# Nonlinear Diffuse fs-Pulse Reflectometry of Harmonic Upconversion Nanoparticles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fundamentals

#### 2.1. Nonlinear Optics

#### 2.2. Introducing a Figure of Merit

## 3. Sample Preparation, Linear Optical Analysis, and Nonlinear Setup

## 4. Harmonic Results

#### 4.1. Intensity (In-)Dependence of the Harmonic Ratio

^{15}is achieved.

## 5. Discussion

^{2}. Thus, the applicability of arbitrary fundamental wavelengths can be demonstrated, which is ultimately only limited by the optical absorption characteristics of the material under investigation. Detrimental factors can affect either THG (typically at the band edge), SHG (color centers and other defects), or both. In such case, an appropriate wavelength-triplet between fundamental, second harmonic, and third harmonic wave should be determined prior to nonlinear investigation; i.e., by diffuse reflectance spectroscopy, outlined in Section 3.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Logarithmized harmonic ratio ${\mathrm{log}}_{10}\left({f}_{R}\right)$ as a function of spectral peak intensities according to Equation (6) with $s=1$ (

**left**) and as a function of the spectral peak width and the linear ratio ${A}_{2\omega}/{A}_{3\omega}$ with $\mathrm{max}({A}_{2\omega},{A}_{3\omega})=1$ (

**right**). The white dashed line marks value-pairs where ${f}_{R}=1$, whereas black lines illustrate equal ratios between second harmonic generation (SHG)- and third harmonic generation (THG)-peaks. Values scale from blue over red to yellow.

**Figure 2.**(

**Left**): prepared powder plaque for optical characterization; (

**Right**): schematic experimental setup for nonlinear diffuse fs-pulse reflectometry. Str.: pulse-stretcher, RGA: regenerative amplifier, Cmp.: pulse-compressor, OPA: optical parametric amplifier, F: filter, M: mirror, S: sample. Further information can be found in the accompanying text.

**Figure 3.**Diffuse reflectance spectra of LiNbO${}_{3}$:Yb- (

**left**) and TiO${}_{2}$-nanopowder (

**right**). Insets are corresponding Tauc-plots for determining the indirect allowed band edge. Further information is found in the accompanying text.

**Figure 4.**Harmonic emission of LiNbO${}_{3}$:Yb- (

**top**) and TiO${}_{2}$-nanopowder (

**bottom**) at different fundamental wavelengths in the range ${\lambda}_{\omega}$ = (900–1900) nm photographed with a digital camera. A shortpass filter was placed in front of the camera lens to suppress residue infrared pump radiation.

**Figure 5.**(

**Left**): baseline-corrected emission spectra of LiNbO${}_{3}$:Yb- (

**top**) and TiO${}_{2}$-nanopowder (

**bottom**) as a function of the fundamental wavelength. Dashed lines indicate SHG- and THG-peak positions. Each spectrum’s most significant peak has been scaled to unity; (

**Right**): simulated spectra with their respective emission characteristics based on the spectral properties of the fundamental beam. All spectra are plotted on a logarithmic intensity scale with values exceeding unity clipped to one. Values scale from blue over red to yellow.

**Figure 6.**Baseline-corrected and normalized emission spectra of LiNbO${}_{3}$:Yb- (

**top**) and TiO${}_{2}$-nanopowder (

**bottom**) at a fundamental wavelength ${\lambda}_{\omega}=1400$ nm. The less intense peak has been scaled up to unity with displayed factors for clarity. Fundamental intensities for both samples are on the order of (9 ± 2) × 10

^{15}W/m

^{2}. Peak areas for calculation of the harmonic ratio are shaded.

**Figure 7.**Harmonic ratio ${f}_{R}$ of LiNbO${}_{3}$:Yb- (

**left**) and TiO${}_{2}$-nanopowder (

**right**) as a function of the fundamental peak intensity ${I}_{\omega}$ at a wavelength ${\lambda}_{\omega}=1400$ nm (

**left**) and ${\lambda}_{\omega}=1460$ nm (

**right**).

**Figure 8.**

**Left**: logarithmized harmonic ratio ${\mathrm{log}}_{10}\left({f}_{R}\right)$ as a function of spectral peak intensities according to Equation (6), with $s=46\mathrm{m}\mathrm{e}\phantom{\rule{-0.21251pt}{0ex}}\mathrm{V}$; the colors scale from $-11$ (blue) to 13 (yellow). Harmonic ratios of LiNbO${}_{3}$:Yb (dotted) and TiO${}_{2}$ (dash-dotted) are simulated for $\mathrm{max}({A}_{2\omega},{A}_{3\omega})$ = 50,000, their linear ratio given by the scaling factors of Figure 6, and extrapolated to low intensities.

**Right**: ${f}_{R}$ of LiNbO${}_{3}$:Yb and TiO${}_{2}$ as a function of the fundamental peak width s measured on an energy-scale with the linear ratio taken from Figure 6 and $\mathrm{max}({A}_{2\omega},{A}_{3\omega})$ = 50,000. The horizontal dashed black line marks ${f}_{R}=1$, whereas the vertical one marks $s=46\mathrm{m}\mathrm{e}\phantom{\rule{-0.21251pt}{0ex}}\mathrm{V}$. Shaded in light gray are typically accessible experimental peak widths. Both ratios are separated by a factor of almost 10

^{13}.

**Table 1.**Relevant values for the determination of the harmonic ratio ${f}_{R}$ extracted from Figure 6. FWHM is the full width at half maximum of each peak, the signal S is given by the area under the peak and the indexes $2\omega $ and $3\omega $ denote the second and third harmonic, respectively.

FWHM_{2ω} | FWHM_{3ω} | S_{2ω} | S_{3ω} | f_{R} | |
---|---|---|---|---|---|

LiNbO_{3}:Yb | 55 $\mathrm{m}\mathrm{e}\phantom{\rule{-0.21251pt}{0ex}}\mathrm{V}$ | 91 $\mathrm{m}\mathrm{e}\phantom{\rule{-0.21251pt}{0ex}}\mathrm{V}$ | 7.12 × 10^{−2} | 4.18 × 10^{−3} | 20.7 |

TiO_{2} | 62 $\mathrm{m}\mathrm{e}\phantom{\rule{-0.21251pt}{0ex}}\mathrm{V}$ | 97 $\mathrm{m}\mathrm{e}\phantom{\rule{-0.21251pt}{0ex}}\mathrm{V}$ | 2.90 × 10^{−5} | 1.13 × 10^{−1} | 1.93 × 10^{−12} |

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**MDPI and ACS Style**

Kijatkin, C.; Eggert, J.; Bock, S.; Berben, D.; Oláh, L.; Szaller, Z.; Kis, Z.; Imlau, M.
Nonlinear Diffuse fs-Pulse Reflectometry of Harmonic Upconversion Nanoparticles. *Photonics* **2017**, *4*, 11.
https://doi.org/10.3390/photonics4010011

**AMA Style**

Kijatkin C, Eggert J, Bock S, Berben D, Oláh L, Szaller Z, Kis Z, Imlau M.
Nonlinear Diffuse fs-Pulse Reflectometry of Harmonic Upconversion Nanoparticles. *Photonics*. 2017; 4(1):11.
https://doi.org/10.3390/photonics4010011

**Chicago/Turabian Style**

Kijatkin, Christian, Juliane Eggert, Sergej Bock, Dirk Berben, Laura Oláh, Zsuzsanna Szaller, Zsolt Kis, and Mirco Imlau.
2017. "Nonlinear Diffuse fs-Pulse Reflectometry of Harmonic Upconversion Nanoparticles" *Photonics* 4, no. 1: 11.
https://doi.org/10.3390/photonics4010011