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Small-Polaron Hopping and Low-Temperature (45–225 K) Photo-Induced Transient Absorption in Magnesium-Doped Lithium Niobate^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Decay of Photo-Induced Absorption

## 4. Small-Polaron Recombination and Phonon-Assisted Hopping

## 5. Combining the Decay of Lithium Niobate’s Induced Absorption with Small-Polaron Recombination

## 6. Discussion

## 7. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Normalized photo-absorptions at a wavelength of 785 nm of 6.5 mol% Mg:LN are plotted versus decay time for representative temperatures between 50 K and 225 K. The solid red curves show fits using a single Kohlrausch–Williams–Watts (KWW) stretched-exponential for T < 100 K and the sum of two KWW functions for T > 100 K, respectively.

**Figure 2.**The temperature dependence of the inverse mean decay time of photo-induced absorption in Mg:LN is compared to the small-polaron hopping and recombination rate.

**Figure 3.**Normalized small-polaron hopping activation energy ${E}_{\mathrm{a}}$ over ${E}_{\mathrm{b}}/2$ as a function of temperature. Note the different slopes and absolute values at different phonon frequencies, $\omega $, when lowering the temperature.

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**MDPI and ACS Style**

Messerschmidt, S.; Krampf, A.; Vittadello, L.; Imlau, M.; Nörenberg, T.; Eng, L.M.; Emin, D.
Small-Polaron Hopping and Low-Temperature (45–225 K) Photo-Induced Transient Absorption in Magnesium-Doped Lithium Niobate. *Crystals* **2020**, *10*, 809.
https://doi.org/10.3390/cryst10090809

**AMA Style**

Messerschmidt S, Krampf A, Vittadello L, Imlau M, Nörenberg T, Eng LM, Emin D.
Small-Polaron Hopping and Low-Temperature (45–225 K) Photo-Induced Transient Absorption in Magnesium-Doped Lithium Niobate. *Crystals*. 2020; 10(9):809.
https://doi.org/10.3390/cryst10090809

**Chicago/Turabian Style**

Messerschmidt, Simon, Andreas Krampf, Laura Vittadello, Mirco Imlau, Tobias Nörenberg, Lukas M. Eng, and David Emin.
2020. "Small-Polaron Hopping and Low-Temperature (45–225 K) Photo-Induced Transient Absorption in Magnesium-Doped Lithium Niobate" *Crystals* 10, no. 9: 809.
https://doi.org/10.3390/cryst10090809