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Gap-Free Tuning of Second and Third Harmonic Generation in Mechanochemically Synthesized Nanocrystalline LiNb_{1−x}Ta_{x}O_{3} (0 ≤ x ≤ 1) Studied with Nonlinear Diffuse Femtosecond-Pulse Reflectometry

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mechano-Chemical Synthesis of LNT Nanocrystallites

#### 2.2. Pellet Preparation

#### 2.3. Remission Spectroscopy

#### 2.4. Nonlinear Diffuse Femtosecond Pulse Reflectometry

## 3. Sample Characterization

#### Remission Spectroscopy

## 4. Nonlinear Diffuse fs-Pulse Reflectometry

#### 4.1. Harmonic Generation

#### 4.2. Diffuse fs-Pulse Remission Spectra

#### 4.3. Wavelength Dependence of the Harmonic Intensities

#### 4.4. Intensity Dependencies of Harmonic Emission

#### 4.5. Harmonic Ratio

#### 4.6. Bandwidths of Harmonic Emission

## 5. Discussion

#### 5.1. Application of Nonlinear Diffuse fs-Pulse Reflectometry to LNT Nanoparticle Pellets

#### 5.2. Characterization of LNT Nanocrystallites from the (Non-)linear Optical Perspective

#### 5.3. Harmonic Generation

## 6. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LN | Lithium Niobate |

LT | Lithium Tantalate |

LNT | Lithium Niobate Tantalate |

NLO | Nonlinear optical |

OPA | Optical parametric amplifier |

SHG | Second harmonic generation |

THG | Third harmonic generation |

FHG | Fourth harmonic generation |

UV | Ultra-violet |

VIS | Visual |

NIR | Near-infrared |

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**Figure 1.**(

**Left**): Photo of the loose, as-synthesized LNT nanocrystallites on a microscope slide. (

**Right**): Nanocrystallite LNT pressed into a powder pellet in a custom-made copper holder in accordance with the pellet preparation protocol outlined in Ref. [21]. For temperature stabilization, the holder is in thermal contact with a double-stacked Peltier element with a PID-loop controller and a platinum sensor (wired orange cables).

**Figure 2.**Tauc plot of the remission in the blue-ultraviolet energy spectrum for LN${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$T${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$. Linear functions (dashed lines) are fitted to the experimental dataset (ochre line) for two distinct fit regions in the range from 4.0 to 4.45 eV and 3.9 to 4.55 eV. The zero crossing point, averaged from both fits, is located at a band gap energy of ${\mathrm{E}}_{\mathrm{gap}}=(3.67\pm 0.01)$ eV. An indirect allowed transition is assumed in the analysis.

**Figure 3.**Digital images (spectral detection window of the digital camera ≈ 350–700 nm) of diffuse remission of LN${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$T${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$ nanoparticles under exposure to a train of fs-pulses tuned from 650 to 1700$\phantom{\rule{0.166667em}{0ex}}\mathrm{nm}$ in steps of 50 nm. The respective fundamental wavelengths are below each image.

**Figure 4.**Two-dimensional colormap measurement of LN${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$T${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$. The emission spectra are shown as a function of the fundamental wavelength with a color grade of the intensity, increasing from dark blue to light yellow colors on a log scale. The inset shows the remission spectrum of the second and third harmonic at a fundamental wavelength of 1350 nm on a logarithmic scale.

**Figure 5.**Intensity dependence of the second harmonic signal (arbitrary units) as a function of the fundamental wavelength ${\lambda}_{\mathrm{Fund}}$ for all LNT compositions with $\mathrm{x}=0,0.25,0.5,0.75,1.0$. The signal data were deduced from the individual emission spectra (cf. upper trace in Figure 4) and normalized to the square of the fundamental pulse peak intensity (details in the text). For the sake of clarity, the five plots were mutually displaced to each other along the signal axis. The dotted lines represent fits of functions of type $1/{(\lambda -{\lambda}_{\mathrm{gap}})}^{\mathrm{m}}$ to the datasets (cf. discussion).

**Figure 6.**Intensity dependence of the second- and third-order harmonic signals (triangles and circles, respectively) as a function of the intensity of the fundamental pulse in a double-logarithmic plot. As an example, data are shown for the sample LN${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$T${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$ at a fundamental wavelength of $1400\phantom{\rule{0.166667em}{0ex}}\mathrm{nm}$. The emission intensities at 700 nm (SHG) and 467 nm (THG) show a pronounced increase, with a significant change in both slopes at about $1.43\xb7{10}^{16}$ W/m${\phantom{\rule{-0.2em}{0ex}}}^{2}$. A linear function is fitted to both datasets (dotted black lines) for both slopes. The values of the derived slopes n${\phantom{\rule{-0.2em}{0ex}}}_{\mathrm{SHG}}$, n${\phantom{\rule{-0.2em}{0ex}}}_{\mathrm{THG}}$ of the fit functions are given in the inset. A spectrum of the fourth harmonic generation (FHG) is added to the figure as an inset.

**Figure 7.**Harmonic ratio as a function of the fundamental peak intensity for all LNT compositions under study.

**Figure 8.**Spectral fingerprints of the fundamental, SHG, and THG emission in LN${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$T${\phantom{\rule{-0.2em}{0ex}}}_{0.50}$. The fundamental, second, and third harmonic are normalized to their respective maximum to increase visibility. Two opposing arrows indicate the FWHM of each spectral signature.

**Table 1.**Average crystalline sizes <${d}_{\mathrm{XRD}}$> from XRD, weighted mean size <${d}_{\mathrm{DLS}}$> from DLS, and the corresponding 5th and 95th percentile ranges of the DLS size distribution for the LNT nanoparticles with compositions $x=0,0.25,0.5,0.75,1$.

Composition x | <${\mathit{d}}_{\mathbf{XRD}}$> (nm) | <${\mathit{d}}_{\mathbf{DLS}}$> (nm) | [5th perc, 95th perc] |
---|---|---|---|

Ref. [18] | (nm, nm) | ||

0.00 | 206 | $277\pm 8$ | [190, 396] |

0.25 | 171 | $275\pm 8$ | [220, 342] |

0.50 | 97 | $299\pm 8$ | [220, 459] |

0.75 | 92 | $335\pm 8$ | [220, 531] |

1.00 | 80 | $402\pm 8$ | [122, 825] |

**Table 2.**Energies of the band gaps ${\mathrm{E}}_{\mathrm{gap}}$ and corresponding wavelengths ${\lambda}_{\mathrm{gap}}$, ${\lambda}_{\mathrm{Fund},\mathrm{min}}^{\mathrm{SHG}}$, and ${\lambda}_{\mathrm{Fund},\mathrm{min}}^{\mathrm{THG}}$ (details in the discussion) for all LNT compositions $\mathrm{x}=0,0.25,0.5,0.75,1.0$ determined from remission spectroscopy. Indirect allowed transitions are assumed and a linear fitting procedure with a Tauc plot is used.

Composition x | ${\mathbf{E}}_{\mathbf{gap}}$ (eV) | ${\mathit{\lambda}}_{\mathbf{gap}}$ (nm) | ${\mathit{\lambda}}_{\mathbf{Fund},\mathbf{min}}^{\mathbf{SHG}}$ (nm) | ${\mathit{\lambda}}_{\mathbf{Fund},\mathbf{min}}^{\mathbf{THG}}$ (nm) |
---|---|---|---|---|

0 | 3.76 ± 0.02 | 330 | 660 | 990 |

0.25 | 4.10 ± 0.01 | 303 | 606 | 909 |

0.5 | 3.67 ± 0.01 | 338 | 676 | 1014 |

0.75 | 4.18 ± 0.03 | 297 | 594 | 891 |

1 | 4.53 ± 0.01 | 274 | 548 | 822 |

**Table 3.**Slopes ${\mathrm{s}}_{\mathrm{SHG}}^{\mathrm{b}}$ and ${\mathrm{s}}_{\mathrm{THG}}^{\mathrm{b}}$ as a result of fitting the function ${\mathrm{I}}_{(\mathrm{SHG},\mathrm{THG})}=\mathrm{c}\xb7{\mathrm{I}}_{\mathrm{Fund}}^{{\mathrm{s}}_{(\mathrm{SHG},\mathrm{THG})}^{\mathrm{a},\mathrm{b}}}$ to the intensity dependencies of the second- and third-order harmonic signals for all LNT compositions under study.

Composition x | s${\phantom{\rule{-0.2em}{0ex}}}_{\mathbf{SHG}}$ | s${\phantom{\rule{-0.2em}{0ex}}}_{\mathbf{THG}}$ |
---|---|---|

0 | $1.83\pm 0.01$ | $2.84\pm 0.03$ |

0.25 | $1.81\pm 0.02$ | $2.97\pm 0.05$ |

0.5 | $2.01\pm 0.03$ | $2.84\pm 0.04$ |

0.75 | $1.98\pm 0.02$ | $2.82\pm 0.05$ |

1 | $1.91\pm 0.02$ | $2.70\pm 0.07$ |

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**MDPI and ACS Style**

Klenen, J.; Sauerwein, F.; Vittadello, L.; Kömpe, K.; Hreb, V.; Sydorchuk, V.; Yakhnevych, U.; Sugak, D.; Vasylechko, L.; Imlau, M.
Gap-Free Tuning of Second and Third Harmonic Generation in Mechanochemically Synthesized Nanocrystalline LiNb_{1−x}Ta_{x}O_{3} (0 ≤ *x* ≤ 1) Studied with Nonlinear Diffuse Femtosecond-Pulse Reflectometry. *Nanomaterials* **2024**, *14*, 317.
https://doi.org/10.3390/nano14030317

**AMA Style**

Klenen J, Sauerwein F, Vittadello L, Kömpe K, Hreb V, Sydorchuk V, Yakhnevych U, Sugak D, Vasylechko L, Imlau M.
Gap-Free Tuning of Second and Third Harmonic Generation in Mechanochemically Synthesized Nanocrystalline LiNb_{1−x}Ta_{x}O_{3} (0 ≤ *x* ≤ 1) Studied with Nonlinear Diffuse Femtosecond-Pulse Reflectometry. *Nanomaterials*. 2024; 14(3):317.
https://doi.org/10.3390/nano14030317

**Chicago/Turabian Style**

Klenen, Jan, Felix Sauerwein, Laura Vittadello, Karsten Kömpe, Vasyl Hreb, Volodymyr Sydorchuk, Uliana Yakhnevych, Dmytro Sugak, Leonid Vasylechko, and Mirco Imlau.
2024. "Gap-Free Tuning of Second and Third Harmonic Generation in Mechanochemically Synthesized Nanocrystalline LiNb_{1−x}Ta_{x}O_{3} (0 ≤ *x* ≤ 1) Studied with Nonlinear Diffuse Femtosecond-Pulse Reflectometry" *Nanomaterials* 14, no. 3: 317.
https://doi.org/10.3390/nano14030317