The terahertz

In the opening section of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I provide a table of common prefixes used in the metric system:

giga	G	109
mega	M	106
kilo	k	103
milli	m	10−3
micro	μ	10−6
nano	n	10−9
pico	p	10−12
femto	f	10−15
atto	a	10−18

We went all the way down to “atto” on the small side, but stopped at “giga” on the large side. I now wish we had skipped “atto” and instead included “tera,” or “T”, corresponding to 10¹². Why? Because the prefix tera can be very useful in optics when discussing the frequency of light.

To better appreciate why, take a look at the letter to the editor “Let’s Talk TeraHertz!” in the April 2011 issue of my favorite journal, the American Journal of Physics. There Roger Lewis—from the melodious University of Wollongong—argues that the terahertz is superior to the nanometer when discussing light. Lewis writes

…the terahertz shares the desirable properties of the nanometer as a unit in teaching optics… Like the nanometer, the terahertz conveniently represents visible light to three digits in numbers that fall in the midhundreds… The terahertz has other desirable properties that the nanometer lacks. First, the frequency is a more fundamental property of light than the wavelength because the frequency does not change as light traverses different media, whereas the wavelength may. Second, the energy of a photon is directly proportional to its frequency… The visible spectrum is often taken to span 400–700 nm, corresponding to 749–428 THz, falling in the octave 400–800 THz. …

I suspect that the reason I have always preferred wavelength over frequency when discussing light is that the nanometer provides such a nice, easy-to-remember unit to work with. Had I realized from the start that terahertz offered an equally useful unit for discussing frequency, I might naturally think in terms of frequency rather than wavelength. Incidentally, Planck’s constant is 0.00414 (or about 1/240) in the units of eV/THz.

After reading Lewis’s letter, I checked Intermediate Physics for Medicine and Biology to see how Russ and I characterized the properties of visible light. On page 360 I found our Table 14.2, which lists the different colors of the electromagnetic spectrum in terms of wavelength (nm), energy (eV) and frequency. We didn’t explicitly mention the unit THz, but we did list the frequency in units of 10¹² Hz, so terahertz was there in every way but name. As a rule I don’t like to write in my books, but nevertheless I suggest that owners of Intermediate Physics for Medicine and Biology take a pencil and replace “(10¹² Hz)” in Table 14.2 with “(THz)”.

Russ and I discuss the terahertz explicitly in Chapter 14 about Atoms and Light.

14.6.4 Far Infrared or Terahertz Radiation

For many years, there were no good sources or sensitive detectors for radiation between microwaves and the near infrared (0.1–100 THz; 1 THz = 10¹² Hz). Developments in optoelectronics have solved both problems, and many investigators are exploring possible medical uses of THz radiation (“T rays”). Classical electromagnetic wave theory is needed to describe the interactions, and polarization (the orientation of the E vector of the propagating wave) is often important. The high attenuation of water in this frequency range means that studies are restricted to the skin or surface of organs such as the esophagus that can be examined endoscopically. Reviews are provided by Smye et al. (2001), Fitzgerald et al. (2002), and Zhang (2002).

The citations are to

Fitzgerald, A. J., E. Berry, N. N. Zinonev, G. C. Walker, M. A. Smith and J. M. Chamberlain (2002) “An Introduction to Medical Imaging with Coherent Terahertz Frequency Radiation,” Physics in Medicine and Biology, Volume 47, Pages R67–R84.

Smye, S. W., J. M. Chamberlain, A. J. Fitzgerald and E. Berry (2001) “The Interaction Between Terahertz Radiation and Biological Tissue,” Physics in Medicine and Biology, Volume 46, Pages R101–R112.

Zhang, X-C. (2002) “Terahertz Wave Imaging: Horizons and Hurdles,” Physics in Medicine and Biology, Volume 47, Pages 3667–3677.

So not only is the terahertz useful when talking about visible light, but also it is useful if working in the far infrared, when the frequency is about 1 THz. Such “T rays” (I hate that term) are being used nowadays for imaging during airport security and as a tool to study cell biology and cancer.