A higher-order Poincar\'e sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincar\'e sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.

The first experimental demonstration of a new Pancharatnam-Berry phase for light beams with spatially inhomogeneous, or vector, states of polarization referred to as the higher-order Pancharatnam-Berry phase is presented. This new geometric phase is proportional to light’s total angular momentum, a sum of spin and higher dimensional orbital angular momentum, sharply contrasting the well-known Pancharatnam-Berry phase associated with the plane wave state of polarization of a spatially homogeneous light beam. The higher-order Pancharatnam-Berry phase is directly related to the rotational symmetry of a vortex-bearing electromagnetic field, associated with the rotational frequency shift of a light beam, and has implications in quantum information science as well as other physical systems such as electron vortex beams.

Light scattering and transmission of Gaussian ($G$) and Laguerre–Gaussian (LG) vortex beams with different orbital angular momentum ($L$) in various turbid media were investigated. Transmittance was measured with varied ratios of sample thickness ($z$) to scattering mean free path ($l_s$) of turbid media, $z/l_s$. In the ballistic region, the LG and $G$ beams were found to have no significant difference on transmittance, while in the diffusive region, the LG beams showed a higher received signal than the $G$ beams, and the LG beams with higher $L$ values showed a higher received signal than those with lower $L$ values. The transition points from ballistic to diffusive regions for different scattering media were determined. This newly observed transmittance difference of LG and $G$ beams may be used for deep target detection in turbid media through LG beam imaging.

Raman spectroscopy is a sensitive method to detect early changes of molecular composition and structure that occur in lesions during carcinogenesis. The Raman spectra of normal, benign and cancerous breast tissues were investigated in vitro using a near-infrared (NIR) Raman system of 785 nm excitation and confocal micro resonance Raman system of 532 nm excitation. A total number of 491 Raman spectra were acquired from normal, benign and cancerous breast tissues taken from 15 patients. When the 785 nm excitation was used, the dominant peaks in the spectra were characteristic of the vibrations of proteins and lipids. The differences between the normal and cancerous breast tissues were observed in both the peak positions and the intensity ratios of the characteristic Raman peaks in the spectral region of 700–1800 cm⁻¹. With 532 nm excitation, the resonance Raman (RR) spectra exhibited a robust pattern of peaks within the region of 500–4000 cm⁻¹. The intensities of four distinct peaks at 1156, 1521, 2854 and 3013 cm⁻¹ detected in the spectra collected from normal breast tissue were found to be stronger in comparison with those collected from cancerous breast tissue. The twelve dramatically enhanced characteristic peaks, including the enhanced amide II peak at 1548 cm⁻¹ in the spectra collected from cancerous breast tissue, distinguished the cancerous tissue from the normal tissue. Principal component analysis (PCA) combined with support vector machine (SVM) analysis of the Raman and RR spectral data yielded a high performance in the classification of cancerous and benign lesions from normal breast tissue.

We present an overview and history of terahertz (THz) sources for readers of the biomedical and optical community for applications in physics, biology, chemistry, medicine, imaging, and spectroscopy. THz low-frequency vibrational modes are involved in many biological, chemical, and solid state physical processes.