Optical anisotropy in semiconductors arises from structural or strain-induced asymmetry in their crystal lattice, leading to direction-dependent interactions with light. This property manifests in phenomena such as birefringence, dichroism, and polarization-dependent optical responses, which are critical for designing optoelectronic devices, strain sensors, and anisotropic photonic systems. Unlike isotropic materials, where optical properties are uniform in all directions, anisotropic semiconductors exhibit distinct refractive indices, absorption coefficients, and polarization effects depending on the propagation and electric field orientation of incident light.

Birefringence occurs when a material has different refractive indices for light polarized along different crystallographic axes. In uniaxial crystals like wurtzite GaN or ZnO, the ordinary refractive index (nₒ) applies to light polarized perpendicular to the optical axis (c-axis), while the extraordinary refractive index (nₑ) governs light polarized parallel to the c-axis. The birefringence magnitude Δn = nₑ - nₒ can be positive or negative, depending on the crystal class. For example, GaN exhibits positive birefringence (Δn ≈ 0.02 at 500 nm), whereas calcite shows negative birefringence. Biaxial crystals, such as orthorhombic SnS, have three principal refractive indices (n₁, n₂, n₃), further complicating the optical response. Strain engineering can modulate birefringence; tensile strain along one axis increases the refractive index contrast, enhancing anisotropy.

Dichroism refers to differential absorption of light polarized along different axes. Linear dichroism arises when the absorption coefficient α varies with polarization direction, as seen in layered transition metal dichalcogenides (TMDCs) like MoS₂. Monolayer MoS₂ absorbs strongly for in-plane polarized light (α ≈ 10⁶ cm⁻¹ at excitonic resonances) but weakly for out-of-plane polarization due to its anisotropic band structure. Circular dichroism, observed in chiral semiconductors or magnetized materials, involves selective absorption of left- versus right-handed circularly polarized light. This effect is exploited in spintronics and valleytronics, where chiral optical transitions enable valley polarization in TMDCs.

Polarization-dependent effects extend to emission and scattering processes. Photoluminescence (PL) from anisotropic semiconductors often shows polarization ratios (ρ = (Iₘₐₓ - Iₘᵢₙ)/(Iₘₐₓ + Iₘᵢₙ)) exceeding 0.8 for aligned quantum wells or nanowires. Raman scattering intensity also varies with the angle between the incident polarization and crystal axes, providing a non-destructive probe of crystallographic orientation. In black phosphorus, the armchair and zigzag directions exhibit distinct Raman tensor components, enabling unambiguous identification of crystal alignment.

Rotating analyzer ellipsometry (RAE) is a key technique for quantifying optical anisotropy. It measures the change in polarization state of light reflected from a sample as a function of incident angle and wavelength. The ellipsometric parameters Ψ and Δ relate to the amplitude ratio and phase difference between p- and s-polarized light, respectively. For anisotropic materials, the Jones matrix formalism extends the standard isotropic model:

| rₚₚ rₚₛ |
| rₛₚ rₛₛ |

Here, rₚₚ and rₛₛ are the reflection coefficients for p- and s-polarized light, while rₚₛ and rₛₚ account for cross-polarization due to anisotropy. By fitting RAE data to a stratified optical model, one can extract dielectric tensor components:

ε = | εₓₓ 0 0 |
| 0 εᵧᵧ 0 |
| 0 0 ε_zz |

For biaxial materials, off-diagonal terms may appear under strain or misorientation. Spectroscopic ellipsometry covering UV to IR wavelengths can resolve anisotropy across energy bands, critical for evaluating strained layers or heterostructures.

Strained semiconductor layers exhibit modified optical anisotropy due to lattice distortion. In silicon-germanium (SiGe) alloys grown on Si substrates, biaxial compressive strain splits the degenerate valence band, inducing polarization-dependent absorption edges. The strain-optic coefficients (p₁₁, p₁₂, p₄₄) quantify how strain alters the refractive index tensor. For Si, p₁₁ ≈ -0.09, p₁₂ ≈ 0.017, and p₄₄ ≈ -0.05 at 1550 nm, enabling strain-engineered photonic devices. In GaN/AlN heterostructures, piezoelectric strain enhances birefringence, useful for ultraviolet waveplates.

Anisotropic 2D materials present extreme optical anisotropy. ReS₂, a low-symmetry TMDC, exhibits in-plane anisotropy with a refractive index contrast Δn ≈ 0.3 between its principal axes at 600 nm. Black phosphorus has a wavelength-dependent dichroism ratio exceeding 3:1 in the mid-infrared, ideal for polarization-sensitive photodetectors. The dielectric tensor of these materials often requires ab initio calculations combined with ellipsometry to capture direction-dependent excitonic effects.

Applications leverage optical anisotropy for advanced functionalities. Liquid crystal displays rely on birefringent materials to modulate polarization states. Strain sensors use the shift in anisotropic optical response to monitor mechanical deformation in real time. Van der Waals heterostructures combine anisotropic layers to create artificial optical media with tailored polarization properties, enabling ultra-thin waveplates or optical isolators. In quantum optics, anisotropic semiconductors provide polarization-entangled photon pairs via biexciton decays.

Challenges remain in controlling anisotropy at nanoscale dimensions and integrating anisotropic materials with conventional photonic platforms. Advances in deterministic assembly of 2D heterostructures and strain engineering at the atomic level promise new classes of devices harnessing optical anisotropy for next-generation optoelectronics, sensing, and quantum technologies.