Photonic crystals are optical materials with a regular nanostructure, often characterized by a repetitive change in refractive index. The study of highly specific interactions between light and matter, especially when incident light leads to changes in the optical properties of photonic crystals, falls under the domain of nonlinear optics. For the study of such interactions leading to changes in the optical properties of photonic crystals, a high-intensity emitting medium such as high-energy lasers is required.
A Brief Introduction to Nonlinear Optical Phenomena
A standard nonlinear optical process comprises two primary stages. Initially, high-intensity coherent light stimulates a nonlinear reaction in the medium, and subsequently, this altered medium exerts a nonlinear influence on the optical radiation.
The chapter on nonlinear optical phenomena in the book Nonlinear Optics states that the optical field, in any medium such as photonic crystals, is characterized by Maxwell's equations, incorporating nonlinear polarization. It is worth noting that all media, especially photonic crystals, inherently exhibit some degree of nonlinearity, but these nonlinear coupling coefficients are typically quite minimal and may be amplified through the application of sufficiently intense optical radiation.
How Nonlinear Optical Phenomena Affects Properties of Photonic Crystals?
Photonic crystals (PCs) are materials structured with a regular variation in dielectric constant, giving rise to a range of restricted frequencies known as the photonic bandgap (PBG), similar to the electronic bandgap in semiconductors. The introduction of nonlinearity into photonic crystals offers dynamic control over light propagation.
Incorporating nonlinear elements within photonic crystals presents the potential to design all-optical devices. Of particular significance is Kerr nonlinearity, which involves the modification of the refractive index of photonic crystals and is highly valuable for ultra-fast devices. Kerr nonlinearity was initially utilized in the creation of a 2-dimensional optical switch.
Additionally, a famous research finding was the all-optical switch simulated computationally using the Finite Difference Time Domain (FDTD) method. It was based on the Kerr effect and nonlinear photonic crystals (PC) micro-cavities made from AlGaAs. To model nonlinearity within photonic crystals, various methods can be employed, including the Finite Difference Time Domain Method (FDTD), Finite Element Method (FEM), Plane Wave Expansion (PWE), and Wannier Function Method (WFM).
Nonlinear Optical Phenomena: Enhancing Photonic Crystal Micro-Resonators
Ever since the dawn of nonlinear optics, optical resonators have been utilized to amplify nonlinear optical phenomena, including frequency conversion processes. Nonlinear photonic crystals-based micro-resonators provide distinctive and fundamental approaches to enhance various nonlinear optical processes. This amplification significantly elevates the efficiency of nonlinear photonic crystals-based optical devices to a degree where their operational power levels and switching times become practical for the development of realistic, ultrafast integrated systems.
Cavities based on photonic crystals demonstrating bi-stability attributes have been used to demonstrate the enhancement process during both theoretical and experimental photonic crystal studies. Photonic crystal (PhC) micro-cavities are especially well-suited for geometrically enhancing nonlinear effects. Furthermore, the optical bi-stability of Photonic crystals-based micro-cavities can serve as the foundation for intricate devices capable of executing all-optical logical operations.
Nonlinear Optical Phenomena in Colloidal Photonic Crystals
In addition to the manufacturing and technology limitations, colloidal photonic crystals offer an excellent framework for studying the physics of light propagation in periodic materials. They also serve as a financially viable platform for providing valuable insights essential for the progress of nonlinear optical studies.
The research team from Belgium presented a paper in Chemical Reviews discussing the optical nonlinear properties of colloidal photonic crystals. 3D colloidal photonic crystals are made up of a regular arrangement of uniform colloidal particles forming a repetitive pattern. This structure can be viewed as a crystal, with the colloids often referred to as dielectric atoms.
To understand the photonic band gap peak more simply, it can be envisioned as a diffraction peak resulting from constructive and destructive interferences of light. These interferences in photonic crystals occur due to multiple reflections and refractions from different crystal planes.
However, researchers found that using the density of states formalism offers a more straightforward approach to studying wave propagation in periodic media compared to the explanation based solely on light diffraction and reflection.
Second Order Nonlinear Optical Phenomena in Photonic Crystals
The second-order nonlinear optical phenomena occurrence in photonic crystals was explained in an article published in 2020 Advances in Science and Engineering Technology International Conferences (ASET). To boost nonlinear effects within photonic crystals, it's imperative to have a material with a substantial nonlinear susceptibility (χ(2)), which is commonly associated with non-centrosymmetric materials.
Nonlinear Susceptibility (χ(2)) characterizes the nonlinear response of photonic crystals to intense light, typically at higher intensities. It specifically relates to the second-order nonlinear interactions between the photonic crystals and the electric field of light. Materials that do not possess a center of symmetry are referred to as non-centrosymmetric materials. In these materials, the distribution of charge or electron density is asymmetric, which enables the occurrence of nonlinearity.
Materials scientists meticulously design the structure of photonic crystals to attain phase matching between waves of distinct frequencies. This phase matching is typically accomplished by tailoring the periodic arrangements of photonic crystals, thereby optimizing nonlinear interactions. This optimization results in effects such as second-harmonic generation or parametric amplification of photonic crystals within the desired wavelength range.
More from AZoOptics: The Role of Photonic Crystals in Controlling Light Propagation
References and Further Reading
Y. Benachour (2020). Nonlinear Optics of Photonic Crystals. 2020 Advances in Science and Engineering Technology International Conferences (ASET). 1-8. 19727433. Available at: https://www.doi.org/10.1109/ASET48392.2020.9118251
González-Urbina, L. et. al. (2012). Linear and nonlinear optical properties of colloidal photonic crystals. Chemical Reviews. 112(4). 2268-2285. Available at: https://doi.org/10.1021/cr200063f
Lembrikov, B. I. (2022). Introductory Chapter: Nonlinear Optical Phenomena in Plasmonics, Nanophotonics and Metamaterials. In Nonlinear Optics-Nonlinear Nanophotonics and Novel Materials for Nonlinear Optics. IntechOpen.
Fernando, M. et. al. (2018). Nonlinear optical properties of photonic crystals. World Scientific News, (97), 1-27. Available at: https://bibliotekanauki.pl/articles/1177892.pdf