# Femtosecond laser-induced damage threshold of a thermo-optically addressed spatial light modulator due to giant third-harmonic generation

Loic Ramousse, Vincent Femy, Cyrille Claudet, Gilles Chériaux, Nicolas Forget, Aurélie Jullien

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## ► To cite this version:

Loic Ramousse, Vincent Femy, Cyrille Claudet, Gilles Chériaux, Nicolas Forget, et al., Femtosecond laser-induced damage threshold of a thermo-optically addressed spatial light modulator due to giant third-harmonic generation. Applied optics, 2025, 64 (9), pp.2238. 10.1364/AO.545125. hal-04990603

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# Femtosecond laser-induced damage threshold of a thermo-optically addressed spatial light modulator due to giant third-harmonic generation

LOIC RAMOUSSE,<fnref n="1" />,<fnref n="2" /> VINCENT FEMY,<fnref n="2" /> CYRILLE CLAUDET,<fnref n="1" /> GILLES CHÉRIAUX,<fnref n="1" /> NICOLAS FORGET,<fnref n="1" />,<fnref n="2" /> AND AURÉLIE JULLIEN<fnref n="1" />,*

Received 22 October 2024; revised 29 November 2024; accepted 1 December 2024; posted 12 December 2024; published 13 March 2025

We investigate the resistance to the laser flux of a complex multilayer structure containing liquid crystal, focusing on the behavior of a spatial light modulator operating in the femtosecond regime. Our findings show that exceptionally high third-harmonic generation at the interfaces between the liquid crystal layer and its substrates, driven by the discontinuity in third-order nonlinear susceptibility, is the primary cause of laser damage. A quantitative study of the chromatic laser-induced damage threshold (LIDT) of a thermo-optically addressed spatial light modulator (TOA-SLM) is then presented. Since the device operates over an ultrabroadband spectrum, the study focuses on the behavior in the ultrashort pulse regime. The chromatic analysis offers a detailed map of the device's operational limits in ultrafast optics. With a maximum LIDT value of 500 GW/cm<fnref n="2" />, the modulator is an excellent candidate for integration into ultrafast optical systems. Additionally, the study examines the laser-induced functional threshold (LIFT), showing that the device remains fully operational nearly up to its damage threshold.

Published by Optica Publishing Group under the terms of the [Creative Commons Attribution 4.0 License](https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
https://doi.org/10.1364/AO.545125

## 1. INTRODUCTION

Spatial light modulators (SLMs) are quasiplanar devices, allowing for the modulation of the amplitude, phase or polarization, or a combination of these parameters, of an incident light beam according to the two spatial dimensions of the modulator. SLMs are employed in many different fields and are the subject of continuous technological development [1–3]. To that purpose, nematic liquid crystals (LCs) intrinsically present highly desirable features, i.e., a high birefringence together with the ability of changing their optical properties through molecular reorientation in response to weak electric or magnetic fields. Combined with a large aperture scalability, electro-optic LCs-based spatial light modulators (LC-SLMs) are extensively used for a wide range of applications [4–8]. Some laser applications do require SLMs to operate at high peak fluence and/or high average power, among them polarization control of energetic nanosecond pulses [9], industrial laser processing [10], and the manipulation of femtosecond pulses [5,11–13]. A high laser-induced damage threshold (LIDT) is thus required.

Perhaps counterintuitively, apart from the absorption bands, the molecular structure of the LCs themselves is quite resistant to the laser flux. Indeed, several recent studies have reported

single-shot LIDT measurements of 1 – 2 J/cm<fnref n="2" /> in the picosecond regime at 1053 nm for unorientated LCs in the nematic phase [14], around 4 J/cm<fnref n="2" /> in the nanosecond regime for orientated LCs [15] and even larger for highly saturated glassy LCs [16]. In the femtosecond regime, for single-shot exposition at 1030 nm, a LIDT > 1 J/cm<fnref n="2" /> for three different LC mixtures has been reported [17]. While these parametric studies have shown that single-shot LIDT is dominated by the usual dielectric ionization mechanisms [15,17], exposure to high-repetition-rate pulse trains (> 1 kHz) indicate a breakdown dominated by thermal accumulation due to residual linear absorption [17].

For standard LC-SLM devices exploiting the electro-optic anisotropy of LCs, the electrode (ITO, most of the time) is known to be the LIDT limiting factor [9,18,19]. In order to improve resistance to laser-induced breakdown, the electrode material can be modified [20], or electrical control can be abandoned in favor of other addressing means. As promising candidates to overcome existing restrictions, such electrode-free LC-SLMs have been achieved, for example, by inserting a photosensitive alignment layer to shape single-shot high-energy nanosecond pulses [21]. Another option is to replace the electrode by a metallic layer so as to enable local thermo-optical control of the LC layer. This simplified structure also makes it

<footnote n="1">¹Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), UMR 7010, 17 rue Julien Lauprêtre, 06200 Nice, France</footnote>

<footnote n="2">²Fastlite, 165 route des Cistes, 06600 Antibes, France</footnote>

<footnote>*aurelie.jullien@inphyni.cnrs.fr</footnote>
possible to extend the wavelength coverage of LC-SLMs. Such a device, coined as a “thermo-optically addressed LC-SLM” (TOA-SLM), has enabled large phase control of multioctave light [22] and large aperture phase modulation capacities for adaptive optics [23]. The device’s broad spectral acceptance makes it particularly suited for ultrafast optics, in order to shape femtosecond pulses, but an accurate LIDT measurement in this regime is still missing. An additional question then arises: is the LIDT of the assembled TOA-SLM the same as that of its weakest component?

The problematic addressed in this article is then the resistance to the laser flux, in the femtosecond regime, of a complex multilayer structure in operation. The case of a multilayer structure, with thick layers (several hundreds of µm), raises specific issues: damage localization; additional nonlinear effects such as self-focusing in one or the other of the layers; and nonlinear effects at the interfaces. Moreover, as the device is ultrabroadband, it is also necessary to study the wavelength dependence of the damage threshold. The chromatic dependence of dielectrics LIDT has been moderately treated in the literature, and solely considered from the perspective of multiphoton ionization. It has been shown that the LIDT of a dielectric decreases linearly with the pump photon energy in the vicinity of the bandgap and remains constant with the wavelength otherwise [24–27].

The study presented here then consists in a quantitative chromatic investigation of the LIDT of TOA-SLM in the femtosecond regime and in realistic exposure conditions. Our work points out the critical role of third-order harmonic generation (THG) generated at the interfaces with the LC layer on the LIDT values. A distinction is also made between the laser-induced damage threshold (LIDT) and the laser-induced functional threshold (LIFT [15,28]). The LIDT corresponds to the maximum fluence withstood by the device before irreversible damage occurs. LIFT corresponds to the maximum fluence withstood by the device before its normal operation is disrupted. LIFT has a value lower than or equal to LIDT. The paper first describes our experimental methods and protocols; then, LIDT and LIFT measurements are presented and discussed.

## 2. EXPERIMENTAL METHODS

### A. Samples

The TOA-SLM is an ultrabroadband reflective SLM, developed from prior research on thick thermotropic nematic LC cells [19,29]. Unlike conventional SLMs, it does not require electrodes. Instead, the optical index of the LC layer is modulated by locally altering its temperature, which is controlled by the absorption of a separate control beam. This absorption generates heat, creating a localized thermal gradient through diffusion in the LC layer. Since the LC is thermotropic and birefringent, its ordinary and extraordinary refractive indices are modulated, with a nonlinear dependence on temperature [30].

Here, the beam to be modulated is a femtosecond source, referred to in the following as the pump beam. The device is cold and static, which means that no control beam is applied.

The typical samples used for this study are TOA-SLM composed of: 1) a BK7 window (1 mm), coated on one side by a 100 nm gold layer and by an AR-coating at 450 nm on the other polished side; 2) a thin sapphire window (1 mm) chosen because

<figure><img src="image_4.png" /><figcaption>Fig. 1. Principle of TOA-SLM and view of the multilayer structure.</figcaption></figure>

<table><caption>Table 1. Reported LIDT for Each Individual Component of a TOA-SLM</caption><thead><tr><th>Sample</th><th>Single-shot (J/cm²)</th><th>Single-shot (TW/cm²)</th><th>kHz (J/cm²)</th><th>kHz (TW/cm²)</th></tr></thead><tbody><tr><td>Al₂O₃</td><td>5–10 [31]</td><td>50–100</td><td>4–8<sup>a</sup></td><td>40–80</td></tr><tr><td>Au</td><td>0.6 [32]</td><td>3</td><td>0.4<sup>a</sup></td><td>2</td></tr><tr><td>E7</td><td>1.13 ± 0.21 [17]</td><td>6 ± 1</td><td>0.1 ± 0.01 [17]</td><td>0.6 ± 0.05</td></tr></tbody></table>

of its good thermal conductivity with a broadband AR-coated on one side and uncoated on the other side (Fig. 1). A thin film (1 µm) of polyvinyl alcohol (PVA) is spin-coated on the gold layer and the uncoated sapphire surface and then rubbed to anchor the molecules in a plane parallel to the substrate. Finally, a layer of 80 ± 3 µm of the nematic mixture E7 (Merck) is inserted between the substrates, in contact with the PVA layers. The transverse dimensions are 25 per 25 mm. Reported subpicosecond LIDT values of each layer of the SLM are listed in Table 1. The gold layer exhibits the lowest value. At high repetition rate, the residual linear absorption of the LC leads to a sharp decrease of the LIDT, which is still higher than 0.1 J/cm².

### B. Experimental Setup

The laser source is a femtosecond diode-pumped Ytterbium laser (Pharos PH2-SP-1mJ, Light Conversion) operating at a central wavelength of 1.03 µm. The pulse duration is 180 ± 2 fs, a maximum pulse energy of 500 µJ, and the repetition rate is set to 10 kHz. The pulse-to-pulse energy stability is 0.5% RMS. The laser can pump a two-stage optical parametric amplifier (OPA, Twin STARZZ, Fastlite) delivering a signal with about 25 µJ energy and 60 fs pulse duration, which tunable between 650 and 950 nm. The idler ranges between 1.2 and 2.1 µm, with an energy of 25 µJ and a pulse duration between 110 and 140 fs, depending on the wavelength. The pulse-to-pulse energy stability is 1% RMS [33]. All pulse durations are experimentally controlled with a scanning SH-FROG device (Frozzer, Fastlite). The laser and OPA wavelengths are out of the absorption bands of the tested materials.

These three beams (laser, OPA signal, OPA idler) can be used to seed the LIDT experimental setup, as schematically depicted in Fig. 2. The laser beam is linearly polarized and focused on the sample at 0° incident angle with a plano-convex lens. Two different focusing lenses are used ($f = 150$ mm and $f = 300$ mm) so as to adjust the fluence on the sample (the shorter focal length

<footnote>a To take repetition rate into account, a 20% decrease was applied compared with the single-shot value [32]. Test wavelength is 1.03 µm.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Experimental setup (DM, dichroic mirror; FM, flip mirror; BS, beam splitter; TH, reflected third-harmonic light). The pump source (either the PHAROS laser or the signal or idler of the OPA Twinstarzz) is focused onto the TOA-SLM sample. A He-Ne probe illuminates the sample, and its retroreflection is relay-imaged onto the wavefront sensor (SID4). Reflected TH light is collected with a dichroic mirror and analyzed using a spectrometer or photodiode. Pulse and beam properties are shown for three arbitrarily chosen source wavelengths.</figcaption></figure>

lens is used for the OPA wavelengths that have lower output energy). The Rayleigh length is around 10 mm for the 300 mm lens and >2 mm for the 150 mm lens, i.e., in both cases longer than the sample thickness (1.5 mm). The sample position is adjusted to optimize the TH signal (as detailed later), and relay-imaging provides the pump spot size. The positioning error is approximately 1 mm, which is smaller than the Rayleigh length, ensuring that the beam profile remains largely unaffected. The beam size is comprised between 40 and 200 µm FWHM for all the wavelengths, as listed in Table 2. Some registered beam profiles are plotted in Fig. 2. The energy can be adjusted using an achromatic zero-order half-wave plate combined with a linear polarizer. In a general way, for all the wavelengths considered in this study, the fluence evolves between ~0.01 J/cm² and ~0.350 J/cm², the latter corresponding to a maximum peak intensity of ~500 GW/cm². As shown in Table 2, the

pump parameters vary in terms of beam area and pulse duration according to the wavelength. The results presented here are therefore valid under the assumption that these ranges of variations have little impact on the performed LIDT measurements.

As the front substrate is relatively thick, the self-focusing Kerr effect in the front substrate and LC layer has to be estimated. Considering 1 mm of sapphire and a maximum peak power of 500 GW/cm² (the most favorable case for self-focusing), the focal length of the Kerr lens induced by the entrance window is several meters. The same observation applies to the LC layer, which has a nonlinear index an order of magnitude higher than that of the window but a thickness an order of magnitude smaller [34]. Kerr's lens can therefore be disregarded.

Third-harmonic emission, reflected by the gold mirror of TOA-SLM, is collected with a dichroic mirror and analyzed using a spectrometer (for pump wavelengths $λ ≥ 1.2 µm$) or photodiode (for all wavelengths). The size of the TH beam was not directly measured. However, it is assumed that, consistent with other third-order nonlinear processes, the Gaussian beam size is reduced with a corresponding increase in its divergence, relatively to the pump beam. The THG efficiency is measured for a pump wavelength of 1.5 µm (TH wavelength: 0.5 µm), using a calibrated low-noise microwatt power meter.

### C. Damage Detection

A He-Ne probe enables us to survey the state of the sample under laser irradiation. After sample illumination, the probe is relay-imaged with a 1.8 magnification onto a wavefront sensor based on quadriwave lateral shearing interferometry (SID4-GE, Phasics) [35]. The motivation for this choice of detector is twofold. First, it has been demonstrated as a highly sensitive device for laser damage detection on fused silica samples and optical coatings [36]. The phase change originates from index or mechanical modification, or both, of the damaged surface. Second, phase sensing enables us to detect potential heating of the LC layer preceding the damage of one layer, which would lower the performances of the thermo-optical shaper. Preheating of the LC layer would induce a local phase change with Lorentzian-like spatial distribution [22]. Therefore, the wavefront detection enables us to set a damage criterion (LIDT) and a functional criterion (LIFT).

The damage criterion used here is the detection of a permanent defect in the wavefront leading to a modulation of at least 0.05 $λ$, which defines the LIDT. In the experiments, the onset of damage corresponds to this specific phase change value, which is why it is used to define the threshold. An illustration is shown in Fig. 3. The functional criterion is the detection

<table><caption>**Table 2.** Laser and OPA Pulses Characteristics<sup>a</sup></caption><thead><tr><th>Wavelength (µm)</th><th>0.8</th><th>1.03</th><th>1.2</th><th>1.3</th><th>1.4</th><th>1.5</th><th>1.6</th><th>1.7</th><th>1.8</th><th>1.9</th><th>2</th><th>2.1</th></tr></thead><tbody><tr><td>Duration (fs) (±2 fs)</td><td>60</td><td>183</td><td>119</td><td>111</td><td>115</td><td>115</td><td>120</td><td>128</td><td>120</td><td>120</td><td>120</td><td>120</td></tr><tr><td>Diameter (µm) (±5 µm)</td><td>76</td><td>112</td><td>196</td><td>121</td><td>120</td><td>117</td><td>50</td><td>45</td><td>46</td><td>44</td><td>47</td><td>42</td></tr><tr><td>THG wavelength (nm)</td><td>260</td><td>340</td><td>400</td><td>430</td><td>460</td><td>500</td><td>530</td><td>560</td><td>600</td><td>630</td><td>660</td><td>700</td></tr></tbody></table>

<footnote><sup>a</sup>The uncertainties originate from in the measurement devices, including the FROG error, the camera's pixel size, and the repeatability of the power meter.</footnote>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) Phase change registered when a laser-induced damage occurs in the sample. (b) Microscopic view of a laser damage on the gold layer. A large bubble of LC originates from this damage.</figcaption></figure>

of a reversible wavefront modification originating from self-heating of the device. “Reversible” means that, when the pump is turned off, the wavefront returns to its original state within a few seconds. The minimum phase change that can be detected is 0.01 λ. Consequently, the LIFT was set to twice this resolution, corresponding to 0.02 λ, or 100 mrad, which is two orders of magnitude smaller than the maximum phase shift achievable by the SLM in operation [22]. Given the thickness of the LC layer and the thermo-optical properties of E7 [29,30], it corresponds to a temperature change of 0.1 K. As this study is restricted to the ultrashort pulse regime, LIDT and LIFT will be mostly expressed in GW/cm² in the following.

The objective is to be close to experimental conditions of SLM applications. S-on-one test procedures, with high S, has been implemented, at the OPA repetition rate (10 kHz). The experimental protocol is then as follows: 1) open the laser shutter for 2 min maximum (1.2 × 10⁶ shots); 2) register THG spectrum and signal during exposition; and 3) acquire the SID4 measurement (amplitude and phase) each 30 s. The LIDT search is then binary: after each sequence, the sample is moved to avoid additional fatigue effects, the laser energy is decreased if damage is observed and, conversely, increased if no damage occurs. For each experimental configuration, the data are organized as breakdown probability (1 = damage; 0 = no damage) as a function of pump peak power with a sigmoid fit function [17]. The LIDT is then defined as the peak power for a damage probability of 0.5, and the error bars correspond to damage probability of 0.1 and 0.9.

# 3. RESULTS

## A. LIDT at 1.03 µm

The first set of LIDT measurements is performed at 1.03 µm on TOA-SLM in both polarization directions (extraordinary and ordinary) and on a gold mirror alone for comparison. Two cases were examined for the gold mirror: one with a thin PVA film coated on its surface; and one without.

The detection and microscopic image of an irreversible damage are shown in Fig. 3(a). The observed phase shape is typical of thin film laser ablation [36]. The gold layer is ablated, resulting in the destruction of the anchoring layer and the formation of disordered bubbles of liquid crystal molecules, the organization structure being locally annihilated [Fig. 3(b)].

The measured LIDT values are reported in Table 3. The LIDT measured in the polarization direction, which is the one used by TOA-SLM (extraordinary), is 65 GW/cm², which is

<table><caption>**Table 3.** Measured LIDT for a Pump Wavelength of 1.03 µmª</caption><thead><tr><th>Sample</th><th>LIDT (GW/cm²)</th><th>LIDT (J/cm²)</th></tr></thead><tbody><tr><td>TOA – SLM<sub>r</sub></td><td>65 ± 10</td><td>0.012 ± 2</td></tr><tr><td>TOA – SLM<sub>o</sub></td><td>100 ± 10</td><td>0.02 ± 2</td></tr><tr><td>Au mirror</td><td>2000 ± 20</td><td>0.36 ± 5</td></tr><tr><td>(Au + PVA) mirror</td><td>2000 ± 20</td><td>0.36 ± 5</td></tr></tbody></table>

quite low and nearly twofold lower than in the ordinary polarization direction (100 GW/cm²). These values are found much lower than the LIDT of the gold layer alone, with or without PVA layer, measured under the same conditions and found to be close to 2000 GW/cm². The LIDT of TOA-SLM is also lower than the value listed for E7 at 10 kHz repetition rate and 1.03 µm pump wavelength, from our previous work (around 600 GW/cm², Table 1). Thus, the assembly of the various layers constituting the SLM degrades the laser flux resistance of the component. This degradation is polarization-dependent and results in damage of the metallic layer. For TOA-SLM, the damaging process is concomitant with the emission of visible light corresponding to the pump's third harmonic. There is no TH emission from the gold mirror alone, even when coated with PVA. This is further investigated in the next section. It is worth noting that, during operation, the linear and nonlinear extraordinary refractive indices approach the values of the ordinary axis. As a result, the LIDT of the device under operating conditions is expected to fall between the ordinary and extraordinary values listed in Table 3.

## B. Achromatic THG at Interfaces

LCs are known for their high nonlinear properties, which can result in efficient nonlinear conversions. In nematic LC cells, THG can originate from 1) phase-matched $\chi^{(3)}$ [37–40] or cascaded-$\chi^{(2)}$ processes [41], or 2) nonphase-matched THG at the interfaces between the LC and its substrates [42–44]. As a matter of fact, LC cells are known to efficiently enable THG at the substrate-LC interface, originating from the $\chi^{(3)}$ discontinuity between the two consecutive layers, in the perturbative regime.

The spectrum and energy of the generated TH are monitored as a function of pump wavelength and pump power. The first outcome of the experiment is that, for a pump polarization parallel to the LC director, e.g., along the extraordinary axis, high TH is reflected by the sample, whatever the pump wavelength, as illustrated by the gallery of experimental TH spectra plotted in Fig. 4(a). The THG signal is maximized by moving the position of the SLM with respect to the focus.

A characterization of the TH yield is presented for $\lambda = 1.5$ µm ($\lambda_{TH} = 0.5$ µm). Figure 4(b) shows that the TH signal presents a cubic dependence with the input peak intensity. For a maximum intensity of 325 GW/cm², the TH power is 2 mW (200 nJ), which corresponds to a generation efficiency of ≈5%, higher than other reported values [44]. At this wavelength, the gold layer absorption is ≈70%, based on furnisher data. That means that the overall THG efficiency is much higher.

<footnote>ªThe polarization direction is changed from extraordinary (e) to ordinary (o). A gold mirror and a gold mirror with a PVA layer are tested for comparison.</footnote>
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** (a) Normalized THG spectra registered when the pump wavelength is varied between 0.8 and 2.1 µm. (b) THG signal as a function of input pump peak intensity for $\lambda = 1.5$ µm (blue) and cubic fit of the data (black).</figcaption></figure>

Polarization dependence is also studied and shows that the THG efficiency is twofold lower for linear polarization along the ordinary axis compared with the extraordinary axis.

The achromaticity of the identified process evidences a mechanism not constrained by phase-matching, which supports the occurrence of THG at interfaces. This is attributed to the discontinuity in the $\chi^{(3)}$ tensor components within the multilayer structures. It explains achromaticity and polarization dependence, as the third-order nonlinear tensor of E7 is anisotropic, as was recently shown [34]. The overall efficiency is nevertheless extremely high. Although this is not yet fully understood, it can be explained by the fact that the gold nonlinear susceptibility is two orders of magnitude higher than that of LC, and that this interface, although the gold layer is only 100 nm thick, may be decisive [45]. We have tested TOA-SLMs with no PVA and not-brushed PVA and noticed only 20% decrease in the THG efficiency, which can be attributed to the disordered liquid crystal layer (lower average nonlinear refractive index). Consequently, we treated the thin PVA layer as part of the LC-bulk and LC-gold interfaces. This phenomenon will require additional investigations as well as the precise role of the PVA in the THG process.

The TOA-SLM therefore forms a structure conducive to THG due to the multiple interfaces that make it up and the associated $\chi^{(3)}$ discontinuities. The following section discusses the impact of this phenomenon on the operation of the device.

### C. Chromatic Dependence of the LIDT and Discussion

It is obvious that, for a wide range of pump wavelengths, the TH wavelength generated in TOA-SLM falls within the one-photon absorption band of the gold layer, which will inevitably fasten the laser-induced damage. This is the subject of this section, in which we report the chromatic LIDT of TOA-SLM following the protocol defined in Section 2.

The pump wavelength is varied from 0.8 to 2.1 µm, and the results are illustrated in Fig. 5. Three areas of distinct behavior are identified. In the first region, between 0.8 and 1.2 µm, the LIDT decreases, reaching a minimum at 1.03 µm. This local minimum corresponds to the longest tested pulse duration. In this range, LIDT values are relatively low. In the second region, from 1.2 to 1.8 µm, the LIDT progressively increases, with a maximum value of 500 GW/cm² (60 mJ/cm²) at 1.8 µm. In the third region, above 1.8 µm, a moderate decrease in LIDT is observed.

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (b) Measured chromatic LIDT of TOA-SLM (black) and gold layer absorption as a function of the TH wavelength (blue, based on manufacturer data.)</figcaption></figure>

The absorption of the gold layer at the third-harmonic (TH) wavelength corresponding to each pump wavelength is plotted on the graph. A correlation is observed between the LIDT and absorption: the LIDT decreases as the gold layer's absorption of the TH wavelength increases; and, conversely, it increases when the TH absorption by the metal decreases. This observation supports the hypothesis that the early damage of the gold layer in TOA-SLM is caused by THG one-photon absorption in the metallic layer. This hypothesis not only accounts for the chromatic dependence of the LIDT but also explains its anisotropy, as discussed in the previous section. The LIDT decrease measured for the longest wavelengths could originate from metrology uncertainties or the behavior of another component (PVA, front-most substrate...). To quantify, we consider the data acquired for $\lambda = 1.5$ µm ($\lambda_{TH} = 0.5$ µm). Close to the LIDT (320 GW/cm² or 40 mJ/cm²), we measure a TH signal, which is 5% of the pump energy, leading to a local TH fluence of at least 2 mJ/cm². This is a floor value. Given the gold absorption for this wavelength (≈70%) and the probable beam size reduction, the TH fluence can be roughly estimated between 2 mJ/cm² and 20 mJ/cm². Recent calculations report LIDT of thin gold layers in the femtosecond regime at $\lambda = 0.515$ µm lower than 50 mJ/cm² for 50% absorption [46]. This theoretical value aligns well with our experimental observations.

To conclude this part, our results highlight the significant role of unexpectedly high THG in the damaging process of TOA-SLM. The highest LIDT value is measured for a pump wavelength of $\lambda = 1.8$ µm and is 500 GW/cm² (60 mJ/cm²). This high value indicates that, once the metallic layer is shielded from TH, the device should endure high peak power, maintaining its suitability for ultrafast optics.

### D. LIFT

Finally, we aim at determining whether the damage is preceded by local heating of the LC layer, potentially caused by the absorption of TH light by the LC molecules, which could negatively affect the operation of the TOA-SLM. To investigate this, we measured the laser-induced functional threshold (LIFT), as
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Local wavefront modification as a function of exposure time, for a pump wavelength of 1.4 µm, for different pump peak power. LIFT and LIDT thresholds, as defined in Section 2, are indicated. The two graphs are on a different y scale. The error bars correspond to the sensitivity of the wavefront sensor.</figcaption></figure>

defined in Section 2. The results, presented for a pump wave-
length of 1.4 µm, are representative of the overall experiments,
despite being shown for only one wavelength. Figure 6 illustrates
the amplitude of local wavefront deformations as a function
of exposure time (following the protocol in Section 2) and for
progressively increasing peak power up to the point of damage.

For peak power levels between 100 GW/cm² and 200 GW/cm² (11 – 23 mJ/cm²), the wavefront modifications remain within the sensor sensitivity. For an experimental peak power below the damage threshold (230 GW/cm², or 26 mJ/cm²), phase modifications increase gradually with exposure time but stay just below the LIFT threshold by the end of the sequence. For the peak power found equal to the LIDT (250 GW/cm² or 28 mJ/cm²), the LIDT threshold is crossed after 30 s exposure time. As intermediate peak powers between 230 GW/cm² and 250 GW/cm² were not accessible during the experiment, the former is designated as the LIFT. Consequently, we estimate that LIFT ≈ 0.9 × LIDT. Notably, no parasitic phase modulation disrupts the device’s operation prior to reaching the LIFT.

4. CONCLUSION

In conclusion, we have conducted a quantitative study of the chromatic LIDT of a TOA-SLM in the femtosecond regime. Although each individual layer in the structure exhibits a relatively high LIDT, the assembled multilayer configuration shows greater sensitivity to laser flux, ultimately resulting in damage to the gold layer. We identified exceptionally high THG at the bulk LC and/or metal LC interfaces, driven by the discontinuity in third-order susceptibility (χ<sup>(3)</sup>), as the main cause of damage, resulting from absorption by the gold layer. The chromatic analysis provided a detailed map of the TOA-SLM’s operating ranges in ultrafast optics. The highest LIDT value, 500 GW/cm<sup>2</sup> (60 mJ/cm<sup>2</sup>), observed outside the THG absorption bands, is highly promising. With a solution to

minimize the impact of THG, such as protecting the gold layer
with a high-reflection coating, the device would exhibit excel-
lent resistance to high peak power in the femtosecond regime,
making it an ideal candidate for ultrafast optical systems.

Additionally, we explored the chromatic functional threshold
of the TOA-SLM. Wavefront analysis revealed that, as long as its
peak intensity remains below ≈0.9 × LIDT, the laser pulse has
no negative effect on its operation.

We point out that the measurements presented in this study are specific to the femtosecond regime, where nonlinear effects are more likely to occur, and they do not predict the outcomes that may arise with stretched or longer duration pulses (picosecond, nanosecond).

Finally, we believe that the phenomenon highlighted here
should therefore be taken into account for all LC devices.
Nevertheless, achromatic and efficient generation of the third
harmonic could be of great interest for other applications, such
as microscopy or the temporal characterization of femtosecond
pulses.

**Funding.** Agence Nationale de la Recherche (ANR-19-CE30-0006-01, ANR-21-PRRD-0001-01); Association Nationale de la Recherche et de la Technologie (2019/0660).

**Disclosures.** The authors declare no conflicts of interest.

**Data availability.** Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

REFERENCES

1. C. Rosales-Guzman and A. Forbes, *How to Shape Light with Spatial Light Modulators* (SPIE, 2017).

2. U. Efron, *Spatial Light Modulators: Materials, Technology and Applications* (Uzi Efron, 1995).

3. A. Jullien, “Spatial light modulators,” *Photoniques* **101**, 59 (2020).

4. N. Collings, T. Davey, J. Christmas, et al., "The applications and technology of phase-only liquid crystal on silicon devices," *J. Display Technol.* **7**, 112–119 (2011).

5. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," *Rev. Sci. Instrum.* **71**, 1929 (2000).

6. M. Block, L. V. Grafenstein, U. Griebner, et al., “Generation of millijoule few-cycle pulses at 5 µm by indirect spectral shaping of the idler in an optical parametric chirped pulse amplifier,” *J. Opt. Soc. Am. B* **35**, C18–C24 (2018).

7. A. Camper, "High complexity femtosecond pulse duplicator," *Opt. Express* **28**, 22247-22254 (2020).

8. X. Liu, H. Wang, H. Cao, et al., "Dispersed pulses created by aperi-
odic binary spectral phase jump and applications for pulse shaping,"
*Opt. Express* **29**, 12319–12329 (2021).

9. C. Dorrer, S. K.-H. Wei, P. Leung, et al., "High-damage-threshold static laser beam shaping using optically patterned liquid-crystal devices," *Opt. Lett.* **36**, 4035-4037 (2011).

10. P. S. Salter and M. J. Booth, “Adaptive optics in laser processing,” *Light Sci. Appl.* **8**, 110 (2019).

11. A. Jullien, U. Bortolozzo, S. Grabielle, et al., "Continuously tunable femtosecond delay-line based on liquid crystal cells," *Opt. Express* **24**, 14483-14493 (2016).

12. Y. Liu, H. Liang, C.-W. Chen, et al., “Ultrafast switching of optical singularity eigenstates with compact integrable liquid crystal structures,” *Opt. Express* **26**, 28818–28826 (2018).

13. A.-K. Raab, M. Schmoll, E. R. Simpson, et al., *Highly Versatile, Two-Color Setup for High-Order Harmonic Generation using Spatial Light Modulators* (2024).

14. T. Z. Kosc, A. A. Kozlov, S. Papernov, et al., "Investigation of parameters governing damage resistance of nematic liquid crystals for
high-power or peak-intensity laser applications," *Sci. Rep.* **9**, 16435 (2019).

15. K. L. Marshall, K. R. P. Kafka, N. D. Urban, et al., "Multiparameter laser performance characterization of liquid crystals for polarization control devices in the nanosecond regime," *Sci. Rep.* **12*, 10969 (2022).

16. J. U. Wallace, K. L. Marshall, D. J. Batesky, et al., "Highly saturated glassy liquid crystal films having nano- and microscale thicknesses for high-power laser applications," *ACS Appl. Nano Mater.* **4**, 13–17 (2021).

17. L. Ramousse, G. Chériaux, C. Claudet, et al., "Femtosecond laser-induced damage threshold of nematic liquid crystals 1030 nm," *Appl. Opt.* **60**, 8050–8056 (2021).

18. H. Wang, Z. Huang, D. Zhang, et al., "Thickness effect on laser-induced-damage threshold of indium-tin oxide films at 1064 nm," *J. Appl. Phys.* **110**, 113111 (2011).

19. V. M. di Pietro, A. Jullien, U. Bortolozzo, et al., "Thermally-induced nonlinear spatial shaping of infrared femtosecond pulses in nematic liquid crystals," *Laser Phys. Lett.* **16**, 015301 (2019).

20. Z. Xing, W. Fan, D. Huang, et al., "High laser damage threshold liquid crystal optical switch based on a gallium nitride transparent electrode," *Opt. Lett.* **45**, 3537–3540 (2020).

21. K. L. Marshall, T. Z. Kosc, M. Ordway, et al., "Optically-addressable liquid crystal laser beam shapers employing photoalignment layer materials and technologies (conference presentation)," *Proc. SPIE* **10735**, 107350W (2018).

22. V. M. di Pietro, S. Bux, N. Forget, et al., "Phase-only pulse shaper for multi-octave light sources," *Opt. Lett.* **45**, 543–546 (2020).

23. S. Barland, L. Ramousse, G. Chériaux, et al., "Reconfigurable design of a thermo-optically addressed liquid-crystal phase modulator by a neural network," *Opt. Express* **31**, 12597–12608 (2023).

24. L. Gallais, D.-B. Douti, M. Commandre, et al., "Wavelength dependence of femtosecond laser-induced damage threshold of optical materials," *J. Appl. Phys.* **117**, 223103 (2015).

25. T. Q. Jia, H. X. Chen, M. Huang, et al., "Ultraviolet-infrared femtosecond laser-induced damage in fused silica and CaF₂ crystals," *Phys. Rev. B* **73**, 054105 (2006).

26. D. Grojo, S. Leyder, P. Delaporte, et al., "Long-wavelength multi-photon ionization inside band-gap solids," *Phys. Rev. B* **88**, 195135 (2013).

27. M. Garcia-Lechuga, O. Uteza, N. Sanner, et al., "Wavelength-independent performance of femtosecond laser dielectric ablation spanning over three octaves," *Phys. Rev. A* **19**, 044047 (2023).

28. K. R. P. Kafka, T. Z. Kosc, and S. G. Demos, "Methods and apparatus for laser damage and functional performance characterization of ultrafast laser optics," *Proc. SPIE* **11910**, 119100N (2021).

29. V. M. D. Pietro and A. Jullien, "Broadband spectral domain interferometry for optical characterization of nematic liquid crystals," *Appl. Sci.* **10**, 4701 (2020).

30. J. Li, S. Cauza, and S.-T. Wu, "Temperature effect on liquid crystal refractive indices," *J. Appl. Phys.* **96**, 19 (2004).

31. O. Uteza, B. Bussière, F. Canova, et al., "Laser-induced damage threshold of sapphire in nanosecond, picosecond and femtosecond regimes," *Appl. Surf. Sci.* **254**, 799 (2007).

32. P. Poole, S. Trendafilov, G. Shvets, et al., "Femtosecond laser damage threshold of pulse compression gratings for petawatt scale laser systems," *Opt. Express* **21**, 26341–26351 (2013).

33. V. Femy, M. Neradovskiy, T. Pinoteau, et al., "Microjoule-level femtosecond pulses from 3 to 10 um by DFG in LiGaS₂ at 250 KHz," in *Frontiers in Optics and Laser Science*, C. Mazzali, T. T. Poon, R. Averitt, and E. R. Kaindl, eds., Technical Digest Series (Optica Publishing Group, 2021).

34. B. Maingot, E. Neradovskaia, C. Claudet, et al., "Measurement of nonlinear refractive indices of bulk and liquid crystals by nonlinear chirped interferometry," *Opt. Lett.* **48**, 3243–3246 (2023).

35. P. Bon, G. Maucort, B. Wattellier, et al., "Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells," *Opt. Express* **17**, 13080–13094 (2009).

36. D.-B. L. Douti, M. Chrayteh, S. Aknoun, et al., "Quantitative phase imaging applied to laser damage detection and analysis," *Appl. Opt.* **54**, 8375–8382 (2015).

37. D. Yelin, Y. Silberberg, Y. Barad, et al., "Phase-matched third-harmonic generation in a nematic liquid crystal cell," *Phys. Rev. Lett.* **82**, 3046 (1999).

38. J.-I. Kosugi and K. Kajikawa, "Phase-matched third-harmonic generation from nematic liquid crystals," *Appl. Phys. Lett.* **84**, 5013 (2004).

39. R. S. Pillai, M. Oh-E, H. Yokoyama, et al., "Imaging colloidal particle induced topological defects in a nematic liquid crystal using third harmonic generation microscopy," *Opt. Express* **14**, 12976–12983 (2006).

40. D. Yelin, Y. Silberberg, Y. Barad, et al., "Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy," *Appl. Phys. Lett.* **74**, 3107 (1999).

41. S. M. Arakelyan, G. A. Lyakhov, and Y. S. Chilingaryan, "Nonlinear optics of liquid crystals," *Sov. Phys. Usp.* **23**, 245 (1980).

42. E. C. Barbano, K. Harrington, S. C. Zilio, et al., "Third-harmonic generation at the interfaces of a cuvette filled with selected organic solvents," *Appl. Opt.* **55**, 595–602 (2016).

43. T. Y. F. Tsang, "Optical third-harmonic generation at interfaces," *Phys. Rev. A* **52**, 4116 (1995).

44. T. Tsang, "Third and fifth harmonic generation at the interfaces of glass and liquids," *Phys. Rev. A* **54**, 5454 (1996).

45. R. W. Boyd, Z. Shi, and I. D. Leon, "The third-order nonlinear optical susceptibility of gold," *Opt. Commun.* **326**, 74 (2014).

46. G. D. Tibidis, D. Mansour, and E. Stratakis, "Damage threshold evaluation of thin metallic films exposed to femtosecond laser pulses: the role of material thickness," *Opt. Laser Technol.* **156**, 108484 (2022).