D.H. Auston's Picosecond photoconducting Hertzian dipoles

I was reading a THz paper in which the first line harked 'from the time THz spectroscopy was first proposed [1]'. I followed that [1] and arrived at this paper:

Picosecond photoconducting Hertzian dipoles

D. H. Auston, K. P. Cheung, and P. R. Smith

AT& T Bell Laboratories, Murray Hill, New Jersey 07974

(Received 14 March 1984; accepted for publication 18 May 1984)

Here they discuss in some detail the function of the photoconductive antenna used to generate subpicosecond pulses. They state that with the use of high repetition rate, subpicosecond pulses focused on a photoconductive antenna with patterned electrodes, charge carriers (electrons and holes) can be 'optically injected' into the material, creating a Hertzian dipole. A DC bias is applied across the electrodes, accelerating the carriers. The carriers then decay quickly because of trapping due to the high defect density in the material and radiate picosencond pulses. Inspired by the symmetry of Hertzian dipoles, a detector is fashioned just like the transmitter without the DC bias. A delay signal injects carriers (excites electrons from the valence band to the conduction band) in the detector and the transmitted THz pulse field propagates through the insulating material separating the photoconductors and acts as the detector's bias. The produced /induced photocurrent is measured using optical gating/sampling.Top view of the photoconductive antennas. The left and right sides are photoconductive, Ar⁺ irradiated silicon on sapphire wafers with electrodes. Between them is a slab of insulating alumina with an aperture.

They define the transmitted radiation's field as Where p(t) is the time varying dipole moment (relating to carrier charge and distance between them) and n is the refractive index of the material between the carriers. The 3 terms can be identified as the 'quasi-static', near, and far field components. The time derivative of E should be equal to the product of the photocurrent i(t) and separation l between the electrodes. And the far field term is related to the time dervative of the photocurrent. Because the distance between the photocondutors is less than l²/8λ_c (at distances much greater than this far field takes over) the near-field radiation is not a planar wave so an aperture must be introduced. They determine the approximate expression for the time averaged current produced in the second photoconductive antenna to be

The g terms represent the generation rates (carriers/time) for both photoconductors.

This paper brought up some important issues that I still have to look into such as polarization in both transmitted THz pulses and in the received signals, and the defect traps and how that relates to relaxation times and energy level of the carriers.