# A Brief Review on Nonlinear Photonic Crystals Induced by Direct Femtosecond Laser Writing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. ${\mathbf{\chi}}^{\left(\mathbf{2}\right)}$-Erasing Technique Using Femtosecond Laser

## 3. ${\mathbf{\chi}}^{\left(\mathbf{2}\right)}$-Poling Technique by Femtosecond Laser

#### 3.1. Primary Domain Inversion

#### 3.2. Secondary Domain Inversion

#### 3.3. Two Types of Domain Inversion Simultaneously Occurring

## 4. Laser Writing Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

1D | One-dimensional |

2D | Two-dimensional |

3D | Three-dimensional |

SHG | Secpnd harmonic generation |

DFG | Difference-frequency generation |

SFG | Sum-frequency generation |

OPO | Optical parametric generation |

SH | Second harmonic |

BPM | Birefringence Phase Matching |

QPM | Quasi-phase matching |

RVL | reciprocal vector |

PPLN | Periodically poled lithium noibate |

NPC | Nonlinear photonic crystal |

PC | Photonic crystal |

UV | Ultraviolet |

$\stackrel{\u02d8}{C}$SHM | $\stackrel{\u02d8}{C}$erenkov SH microscopy |

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**Figure 1.**(

**a**) ${\chi}^{\left(2\right)}-$poling 1D QPM and (

**b**) ${\chi}^{\left(2\right)}-$erasing 1D QPM. In both (

**a**) and (

**b**), the periodicity is $\Lambda =2{l}_{C}$ and the duty cycle is 0.5. (

**c**) The amplitude of SH and (

**d**) the relative ${\chi}^{\left(2\right)}$ value vs. the reacting length. The red line indicates the no-maching case, the blue lines indicate ${\chi}^{\left(2\right)}-$poling case and the yellow lines indicate ${\chi}^{\left(2\right)}-$erasing case.

**Figure 3.**Three examples of LIQPM. (

**a**–

**c**) The first ${\chi}^{\left(2\right)}$-erasing grating sample. (

**a**) Schematic of the sample and inscription setup, the coordinate system is principle axes of the crystal. (

**b**) Each ${\chi}^{\left(2\right)}$-erasing volume is complished layer by layer, and each layer is completed line by line. Shutter is on for red line and off for black line. The layers were described from surface to bottom. (

**c**) An optical microscope image of a LIQPM structure. The period of the grating is 19.2 $\mathsf{\mu}$m corresponding to a fundamental wavelength of 1545 nm. © 2013 WILEY–VCH Verlag GmbH & Co. KGaA, Weinheim; (

**d**–

**f**) A LIQPM grating integrated with waveguide. (

**d**) Schematic of the LIQPM-waveguide design, and the grating period is 6.7 $\mathsf{\mu}$m with a fundamental wavelength of 1064 nm. (

**e**,

**f**) Optical microscope images of the circular waveguide structure. The refractive index change of the cladding waveguide is TypeII modification which is relatively dark, while that of the grating is TypeI modification which is relatively bright. © 2015 AIP Publishing LIC. (

**g**) Microscope image of LIQPM inside a Type II waveguide, with a period of 6.9 $\mathsf{\mu}$m. Journal © 2023.

**Figure 4.**Characterization of 3D NPC. (

**a**) A $\stackrel{\u02d8}{C}$SHM of the first two layers of the 3D NPC, with the inserted image showing a clear periodic structure. (

**b**) An image in the $xoy$ plane through a general confocal SH microscopic system. (

**c**) The intensity distribution along the black line in (

**b**). The average values of SH intensity are also presented in (

**c**) as black lines. The SH intensity is much lower in the engineered area than that in the nonengineered area, which proves the reduction in ${\chi}^{\left(2\right)}$ due to laser inscription. The average minimal SH intensity is 0.225, which indicates that ${\chi}^{\left(2\right)}$ can be further reduced. Reprinted with permission from Ref. [82], © 2018 $NaturePhotonics$.

**Figure 5.**Far-field diffraction patterns for the 3D nonlinear fork-grating array. (

**a**) $\stackrel{\u02d8}{C}$SHM images of the 3D structures in the $xoz$ plane and $xoy$ plane. Here, ${\Lambda}_{x}={\Lambda}_{y}=3\mathsf{\mu}$m. (

**b**–

**d**) SH diffraction patterns and their corresponding wave vector configurations. The 1st, 2nd, and 3rd diffraction orders are enhanced through nonlinear QPM processes at the input wavelengths of 820 nm, 802 nm and 781 nm, respectively. © 2019 Optical Society of America.

**Figure 6.**Comparison of the Hermite-Gaussian patterns of HG${}_{\left(10\right)}$, HG${}_{\left(11\right)}$, and HG${}_{\left(12\right)}$. (

**a**–

**c**) Calculated patterns. (

**d**–

**f**) Optical images of the three type patterns. (

**g**–

**i**) $\stackrel{\u02d8}{C}$SHM images of the three type patterns. © 2019 Optical Society of America.

**Figure 7.**Ferroelectric-domain inversion induced by tightly focused femtosecond laser in the BCT crystal. (

**a**) The $\theta $ -like domain structure created by femtosecond laser pulses, imaged by $\stackrel{\u02d8}{C}$SHM. The weak random patterns surrounding the $\theta $ domain originates from random inherent submicrometre-period domains in the BCT crystal. (

**b**–

**f**) Mechanism of domain inversion. (

**b**) Temperature gradient represented by arrows in induced by nonlinear absorption in the laser focal region acts as a thermoelectric field source. (

**c**) The z component of the temperature gradient leads a bipolar electric field. (

**d**) When the bipolar electricfield in (

**c**) exceeds the coercive field ${\mathbf{E}}_{C}$, it inverts microdomains in (

**e**) to form two larger antiparallel domains in (

**f**). Reprinted with permission from Ref. [113], © 2018 $NaturePhotonics$.

**Figure 8.**Schematic of evolution of nonlinear hologram of NPC. (

**a**) A fork pattern leads to a second-harmonic emission of a standard optical vortex. (

**b**) The fork pattern in (

**a**) combined with an external axicon results in the formation of a perfect vortex harmonic. (

**c**) A curved fork pattern instead of the combination in (

**b**) also leads to a perfect vortex second harmonic. © 2020 Author(s).

**Figure 9.**The working principle of non-reciprocal laser writing for LiNbO${}_{3}$ ferroelectric-domain engineering. (

**a**–

**c**) The simulated electric field. (

**a**) The 3D thermoelectric field induced by the temperature gradient. (

**b**) The threshold of LiNbO${}_{3}$ for domain inversion, whose magnitude depends on local temperature. (

**c**) The z components of the thermoelectric field. Within the enclosed ellipsoidal areas, these are denoted by a and b. The z components ${\mathbf{E}}_{1}$ and ${\mathbf{E}}_{2}$ of the thermoelectric fields are higher than the threshold field. Only the one antiparallel to the spontaneous polarization of LiNbO${}_{3}$ can pole the domain. (

**d**–

**g**) The principle of the nonreciprocal laser poling and erasure in LiNbO${}_{3}$, which strongly depends on the applied sequence of ${\mathbf{E}}_{1}$ and ${\mathbf{E}}_{2}$. (

**d**) Firstly, ${\mathbf{E}}_{1}$ poles the ferroelectric domains; subsequently, ${\mathbf{E}}_{2}$ inverts the domain inverted by ${\mathbf{E}}_{1}$, resulting in no inversion of the domain at the end. (

**e**) When laser is moving along the $-z$ axis, ${\mathbf{E}}_{2}$ does not work, but ${\mathbf{E}}_{1}$ works to invert the domain. (

**f**) When the laser scans along y axis, ${\mathbf{E}}_{1}$ and ${\mathbf{E}}_{2}$ separately interact with the spontaneous polarization, leading to an inverted domain of width b. (

**g**) Supposing that the domain is inverted at the beginning, it is flipped back by scanning laser along $+z$ axis. Reprinted with permission from Ref. [107], © 2022.

**Figure 10.**The pyroelectric field changes with temperature. (

**a**) The pyroelectric field is zero at room temperature. (

**b**) It is not zero any more and parallel to the spontaneous polarization (${\mathbf{P}}_{s}$) during heating, with

**E**${}_{dep}$ decreasing as temperature increases. (

**c**) It is zero again at $200{\phantom{\rule{3.33333pt}{0ex}}}^{\circ}$C due to the electric field induced by charges. (

**d**) It is antiparallel to ${\mathbf{P}}_{s}$ when cooling down to room temperature. During cooling, ${\mathbf{E}}_{dep}$ increases, and ${\mathbf{E}}_{pyr}$ is opposite to ${\mathbf{P}}_{s}$; then, the polarization is flipped when ${\mathbf{E}}_{pyro}>{\mathbf{E}}_{threshold}$.

**Figure 11.**Square lattic pattern with a period of 20 $\mathsf{\mu}$m. (

**a**) Microscopy image of the lower surface of the crystal after selective chemical etching. (

**b**) $\stackrel{\u02d8}{C}$SHM image of the same plane as in (

**a**). (

**c**) The structure in the volume of the crystal measured in 3D with $\stackrel{\u02d8}{C}$SHM. © 2018 Author(s).

**Figure 12.**$\stackrel{\u02d8}{C}$SHM images of the primary and secondary ferroelectric domains in PMN-38PT. (

**a**) Laser-induced domains located at different depths inside a single-domain PMN-38PT crystal. (

**b**) The view of the $yoz$ cross-section corresponding to the single row bounded by the dashed line in (

**a**). (

**c**) The view of the $xoy$ cross-section corresponding to the dashed lines in (

**b**); C-C shows only primary domain inversion, B-B presents both primary domain inversion in the center and secondary domain inversion in the surrounding area, and A-A shows only secondary domain inversion. (

**d**) Another example of secondary domain pattern. (

**e**,

**f**) Erasure of secondary domains by laser inside PMN-38PT. (

**e**) Secondary domain formed with separation distance $\Lambda =45,15,11,8\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m. (

**f**) Linear secondary domain patterns formed with separation distance $\Lambda =2\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m for the top two patterns and $\Lambda =1\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m for the bottom one. © 2021 Wiley-VCH GmbH.

**Figure 13.**(

**a**) $\stackrel{\u02d8}{C}$SHM images of domains in $xoy$ plane for pulse energies from 220 nJ to 550 nJ, and addressed depths of the laser-induced filaments. (

**b**) The single domain marked with an arrow is shown in detail. Width of domain in (

**a**) as a function either of pulse energy (

**c**) or of addressed filament depth (

**d**). © 2022 Author(s).

**Figure 14.**Average domain diameter dependent on the set temperature in a secondary domain inversion with pulse energy of 250 nJ. (

**a**–

**c**) $\stackrel{\u02d8}{C}$SHM images of domains at the bottom +z-surface. ${\Lambda}_{y}$ keeps 6.3 $\mathsf{\mu}$m all three figures, while ${\Lambda}_{x}$ = 15 $\mathsf{\mu}$m in (

**a**), ${\Lambda}_{x}$=10 $\mathsf{\mu}$m in (

**b**), and ${\Lambda}_{x}$=6 $\mathsf{\mu}$m in (

**c**). The average domain diameter of either edge domains (

**d**) or in the center of lattice (

**d**) dependent on the maximum heating temperature. Journal © 2022.

${\mathit{\chi}}^{\left(2\right)}$-Erasing | Reference | Nonlinear Crystal | Repeat Frequency | Bandwidth | Wavelength | Pulse Energy | Scan Speed | N.A. |
---|---|---|---|---|---|---|---|---|

Ref. [79] | LiNbO${}_{3}$ | 100 kHz | 170 fs | 800 nm | 650 nJ | 1 mm/s | 0.5 | |

Ref. [80] | LiNbO${}_{3}$ | 1 kHz | 120 fs | 800 nm | 60–72 nJ | 80 $\mathsf{\mu}$m/s | 0.8 | |

Ref. [82] | LiNbO${}_{3}$ | 1 kHz | 104 fs | 800 nm | 100–200 nJ | 55–100 $\mathsf{\mu}$m/s | 0.8 | |

Ref. [84] | MgO-doped LiNbO${}_{3}$ | 1 kHz | 500 fs | 1030 nm | 900 nJ | 280 $\mathsf{\mu}$m/s | 0.5 | |

Ref. [86] | LiNbO${}_{3}$ | 200 kHz | 350 fs | 1040 nm | 16/20 nJ | 1 mm/s | 0.3 | |

Quartz | 8/12 nJ | |||||||

${\mathbf{\chi}}^{\left(\mathbf{2}\right)}$-Poling | References | Nonlinear Crystal | Repeat Frequency | Bandwidth | Wavelength | Pulse Energy | Scan Speed | N.A. |

Ref. [104] | LiNbO${}_{3}$ | 76 MHz | 180 fs | 800 nm | 0–5 nJ | 10 $\mathsf{\mu}$m/s | 0.65 | |

Ref. [113] | BCT | 76 MHz | 180 fs | 800 nm | ∽6 nJ | 10 $\mathsf{\mu}$m/s | 0.65 | |

Ref. [117] | CBN | 76 MHz | 180 fs | 800 nm | 3.6–6.6 nJ | 10 $\mathsf{\mu}$m/s | 0.65 | |

Ref. [128] | PMN-38PT | 80 MHz | 180 fs | 800 nm | 0–5 nJ | 0.4 | ||

Seeds | Ref. [106] | MgO-doped LiNbO${}_{3}$ | 1 kHz | 100 fs | 800 nm | 50–500 nJ | 0.8 | |

LM | Ref. [108] | MgO-doped LiNbO${}_{3}$ | 1000 kHz | 170 fs | 1026 nm | 150 nJ | 0.42 | |

LI | 500 kHz | 300–900 nJ |

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**MDPI and ACS Style**

Tian, Y.; Li, Q.; Yan, L.; Cao, X.; Zhao, X.
A Brief Review on Nonlinear Photonic Crystals Induced by Direct Femtosecond Laser Writing. *Photonics* **2023**, *10*, 833.
https://doi.org/10.3390/photonics10070833

**AMA Style**

Tian Y, Li Q, Yan L, Cao X, Zhao X.
A Brief Review on Nonlinear Photonic Crystals Induced by Direct Femtosecond Laser Writing. *Photonics*. 2023; 10(7):833.
https://doi.org/10.3390/photonics10070833

**Chicago/Turabian Style**

Tian, Yaolan, Qingbo Li, Lili Yan, Xiangdong Cao, and Xian Zhao.
2023. "A Brief Review on Nonlinear Photonic Crystals Induced by Direct Femtosecond Laser Writing" *Photonics* 10, no. 7: 833.
https://doi.org/10.3390/photonics10070833