Higher-order nonlinearity of refractive index: The case of argon

Unraveling the role of superalkalis in modulating the static and dynamic hyperpolarizabilities of emerging calix[4]arenes

Calixarenes, as novel organic materials, can play a pivotal role in the development of high-performance nonlinear optical materials due to the ease of design and fabrication. In this study, DFT simulations were employed to investigate the geometric, electronic, and NLO responses of calix[4]arene doped with Li3O, Na3O, and K3O superalkalis. The computed values of the vertical ionization energies and interaction energies indicate the chemical and thermodynamic stabilities of the targeted M3O@calix[4]arene complexes. The corresponding energy gaps (2.01 to 3.49 eV) are notably reduced, indicating the semiconductor nature of the materials. Surprisingly, the M3O@calix[4]arene complexes exhibit transparency in the UV/visible range as the absorption peaks are shifted in the near infrared (NIR) region. The highest values of 5.9 × 105 a.u. and 2.3 × 108 a.u. for the respective first and second hyperpolarizabilities are observed for Na3O@calix[4]arene. Furthermore, the Na3O@calix[4]arene complex exhibits maximum values of 2.3 × 105 a.u. for second harmonic generation (SHG) and (K3O@calix[4]arene) 2.3 × 106 a.u. for the electro-optical Pockels effect (EOPE) at 1064 nm. Similarly, approximations are made for the dynamic second hyperpolarizability coefficients (EOKE and EFISHG) at different wavelengths. Notably, the Na3O@calix[4]arene complex demonstrates the highest quadratic nonlinear refractive index (n2) of 9.5 × 10-15 cm2 W-1 at 1064 nm. This research paves the way for the development of stable calix[4]arenes doped with superalkalis, leading to an improved nonlinear optical (NLO) response.

Non-instantaneous third-order optical response of gases in low-frequency fields

It is commonly assumed that for low-intensity short optical pulses far from resonance, the third-order optical nonlinear response is instantaneous. We solve the three-dimensional time-dependent Schrödinger equation for the hydrogen atom and show that this is not the case: the polarization is not simply proportional to the cube of the electric field even at low intensities. We analyze the fundamental-frequency and third-harmonic nonlinear susceptibilities of hydrogen, investigate their dependence on intensity, and find that the delays in the Kerr response rapidly approach the femtosecond time-scale at higher intensities, while the delays in the third harmonic generation remain much lower. We also propose an experimental scheme to detect and characterize the above effects.

Mixed superalkalis are a better choice than pure superalkalis for B12N12 nanocages to design high-performance nonlinear optical materials

Mixed superalkali clusters are a source of excess electrons, as their vertical ionization energies (2.81-3.36 eV) are much lower than those of alkali metals (even cesium (∼3.85 eV)) and the superalkali Li₃O (3.42 eV). In the present work, the geometric, electronic, and nonlinear optical (NLO) properties of mixed superalkali cluster-doped B₁₂N₁₂ nanocages are studied theoretically. All complexes, A-G, have very high interaction energies (-98.02 to -123.13 kcal mol^-1) and are thermodynamically stable when compared to previously reported Li₃O@B₁₂N₁₂ (-92.71 kcal mol^-1). The designed complexes have smaller HOMO-LUMO energy gaps (3.36-4.27 eV) than pristine B₁₂N₁₂ (11.13 eV). Charge transfer in the complexes is studied through natural population analysis and non-bonding interactions are evaluated through quantum theory of atoms in molecules (QTAIM) and non-covalent interaction analyses. These complexes have absorption maxima (1076-1486 nm) in the near-infrared region (NIR) and they are transparent in the UV region. The first hyperpolarizability of complex C is 1.7 × 10⁷ au, which is much higher than the value of 3.7 × 10⁴ au for a pure Li₃O superalkali-doped B₁₂N₁₂ complex calculated at the same level of theory, as reported by Sun et al. (Dalton Trans., 2016, 45, 7500-7509). The large second hyperpolarizability values also reflect the enhanced nonlinear optical response. The best computed values for the electro-optical Pockels effect, second harmonic generation, and hyper-Rayleigh scattering are 3.29 × 10¹⁰ au, 1.17 × 10¹⁰ au, and 6.71 × 10⁶ au, respectively. Furthermore, the electro-optic dc-Kerr effect and electric-field-induced second harmonic generation have maximum values of 3.96 × 10¹¹ au and 3.46 × 10¹⁰ au at 1064 nm. There are enhancements in the quadratic nonlinear refractive index (n₂) values for complexes A-G, with a highest n₂ value of 3.35 × 10^-8 cm² W^-1 at 1064 nm. These results suggest that mixed-superalkali-doped B₁₂N₁₂ nanoclusters are potential candidates when designing high-performance NLO materials.

Remarkable static and dynamic NLO response of alkali and superalkali doped macrocyclic [hexa-]thiophene complexes; a DFT approach

In this study, the nonlinear optical (NLO) response of alkali metal atom (Li, Na and K) and their corresponding superalkali (Li₃O, Na₃O and K₃O) doped six membered cyclic thiophene (6CT) has been explored. The optimized geometries of complexes; Li@6CT, Na@6CT, K@6CT, Li₃O@6CT, Na₃O@6CT and K₃O@6CT depict that the superalkalis and alkali metals interact through the active cavity of 6CT. Interaction energies reveal that superalkalis have higher interaction with 6CT than alkali metals. The nonlinear optical (NLO) response of the reported complexes is estimated via both static and dynamic hyperpolarizabilities which are further rationalized by the HOMO–LUMO gap, natural bond orbital (NBO) charge transfer, dipole moment, polarizabilities and β_vec. A remarkably high NLO response is computed for Na₃O@6CT among all of the complexes. The static hyperpolarizability of the Na₃O@6CT complex is 5 × 10⁴ au along with the highest β_vec value (2.5 × 10⁴ au). High charge transfer (1.53e⁻) and small E_H–L gap (2.96 eV) is responsible for such a large NLO response. For dynamic NLO responses, electro-optic Pockel's effect (EOPE) and second-harmonic generation (SHG) are explored. A very large quadratic nonlinear optical response (3.8 × 10⁻¹² au) is observed for the Na₃O@6CT complex. Moreover, the absorption spectrum of the Na₃O@6CT complex shows ultra-high transparency in the ultraviolet and visible regions unlike any other of its counterparts.

In this study, the nonlinear optical (NLO) response of alkali metal atom (Li, Na and K) and their corresponding superalkali (Li₃O, Na₃O and K₃O) doped six membered cyclic thiophene (6CT) has been explored.

Nonlinear polarization and ionization in O2: metastable electronic state model

We present a computational model for the nonlinear response of molecular oxygen exposed to strong mid-wavelength and long-wavelength infrared optical fields. Based on a non-Hermitian approach utilizing metastable electronic states, the nonlinear polarization and strong-field ionization are described as intimately connected properties. Good agreement with the measured nonlinear index and ionization rates is shown, and parameterized response functions are provided to facilitate applications in large-scale simulations of infrared optical pulses interacting with gaseous media.

Remarkable second and third order nonlinear optical properties of organometallic C6Li6–M3O electrides

Electrides are excess electron compounds with excellent nonlinear optical properties.

Superhalogen doping: a new and effective approach to design materials with excellent static and dynamic NLO responses

The first-ever example where superhalogen doping alone is introduced as a new and effective approach to impart large NLO responses.

True versus effective Kerr nonlinear response in optical filamentation

The optical Kerr effect, and the nonlinear polarization in general, represents an important light-matter interaction governing many regimes encountered in the nonlinear optics. We reason that in the context of optical filamentation one should distinguish the third-order Kerr effect occurring at relatively low light intensities from the effective Kerr nonlinearity relevant to higher intensity. While many properties of filaments can be captured well with a third-order nonlinear polarization model with a nonlinear index chosen somewhat higher than the true nonlinear index operative at low intensities, our comparative simulations indicate that some filamentation aspects carry significant signatures from the higher-order nonlinearity.