1 Fundamentals of Terrestrial Millimeter-Wave and THz Remote Sensing E.R. Brown Professor of Electrical Engineering University of California, Los Angeles Los Angeles, CA 90095 Email: [email protected] ; [email protected] Abstract Having long been the realm of molecular chemistry, astronomy, and plasma diagnostics, the upper millimeter-wave band (~100 to 300 GHz) and the THz region above it have recently become the subject of heightened activity in the engineering community because of exciting new technology (e.g., sub-picosecond optoelectronics) and promising new “terrestrial” applications (e.g., counter-terrorism and medical imaging). The most challenging of these applications are arguably those that demand remote sensing at a stand-off of roughly 10 m or more between the target and the sensor system. As in any other spectral region, remote sensing in the THz region brings up the complex issues of sensor modality and architecture, free-space electromagnetic effects and components, transmit and receive electronics, signal processing, and atmospheric propagation. Unlike other spectral regions, there is not much literature that addresses these issues from a conceptual or system-engineering viewpoint. So a key theme of this chapter is to review or derive the essential engineering concepts in a comprehensive fashion, starting with fundamental principles of electromagnetics, quantum mechanics, and signal processing, and building up to trade-off formulations using system-level metrics such as noise-equivalent power and receiver operating characteristics. A secondary theme is to elucidate aspects of the THz region and its incumbent technology that are unique, whether advantageous or disadvantageous, relative to other spectral regions. The end goal is to provide a useful tutorial for graduate students or practicing engineers considering the upper mm-wave or THz regions for system research or development. Keywords Active and passive sensor, direct and coherent detection, heterodyne and homodyne receiver; blackbody and thermal radiation, Planck distribution, Rayleigh-Jeans limit, brightness temperature; atmospheric propagation, water vapor absorption, PCLnWin, HITRAN96 database; waveguide, feedhorn, planar antenna, parabolic dish, lenses, hyperhemisphere, antenna theorem, antenna directivity and gain, effective aperture, diffraction limit; Gaussian beams, beam waist, Rayleigh length, ABCD matrix; radiation noise, shot and thermal noise, quantum noise; classical and quantum mixer, classical and quantum square-law detection, bolometer, Golay cell, Schottky diode, low-noise amplifier; coupling and quantum efficiency, responsivity, conversion gain, noise figure, RF, IF, and post-detection bandwidth; Gaussian, Boltzmann, Poisson, Rayleigh, and Rician statistics; signal-to-noise ratio (SNR), noise-equivalent power (NEP), noise-equivalent delta temperature (NE∆T), probability of detection, probability of false alarm, receiver operating characteristics (ROC); Poynting’s theorem, Friis’ transmission formula, Johnson-Nyquist theorem, Nyquist’s sampling theorem, North’s theorem, Whittaker-Shannon theorem.2 I. INTRODUCTION .................................................................................................................5 A. Background and Purpose......................................................................................................... 5 B. Sensor systems ........................................................................................................................ 6 C. THz Solid-State Devices: A Longstanding Challenge ............................................................ 7 II. THZ RADIATION...............................................................................................................10 A. Poynting’s Theorem: Classical Picture ................................................................................. 10 B. Harmonic-Oscillator States: Quantum Picture ...................................................................... 11 C. Types of Radiation ................................................................................................................ 12 C.1 Coherent Radiation .................................................................................................................. 12 C.2 Thermal Radiation.................................................................................................................... 13 C.2 The Special Case of Blackbody Radiation ............................................................................... 15 D. Fluctuations of Radiation ...................................................................................................... 17 D.1 Quantum Derivation ................................................................................................................ 17 D.2. Coherent Radiation: Poissonian photon statistics ................................................................... 19 D.3 Incoherent or Thermal radiation: Boltzman Photon Statistics ................................................. 20 D.4 Low-Frequency Limit: The Johnson-Nyquist Theorem........................................................... 20 D.5. High-Frequency Limit: Photon Shot Noise............................................................................. 21 E. THz propagation.................................................................................................................... 22 E.1 Atmospheric absorption .......................................................................................................... 22 E.3. Effect on THz signals: Radiative transfer................................................................................ 23 E.3. Atmospheric scattering........................................................................................................... 25 F. Measurement of THz power.................................................................................................. 25 III. COUPLING OF THZ SENSORS TO FREE SPACE ......................................................26 A. Routing between devices: THz Transmission Lines ............................................................. 26 A.1. Metallic waveguides ............................................................................................................... 26 B. Coupling to free space: THz