Babinet's Principle for non linear optics

Babinet’s principle states that if you have an opaque object and its complementary aperture, they should produce identical diffraction patterns when light passes through them. Ex. A thin metal rod blocking light should create the same diffraction pattern as a slit of the same shape cut into a metal sheet.

Babinet’s principle does not hold for nonlinear optics.

super-resolution effect:

In linear optics, only Fourier components inside the fundamental resolution limit (2π/λ) contribute to the far-field pattern. This means that small details in the near-field do not appear in the far-field image.

In nonlinear optics,  The third-harmonic wave has a much shorter wavelength (λ/3), so the far-field image contains Fourier components up to 3 times and allows finer details visible.

Eddy current in slits:

In the rod, the polarization is mostly cosine-shaped, aligned with the electric field.

The Third Harmonic Generation process is highly localized and depends on the third power of the electric field.

The eddy currents in slits create extra localized hot spots, which do not appear in rods.

These extra hot spots cause the THG pattern of slits and rods to be completely different, violating Babinet’s principle.

Source: 

https://arxiv.org/html/2503.14773v1

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Study of birefringence in shear thinning fluid

Birefringence is an optical property of materials where light splits into two different rays, each traveling at a different speed and direction when passing through the material.

Phase retardation (∆) refers to the difference in the phase of light waves as they pass through a birefringent material (like a flowing fluid with aligned molecules). 

∆ is Phase retardation, C₁: First-order stress-optic coefficient, σxx, σyy: Stress components in x and y directions

The second-order stress-optic law is needed to accurately predict birefringence in thin fluid flows. Shear-thinning affects birefringence, mainly due to changes in second order Stress optics coefficient c2 rather than just viscosity.

As shear rate increases, C₂ decreases and phase retardation increases. The phase retardation decreases in the radial direction and increases with increasing flow rate.

source:

https://arxiv.org/html/2503.10261v1

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Symmetry change in Magnetite

Below the Verwey transition temperature (~110K in this experiment), Magnetite Fe3O4 structure distorts into a monoclinic shape, where one of the angles slightly deviates from 90° (β ≈ 90.23°). This distortion introduces a shear strain. 

The change is accompanied by charge ordering of the Fe2+ and Fe3+ ions to form “trimerons”, valence-ordered Fe3+-Fe2+-Fe3+ linear structures, which confine the electrons and lead to an insulating behavior at low temperatures.

The transition involves both electronic localization and a significant lattice distortion, evidenced by a change in symmetry and unit cell dimensions.

Below the Verwey transition, the strain distribution becomes increasingly fragmented, which indicates localized stress concentrations due to internal layered phase variations. Here higher temperatures allow for stress relaxation, while lower temperatures promote strain localization.

Bragg Coherent X-ray Diffraction Imaging method was used here.

Source:

https://arxiv.org/html/2503.10417v1

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two superconducting gaps observed for CsV₃Sb₅

The two superconducting gaps have been observed for CsV₃Sb₅ material. 

A charge density wave (CDW) is a state where the electron density in a material forms a periodic pattern instead of being uniform. This happens because of electron-phonon interactions, where electrons couple with vibrations in the crystal lattice.

As per CDW in CsV₃Sb₅, electron density and lattice distortions repeat every two unit cells in different directions. 

Ginzburg-Landau Theory, Tinkham Model were used here.

In a conventional superconductor, the energy gap is uniform, meaning all Cooper pairs have the same energy. In a nodal superconductor, the superconducting gap has zero-energy points (nodes) where quasiparticles can exist even in the superconducting state.

The charge order changes the natural symmetry of the kagome lattice from having six-fold rotational symmetry to only two-fold symmetry. When a magnetic field is rotated within the plane of the material, the upper critical field also follows a two-fold pattern. The superconducting state itself has become nematic, meaning different along different directions-not uniform.

https://arxiv.org/abs/2411.15333

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Chromium based tantalum disulfide properties

Study was done on Cr₁/₃TaS₂ (Cr atoms are inserted into a layered compound TaS₂ (tantalum disulfide)). The Raman Scattering method was used here.

Pressure changes bond lengths and angles and, at the same time, systematically reduces the van der Waals distance and modifies the structural c/a ratio.

Cr₁/₃TaS₂ has a smaller van der Waals gap, making it less change to structural distortions than Fe based material.

When pressure increases Cr₁/₃TaS₂ magnetic properties remain stable but Fe₁/₃TaS₂ magnetic property decreases drastically.

source:

https://link.springer.com/article/10.1038/s41535-025-00734-x

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Study of Cesium lead bromide- local polarization

Material CsPbBr₃ (cesium lead bromide) was studied here. It is widely used in solar cells, LEDs.

At high temperatures (>100K), transport shifts to a band-like motion, where charge carriers move smoothly.

At low temperatures (<100K), charge carriers move by hopping transport (jumping between localized spots). spontaneous grain boundaries form inside the material. 

These grain boundaries create regions of local polarization meaning certain parts of the material develop an electric dipole moment. Here Displacement of Pb Ions occurs. This shift causes an imbalance in charge distribution, leading to localized electric fields.

GB⊥ have been observed here. It means the crystal tilts in a direction that is perpendicular to the boundary. Twinning boundaries have lower energy( more stable) when the in-phase octahedral tilting axis is rotated perpendicularly rather than twisted.

Low temperature (<100K) transport can be explained by the Mott’s variable range hopping (VRH) equation. Its conductivity is given by,

P is Local polarization, V is volume, d is displacement of ion

Source: https://arxiv.org/html/2502.20261v1

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