# Applications of Random Nonlinear Photonic Crystals Based on Strontium Tetraborate

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}= π/Δk(λ

_{0}) is approximately described by (sin(x)/x)

^{2}function, where x = [Δk(λ) − Δk(λ

_{0})]d

_{0}N/3.5, N being the number of domains. It was shown [4] that in case of special kind of deviations this spectral dependence becomes modified and can be, for instance, a triangular or quasi-rectangular shape.

## 2. Orthorhombic Strontium Tetraborate (α-SBO)

_{caa}, d

_{cbb}, d

_{ccc}, d

_{aac}, and d

_{bbc}, d

_{ccc}being largest of them.

**Figure 1.**Domain structure in strontium tetraborate visualized by etching. Crystallographic axes are shown by arrows. Thickness of structure in a direction is 1 mm.

## 3. Applications of NPC SBO

#### 3.1. Generation of Deep UV Radiation in NPC SBO

**Figure 2.**(

**a**) Angular dependence of the second harmonic for nonlinear photonic crystals (NPC) and strontium tetraborate (SBO); (

**b**) Maker fringes for single domain sample of SBO. Input radiation (532 nm) direction k, polarization of input radiation and second harmonic (266 nm) E.

**Figure 4.**Spectral dependence of the second harmonic for a sample of NPC SBO (blue) and single domain sample (black) calculated by varying the fundamental wavelength. Real domain structure of NPC SBO mapped via optical microscopy was used in the calculation.

^{2}in the direction of RQPM. The doubling of the frequency of input radiation in NPC SBO resulted in generation of DUV in the region of 200 nm. The spectra of DUV were not smooth but contained multiple peak structures with the characteristic width of individual peak in the order of several tenths of a nanometer (Figure 5). These structures are found to be independent of the power of input radiation and therefore they cannot be due to any process of the nonlinearity higher than the second one. Obviously, they are the manifestation of the multiple peak structure seen in the spectrum in Figure 4. Different panels in Figure 5 show spectra obtained in the NPC samples from different growth experiments. These samples had different domain structures but the control of this structure by the growth conditions is presently above our experimental abilities. The quality of spectra is not perfect, but comparison of spectra from samples S2 and S4, from one side, and those from samples S7 and S8, from the other side, show that the degree of spectra deterioration can be in principle controlled by the growth process of SBO crystals using more advanced growth installations. From Figure 4 and Figure 5, one can expect that DUV tuning curve might exhibit strong influence of the same multipeak structure. However, for typical bandwidth of input femtosecond pulse and NPC structure typical for SBO it was found that it is not so.

**Figure 5.**The spectra of deep ultraviolet (DUV) generated in several samples (S2, S4, S7, S8) obtained in separate growth experiments.

^{2}[20], so to increase generated power by 10–100 is expected in view of the high radiation breakdown threshold of SBO. The decrease of generated power at shorter wavelength is mainly due to air absorption. The decrease of RSV amplitudes is present in this spectral region too, but it plays a secondary role. The tuning curve bears no signs of narrow multiple peak structure in Figure 5, but variations in RSV amplitudes at the scale of several nanometers are well observable.

**Figure 6.**DUV tuning curves for several samples (S2, S4, S7, S8) obtained in separate growth experiments. DUV power is normalized to the square of the power of the fundamental beam.

**S**pectral and angular dependences of generated power in NPCs are connected through the concept of the NPC band structure [10,21]. Peaks observed in both dependences can be associated with the same set of RSV. An example of angular dependence of DUV power is presented in Figure 7. This curve is in general terms symmetrical with respect to the case of normal incidence, deviations from this symmetry being due to the instability of some experimental parameters, i.e., the temperature fluctuations. The range of power variation in the order of three within 30 degrees can be considered as super-critical angular sensitivity of RQPM. Similarly, slow quasi-monotonic decrease of generated power with its central wavelength can be treated as super-critical spectral sensitivity of RQPM.

#### 3.2. Fs Pulses Diagnostics Using NPC SBO

#### 3.2.1. RQPM Scheme

**Figure 8.**RQPM autocorrelation trace of Tsunami oscillator measured with NPC SBO (blue) and BBO (black). Central wavelength 780 nm. SBO: pulse duration 83.3 fs; power 3.49 microwatts; SNR-2992; BBO: pulse duration 83.7 fs; power 929.9 microwatts; SNR-15079.

**Figure 10.**Pulse duration of Tsunami oscillator measured with NPC SBO throughout the tuning range at fixed angular position of the crystal.

**Figure 11.**Variation of autocorrelation beam spectra on the NPC position. (

**a**) Net data; (

**b**) Data normalized to the maximal value in every section of constant coordinate.

#### 3.2.2. Autocorrelation Measurements Using Nonlinear Diffraction from Virtual Beam

_{caa}and d

_{ccc}, respectively. In view of larger value of d

_{ccc}, the latter scheme must be more efficient and enable larger dynamic range of measurements. To avoid beam overlapping, NPC must be rotated off the normal incidence position around the axis perpendicular to the intersection plane. This rotation does not affect the effective nonlinear coefficient that remains to be equal to d

_{ccc}. The angle of rotation can be found experimentally from the considerations of minimizing the overlap contribution to the background and maximum contribution of RSV spectrum. Sufficient rotation angle value for our samples was found to be of below ten degrees. The scheme of experimental set-up is presented in Figure 12. Typical autocorrelation curve is presented in Figure 13 in comparison with reference crystal. The agreement is as good as in the case RQPM scheme. The background-to noise ratio was 1600, that is approximately two times smaller than in RQPM geometry. This difference, in our opinion, is not fundamental and can be decreased by careful adjustment of the experimental setup. In case of NLDVB, the propagation angle of autocorrelation beam changes when tuning the central frequency of the fundamental. The autocorrelation measurements in the course of tuning the central frequency of the fundamental radiation are, therefore, slightly more complicated since it is necessary to monitor this change, but for large aperture detector this difficulty is not severe.

**Figure 12.**Optical scheme of autocorrelation measurement in nonlinear diffraction from virtual beam (NLDVB) geometry. 1-Tsunami oscillator; 2-beamsplitter; 3-mirror; 4-delay line; 5-focusing lens; 6-NPC SBO; 7-BG39 filter; 8-918D-UV-OD3 sensor.

**Figure 13.**NLDVB autocorrelation trace of Tsunami oscillator measured with NPC SBO (blue) and BBO (black). Central wavelength 840 nm. SBO: pulse duration 75.7 fs; power 5.99 microwatts; SNR-1877; BBO: pulse duration 77.0 fs; power 770 microwatts; SNR-17510.

## 4. Conclusions

## Acknowledgments

## Conflict of Interest

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**MDPI and ACS Style**

Aleksandrovsky, A.S.; Vyunishev, A.M.; Zaitsev, A.I.
Applications of Random Nonlinear Photonic Crystals Based on Strontium Tetraborate. *Crystals* **2012**, *2*, 1393-1409.
https://doi.org/10.3390/cryst2041393

**AMA Style**

Aleksandrovsky AS, Vyunishev AM, Zaitsev AI.
Applications of Random Nonlinear Photonic Crystals Based on Strontium Tetraborate. *Crystals*. 2012; 2(4):1393-1409.
https://doi.org/10.3390/cryst2041393

**Chicago/Turabian Style**

Aleksandrovsky, Aleksandr S., Andrey M. Vyunishev, and Alexandre I. Zaitsev.
2012. "Applications of Random Nonlinear Photonic Crystals Based on Strontium Tetraborate" *Crystals* 2, no. 4: 1393-1409.
https://doi.org/10.3390/cryst2041393