# Laser-Inscribed Stress-Induced Birefringence of Sapphire

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## Abstract

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## 1. Introduction

## 2. Experimental

## 3. Results and Discussion

#### 3.1. Direct Write of Nano-Planes

#### 3.2. Engineering of Birefringence

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Inscription of sapphire with Bessel-beam at different stretch factors ${f}_{st}$ (0 corresponds to the spherical aberration compensation while the largest value of 12 was for the maximum stretch to obtain a linear intensity distribution over the entire pulse length $c{t}_{p}/n$, here ${t}_{p}$ is the pulse duration). SEM side-view images of as fabricated sample after breaking it on a xy-plane (see the inset) (

**a**) and after wet etching in HF 20% vol. for 60 min (

**b**,

**c**) with same single pulse ${E}_{p}=847$ nJ at different pulse frequency: 1 kHz (

**a**,

**b**), 10 kHz (

**c**); the beam was scanned at ${v}_{s}=0.5$ mm/s along z-axis. Some lines do not appear straight in SEM images due to the uneven surface of the cleaved region.

**Figure 2.**SEM images of the highest resolution single-line pattern inscribed in sapphire at the largest stretch factor ${f}_{st}=12$; conditions as in Figure 1a. The sample was cleaved (image plane) at some depth along the inscribed pattern and wet-etched for the SEM observation. The single line was inscribed by Bessel-like beam scanning without formation of periodicity nano-gratings (${f}_{st}\le 9$) nor transitional irregular pattern at low frequency and high pulse energy (Figure 1b). Wet-etched patterns reached aspect ratio $50/0.2=250$.

**Figure 3.**Optical (

**a**), cross-polarized (

**b**) and color-shifted birefringence with $\lambda =530$ nm waveplate at two orientations (

**c**) images of the sample between polarizer (P) and crossed-oriented analyzer (A). The inset in (

**a**) shows the pattern of 10 $\mathsf{\mu}$m inscribed regions with nano-planes with separation of $\Delta x$. The form-birefringent pattern of negative uniaxial crystal $\Delta x={t}_{1}+{t}_{2}$ and the orientation of ordinary and extraordinary fields ${E}_{o,e}$; OA is the optical axis (inset in (

**b**)). The stretch parameter of 11 corresponds to ∼$40\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m axial extent of the laser-inscribed region, 10 corresponds to ∼$30\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m. The Michel-Levy birefrincence color chart is shown in the inset of (

**c**).

**Figure 4.**Retardance $|\Delta n|d$ measured at several wavelengths from 475 nm to 650 nm with 10-nm-bandpass filters. Sample was fs-laser-inscribed at pulse energy ${E}_{p}=574$ nJ; sample is shown in Figure 3. Rectangular regions of interest (ROIs) show locations from where an average retardance was measured. Two lines of gratings with different stretch factors of 11 (the length of inscribed line $d=40\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m) and 10 ($d=30\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m) were analyzed using liquid crystal compensator [33]. Note logarithmic ordinate was used to reveal single exponential decay of retardance with $\Delta x$.

**Figure 5.**Retardance $|\Delta n|d/\lambda $ [waves] measured at 650 nm; sample are shown in Figure 3. (

**a**) Retardance map calculated at a single pixel level for VGA 640 × 480 pixel area. The $\delta n=0$ contour lines are shown to distinguish regions affected by stress-induced birefringence; the maximum was 0.22. Horizontal single-pixel cross sections are plotted in (

**b**). The slope of retardance $\gamma =4.8\times {10}^{-4}/$pixel or $(3.27\times {10}^{-4})/\mathsf{\mu}$m at the used magnification was achieved. One pixel corresponds to 1.4 $\mathsf{\mu}$m in the image while the optical resolution for the $NA=0.2$ lens was $0.61\lambda /NA=2\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m.

**Figure 6.**Retardance $|\Delta n|d/\lambda $ [waves] measured at 625 nm with higher resolution $NA=0.4$; sample are shown in Figure 3 and Figure 5. Retardance map calculated at a single pixel level. Cross sections for two regions inscribed with stretch factors ${f}_{st}=11$ and 10 are shown as one-pixel line for $\Delta x=200$ nm; for ${f}_{st}=10$ five separate lines and their average (× marker in red line) are plotted. The optical resolution for the $NA=0.4$ lens was $0.61\lambda /NA=0.95\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m. Rectangular markers show positions of the inscribed regions for the ${f}_{st}=11$ grating.

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## Share and Cite

**MDPI and ACS Style**

Fan, H.; Ryu, M.; Honda, R.; Morikawa, J.; Li, Z.-Z.; Wang, L.; Maksimovic, J.; Juodkazis, S.; Chen, Q.-D.; Sun, H.-B.
Laser-Inscribed Stress-Induced Birefringence of Sapphire. *Nanomaterials* **2019**, *9*, 1414.
https://doi.org/10.3390/nano9101414

**AMA Style**

Fan H, Ryu M, Honda R, Morikawa J, Li Z-Z, Wang L, Maksimovic J, Juodkazis S, Chen Q-D, Sun H-B.
Laser-Inscribed Stress-Induced Birefringence of Sapphire. *Nanomaterials*. 2019; 9(10):1414.
https://doi.org/10.3390/nano9101414

**Chicago/Turabian Style**

Fan, Hua, Meguya Ryu, Reo Honda, Junko Morikawa, Zhen-Ze Li, Lei Wang, Jovan Maksimovic, Saulius Juodkazis, Qi-Dai Chen, and Hong-Bo Sun.
2019. "Laser-Inscribed Stress-Induced Birefringence of Sapphire" *Nanomaterials* 9, no. 10: 1414.
https://doi.org/10.3390/nano9101414