Hybrid perovskites have emerged as a promising class of materials for nonlinear optical (NLO) applications due to their exceptional optoelectronic properties and structural versatility. Their unique combination of strong light-matter interactions, tunable bandgaps, and high defect tolerance makes them ideal candidates for nonlinear processes such as two-photon absorption, harmonic generation, and Kerr effects. The compositional flexibility of hybrid perovskites further allows for precise engineering of their nonlinear responses, enabling optimization for specific applications.

Two-photon absorption (TPA) is a third-order nonlinear process where a material simultaneously absorbs two photons to excite an electron from the valence band to the conduction band. Hybrid perovskites exhibit strong TPA coefficients due to their high absorption cross-sections and intermediate bandgaps. For instance, methylammonium lead iodide (MAPbI3) demonstrates a TPA coefficient in the range of 5 to 15 cm GW−1 at near-infrared wavelengths, which is comparable to conventional semiconductors like GaAs. The TPA response can be enhanced by tailoring the organic cations and halide composition. Formamidinium-based perovskites, for example, show broader spectral coverage due to their narrower bandgaps, while mixed halide perovskites (e.g., MAPb(Br,I)3) allow tuning of the TPA resonance peaks. The inorganic framework, particularly the B-site metal, also plays a critical role; replacing lead with tin can reduce the bandgap and shift the TPA onset to longer wavelengths.

Harmonic generation, including second-harmonic generation (SHG) and third-harmonic generation (THG), is another key NLO phenomenon in hybrid perovskites. SHG requires non-centrosymmetric crystal structures, which are present in certain perovskite phases such as the ferroelectric variants of MAPbI3. The SHG intensity is highly dependent on crystalline orientation and domain size, with reported nonlinear susceptibilities (χ(2)) reaching up to 100 pm V−1. THG, a third-order process, is less restrictive and occurs even in centrosymmetric structures. Hybrid perovskites exhibit strong THG due to their high third-order susceptibility (χ(3)), with values ranging from 10−19 to 10−17 m2 V−2. The harmonic generation efficiency can be modulated by strain engineering or applying external electric fields to align polar domains in the material.

The Kerr effect, a refractive index change proportional to the square of the electric field, is another important NLO property of hybrid perovskites. These materials exhibit large Kerr coefficients (n2) due to their high polarizability and strong excitonic effects. For MAPbI3, n2 values on the order of 10−15 m2 W−1 have been reported, making them suitable for all-optical switching and modulation applications. The Kerr response is influenced by exciton binding energy and carrier mobility, which can be tuned via compositional adjustments. Incorporating larger organic cations, such as butylammonium, can enhance the Kerr effect by increasing the lattice polarizability, while halide mixing can adjust the excitonic contributions.

Compositional tuning is a powerful strategy for enhancing the nonlinear optical properties of hybrid perovskites. The organic cation influences the dielectric environment and electron-phonon coupling, which directly affect NLO responses. For example, replacing methylammonium with formamidinium reduces the bandgap and increases the TPA cross-section. The inorganic framework, particularly the halide composition, allows for precise control over the bandgap and excitonic properties. Iodide-rich perovskites exhibit stronger NLO effects in the visible to near-infrared range, while bromide-rich compositions extend the response toward the ultraviolet. Mixed-cation and mixed-halide approaches further enable fine-tuning of the nonlinear coefficients across a broad spectral range.

Dimensionality engineering is another effective method for optimizing NLO performance. Lower-dimensional perovskites, such as 2D Ruddlesden-Popper phases, exhibit enhanced excitonic effects due to quantum confinement, leading to higher TPA and harmonic generation efficiencies. The interlayer organic spacers also introduce additional design knobs for modulating nonlinear responses through changes in dielectric contrast and charge carrier localization. Quasi-2D perovskites, with varying numbers of inorganic layers, provide a balance between confinement effects and charge transport, enabling tailored NLO properties for specific applications.

Defect engineering plays a subtle but important role in the NLO behavior of hybrid perovskites. While defects are often detrimental to linear optoelectronic properties, certain defects can enhance nonlinear processes by introducing mid-gap states that facilitate multi-photon transitions. Controlled incorporation of vacancies or interstitial ions can modify the density of states and increase the NLO coefficients. However, excessive defects may lead to unwanted absorption losses or scattering, necessitating careful optimization.

The nonlinear optical properties of hybrid perovskites are also influenced by external factors such as temperature and pressure. Phase transitions, which are common in these materials, can dramatically alter the symmetry and electronic structure, thereby affecting NLO responses. Applying hydrostatic pressure can induce bandgap changes and enhance nonlinear susceptibilities through lattice compression. Temperature-dependent studies reveal that the NLO coefficients peak near phase transition points due to critical fluctuations and soft phonon modes.

In summary, hybrid perovskites exhibit rich and tunable nonlinear optical properties, making them attractive for applications such as frequency conversion, optical limiting, and ultrafast photonics. Their compositional flexibility allows for precise control over two-photon absorption, harmonic generation, and Kerr effects, while dimensionality and defect engineering provide additional avenues for optimization. Continued research into the fundamental mechanisms governing these NLO processes will further unlock the potential of hybrid perovskites for advanced photonic technologies.