane, a parabolic phase term may be added to the calcu-
lation). Thus, the calculation of the proper phase modu-
lation φ<sub>M</sub> for a desired intensity distribution can be
based on optimization algorithms relying on one or sev-
eral Fourier transforms. Three main calculation strate-
gies are illustrated by Fig. 3.

The most famous one is the gerchberg-saxton algo-
rithm or iterative Fourier transform algorithm (IFTA)⁸⁷.
This deterministic algorithm performs back and forth
propagation steps between the phase modulation plane
and the focal intensity target plane, with the constraints
of the desired focal target intensity and the original laser
beam profile. Iterations go on until a phase mask per-
mits to obtain a intensity in the focal plane close enough
to the target. Many improvements have been proposed
for this algorithm, such as extension to N-planes (in 3 di-
mensions)⁸⁸, dynamic adaptation of the target
intensity⁸⁹,⁹⁰, introduction of a 'numb' region for high fi-
delity shaping⁹¹,⁹² and so on. It is interesting to note that
many of these improvements have been triggered by the
fields of optical tweezers and atomic cooling. More de-
tails on these recent advances permitting to overcome
the SLMs limitations are given in Section 4.

When the intensity target is an array of distinct spots,
the lens and gratings (LG) techniques are particularly
adapted. The LG is based on the fact that each desired
laser spot in the focal region corresponds to a given
beam deflection and defocusing i.e a phase tilt and phase
second order curvature. A complex sum of each contri-
bution permits to generate the desired phase mask, with-
out the need of any optimization step⁹³,⁹⁴ as illustrated in
Fig. 3(b). This strategy can also include position-dep-
dent aberration correction and arbitrary intensity
levels⁹⁵. The LG strategy is similar to the generation of
spot arrays with kinoforms from the optimization rota-
tion angle algorithm⁹⁶ or with Dammann cells⁹⁷ that has
also been extended in the 3D⁹⁸. The phase modulation
can also be calculated based on an ensemble of Fresnel
lenses, each lens corresponding to one laser spot³⁶. Re-
searchers have also taken advantage of the Talbot effect,
also enabling multispot generation in the 3 dimensions
with the possibility to combine it with helical wavefront
shaping⁹⁹.
<figure><img src="image_11.png" /><figcaption>**Fig. 3** | Main calculation strategies for determination of the spatial phase modulation $\phi_M$. (a) The iterative fourier transform algorithm (IFTA) based on FFT iterations between the modulation and the shaping planes. (b) The lens and grating (LG) calculation relies on the complex sum of phase masks to generate arrays of laser spots in 3D. (c) The global optimization algorithms encompass all the strategies that permit to 'guess' the optimal $\phi_M$ through stochastic optimization (simulated annealing, evolutionary algorithm etc.) or machine learning strategies (neural network etc.).</figcaption></figure>

The third calculation strategy concerns global optimization algorithms (GOA). For this report, we include non-deterministic algorithms encompassing both randomized optimization algorithms and machine learning strategies. The goal is to determine the phase modulation mask $\phi_M(x, y)$ that permits to achieve a user-defined intensity distribution. The algorithm must walk a very large search space constituted by all the phase values that the phase modulator offers. The optimization can be performed numerically using e.g FFT or experimentally by measuring the laser intensity distribution. Thus, probabilistic techniques have been used for spatial beam shaping like gradient descent¹⁰⁰ simulated annealing⁵⁶, evolutionary algorithms¹⁰¹ for spatial beam shaping but also for aberration corrections. More recently, machine learning has gained interest for laser beam shaping as discussed in Section *Advances in dynamic spatial beam shaping*.

## Surface and bulk structuring with spatially shaped ultrafast laser

### At the micrometric scale

In order to increase the efficiency and flexibility of the process, spatial beam shaping was rapidly included to ultrafast laser processing set-ups. The possibility offered by

femtosecond pulses to produce surface and bulk structuring on multiple scale, from the nanometer to the millimeter range has motivated the researchers to make the most of all the available laser energy. Figure 4(i) illustrates various examples of surface ablation and structuring performed with the help of dynamic spatial beam shaping. An array of laser spots evidently enables parallel micromachining, thus reducing the operation cost and time. Static microlens arrays have been used quite early for parallel machining, for example to perform parallel photopolymerisation¹⁰⁶. Examples of surface structuring with dynamic spatial shaping using SLMs are illustrated in Fig. 4(a–d) with the pioneering results of G Dearden team³⁷. Note that the array of impacts on silicon forming the 'Liverpool' word is the result of 15 irradiation steps with different arrays of 7–9 laser spots and no sample displacement, illustrating another advantage of using spatial beam shaping for rapid processing (see Fig. 4(a)). Similar results on tempered glass were reported (see Fig. 4(b)) with an array of 9 laser spots. Interestingly, the treatment confers anti-reflection properties to the surface¹⁰² thanks to the presence of laser induced surface structures (LIPSS) with nanometric surface modulation prone to optical effects in the visible range¹¹,¹⁰⁷,¹⁰⁸. Noteworthy, these LIPSS patterns can be orientated with the laser polarization offering a precise control of the
related diffractive effect¹⁰⁹. Thus, by generating large and uniform laser intensity distributions combined with fast scanning, rapid surface structuring at the nanometric scale is rendered possible¹¹⁰,¹¹¹. Surface processing with an array of spots combined with fast scanning of the femtosecond laser beam is shown on Fig. 4(c). The structuring permits to control the surface tribological properties in a lubricated environment¹¹². Another interesting example of parallel spot structuring involves the use of 15 parallel spots to generate oleophilic and hydrophobic properties on copper mesh¹¹³ (not shown). The spot parallelization has also an interest for more rapid cutting when the processing direction follow the laser spot array orientation thus reducing the number of scans while keeping the proper fluence level¹¹⁴. Pushing the limit of the number of parallel spots to more than 1000 was demonstrated by the team of Y Hayasaki⁴⁸. Even though numerical optimizations were put into play, it can be observed that difficulties arise to maintain a good level of homogeneity for each of the multiple laser spots (see the corresponding irradiation impact on Schott B270 glass on Fig. 4(d)).

Shaping the spot form itself can also increase processing efficiency. Contrary to the regular Gaussian distribution, top-hat intensity repartitions allow for more uni-

form irradiation level on the sample, thus several static optical elements are commercially available to perform the Gaussian to top-hat conversion⁶⁴,¹¹⁵ with an interest for a better control of the pulse overlap for surface machining¹¹⁶. By using an all-optical SLM, Sanner et al. have early demonstrated the generation and use of squared top-hat beam for ultrafast machining Fig. 4(e1) and 4(e2))³⁵,¹¹⁷). More advanced intensity distributions such as data-matrix or Fresnel lens patterns were achieved as illustrated in Fig. 4(f) and 4(g) with SLM.

We would like to point out here two limiting factors that deteriorates the beam shaping fidelity and energetic efficiency. First, the so-called 0th order is an unwanted laser spot that gathers all the non properly addressed parts of the beam due to fill factor and other limits of the SLMs. If not taken care of, this additional spot is a detrimental waste of energy and may even badly impacts the surface as clearly visible on Fig. 4(a), 4(d) and 4(f2). Researchers have developed many strategies to overcome this issue that are discussed in Section *Advances in dynamic spatial beam shaping*. Second, the speckle effect deteriorates the homogeneity of continuous beam shapes as visible on Fig. 4(e1) and 4(f1). Usually, the phase value on the SLM (or DM/AOM) is adjusted to control the intensity distribution (i.e the amplitude) in the target

<figure><img src="image_12.png" /><figcaption>**Fig. 4** | Surface structuring with dynamic wavefront shaping. (a) Array of impacts on silicon using 15 irradiation steps, the unwanted 0th order leaves a strong crater at the top of the array. (b1) Parallel structuring of tempered glass using an array of 6 laser spots with anti-reflection properties due to the LIPSS (b2). (c) Combination of multispot shaping and beam scanning for stainless steel surface processing conferring friction reduction properties. (d) Reaching more than 1000 laser spots in a single irradiation on glass (Schott B270), note the effect of the unwanted 0th order. (e1) Square top hat beam with corresponding crater on steel (e2). (f1) Shaping of arbitrary intensity distributions with the detrimental speckle effect and its marking on photoresist (f2) with a strong crater at the 0th order position (bottom right). (g1) Fresnel zone plate fabrication by successive shaped beam irradiations (g2) stitched together on Au film on SiO2. Figure reproduced with permission from: (a) ref.³⁷, the author; (b) ref.¹⁰², (c) ref.¹⁰³, under a Creative Commons Attribution License; (d) ref.⁴⁸, Optical Society of America; (e) ref.³⁵, the author; (f) ref.¹⁰⁴, the authors; (g) ref.¹⁰⁵, under a Creative Commons Attribution License.</figcaption></figure>
plane. Thus, the spatial phase remains a free parameter in this target plane. This generates random phase jumps eventually leading to a superimposed random interference pattern on the laser intensity distribution¹¹⁸. The resulting speckle pattern strongly deteriorates the desired laser intensity distribution with a random pattern of darkening spots all over the beam shape. Again, several developments have been conducted to limit this effect (see Section *Advances in dynamic spatial beam shaping*). Note that for thin film ablation, polymerization or drilling, this effect may not be so problematic as the successful processing result mostly rely on overcoming a certain fluence threshold (see Fig. 4(f2, a, d, g1)). Controlling the beam shape opens the door to efficient processing of surfaces thanks to the possibility to directly 'stamp' the desired structuring map with the adequate beam shape. Using this technique, fast marking of surfaces is made possible. More advanced structures can also be achieved like this recent demonstration of super microcapacitors obtained by a single pulse laser photonic-reduction stamping based on graphene¹¹⁹. Also, advanced surface processing can be envisaged using other beam shapes like lines and rings for post-irradiation cleaning or more precise ablation compared to scanned laser spots¹²⁰,¹²¹ (not shown).

Ultrafast laser pulses have a particular interest in the case of structuring in the three dimensions inside the bulk of transparent materials¹. Due to the non-linear aspect of the laser-matter interaction, the laser energy deposition can be achieved with a high degree of precision, reaching the micrometric and sub-micrometric levels depending on the laser focal spot size and the local modification threshold. As for surface structuring, spatial beam shaping can parallelize the process with the advantage of producing intensity distribution geometries in the 3D as illustrated by Fig. 5. In particular, 3D arrays of laser spots have been used to generate micro-modifications at multiple depths inside transparent materials³⁶,¹²⁸ with the possibility to correct for depth related wavefront aberration⁹⁵ (see Fig. 5(a)). Another illustration of the interest of spatial beam shaping concerns the cataract surgery where an array of femtosecond laser spots can achieve the full emulsification of the crystalline lens thus reducing the need of the ultrasound handpiece for a significant increase of patient safety⁹,¹²³ (see Fig. 5(c)). Also in relation to the biomedical field, there is a general challenge to achieve efficient focusing of coherent light through opaque and/or scattering media, like skin or

edematous cornea. There, dynamic phase modulation by SLMs can play a significant role, allowing for compensation of the tissue aberrations and/or scattering¹²⁹⁻¹³¹. The principle here is to counterbalance the beam wavefront distortions, caused by the medias non-homogeneity¹³². Spatial light modulators can be used for microscopy and spectroscopy as well thanks to the possibility to generate multiplexed beam steering for faster sample characterization or particle trapping¹³³. Other biomedical applications include the use of an array of laser spots obtained by SLM phase shaping for microsurgery, achieving multi site ablation on a Drosophila embryo¹³¹. Another application is related to fact that the growth cone of a developing neuron can be guided using an infrared laser beam. This intriguing phenomenon can be better controlled using a computer-driven spatial light modulator, allowing for a higher flexibility of the laser field spatial distribution¹³⁴.

Parallel structuring in glass has shown the possibility to generate photonic functions in fused silica using two processing spots¹²⁴ (see Fig. 5(d)). The direct laser writing technique inside transparent materials permits the fabrication of complex optical functions¹,¹⁵,¹³⁵. The 3D shaping potential with CGH has also been nicely illustrated using laser induced plasma in the air, thus providing 3D rendering of aerial graphics as reported by Ochiai et al.¹³⁶ (not shown). Tightly related to spatial beam shaping, aberration correction is also based on dynamic wavefront modulation that compensates for various beam deteriorations. A comprehensive review of this topic for ultrafast processing can be found here⁵⁰. Without entering into details, let us underline that both techniques share the interest of dynamic reconfigurability offered by SLMs. In particular, when processing inside high index transparent materials, depth-dependent spherical aberrations spread out the laser intensity along the optical axis. Dynamic wavefront shaping can compensate this¹²⁵ as illustrated on Fig. 5(e). There, gyroid photonic crystals with circular dichroism properties could be fabricated in the high-index chalcogenide glasses. Likewise, photonic crystals in lithium niobate were also demonstrated¹²⁶ (see Fig. 5(f)) as well as laser-induced micro-wires inside diamond¹²⁷ (see Fig. 5(g)).

## Towards the nanometric scale

In order to reach the sub micrometric range for surface and bulk structuring, researchers have considered the use of non-diffractive beams. The pioneering work of
<figure><img src="image_13.png" /><figcaption>**Fig. 5** | Examples of ultrafast laser bulk photoinscription with the help of spatial beam shaping. (a) Structuring of glass at the microscale level using 3D arrays of spots achieved in a single irradiation using LG algorithm including depth-related aberration correction. (b) Photoinscription in glass using the fractional Fourier transform iterative algorithm generating arrays of laser spots in multiple planes. (c) Photo emulsification of the crystalline lens for the cataract surgery with the help of spatial beam shaping of ultrafast laser. (d) Photoinscription of photonic devices inside fused silica with optical functions (here light division). (e) Fabrication of gyroid photonic crystals using wavefront compensation of the depth-related strong spherical aberration in chalcogenide glass generating circular dichroism (RCP: right handed circular polarization). (f) Photonic crystal in lithium niobate with adaptive control of the wavefront to compensate for the spherical aberrations. (g) Structuring of diamond in three dimension yielding conductive wires in the bulk. Figure reproduced with permission from: (a) ref.⁹⁵, the author; (b) ref.¹²², the author; (c) ref.⁹, the author, ref.¹²³, under a Creative Commons Attribution License; (d) ref.¹²⁴, Optical Society of America; (e) ref.¹²⁵, the author; (f) ref.¹²⁶, the author; (g) ref.⁹⁵,¹²⁷, the author.</figcaption></figure>

Courvoisier et al. has shown the interest of these Bessel beams for surface processing¹⁴⁴. The experimental realization of such beam usually relies on an axiconic phase modulation that can be seen as a biprism with a cylindrical symmetry. Thus, a interference pattern is formed right after the axicon with a high intensity central lobe along a distance that mostly depends on the beam size and axicon angle. The beam formation is supported by the concentric interference of the paraxial and marginal rays, yielding a particularly long 'propagation' without diffraction and associated with remarkable self-reconstruction properties¹⁴⁵,¹⁴⁶. This results in an 10–30 × confocal length increase if compared to a regular Gaussian beam of similar size. The sample surface positioning at the plane of peak intensity is therefore facilitated. Moreover, the central lobe of the bessel beam offers a tightly focused intensity easily reaching sub-micrometric dimensions. Let us be precise here that the ring pattern around the central lobe may not intervene on the structuring by properly adjusting the laser intensity so that

the modification threshold remains too large for the ring patterns to permanently modify the material. Consequently, first demonstrations of structuring have shown remarkable high aspect ratio channels and stems with as little as 200 nm cross section (4 times below the laser wavelength) in fused silica and sapphire¹³⁷,¹³⁸ (see Fig. 6(a)). Following this, industrial applications of such beams have risen for rapid glass cutting with low cracking¹⁴⁷. Following this opportunities, reflective axicons have been developed in order to withstand high power sources with high energy pulses and wide spectrum¹⁴⁸. Non diffractive and multispot shaping has also been combining to sequentially fabricate embedded spectrometers and saturable absorbers inside sulfur-based chalcogenide mid-infrared glasses¹⁴⁹.

Other applications taking advantage of the elongated confocal volume concern welding of transparent materials by ultrafast laser¹⁵⁰,¹⁵¹. In that case, the gain of positioning tolerance renders the process more reliable even though several processing challenges remain, such as the
<figure><img src="image_14.png" /><figcaption>**Fig. 6** | Surface and bulk structuring towards the sub micrometric scale using non-diffractive beams with the help of spatial beam shaping. (a) Bessel beam generation and high aspect ratio structuring of glass with single femtosecond pulses. (b) Turning non diffractive beam (or Airy beam) enabling curved machining of silicon. (c) Hollow core non-diffractive beam based on vortex phase modulation yielding tubular bulk photo inscription in a single irradiation. (d) Modulated axiconic phase mask forming a multiple lobes non diffractive beam permitting dynamic crack orientation control for glass cutting. (e) Drilling of stainless steel using non-diffractive beam with enhanced efficacy. (f) Machining of grooves using superimposed bessel beams associating an axicon and an SLM. Figure reproduced with permission from: (a) ref.¹³⁷, the author, ref.¹³⁸, under a Creative Commons Attribution License; (b) ref.¹³⁹, the author; (c) ref.¹⁴⁰, under a Creative Commons Attribution License; (d) ref.¹⁴¹, SPIE; (e) ref.¹⁴², under a Creative Commons Attribution License; (f) ref.¹⁴³, the author.</figcaption></figure>

need of optical contact during irradiation¹⁵²,¹⁵³ (not shown). More advanced non diffractive beams have been also demonstrated involving curved trajectories permitting round edge cutting of wafers¹³⁹ (see Fig. 6(b)). Shaping the transverse intensity distribution of non-diffractive beam has also been reported with a vortex phase modulation. In that case, a tubular bulk photo inscription in glass can be achieved in a single irradiation¹⁴⁰ (see Fig. 6(c)) with the possibility to generate type I and type II 3D structuring¹⁵⁴. Controlling further the conical wavefront with an SLM also renders possible the inhibition or enhancement of Kerr lensing, plasma defocusing, and surface aberration effects offering means for compressing and stretching of the focal interaction volume inside transparent materials despite the strong and hard-to-bypass influence of these unstable propagation distortions¹⁵⁵.

Elliptical Bessel beam can also be obtained using an asymmetric phase-modulation technique with an SLM. They permit to transfer these asymmetries in the induced fields of thermo-mechanical constraints relevant for material structuring¹⁵⁶. Multiple central intensity cores can also be obtained by modulating the axiconic

phase mask. A better control the crack during glass cutting is then attainable in a dynamic manner along user-defined trajectories¹⁴¹ (see Fig. 6(d)). Quite counter-intuitively, those beams have also shown some interest for non-transparent materials processing. Indeed, an enhanced drilling efficacy on steel when compared to equivalent fluence Gaussian beams has been reported (see Fig. 6(e)) probably due to the self-healing capacity of these beams in the presence of scattered debris¹⁴². Surface groove machining can also be optimized by associating axicons and SLMs. By generating superimposed bessel beams, the side ring pattern potentially producing undesired marking can be canceled¹⁴³ (see Fig. 6(f)).

Advanced nanometric structuring is also readily achievable by finely tuning the laser beam polarization with the help of spatial beam shaping. Vortex beam possessing an orbital angular momentum (OAM) have recently attracted a large attention due to their capacity to convey information within their OAM state, but also to spin micro objects or generate new imaging systems¹⁶⁴. Several optical systems have been proposed to obtain such beam for ultrafast lasers¹⁶⁵. This type of beams present an interest also for surface processing as illustrated
on Fig. 7(a)) where a spatial light modulator imprints an helical wavefront on the femtosecond laser beam associated with an S-waveplate. In that case, a particular orientation of the nanometric LIPSS can be observed on metal with a spiral geometry¹⁵⁷. Dynamic change of advanced polarization states like azimuthal or radial show an particular interest when combined with surface scanning of the laser beam, producing complex LIPSS orientation reminding a soft breeze swaying over a wheat field¹⁶⁶,¹⁶⁷. Skoulas et al. have also reported on biomimetic structuring with this types of polarization using a S-waveplate only (no wavefront modulation) with the generation of complex LIPSS shapes resembling the shark's skin morphology scaled down to the sub micrometric level¹⁶⁸. Hasegawa et al. have also shown the possibility to control the individual polarization of laser spots within an array of 20 lasers spots, permitting to dynamically control the LIPSS pattern¹⁵⁸ (see Fig. 7(b)). Interestingly, efforts have been conducted to propose compact apparatus where a single SLM simultaneously control both the holographic image and its polarization state (see Fig. 7(c)), with an interest for laser induced 5D optical storage inside glasses¹⁶⁹.

Going further in the structuring precision, Allegre et al. have proposed the combination of ring shaping with high numerical aperture (0.95) and polarization control to reach 10 nm surface holes on sapphire¹⁶⁰ (see Fig. 7(d)). It is interesting to note that such nano structuring relies on the particular nature of the laser-matter interaction at ultrafast timescales that permits to combine laser intensity distribution control with threshold effect to achieve this degree of energy localization.

Beam shaping and polarization control has recently been extended to the 3D enabling the position, polarization state and intensity control of each focal spot (see Fig. 7(e)), although not with an ultrafast beam¹⁶¹. Even if the primary applications mentioned by the authors concern optical tweezers or microscopy, the interest of this technique for ultrafast processing is evident, especially for optical data storage or the fabrication of advanced photonic components inside transparent materials. This high degree of control has also been shown for continuous beam shapes with an SLM inserted in a Sagnac interferometric set-up. In this experiment mostly dedicated to

<figure><img src="image_15.png" /><figcaption>**Fig. 7** | Spatial beam shaping with polarization control to achieve nanometric structuring. (a) Helical wavefront shaping using an SLM associated with an S-waveplate yielding a vortex beam generating spiral orientation of LIPSS on metal. (b) Array of laser spots with individual polarization control. The laser-induced surface tracks show the corresponding LIPSS orientation. (c) Example of integrated advanced dynamic polarization control using a single sLM. (d) 10 nanometer surface hole on sapphire combining annular beam shaping, polarization control and high numerical aperture focusing. (e) Generation of spot arrays in 3D with controlled polarization (not ultrafast laser). (f) Arbitrary intensity distribution controlled polarization distribution (not ultrafast laser). (g) Cutting of cornea using vortex beam shaping (right) compared with regular Gaussian beam (left) showing a smoother and more precise cut. Figure reproduced with permission from: (a) ref.¹⁵⁷, the author; (b) ref.¹⁵⁸, the author; (c) ref.¹⁵⁹, (d) ref.¹⁶⁰, under a Creative Commons Attribution License; (e) ref.¹⁶¹, the author; (f) ref.¹⁶², the author; (g) ref.¹⁶³, under a Creative Commons Attribution License.</figcaption></figure>
imaging applications, the beam polarization distribution
can be tuned quasi-independently of beam intensity (see
Fig. 7(f))¹⁶². Again, the interest of this result to increase
flexibility of ultrafast laser processing seems obvious. As
a remarkable combination of Fig. 6 and Fig. 7, the teams
of Courvoisier and Lancry have lately demonstrated the
generation of a non-diffractive ultrafast beam with a
controlled state of polarization along its propagation axis.
This advanced laser intensity distribution has been
shown to imprint tunable chiral properties inside glass in
a single irradiation¹⁷⁰. We also like to point out some recent
results in the ophtalmic domain with ultrafast lasers. A
vortex beam obtained by helical wavefront has been used
for more precise cutting of the cornea, with a lower on-
set of bubbles and a smoother surface finish (see Fig.
7(g))¹⁶³. A possible explanation proposed by the authors
mentions a better efficiency of the laser excitation with
the ring-shaped beam due to the collagen orientation be-
ing arallel to the laser ring, contrary to the Gaussian spot,
allowing for a better horizontal disruption propagation
in the stroma as observed in high speed photography¹⁷¹.

Following the quest of nano structuring, spatial beam
shaping has also invaded additive processes like 2 pho-
ton polymerisation (2PP) and laser induced forward
transfer (LIFT) that are dedicated to micro and nano fab-
rication to control photonic properties¹⁷⁹,¹⁸⁰. The same
holds for other fields of additive fabrication involving
much higher laser energy and larger processing scales
like laser powder bed fusion (LPBF) and laser welding
(LW), a review of the recent advances of ultrafast laser
based techniques and their impact on these fields can be
found here¹⁸¹. The interest of dynamic beam shaping for
industrial laser processes is also discussed in ref.¹⁸² out-
lining the benefit of the possibility to dynamically tune
the laser energy deposition for optimized processes.

Concerning 2PP, arbitrary beam shape permits to
rapidly fabricate complex structures with fine resolution
in 3D by generating controlled beam shapes¹⁷² or arrays
of spots combined with beam movements¹⁷³. This en-
ables quick fabrication of periodic structures in 3D
showing photonic band gap properties (see Fig. 8(a)) and
b) respectively). Noteworthy, static microlens arrays
have also been used to obtain more than 200 spots for
2PP fabrication¹⁰⁶. The potential of dynamic shaping of
the beam has also triggered the use of amplitude modula-
tion device instead of wavefront modulation device. De-
spite the loss of energy, the quick refresh rate of digital
micro mirror devices (DMD) was used to demonstrate

the fabrication of 3D structures in 2PP in a continuous
manner¹⁷⁴ (see Fig. 8(c)) or to generate an array of 10
laser spots for parallel 2PP fabrication¹⁸³. LIFT can also
benefit from these arbitrary beam shapes, by direct im-
printing of the modulated laser intensity distribution¹⁷⁵
(see Fig. 8(d)). There also, DMD have shown an interest
for the LIFT process, here in the UV range with longer
pulse durations (not shown)¹⁸⁴. In photo polymerization
processes, the fabrication precision can be adjusted by
the laser fluence level with respect to the polymerization
threshold (not only with ultrafast lasers¹⁸⁵). Noteworthy,
this threshold can also configured by optimizing the
chemistry of the light sensitive polymer¹⁸⁰ which can
even be tuned to allow for write and erase operations¹⁸⁶.
Adjusting the laser fluence further also permits to
achieve both local polymerization and ablation in a con-
trolled manner during the same fabrication step¹⁸⁷,¹⁸⁸. Re-
markably, the 2PP field took inspiration from the fa-
mous stimulated emission depletion microscopy (STED)
technique¹⁸⁹,¹⁹⁰ thanks to the possibility to finely and lo-
cally control the excitation levels. There, the gaussian ex-
citation beam is accompanied by a ring-shaped beam
that triggers depletion of the excitation levels, inhibiting
locally the polymerization for fabrication resolution
thinner than 100 nm (see Fig. 8(e))¹⁷⁶. Even if the tech-
nique does not require a dynamic beam shaping system
like an SLM to generate the ring shaped beam, it is inter-
esting to note that recent developments imply the use of
an SLM to obtain a more advanced depletion beam able
to better resolve the axial origin of fluorescence
photons¹⁹¹. In the same manner, the field took inspira-
tion from the light sheet microsopy technique in order to
achieve higher peak printing rates with continuous laser
and optimized resins¹⁹². More advanced beam shaping
has also been used for 2PP like helical wavefront modu-
lation associated with coaxial beam interference that was
shown to enable the fabrication of chiral microstruc-
tures depending on the beam topological charge (see Fig.
8(f))¹⁷⁷. Likewise, optical vortex laser beams were used
for LIFT¹⁹³ to fabricate a twisted ferrite microcrystal ar-
ray by twisting and confining the sintered nanoparticles
within their dark core to form chiral spinel monocrys-
talline dots (not shown)¹⁹⁴.

Concerning larger scale additive manufacturing like
LPBF of LW, it is interesting to note that femtosecond
laser pulses are also gaining more and more attention in
these fields¹⁸¹. For example, the challenge of LPBF of
high melting temperature metals like Tungsten has been
<figure><img src="image_16.png" /><figcaption>**Fig. 8** | Additive fabrication using spatial beam shaping. Two photon polymerization using arbitrary beam shapes (a) and an array of laser spots (b). (c) Continuous projection of femtosecond pulses using digital micro-mirror device with spatio temporal focusing permits high throughput photo-polymerization. (d) Laser induced forward transfer of polymer on PDMS based on spatial intensity shaping using digital micro mirror device. (e) Stimulated emission depletion inspiring two photon polymerization combining the polymerizing beam with a ring shaped depletion beam for improved fabrication resolution. (f) Chiral micro structures achieved with helical phase wavefront on isotropic polymers with coaxial interference second laser beams for different topological charge. (g) Side wall polishing of laser powder bed fusion manufactured parts using non diffractive femtosecond beam. Figure reproduced with permission from: (a) ref.¹⁷³, the author; (b) ref.¹⁷², the author; (c) ref.¹⁷⁴, under a Creative Commons Attribution License. (d) ref.¹⁷⁵, the author; (e) ref.¹⁷⁶, Optical Society of America; (f) ref.¹⁷⁷, (g) ref.¹⁷⁸, under a Creative Commons Attribution License.</figcaption></figure>

recently addressed thanks to the better thermal control of the heat affected zone offered by femtosecond pulses with tunable repetition rates¹⁹⁵⁻¹⁹⁷. Surface roughness control and post processing of the additively manufactured parts can also be advantageously achieved by ultrafast pulses¹⁹⁸,¹⁹⁹. It can also be observed here that, as in other fields, femtosecond pulses processes are often quickly followed by spatial beam shaping developments. As an example, non-diffractive beam shaping has been proposed for side wall polishing of LPBF manufactured parts taking advantage of the longer beam confocal region (see Fig. 8(g))¹⁷⁸.

All these application examples, covering multiple fabrication and structuring scales, tend to show the tight link between ultrafast laser processes and dynamic spatial beam shaping. In all these cases, dynamic spatial beam shaping permits not only to push the limits in almost all matters like processing throughput or ultimate precision but also to open new doors that were previously unthought of, like curved machining with self-accelerating beams or chiral structuring with helical wavefront-shaped beams. These remarkable laboratory achievements must now face the wall of industrial-level and/or

medical-level applications with the challenges of day-to-day repeatability and robustness of the process. This is where the performance of spatial beam shaping, in terms of beam intensity distribution regularity and fidelity to the target and of energy efficiency comes to play. Thus, the following section gives an overview of the numerous research efforts to ameliorate the beam shaping quality and efficiency despite the non-perfect physical beam shaping tools like SLMs and DMs.

## Advances in dynamic spatial beam shaping

### Towards higher beam shaping fidelity and efficiency
As the physical apparatus permitting dynamic wavefront modulation have inherent physical limitations such as limited fill factor, phase range, phase resolution (quantization) etc.; their optical response is not perfect (see a detailed review on the SLM's limitations here²⁰⁵). Concerning SLMs, the technological trends orientate towards a larger resolution with a thinner pixel pitch⁴⁹. Despite these efforts, the aforementioned limits have a detrimental impact on the experimental laser beam shaping fidelity
to the desired target intensity distribution. Parts of the
beam that are not properly modulated end up the focal
spot of the focusing lens yielding the so-called stray 0th
order and a superimposed random interference (speckle)
pattern on the beam shape as discussed in Section Surface and bulk structuring with spatially shaped ultrafast laser and illustrated by Fig. 4(a, d, f2) and 4(f1). When
generating arrays of laser spots for parallel machining,
the stray order is usually the main challenge to over-
come. A simple approach consists in adding a phase tilt
to the wavefront modulation. That way, the stray 0th or-
der can be blocked in an intermediate Fourier plane,
however this drastically reduces the energy efficiency of
the process²⁰⁶. Researchers have also proposed to dis-
place axially this stray spot out of the processing plane by
moving the beam shaping plane out of the lens focal
plane. This can be done by superimposing a lens-type
phase modulation on modulation mask²⁰⁷ or by moving
the coordinates of the desired spot array out of the focal
plane with LG-type beam shaping strategies²⁰⁸. Another
approach proposed by M. Booth teams takes advantage
of the LG algorithm. The principle is to purposely add
the 0th spot in the phase mask calculation with an experi-

mentally adjusted piston phase at the position of the
stray order in order to produce a destructive interfer-
ence, allowing for more controlled processing inside
transparent materials (see Fig. 5(a)) where no stray dam-
age is visible within the 3D array of impacts)⁹⁵. Another
method has been also described by Rontizi and al.²⁰⁹.
With a preliminary characterization of the SLM, the pix-
el cross talk effect can be counteracted permitting a re-
duction of 96% of the 0th order.

One of the most evident physical limitations is related
to the limited resolution of the wavefront modulator. Be-
cause of the finite spatial dimension of pixels of SLMs (or
actuators for DMs), the device acts as a low-pass filter
with respect to the spatial frequencies of the desired
phase modulation pattern. To a certain extent, this prob-
lem can be compensated by enhancing the part of higher
frequencies of the phase mask permitting to obtain a
more homogeneous array of laser spots (see Fig. 9(a))²⁰⁰.
Interestingly, the use of an SLM in combination with mi-
crolens arrays (MLA) was recently presented²¹⁰. The
technique allows to control the individual laser spot int-
tensities orders by varying the absolute phase with the
SLM with a strong interest for coherent beam combining.

<figure><img src="image_17.png" /></figure>

**Fig. 9** | Examples of recently developed to improve the fidelity and/or efficacy of spatial beam shaping. (a) Compensating the limited spatial resolution of SLM by using spatial frequency filtering of the phase modulation. (b) Averaging the detrimental speckle effect by addressing different phase masks on the SLM for uniform multi-pulse ablation. (c) Incorporating Vortex elimination during the phase modulation calculation step. (d, e) High fidelity intensity distribution shaping in the region of interest with the compromise of energy losses for atom trapping. (f) Parallel surface structuring using multi-spot arrays with individually controlled spot intensity based on an optical feedback of the experimental intensity distribution. (g) Smooth top hat generation using optical feedback to adjust the intensity pattern in the iterative Fourier transform algorithm. (h) Arbitrary intensity distribution using the GPC technique. (i) Groove machining with controlled intensity distribution using Zernike polynomials optimization. (j) Spatial beam shaping based on diffractive optical neural network. Figure reproduced with permission from: (a) ref.²⁰⁰, the author; (b) ref.²⁰¹, under a Creative Commons Attribution License; (c) ref.¹¹⁸, Optical Society of America; (d) ref.²⁰², (e) ref.⁹², under a Creative Commons Attribution License; (f) ref.⁹⁰,⁹², Optical Society of America; (g) ref.²⁰³, the author; (h) ref.⁶⁵,⁶⁸, the author; (i) ref.²⁰⁴, Optical Society of America; (j) ref.²²⁶, under Optica Open Access Publishing Agreement.
Another study has identified phase modulations that an SLM with limited resolution and phase depth can still correctly reproduce²¹¹.

Concerning the detrimental speckle effect which is more related to continuous intensity distributions like round, square top-hats or arbitrary shapes, researchers have taken advantage of its random character to correct for its effect. By applying a series of similar phase masks with slight differences (e.g adding a phase piston), similar intensity distributions are obtained with a distinct speckle pattern. By displaying these various phase masks during surface ablation, an averaging effect occurs in the machining region yielding much more uniform ablation profile¹⁰⁴. The technique adds a time constraint on the machining pace directly related to the relatively low refresh rate of SLMs (≈ 50 Hz) and the number of necessary irradiation overlaps. However this delay can be reduced by scanning the beam on a the surface of a single SLM displaying this collection of phase masks (see Fig. 9(b))²⁰¹,²¹². This solution is still limited to multi-pulse process. Note that simple beam scanning also yields an averaging effect²¹³. However this confines ultrafast processes to multi-pulse machining.

Looking at solution without pulse averaging, developments around the phase calculation have also been conducted especially on the IFTA thanks to the possibility to add all sorts of constraints to this algorithm. One of them implies the elimination of vortex-like phase micro-patterns within the phase modulation map directly generating zeroes of intensity in the beam shaping plane (see Fig. 9(c))¹¹⁸. Going further in this type of constraints, the IFTA was completed with the mixed-region-amplitude-freedom (MRAF) strategy by researchers mostly dedicated to atom trapping, where the fidelity of the shaped intensity distribution is much more important than the energy efficiency. In short, the MRAF consists in allowing the IFTA to freely redirect laser intensity out of a region of interest to avoid the phase vortices mentioned above. By doing so, a significant amount of the laser energy is then wasted in the numb area and in the stray 0th order (more than 50%)⁹¹. However, the degree of beam shaping control is remarkable (see Fig. 9(d, e))⁹²,²⁰². A similar idea was also proposed by adding the constraint of an uniform phase within the region of interest in the image plane during the IFTA²¹⁴. Further control of the beam involves both amplitude and phase control with the use of two modulators, or two portions of a single SLM surface permitting a significant reduction of the speckle effect as

well as 0th order suppression, however the amplitude modulation implies a certain energy loss²¹⁵. Beam transformation from gaussian to high quality top-hat intensity distributions has also been shown using a phase-only SLM to achieve full amplitude and phase control with physical filtering of the 0th order¹¹⁰.

Another type of strategy to circumvent the SLMs limitations, as well as some of the experimental imperfections (aberrations, misalignements etc.) is based on real-time characterization of the targeted intensity distribution, thus providing an experimental feedback. The technique is tightly linked to the IFTA algorithm as the target intensity, instead of being constant during the IFTA optimization, is gradually adapted to include and compensate for the differences between the used defined target and the experimental intensity profile. A self-explanatory example is the generation of an array of uniform spots. For the first IFTA run, the numerical intensity target is the desired array of homogeneous spots. By capturing the experimental array (which is very likely to be not homogeneous) a new weighted target is defined to compensate for the array inhomogeneities, with higher spot intensities where the experimental ones were too weak and lower spot intensities for too high spots. This new target feeds a novel IFTA iteration. This weighted IFTA (WIFTA) process is repeated until a sufficient degree of experimental precision is reached. The technique has been used to generate arrays of laser spots with precisely controlled intensity for surface marking (see Fig. 9(f))⁹⁰, structuring of highly regular dimples on steel¹⁰³ and reach more than 1300 parallel laser spots with a optimized spot homogeneity⁴⁸. Noteworthy, spot array homogenization can also be factorized by identifying and removing undesired phase rotations during the IFTA²¹⁶. The WIFTA strategy based on optical feedback has also recently been used to produce smooth top-hat beams with no speckle effect neither 0th order (see Fig. 9(g))²⁰³.

Although not being easily adaptable for ultrafast pulses as discussed in Section *Dynamic spatial beam shaping apparatus*, the high quality of intensity distribution obtained with the GPC technique has to be mentioned here (see Fig. 9(h))⁶⁸. The technique is elegantly based on phase contrast microscopy and thus doesn't require any phase mask calculations. However, the indispensable phase filtering at the focal position of a Fourier plane is easily affected even by slight non linear propagation effects associated with femtosecond pulses, degrading the beam shaping quality (not shown). Nevertheless, recent
improvements of the technique were achieved by combining it with an additional SLM to achieve multi-plane GPC in the 3D<sup>217</sup>. A similar technique was used to produce highly uniform squared top hat beam, by using a superimposed diagonal phase grating for easier filtering in the intermediate Fourier plane<sup>218</sup>.

As the main challenges related to high fidelity beam shaping are related to the limitations of the phase modulators, we recently proposed a phase mask calculation that can take into account the light modulator limits from the start, contrary to the usual IFTA or LG approaches. The key idea is to run the phase modulation calculation on a set of Zernike polynomials that the modulator can correctly reproduce. The technique is valid for SLMs, DMs and more generally any phase only modulator whose optical response can be well-characterized this way. Groove machining with a controlled ablation profile distribution could be achieved using the technique (see Fig. 9(i))<sup>204</sup>.

Let us also mention the current strong push of machine learning strategies. Several studies compare its performance with IFTA<sup>219</sup> or associating it with IFTA methods<sup>220</sup>. An interesting review of the latest developments can be found here<sup>221</sup>. Usually based on neural networks, a collection of phase masks and propagated intensity distributions constitutes the training dataset permitting a faster determination of the proper phase mask generating the desired intensity distribution than IFTA methods (once the training is correctly completed)<sup>222,223</sup>. However, several studies outline the fact that the beam shaping quality using CNN does not surpass IFTA-based optimizations for 2D beam shaping<sup>219</sup> as well as multi-plane beam shaping<sup>223</sup>. Machine learning has also been used to correct for optical aberration in the case of multiple spot laser beam surface machining using adaptive optic convolutional neural network on Zernike polynomials<sup>224</sup>. Let us precise that this type of dynamic aberration correction during parallel machining was already achieved without machine learning<sup>50,225</sup>. Following the machine learning trend, SLMs were also employed as diffractive neural network with the scope to define efficient beam shaping modulations for better performance against misalignments or when using binary DOEs<sup>226</sup> but also with a lower stray 0<sup>th</sup> order<sup>227</sup>. Although not directly related to beam shaping, let us mention here the current widespread trend to use machine learning and optimizations strategies with rapid monitoring of the processed area<sup>228</sup>. Examples of using such techniques for improved

ablation efficiencies or LIPSS generation are flourishing in the literature<sup>229-231</sup>, even if this concept of self-learning ultrafast processes with in-situ feedback loop was demonstrated much earlier for transparent material machining<sup>232,101</sup>. There is no doubt that such optimization strategies will increasingly involve advanced spatial beam shaping in the near future.

Several efforts were also conducted on the SLM architecture itself in order to obtain better performance for dedicated beam shapes. For example a transmitting SLM based on LC with electrodes having a sector geometry has been proposed, allowing for helical wavefront shaping and vortex beam generation<sup>233</sup>. In the same trend, a polymerizable nematic liquid crystal was used as the active wavefront medium in a custom SLM. By achieving local polymerization by 2PP, the authors could imprint in the LC layer an arbitrary static phase modulation that can be activated and deactivated with the application and removal of an external applied voltage. The technique was shown to be efficient for aberration correction<sup>234</sup> or multi-spot pattern generation based on Dammann gratting<sup>235</sup>. The quest of faster response time has also led to several studies. In is known that increasing the temperature of the LC permits to decrease the viscosity, offering a higher reorientation speed. However, this degrades the phase modulation stability, augmenting the flickering effect<sup>236</sup>. Thus, ferroelectric LC layers were employed to reach faster response time, up to 6.3 kHz for binary phase modulation<sup>54,237,238</sup>. Let us briefly mention here that in many laser processing situations, the need for rapid beam shape change is not mandatory. In many cases, surface or volume structuring/cutting is conducted with a constant phase modulation throughout the laser processing (see for example<sup>103,200,144</sup>. If this remark pleads in favor of static phase modulation apparatus (DOEs, MPLC etc.), it is worth noting that the possibility to dynamically change the phase modulation, even at a limited rate, significantly increases the processing flexibility by e.g addressing depth-related aberrations<sup>50,125</sup> changing the marking or ablation target shape<sup>90,105</sup> or correct for beam distortions<sup>203</sup>.

More recently, the question of power handling has become a central issue because of the remarkable advances of the commercially ultrafast laser sources in terms of available power<sup>3,4</sup> and the growing demand of ultrafast laser processing with the use of spatial beam shaping (see various application examples in these references<sup>103,123,141,239</sup>). Thus, a technique permitting to
optimize the beam size on dual-SLMs set-up in order to
decrease the impinging laser fluence was proposed<sup>240</sup>. It
also has been shown that the temperature-dependence of
the LC layer phase modulation can be taken into ac-
count for stable multispot generation<sup>241</sup>. Investigations of
the SLMs behavior at high laser powers (around 200 W)
have been reported<sup>53,242</sup>. The heat accumulation on the
SLMs implies a decrease of the available modulation
phase range, yielding a degradation of the beam shaping
quality with more wasted energy in the stray 0th order<sup>53</sup>.
A study of optically-induced thermal non-linear effect in
a nematic liquid-crystal has been done using an optically
addressed SLM through weak light-absorption of the
photoconductive material, showing beam distortion such
as spatial self-phase modulation<sup>243</sup>. Noteworthy, the same
research team has proposed an interesting SLM architec-
ture taking advantage of the thermo-optical effect for
large spectral bandwitdh with a large modulation dy-
namic range, the so-called Thermo-Optically-Addressed
Spatial Light Modulator (TOA-SLM)<sup>244</sup>. By impinging a
single gold layer with a modulation beam, a local tem-
perature gradient is generated, affecting the attached LC
layer yielding a corresponding phase modulation on the
readout laser beam. There also, machine learning was
used, in order to generate prescribed low-order spatial
phase modulations with a little amount of experimental
data<sup>245</sup>.

Research involving the use of other devices than SLMs
has also been conducted. For example, beam shaping us-
ing AOD was studied to achieve flat top intensity distri-
butions (see⁶⁰ and references therein). Turning beams
similar to those obtained with SLMs (see Fig. 6(b)) were
also demonstrated by using an acoustooptic cell with a
cubic phase transmittance, as well as other interesting ac-
celerated beams²⁴⁶,²⁴⁷. Developments around the MPLC
device, particularly interesting thanks to its inherent high
power handling capability, have also involved the use of
machine learning to find optimal triangular beam shapes
for Fresnel lens fabrication²⁴⁸. The so-called grating light
valves (GLV) are also gaining attention for laser process-
ing thanks to their very high refreshing rate (more than
300 kHz)²⁴⁹, even though the optical configuration is
based on a one-dimensional SLM and imaging which
renders the optical set-up more complex. Interestingly,
researchers have also combined DOEs with AOD to ob-
tain rapid reconfigurability of spatial beam shaping
thanks to the quick response time of AODs²⁵⁰. Amplitude modulation was also studied in combination with

phase modulation using two SLMs, the first one en-
abling beam shape control by imaging⁴⁴ and the second
one multiplying the number of shaped spots for parallel
processing through phase modulation²⁵¹. Inspiration for
ultrafast processes with advanced beam shaping can also
be taken from the field of LPBF where various con-
trolled beam shapes (top-hat, ring, elliptical, Bessel) have
a strong impact on the melting pool dynamics and the fi-
nal structural properties of the fabricated parts²⁵².

A promising research direction for dynamic beam
shaping concerns tunable meta surfaces<sup>253</sup>. In these 2D
devices, the properties of subwavelength elements are
controlled on order to modulate the impinging light
phase, amplitude and/or polarization. With a very high
potential in terms of integration to optoelectronic de-
vices, several schemes have been proposed achieving
beam steering<sup>254</sup> (related to the key application of LI-
DAR), beam focusing<sup>255</sup> and advanced holography<sup>256</sup>.
Noteworthy, ultrafast lasers can play a key role in the
fabrication of these surfaces<sup>257</sup> thanks to the possibility to
highly localize the laser structuring with recent results
involving SLM-based laser beam shaping for the process-
ing<sup>258</sup>. Several materials of interest are under investiga-
tion (e.g phase-change materials such as Ge-Sb-Te
(GST), noble metals whose optical properties can be
switched through hydrogenation and subsequent dehy-
drogenation, liquid crystals, transparent conductive ox-
ides, graphene etc.)<sup>253</sup>. Applications for ultrafast laser
processing with meta surfaces based spatial beam con-
trol are now at reach, also facing the challenges of effi-
ciency, power handling and shaping quality.

In short, research efforts around ultrafast laser pro-
cessing using dynamic spatial beam shaping are mainly
addressing the issues of beam shaping fidelity and effi-
ciency, trying to counteract the detrimental effects of the
physical optical response of light modulators. The in-
crease of available power handling pushes the work
around efficient spot parallelization, controlled beam
forming and reflective solutions able to withstand both
high average power and peak intensities. Machine learn-
ing has already gained a strong interest in the field
thanks to its quick phase mask determination and to its
adaptability to various laser processes especially when a
rapid and/or in-situ feedback is available. The near-fu-
ture trends comprehend technological developments for
high power laser handling along with machine learning
strategies to increase the beam shaping speed and quali-
ty. In the following, we strive to foresee some future and
more fundamental research trends based on a careful consideration of the spatio-temporal effects associated with spatial beam manipulation.

## Perspectives offered by spatio-temporal

As often in science, something that is at first considered as a problem to solve is likely to become an interesting subject to explore, e.g the ultraviolet catastrophe. This also stands true for ultrafast laser processes and temporal effects associated with spatial beam shaping in general. Contrary to the quasi-monochromatic assumption taken at the beginning of this paper, ultrafast pulses carry a non negligible spectral content with consequences on their spatio-temporal characteristics during the beam propagation depending on the optical elements met on the beam path. We will not discuss here the details of temporal pulse shaping and its interest for ultrafast laser processing as this subject is beyond the scope of the review<sup>265-269</sup>. However, a closer look at the specificity of ultrafast pulses when spatial beam shaping is employed reveals situations where the pulse temporal excitation during processing is greatly affected, even for simple beam shaping elements. Considering the spatio-temporal characteristics of femtosecond pulses leads to the notion of pulse front. This quantity corresponds to the spatial surface that comprehends the intensity peak of the pulsed laser beam. In vacuum, the phase and the pulse fronts are identical as they travel respectively at the phase and group velocity that are also equal. However, in a isotropic and dispersive media like glass, their speed differs due to the variation of refractive index with respect to the wavelength. In this simple case, a delay takes place between the pulse front and the phase front while they keep an identical spatial distribution. The situation becomes more complex when a beam passes through a non-flat optical element constituted of a dispersive material, like a fused silica lens. Z. Bor has conducted several pioneering theoretical and experimental studies, revealing the effect of pulse front distortion occurring when using lenses and telescopes<sup>270,271</sup>. For example, the use of a non-treated fused silica lens for ultrafast beam focusing can turn a spectral bandwidth-limited 100 fs pulse into a more than a picosecond excitation at the focal point, primarily due to the pulse front distortion, the group velocity dispersion being of much weaker importance<sup>259</sup>. The spatio-temporal cartography of corresponding pulse front distortion before and after the focal point is depicted on Fig. 10(a)). The marginal part of the pulse front-

encountering less glass thickness-reaches the focal point earlier than the paraxial part, yielding a drastic increase of the local excitation. Experimentally, the team was able to precisely quantify this type of pulse front distortions using a Michelson-type interferometric set-up<sup>270</sup>. Naturally, the very first reaction of any well-minded scientist is to find ways to avoid this alteration of the laser excitation. Indeed, it can simply be achieved by using achromat lenses and more generally by avoiding any chromatic aberrations on the beam path. However, the pulse front can also be considered as an additional control knob for ultrafast laser processing. One of the first interesting results that was reported being related to the pulse front control of ultrafast laser pulses is the so-called quill-writing effect. The team of P. Kazansky has thus reported the intriguing phenomenon of non-reciprocal photo-writing using ultrafast pulses depending on an onset of spatial chirp and pulse front tilt (see Fig. 10(b))<sup>260</sup>. This type of pulse front distortion coupled with spatial chirp is often met at the output of amplified ultrafast sources because of the the recompression stage geometry<sup>272</sup>. The results reported by P. Kazansky can be seen as the first developments around advanced processing using pulse front control<sup>273</sup>. The possibility to control not only the wavefront but also the pulse front has opened a new avenue for dynamic control of the region of highest laser intensity within the focal volume. As well-explained in ref.<sup>263</sup>, considering a laser beam with a linear spatial chirp passing through a lens with chromatic aberrations yields a space and time-varying focal spot. This is because the bluer part of the beam is focused earlier than the redder part. This can be extended to more complex pulse front shapes. M. Booth and colleagues have proposed an interesting setup combining SLM and DM to control both the phase and the pulse fronts<sup>261</sup> see Fig. 10(c)). This permits to control the focal intensity velocity, yielding the so-called flying focus, with arbitrary controlled subluminal or superluminal speeds (see Fig. 10(d))<sup>262</sup>. Numerical simulations permit to precisely anticipate the spatiotemporal behavior of the laser pulse around the focus in *z* versus time diagrams like the one depicted on Fig. 10(e)) with the possibility to generate several accelerating and decelerating steps of the local excitation peak<sup>263</sup>. This advanced level of excitation control might constitute a decisive advance in the field of ultrafast processing, especially of in-volume processing of materials that are transparent to the laser wavelength. Looking closer, the possibility to drive an excitation
<figure><img src="image_18.png" /><figcaption>**Fig. 10** | Future research trends taking advantage of the temporal effects associated with spatial shaping. (a) Illustration of the pulse front distor- tion around the focal point implying complex consequences on the spatial and temporal properties of the local excitation. (b) Pulse front tilt and spatial chirp involving non reciprocal photo inscription on glasses. (c) Concepts for pulse front and wavefront modulation based on an SLM and a DM. (d) Controlling the velocity of the intensity focal point in the focal region along z by tuning the pulse and phase fronts. (e) Simulation of a con- trolled intensity trajectory with accelerating and decelerating steps. (f) Overcoming ionization induced refraction by controlling the flying focus speed. Figure reproduced with permission from: (a) ref.²⁵⁹, Springer Nature; (b) ref.²⁶⁰, under a Creative Commons Attribution License; (c) ref.²⁶¹, the author; (d) ref.²⁶², under the Optica Open Access Publishing Agreement; (e) ref.²⁶³, the author; (f) ref.²⁶⁴, the author.</figcaption></figure>

region spatially at superluminal speeds offer a much higher degree of control (see the visualizations in ref.²⁶³), possibly overcoming light delocalization effects like plasma shielding due to the material transient response that are detrimental for precise bulk processing. A well-known example of this challenge concerns precise bulk microstructuring inside crystalline silicon (c-Si) using ultrafast pulses. Remarkable efforts have been made to bypass the very high degree of light delocalization of this material by using longer pulses (in the picosecond and nanosecond regime), femtosecond-pulse trains, and surface-seeded bulk modifications²⁷⁴. Recently, Froula et al. have experimentally reported the generation of a flying focus quicker the ionization-induced refraction in air (see Fig. 10(f))²⁶⁴. It can be anticipated that similar developments take place for highly localized bulk processing of c-Si or other transparent materials.

## Conclusions

In conclusion, the use of ultrafast lasers for surface and bulk processing has gained a strong interest, due to their capacity to achieve high precision in ablation, cutting, and structuring processes with relatively low thermal side effects. Dynamic spatial beam shaping, particularly

using spatial light modulators, emerges as a promising solution to efficiently use the growing laser power or commercially available sources. This technique gains particular relevance with the emergence of Ytterbium-based laser sources, distinguished by their much higher power and repetition rates when compared to conventional Ti:Sa lasers.

Several factors underscore the critical role of spatial beam shaping in the realm of ultrafast laser processing. Spatial beam shaping permits the sculpting of the laser intensity distribution in a quasi-arbitrary fashion, increasing the processing precision by spatially tailoring fluence levels. This is of great benefit for applications requiring micrometric spatial structuring resolution, especially when the interaction involves a rigorous control with respect to structuring threshold (LIPSS formation, 2PP, ablation etc.). Precision alone is not enough for game changing processes. Efficiency also stands as key advantage offered by the technique. By controlling the beam shape, the available laser energy can be distributed more effectively, facilitating parallel processing and enabling the creation of customized beam shapes that can be designed for specific applications, non diffractive beams being a very illustrative example in quest for
submicrometric cutting/ablation. Thirdly, flexibility is a
noteworthy benefit. Dynamic spatial beam shaping of-
fers the agility to dynamically adjust the laser beam shape
during processing, adapting to depth-related aberrations,
evolving target shapes, or rectifying beam distortions on
the optical set-up.

It is however essential to acknowledge the inherent
limitations associated with dynamic spatial beam shap-
ing, primarily stemming from the physical apparatus em-
ployed for wavefront modulation. Spatial light modula-
tors (SLMs), while extensively utilized for dynamic phase
retardation, encounter constraints in both power han-
dling and response time. These devices are also suscepti-
ble to issues such as limited fill factor and phase resolu-
tion involving undesirable effects, including the emer-
gence of stray 0th order beams and the formation of
speckle patterns. Deformable mirrors (DMs), while af-
fording superior power handling capabilities, grapple
with restricted spatial resolution and protracted re-
sponse times in contrast to SLMs. Alternative techniques,
including general phase contrast (GPC), present mini-
mal energy losses but exhibit heightened sensitivity to
high-intensity femtosecond lasers. Multi-plane light con-
version (MPLC) as well as direct laser interference
patterning (DLIP) permit the creation of tunable intensi-
ty distributions but present constrained dynamic
reconfigurability.

Recent efforts in dynamic spatial beam shaping aim at
surmounting these limitations and augmenting beam
shaping fidelity and efficiency. These advancements en-
compass aberration correction, wherein dynamic wave-
front shaping compensates for depth-dependent spheri-
cal aberrations, particularly when conducting processing
inside transparent materials. Furthermore, optimization
algorithms, including iterative techniques such as the IF-
TA and machine learning strategies, are deployed to ob-
tain phase modulation masks less prone to the forma-
tion of 0th order and speckle patterns, thus realizing de-
sired intensity distributions. Real-time characterization
of the targeted intensity distribution has been used as ex-
perimental feedback, to rectify SLM limitations and ex-
perimental imperfections. Novel techniques, like GPC
and Zernike polynomial optimization, offer alternative
methodologies for attaining high-fidelity beam shaping.
Tunable meta surfaces hold considerable promise for dy-
namic beam shaping, characterized by elevated integra-
tion potential.

Power handling constitutes a critical consideration in

the context of dynamic spatial beam shaping. Various
devices and techniques exhibit disparate capacities for
managing laser power and fluence. Methods based on re-
flection, such as those employing DMs, DMDs, and
MPLC, can benefit from the possibility to have high
laser-induced damage threshold (LIDT) reflective layers.
Conversely, devices necessitating transmission through a
modulating medium, like SLMs, GPC, AOD, and TAG
lenses, may confront challenges pertaining to LIDT espe-
cially at high repetition rates.

Looking ahead, research groups are progressively ex-
ploring the spatio-temporal effects intertwined with spa-
tial beam shaping. Controlling the pulse front, in con-
junction with the wavefront, unlocks novel possibilities
for ultrafast laser processing. For instance, the flying fo-
cus technique, which enables a certina control of the fo-
cal intensity velocity, has the potential to circumvent
light delocalization effects and increase bulk microstruc-
turing precision.

The successful transfer of dynamic spatial beam shap-
ing from laboratory experimentation to robust industri-
al and medical applications relies on carefully address-
ing the challenges of repeatability, robustness, and ener-
gy efficiency. Future trajectories include technological
innovations related to high-power laser handling, ame-
liorated optical performances (resolution, fill factor), de-
ployment of efficient algorithmic strategies for refined
beam shaping, tunable meta surfaces and control of spa-
tio-temporal effects.

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## Acknowledgements

This was supported by the French ANRT agence nationale de la recherche

technologique under the CIFRE conventions industrielles de formation par la recherche framework.

## Competing interests

The authors declare no competing financial interests.

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