Terahertz Time-Domain Spectroscopy of Metallic Particle Ensembles

The terahertz (THz) frequency range is the region of the electromagnetic spectrum between the microwave and optical bands spanning from 0.1 THz to 10 THz. Historically, electromagnetic radiation in this frequency range has been inaccessible due to the lack of widespread electronic or laser-based radiation sources. Electronic radiation sources such as crystal oscillators are generally confined to operate at frequencies below ~ 100 GHz, while laser radiation sources are generally confined to operate at frequencies above ~ 30 THz. In recent years, the development of femtosecond lasers and quantum electronics have enabled a wide range of implementations to both generate and detect THz radiation [14]. One of the earliest and most widespread techniques is THz time-domain spectroscopy. THz timedomain spectroscopy is based upon the generation of a broad-band, free-space THz transient, which is detected using a femtosecond pulse to sample the THz electric field in the time-domain. THz spectroscopic measurements are performed by illuminating materials with a THz pulse and measuring the pulse after reflection from or transmission through the material. The electromagnetic properties of the material are inferred from changes in the amplitude and phase of the measured electric field pulse relative that of the incident electric field pulse. THz time-domain spectroscopy has been applied in transmission mode to characterize the THz-frequency optical constants of dielectrics and superconductors [5, 8, 15, 16] and in reflection mode to characterize the reflection amplitude and associated phase change due to semiconductors such as InSb [6] and highly doped silicon [17, 18]. The implementation of THz time-domain spectroscopy requires that the reflected/ transmitted THz pulse undergo measurable transformation upon interacting with the material; spectroscopic measurements made in transmission mode require that the investigated material exhibit partial transparency to THz radiation (that is, some radiation must pass through the material), while spectroscopic measurements made in reflection mode require that the material exhibit partial reflectance to THz radiation (that is, the reflected radiation must be altered relative to the incident radiation). Highly reflective materials such as bulk metals are not amenable to THz time-domain spectroscopy in either transmission or reflection modes. Due to the large and negative real part of the relative permittivity of most metals at THz frequencies (where typically 5 R [ ( ) 10 ] e ε ω − ∼ ), incident THz radiation penetrates only a short, subwavelength distance δ ~ 100nm into the surface of the metal and nearly all the incident electromagnetic energy is reflected. The high