Second-harmonic generation (SHG) is a nonlinear optical process where two photons of the same frequency interact with a material to produce a single photon with twice the energy and half the wavelength of the incident photons. This phenomenon is particularly significant in II-VI semiconductors such as ZnSe and CdTe due to their high nonlinear susceptibility and transparency in the visible to mid-infrared range. Understanding SHG in these materials requires an analysis of their crystal structures, phase-matching conditions, and interactions with ultrafast laser pulses.

ZnSe and CdTe crystallize in the zinc-blende structure, which lacks inversion symmetry—a prerequisite for non-zero second-order nonlinear susceptibility. The absence of inversion symmetry allows for efficient SHG, as the nonlinear polarization induced by an electric field does not cancel out. The second-order nonlinear susceptibility (χ⁽²⁾) in these materials is a tensor quantity, with ZnSe exhibiting values around 30 pm/V and CdTe around 100 pm/V, depending on wavelength and crystal orientation.

Phase-matching is critical for efficient SHG, as it ensures constructive interference between the generated second-harmonic wave and the nonlinear polarization driving it. In bulk ZnSe and CdTe, birefringent phase-matching is not possible due to their cubic symmetry. Instead, quasi-phase-matching (QPM) or angle tuning in thin films or waveguides can be employed. QPM involves periodic poling of the material to compensate for phase velocity mismatch, but this is challenging in II-VI semiconductors due to their high resistivity and hardness. Alternatively, non-collinear phase-matching schemes using ultrafast pulses can enhance SHG efficiency by exploiting temporal and spatial walk-off effects.

Ultrafast laser interactions introduce additional considerations for SHG in ZnSe and CdTe. When excited by femtosecond pulses, these materials exhibit transient changes in refractive index due to carrier generation and lattice heating. The high peak intensities of ultrafast pulses can drive strong nonlinear responses, but they also risk inducing two-photon absorption (TPA) or free-carrier absorption (FCA), which compete with SHG. For ZnSe, the bandgap (~2.7 eV) means that SHG at 800 nm (1.55 eV) is below the TPA threshold, whereas CdTe (~1.5 eV bandgap) may experience TPA at this wavelength. Pulse duration and repetition rate must be optimized to balance SHG efficiency with thermal effects.

The dispersion properties of ZnSe and CdTe also influence SHG dynamics. ZnSe has a relatively flat dispersion curve in the near-infrared, reducing group velocity mismatch between fundamental and second-harmonic pulses. CdTe, with higher dispersion, requires precise control of pulse bandwidth to maintain phase-matching over a broad spectrum. Chirped pulses or adaptive pulse shaping can mitigate these effects in ultrafast experiments.

Applications of SHG in these materials extend to nonlinear microscopy and spectroscopy, where their high damage thresholds and broad transparency are advantageous. ZnSe is often used in mid-infrared frequency doubling, while CdTe’s higher nonlinearity makes it suitable for compact visible light sources. However, thermal management remains a challenge, particularly under high average power irradiation, as thermal lensing can degrade phase-matching conditions.

In summary, SHG in ZnSe and CdTe is governed by their zinc-blende crystal symmetry, requiring innovative phase-matching approaches due to their isotropic refractive indices. Ultrafast laser interactions introduce dynamic effects that must be carefully managed to optimize conversion efficiency. These materials continue to be important for nonlinear optical applications, provided their thermal and dispersive properties are accounted for in system design.