# Dynamical Control of Broadband Coherent Absorption in ENZ Films

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## Abstract

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## 1. Introduction

## 2. Theoretical Investigation

^{15}rad/s. We vary the Drude model damping coefficient, thus increasing losses and reducing the dispersion gradient in n, from (a) to (c) $\gamma $ = 1.0073 × 10

^{13}→ 2.4745 × 10

^{14}rad/s. Figure 2d–f show the visibility ${V}_{tot}$ of the total energy as a function of the ENZ film’s thickness for the three cases shown in Figure 2a–c. In Figure 2d (${\gamma}_{a}$), we do not observe coherent modulation of the total energy for thickness below 1000 nm. Due to the high transmission of the thin film, the interference between the reflected and transmitted field is weak. For thicker films, r and t become more similar and stronger interference is observed. The TMM model predicts visibility with a maximum value close to one that is pinned to a wavelength slightly shorter than ${\lambda}_{ENZ}$. When we increase the optical losses of the ENZ slab, Figure 2e,f, the peak of the visibility becomes broader, exhibiting multiple resonances as the thickness increases but all with maximum absorption at a wavelength just below ${\lambda}_{ENZ}$. These results show that the system exhibits broadband coherent modulation of the energy with a maximum value close to one just below ${\lambda}_{ENZ}$, independently of the thickness and of the single-pass absorption. We associate this maximum to a Fabry–Perot (FP) like resonance due to interference effects in the Air/AZO/glass system. The fact that the FP resonance is ‘locked’ before the ENZ wavelength irrespectively of the thickness is due to the ENZ condition [42,43].

## 3. Coherent Absorption and Its Dynamical Control

^{2}without showing damage of the sample or saturation of the optical Kerr effect. In the same work, at $\lambda $ = 1310 nm a nonlinear susceptibility of $Re\left[{\chi}^{\left(3\right)}\right]\sim 4.73\times {10}^{-20}$ V

^{2}/m

^{2}and $Im\left[{\chi}^{\left(3\right)}\right]\sim 0.57\times {10}^{-20}$ V

^{2}/m

^{2}was extrapolated. We therefore illuminated the AZO film in the Sagnac interferometer with two high intensity pulses at normal incidence and same wavelength. The intensities on each side are 0.8 and 0.6 TW/cm

^{2}, respectively. By increasing the intensities from the linear regime to these maximum values, we observe that the CPA visibility passes from 68% of the linear case to 35% (Figure 5a,b). The peak of the normalized visibility also redshifts and becomes broader for both the samples, with a nearly 50 nm-shift for the 500 nm sample. Following the recent works in TCOs, this can be explained by the fact that the dielectric permittivity, and so the optical constants including ${\lambda}_{ENZ}$, exhibit a redshift when it is optically pumped across the ENZ wavelength [31,44]. The redshift of the ${\lambda}_{ENZ}$ is also associated to a positive $\Delta n$ and to a negative $\Delta k$ [30,32]. Due to the decreasing of k, the visibility drops, as we observed for the linear case. While, the shift of the visibility peak is related to the shift of ${\lambda}_{ENZ}$ in the same direction, and therefore to the shift of the strong dispersion which the material exhibits at wavelength shorter than the zero-crossing frequency. In Figure 5c,d we plot the experimental results together with TMM simulations. The TMM simulations are obtained considering a ∼60 nm shift of ${\omega}_{p}$ and a decreasing of $\gamma $ ($0.15\times {10}^{15}$→$0.09\times {10}^{15}$). This correspond to a $\Delta {\lambda}_{ENZ}\sim 60$ nm and to a ${k}_{500}=0.38$ and ${k}_{900}=0.24$. These results show that enhanced nonlinearities in ENZ materials can be used to add a degree of freedom to tune the efficiency and the bandwidth of coherent absorption.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Bi-directional coherent perfect absorption (CPA) scheme. (

**b**) Intensity of the two output beams, C and D, and its sum as we scan the sample position in the propagation direction. This is equivalent to changing the relative phase between the two input fields $\varphi $.

**Figure 2.**(

**a**–

**c**) Real and imaginary part of the refractive index of the three cases with ${\lambda}_{ENZ}$ ≈ 1350 nm. (

**d**–

**f**) Normalized visibility of the total energy as a function of the wavelength for different thicknesses. The dashed red line indicates the ${\lambda}_{ENZ}$. For the dispersion we use ${\u03f5}_{\infty}=3.18$ and ${\omega}_{p}$ = 2.4745 × 10

^{15}rad/s. For the damping constant we use ${\gamma}_{a}=1.0073\times {10}^{13}$, ${\gamma}_{b}=0.8053\times {10}^{14}$ and ${\gamma}_{c}=2.3614\times {10}^{14}$ rad/s.

**Figure 3.**(

**a**) Schematics of the Sagnac interferometer. (

**b**) An example of measurement for ${\lambda}_{0}$ = 1280 nm, assuming energy equal to 1 at the interferometer input. The total modulation of the energy (or absorption) is given by the sum of C and D (green curve). The inset shows a zoom of the interferogram. (

**c**) ellipsometer measurement of the index of refraction of AZO 900 nm thick film, (

**d**) experimental (dots) and TMM simulation (solid line) of R, T and abs for the same sample.

**Figure 4.**Experimental (circles) and transfer matrix method (TMM) simulation (solid line) of normalized visibility of the total energy for aluminum-doped zinc oxide (AZO) 500 nm and 900 nm with different values of k. (

**a**,

**b**) High losses ${k}_{1}$, (

**c**,

**d**) middle losses ${k}_{2}$ and (

**e**,

**f**) low losses ${k}_{3}$. For the TMM simulation we suppose $\Delta \lambda \sim $60 nm.

**Figure 5.**(

**a**,

**b**) Normalized visibility of the total energy for both samples, 500 nm (

**a**) and 900 nm (

**b**). The dashed blue curve represents the linear characterization, while the circles is the nonlinear CPA with high beam intensity. (

**c**,

**d**) Experimental (circles) and TMM simulation (solid line) of normalized visibility of the total energy for AZO 500 nm and 900 nm for the nonlinear CPA.

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**MDPI and ACS Style**

Bruno, V.; Vezzoli, S.; DeVault, C.; Roger, T.; Ferrera, M.; Boltasseva, A.; Shalaev, V.M.; Faccio, D.
Dynamical Control of Broadband Coherent Absorption in ENZ Films. *Micromachines* **2020**, *11*, 110.
https://doi.org/10.3390/mi11010110

**AMA Style**

Bruno V, Vezzoli S, DeVault C, Roger T, Ferrera M, Boltasseva A, Shalaev VM, Faccio D.
Dynamical Control of Broadband Coherent Absorption in ENZ Films. *Micromachines*. 2020; 11(1):110.
https://doi.org/10.3390/mi11010110

**Chicago/Turabian Style**

Bruno, Vincenzo, Stefano Vezzoli, Clayton DeVault, Thomas Roger, Marcello Ferrera, Alexandra Boltasseva, Vladimir M. Shalaev, and Daniele Faccio.
2020. "Dynamical Control of Broadband Coherent Absorption in ENZ Films" *Micromachines* 11, no. 1: 110.
https://doi.org/10.3390/mi11010110