# Broad Frequency Shift of Parametric Processes in Epsilon-Near-Zero Time-Varying Media

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## Abstract

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## 1. Introduction

## 2. Results

## 3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**,

**b**) describe the two four-wave mixing processes that generate the PC and NR signals, respectively. The pump beam is illustrated with a green arrow while the input seed is shown with a blue arrow. Red arrows show the result of the parametric amplification process, while blue dashed arrows show the linear reflection and transmission. For each of these two four-wave mixing processes, the seed field is amplified and emerges along both the transmitted and reflected directions. (

**c**) Sketch of the experimental setup. Pump and seed fields have the same wavelength (1400 nm) and vertical polarisation. The seed is overlapped to the pump with an angle of $\simeq 6\xb0$. The delay between the pump and seed pulses is controlled by a delay line (not shown). A spectrometer is used to collect the radiation emerging along the direction of the seed reflection and transmission ($\mathrm{RS}+{\mathrm{AS}}_{\mathrm{b}}$ and $\mathrm{TS}+{\mathrm{AS}}_{\mathrm{f}}$), as well as to characterise the PC and NR.

**Figure 2.**Measured spectrograms (normalised power spectral density (PSD)) for (

**a**) the PC, (

**b**) the NR, (

**c**) the reflection, and (

**d**) the transmission of the input seed field. See the colour bar for the PSD above panels (

**a**,

**b**). The horizontal axis in each panel denotes the delay between the pump and the seed pulses. The vertical axis indicates the wavelength. The dashed line is at the seed carrier wavelength (1400 nm), while the dotted line refers to the amplified seed measurement (see text for details).

**Figure 3.**(

**a**) Carrier wavelength shift of the PC signal as a function of the pump-probe delay $\Delta \tau $ (blue-curve) overlapped with the PC generation efficiency (red curve). (

**b**) Carrier wavelength shift of the NR signal as a function of the pump-probe delay $\tau $ (blue curve) overlapped with the NR generation efficiency (red curve). (

**c**) Reflection spectrogram as in Figure 2c, with a dashed blue line at the input seed carrier wavelength and a black dotted line at the carrier wavelength of the PC peak. (

**d**) Measured wavelength shifts for the PC (blue) and the NR (red) nonlinear products, as a function of the pump intensity.

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## Share and Cite

**MDPI and ACS Style**

Bruno, V.; Vezzoli, S.; DeVault, C.; Carnemolla, E.; Ferrera, M.; Boltasseva, A.; Shalaev, V.M.; Faccio, D.; Clerici, M.
Broad Frequency Shift of Parametric Processes in Epsilon-Near-Zero Time-Varying Media. *Appl. Sci.* **2020**, *10*, 1318.
https://doi.org/10.3390/app10041318

**AMA Style**

Bruno V, Vezzoli S, DeVault C, Carnemolla E, Ferrera M, Boltasseva A, Shalaev VM, Faccio D, Clerici M.
Broad Frequency Shift of Parametric Processes in Epsilon-Near-Zero Time-Varying Media. *Applied Sciences*. 2020; 10(4):1318.
https://doi.org/10.3390/app10041318

**Chicago/Turabian Style**

Bruno, Vincenzo, Stefano Vezzoli, Clayton DeVault, Enrico Carnemolla, Marcello Ferrera, Alexandra Boltasseva, Vladimir M. Shalaev, Daniele Faccio, and Matteo Clerici.
2020. "Broad Frequency Shift of Parametric Processes in Epsilon-Near-Zero Time-Varying Media" *Applied Sciences* 10, no. 4: 1318.
https://doi.org/10.3390/app10041318