Anisotropic terahertz microspectroscopy

Original ATM techniques involve rotating the sample at the focal point of a linearly polarized THz beam using a mechanically rotated sample mount. For this reason, the configuration is typically a far-field instrument in which a balanced detector (sensitive to infrared light) is placed a considerable distance from the sample. In the terahertz time-domain spectroscopy configuration, both the infrared and THz beams are transmitted through an electro-optic (EO) crystal like ZnTe or GaP. Here, the infrared beam detects the change in birefringence of the EO crystal due to the THz beam. When a sample is placed in the THz beam, the polarized THz beam is perturbed and the resulting degree of birefringence in the EO crystal is changed. The resulting perturbation of the infrared beam is sensed at the balanced detector.

Far-field anisotropic terahertz microspectroscopy (ATM) system using a terahertz time-domain spectroscopy (THz-TDS) configuration. Diagram created using The Optics Library.[1]

Rotated sample ATM is very useful for large samples (0.1 to 1 cm). However, when measuring samples such as protein crystals that must be isolated inside a hydration chamber, for example, the sample cannot be easily rotated. Additionally, it is challenging to maintain the same location of a rotated sample at the precise focal point of a THz beam.

An ATM designed with a rotated sample is typically a far-field measurement configuration using a time-domain spectroscopy strategy.

A high power infrared laser is typically used. Its beam is split by a beamsplitter into two optical paths: a probe beam and a THz generation beam.

The THz generation beam typically receives the greater fraction of NIR power in order to maximize the power of the THz light commonly generated by a voltage-pulsed photoconductive antenna. The generated THz light is collected through a hyper-hemispherical silicon lens and passed to an off-axis parabolic mirror that collimates the THz beam for polarization by a THz polarizer that is often made of a simple wire-grid. The linearly polarized THz beam is then focused by a second off-axis parabolic mirror onto the sample. The THz beam transmitted through the sample is again collected by a third off-axis parabolic mirror, collimated onto a fourth parabolic mirror that then focuses the beam onto an electro-optic (EO) crystal whose birefringence is perturbed by the strength of the THz beam.

The NIR probe beam is passed through the EO crystal to probe the induced degree of birefringence caused by the THz beam and passed to a detection module that often consists of an NIR quarter wave plate, a Wollaston prism that spatially separates orthogonal polarization states of the probe beam into two optical paths that are individually detected at a balanced detector. The resulting signal reported by the balanced detector is a measure of the difference in magnitude of these two orthogonal components of the NIR probe beam and therefore a direct correlation of the degree of birefringence induced in the EO crystal by the THz beam passed through the sample.

Previously called "ideal ATM" and "polarization-varying ATM,"[2] stationary sample ATM (SSATM) involves rotation of the linearly polarized state of the THz beam in a time-domain spectroscopy (TDS) configuration parallel to the interrogated material sample. In a SSATM configuration, the THz beam polarization is rotated through 360° in a plane perpendicular to the propagation direction of the beam. Measurements of the sample's anisotropy is measured at several THz polarization angles.

At least two methods to achieve THz polarization rotation for SSATM have been demonstrated: 1) by using a THz quarter waveplate (THz-QWP) together with an infrared polarizer[3] and 2) by rotating the photoconductive antenna.[4]

In the case of employing a THz-QWP and an infrared polarizer, the magnitude of the measured signal, ${\displaystyle {\rm {Sig}}(\tau ,\alpha _{\rm {THz}},\phi _{\rm {NIR}})}$, where ${\displaystyle \tau }$ is a time delay between THz generation and the detected pulses in a THz-TDS system is dependent on the relative polarization angle of the THz light, ${\displaystyle \alpha _{\rm {THz}}}$ and the polarization angle of the ultrafast near-infrared (NIR) probe beam, ${\displaystyle \phi _{\rm {NIR}}}$, at the sample by the relationship[5]

$${\displaystyle {\rm {Sig}}(\tau ,\alpha _{\rm {THz}},\phi _{\rm {NIR}})\propto \left|\left[\cos(\alpha _{\rm {THz}})\sin(2\phi _{\rm {NIR}})+2\sin(\alpha _{\rm {THz}})\cos(2\phi _{\rm {NIR}})\right]\right|.}$$

The objective is to maintain equal magnitude of the THz electric field at the sample for all measurement angles, ${\displaystyle \alpha _{\rm {THz}}}$. This requires adjustment of ${\displaystyle \phi _{\rm {NIR}}}$ for every ${\displaystyle \alpha _{\rm {THz}}}$.

Far-field anisotropic terahertz microspectroscopy (ATM) system using a terahertz time-domain spectroscopy (THz-TDS) configuration. Diagram created using The Optics Library.[6]

A SSATM instrument is typically designed in a time-domain spectroscopy configuration in which a high power infrared laser beam is divided into two optical paths by a beamsplitter.

The first optical path often receives a greater fraction of the optical power of the laser to maximize the output power of generated THz light. THz light is often generated with a voltage-pulsed photoconductive antenna, collected with a hyper-hemispherical silicon lens, collimated using an off-axis parabolic mirror that is then passed through a THz polarizer, made circular by a THz quarter waveplate constructed of two planar mirrors and a right-angled high-resistivity silicon prism to form circularly polarized light. A second THz polarizer selects from the circularly polarized THz light the angle at which each measurement is made once the light reaches a sample located at a focal point of the beam and mounted in direct contact with an electro-optic crystal often made of either ZnTe or GaP.

The second optical path includes a retroreflector mirror mounted on a delay stage that adjusts the time-of-flight of the NIR beam to match the delay time, ${\displaystyle \tau }$, of the THz light at the sample. The NIR beam is linearly polarized and chopped at a frequency suitable for detection, directed to the EO crystal to measure the change in its birefringence due to the degree of THz absorption by the sample. The NIR beam is reflected by the sample/EO crystal interface and directed to the detection module that often consists of an NIR quarter waveplate, a Wollaston prism that spatially selects perpendicular polarization states of the light toward two detectors in a balanced detector. The detected signal is a measure of the difference of the magnitude of the two perpendicular polarization states and corresponds to the degree of birefringence induced in the EO crystal by the THz light as-perturbed by the sample.

One strategy to provide full 360° rotation of THz polarization of equal electric field magnitude at the sample is to generate a circular state of polarization, then select particular linear polarization states from the circularly polarized beam with a THz polarizer.

A circular polarization state may be generated by a quarter waveplate, however, common optical waveplates are typically designed for visible, near- and mid-infrared regions of the electromagnetic spectrum. A quarter waveplate designed for use in the THz frequency range consists of a right-angle silicon prism together with metal-coated planar mirrors as input/output. In particular, the silicon prism acts analogously to a Fresnel rhomb with a single total internal reflection on the longer face of the prism and is a passive broadband component that permits a wide frequency sweep during measurements.

Far-field anisotropic terahertz microspectroscopy (ATM) system using a terahertz time-domain spectroscopy (THz-TDS) configuration. Diagram created using The Optics Library.[7]

A key characteristic of ATM is the orientation of the polarized electric field of THz light at the sample. In particular, unlike other microspectroscopy techniques like scattering scanning near-field optical microscopy (s-SNOM), the electric field of the interrogating THz field is parallel to the surface of the sample. In s-SNOM, the shape of the oscillating metallic probe tip directs the THz polarization into a direction predominantly perpendicular to the sample surface.

Living organisms typically consist of large quantities of water. Many anisotropic materials of interest are biological in nature and as such require hydration during spectroscopic measurements. While some limited novel techniques to measure properties of materials inside a hydrated sample chamber have been recently reports, the primary design requirement of ATM is that the material is accessible through a window that is transparent to THz light such as quartz. Similarly, samples requiring cryo-cooling or low pressure vacuum environment are readily interrogated in ATM using THz-transparent window materials.

ATM is uniquely suited to measure resonant molecular vibrations in proteins.[9] Molecular motions in proteins occur with frequencies in the terahertz range of the spectrum (0.3 THz to 3 THz). These structural changes include hinge motions in which two regions of molecules are connected together in a flexible way that bends like a mechanical hinge or joint and other conformational changes that occur within systems of protein molecules.

Protein molecules are typically surrounded by water molecules and are arranged in random orientations. For this reason, it is common to arrange protein molecules in crystal form such that their orientations all the same. In particular, in a protein crystal the dipole of all protein molecules are naturally aligned. This allows us to perform microspectroscopy with polarized THz light and ascertain the spatial orientation of vibrations within molecules.