Author:
Hazal Orman, Summer Semester 2025

THz time-domain spectroscopic ellipsometry is a non-destructive testing method that combines the self-referencing features of ellipsometry with the broadband and coherent detection capabilities of THz time-domain spectroscopy. It enables the derivation of material properties such as refractive index, permittivity, and layer thickness in the terahertz frequency range.

• 1 Basic Principles
  • Basics of Ellipsometry
    • Polarization of Light
    • Fundamental Ellipsometry Parameters
  • THz Time-Domain Spectroscopy Basics
  • Combining Time- Domain Spectroscopy with Ellipsometry
• 2 Instrumentation
  • THz Generation
    • Photoconductive Antennas (PCAs)
    • Nonlinear Crystals
  • THz Detection; Coherent Pump-Probe Principle
    • Photoconductive Antennas (PCAs)
  • Experimental Configuration
    • PSA Configuration
    • Dependence On Incidence Angle
  • 4 Applications
  • 5 Literature

1. Basics of Ellipsometry

Polarization of Light

To understand ellipsometry, it is crucial to understand polarization of light. Light is an electromagnetic wave that consists of electric and magnetic field which propagates always perpendicular together. If the fluctuations of electric field are restricted to a single plane, the light is polarized. Ellipsometry gets its name from the most generalized form of polarizations; elliptical. ^[1] If two waves propagate with different phases or amplitudes light is elliptically polarized. When a sample is subjected to a polarized beam, the polarization state of the light changes.

Fundamental Ellipsometry Parameters

Figure 1: Polarization of Light upon Reflection
Daniel Rüdisser, Polarization upon specular reflection.png  CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons

Ellipsometry uses the changes of polarization to determine the optical properties of specimen that the light is reflected off, at a certain frequency. ^[3] An illustration of this occurrence is given in Figure 1. Here, , , and  represent the incident beam, reflected beam, and transmitted beam respectively. The plane of incidence is the plane defined by the surface normal ( and the propagation direction of reflected light. If the polarization component of light is parallel to the plane of incidence it is described as p-polarized (given as  in Figure 1). If the light oscillates perpendicular to this plane it is defined as s-polarized (given as  in the figure).

A standard ellipsometer can be seen in Figure 2. Ellipsometry measures the materials optical constants using the ellipsometry parameters called ellipsometric angles; Ψ and Δ. Tan Ψ is the amplitude ratio between s-polarized and p-polarized reflected light. And Δ is defined as the phase difference between s-polarized and p-polarized reflected light.^[1] The p and s reflection coefficient ratio of is equal to the complex value ρ. This relation can be summarized with the following fundamental equation of ellipsometry

ρ can be obtained as a function of properties of sample by using Fresnel coefficients written in Jones formalism. Ellipsometry eliminates the need of a standard reference sample by self-referencing the s and p polarization electric field from the sample.  For more information regarding Ellipsometry see Ellipsometry. ^[2][3]

Figure 2: Standard Ellipsometry Setup
Buntgarn, at the English Wikipedia project, Ellipsometry setup.svg CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons

THz Time-Domain Spectroscopy Basics

THz Time Domain Spectroscopy investigates how materials interact with light using terahertz radiation. Terahertz radiation is a electromagnetic radiation ranging in the frequencies between microwave and infrared radiation corresponding to energy window between 10^-22 -10^-20 J. this is linked with the vibrational and rotational level energy state changes. Additionally, The penetration depth of THz radiation varies strongly depending on material conductivity. It is relatively high for low conductivity materials making them suitable for precise imaging with THz radiation. ^[1][2]

 One of the well-established approaches for spectroscopy is the time domain spectroscopy. TDS uses ultrashort THz radiation pulses typically lasting around 1 ps (picosecond). These pulses are broadband and coherent, covering the THz frequency range. For more information on THz spectroscopy see Terahertz spectroscopy.

Combining Time-Domain Spectroscopy with Ellipsometry

In the previous section it is stated that THz Time-Domain Spectroscopy enables a coherent signal detection. With THz TDS spectroscopic ellipsometry, this is combined with the self-referencing ability of ellipsometry creating a broader non-destructive testing way for characterization of materials. ^[1]

2. Instrumentation

THz TDS spectroscopic ellipsometers mostly have similar functioning mechanisms. Possible ways for THz pulse generation and detection are nonlinear crystals and photoconductive antennas. Recent studies also report using air-plasma filament polarimetry as an alternative way.^[2] There are also several setup configurations exist, difference being the way polarization control is handled and the lights interaction with the specimen. 

THz Generation

Photoconductive Antennas (PCAs)

Photoconductive Antennas are highly recommended for THz generation due to their abilities to precisely set and measure the incident angle together with fast response and easy handling. ^[1][2] The primary basis for the THz signal is the transformation of a femtosecond laser pulse into a picosecond pulse.

PCAs are antenna structures produced on a special semiconductor with a sub-picosecond carrier lifetime. Across the antenna gap, a DC bias voltage is applied. The semiconductor is excited with a femtosecond laser pulse with wavelength between 800 and 1500 nm and photocarriers are generated. DC field accelerates these carriers. The current produces a burst of electromagnetic radiation, a broadband THz pulse lasting around a picosecond. ^{[1] [2]}

Figure 3: Photoconductive Antennas
KiarashKevin86, Reflection Setup THz.PNG CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons

Nonlinear Crystals

Another method proposed for THZ emission based on optical rectification is using femtosecond laser-excited GaP and GaSe crystals. These illuminated crystals generate broadband THz pulses. ^[1]

Further THz generation mechanisms include accelerator-based and free electron laser (FEL) based sources. ^[1]

THz Detection; Coherent Pump-Probe Principle

Similar to THz Generation, there are several methods proposed for THz detection.

Photoconductive Antennas (PCAs)

Photoconductive antennas can also be used to detect THz signals. Different from the emission arm no external DC field is applied. The femtosecond laser is divided into pump and probe beams. The pump pulse generates the THz pulse in the emitter. The probe pulse is guided toward the detector placed at a controlled delay by the optical delay unit. The detection mechanism detects a signal when the THz pulse that is reflected or transmitted through the specimen overlaps the probe pulse on the detector gap and Compared to the THz beam, the laser beam's pulse duration is significantly shorter. By considering the delay, the electric field of the THz signal is measured as a function of time enabling coherent detection. ^[3][1]

Alternatives to PCAs for THz generation can be electro-optic sampling, air plasma filament detection, and golay cells. ^[2][1]

Experimental Configuration

PSA Configuration

PSA Configuration stands for Polarizer–Sample–Analyzer ellipsometer. In standard ellipsometry, three polarizers are usually required for an accurate polarization manipulation. First one, placed before the emitter to ensure the THz beam is polarized into equal s and p components. Usually set at 45^○ to the s direction. Second polarizer is positioned after the sample, acting as an analyzer to catch the s or p reflected components. Polarization of the of the equal s, p component of the beam passing first polarizer is disturbed by reflection or emission through sample. This is rebuilt by rotation of polarizer.  Third polarizer which is placed in front of the detector positioning at 45^○ to secure equal sensitivity for both s and p polarized fractions. ^[2]

Several alternative experimental setups are proposed to satisfy different measurement requirements for THz TDS spectroscopic ellipsometers.

Dependence On Incidence Angle

The high sensitivity of ellipsometric parameters (Ψ and Δ) to a material’s optical properties is closely related to the choice of angle of incidence. These parameters show the strongest variation particularly around the Brewster angle (θ_B) which the angle of incidence at which p-polorized component of light reaching the surface is perfectly transmitted with no reflection. The Brewster angle varies for different materials therefore θ scan can be applied to preliminarily obtain the sample characteristics. ^[2][1]

To investigate the Brewster angle, fiber-coupled antennas (an alternative THz generation and detection device) is suggested as they allow the adjust the angle of incidence without disturbing the alignment of the laser beams. ^[2]

3. Data Analysis

THz TDS spectroscopic ellipsometry directly measures the time dependent electric field of p and s polarizations of beam separately. The time domain data is then transformed into frequency domain data using fast Fourier transformation. From the frequency domain data ellipsometric parameters are calculated. To determine material properties such as refractive index, thickness, or dielectric function, the measured Ψ and Δ spectra are then fit to a theoretical model of the sample structure. ^[1][3]

4. Applications

Even though THz time-domain spectroscopic ellipsometry is a relatively new characterization technique, it has gained significant attention due to its wide range of interdisciplinary applications.

One major application is the measurement of the complex dielectric function of materials, allowing the extraction of both refractive index and absorption coefficients with absolute numerical values. ^[1] It is also frequently used to characterize multilayered structures and conductive thin films, like semiconductors and polymer coatings, where the thickness, conductivity, and interfacial characteristics can be determined with high precision. ^[2]

Additionally, the non-ionizing nature of THz radiation makes it highly promising for biomedical applications. Current research focuses on developing rapid, label-free, and convenient biosensors for tasks such as blood cell detection, cancer cell characterization, bacterial identification, and biological tissue discrimination. ^[6]

Using THz-TDS Ellipsometry in measuring both the material’s anisotropic responses such as stress or magnetic field as well as the material’s anisotropic characteristics such as optical activity, or birefringence in metal hole arrays, polymers, and fibrous materials are possible. ^[5]

An emerging application is THz-TDS Magneto-optic Ellipsometry. With this technique, the transport properties of free carriers in materials are obtained. Essential parameters such as effective mass, scattering time, carrier density can be derived without prior assumptions by analyzing diagonal and off-diagonal components of the dielectric tensor. ^[5]

5. Literature

1. Mazaheri, Zahra, et al. "Terahertz time-domain ellipsometry: Tutorial." Journal of the Optical Society of America A39.8 (2022): 1420-1433.
2. Chen, Xuequan, and Emma Pickwell-MacPherson. "An introduction to terahertz time-domain spectroscopic ellipsometry." APL Photonics7.7 (2022).
3. Neshat, Mohammad, and N. P. Armitage. "Terahertz time-domain spectroscopic ellipsometry: instrumentation and calibration." Optics express20.27 (2012): 29063-29075.
4. Matsumoto, Naoki, et al. "Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry." Optics letters36.2 (2011): 265-267.
5. Nagashima, Takeshi, Masahiko Tani, and Masanori Hangyo. "Polarization-sensitive THz-TDS and its application to anisotropy sensing." Journal of Infrared, Millimeter, and Terahertz Waves34.11 (2013): 740-775.
6. Yu, Liu, et al. "The medical application of terahertz technology in non-invasive detection of cells and tissues: opportunities and challenges." RSC advances9.17 (2019): 9354-9363.

Figure 1: Daniel Rüdisser, Polarization upon specular reflection.png  CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons

Figure 2: Buntgarn, at the English Wikipedia project, Ellipsometry setup.svg CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons

Figure 3: KiarashKevin86, Reflection Setup THz.PNG CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons