Terahertz radiation (1 THz=1012 Hz) is the part of the electromagentic spectrum between microwaves and infrared. It encompasses frequencies invisible to our eyes in the range from 100 GHz up to roughly 10 THz. Terahertz radiation was discovered in 1986 by H. Rubens and E. Fox Nichols at the University of Berlin. In 1900 Rubens succeeded to isolate wavelengths of 6 THz (50 microns) and made careful measurements enabling M. Planck to derive after that the well known Radiation Law.
The interest to terahertz-rays is due to the fact that they can shine through matter and are therefore of interest for many applications from luggage scanners at airports to biological imaging and study of superconductors.
Semiconductor surfaces have been considered as suitable candidates for THz emission as well. Generally, THz generation mechanisms from semiconductor surfaces can be classified into two distinct categories:
Non-linear contributions may come from bulk  or surface second-order nonlinearity of the semiconductor , or through higher-order nonlinear effects . Photocarrier related effects arise as a consequence of transient photocurrents, resulting from either acceleration of carriers in the surface depletion field  or from diffusion of carriers into the sample away from the surface . It is important to note that at high excitation fluence, the contribution from the nonlinear response of the material is quite large .
Figure 4.21: Experimental setup for investigating THz emission from InP. The InP samples are oriented at an angle of incidence of 45o. BS is a beam splitter, HWP is a half-wave plate, P is a polarizer, M are mirrors, ODL is an optical delay line, L1 and L2 are lenses, PM are parabolic mirrors, QWP is a quarter-wave plate, WP is a Wollaston prism, PD are photodiodes, and LIA is a lock-in amplifier.
As discussed in the previous chapter, electrochemical etching of pores can introduce a large birefringence into the semiconductor, allowing phase matching and consequently an enhancement in optical second-harmonic generation as compared with bulk . In this connection one may expect that porosity will have an impact upon THz emission, too. More than that, changes in the sample surface architecture could affect transient currents generated in semiconductors, which may lead to changes in the THz emission characteristics.
The enhancement of THz emission from a porous InP membrane was for the first time reported by Reid et al . The experimental setup is presented in Figure 4.21. A regeneratively amplified Ti:Sapphire laser system is used as a source (center wavelength of 800 nm). The probe pulse is delayed with respect to the pump using a scanning optical delay line. A variable attenuator (l/2 plate and polarizer) is used in the pump beam to vary the fluence. The THz radiation from the surface of the sample, oriented at angle of incidence, is collected in the specular direction and imaged onto a detector using four F/2 parabolic mirrors. A ZnTe (110) electro-optic crystal is used as detector, oriented for sensitivity to p-polarized THz emission  and can be reoriented to attain sensitivity to the s-polarized THz emission.
Figure 4.22: Measured THz wave forms in the time domain from bulk (a) and porous (b) InP samples. Insets show the frequency spectrum, taken as the Fourier transform of the time domain signals .
A typical wave form and spectrum from bulk and porous InP is presented in Figure 4.22. The wave forms are similar, with the bulk semiconductor exhibiting slightly higher field amplitudes at higher frequencies. In order to determine if there is a measurable difference between the radiated THz fields from the bulk and porous InP, the authors varied the fluence of the laser beam. Figure 4.23 shows the peak detected THz field as a function of the pump fluence for bulk and porous InP samples. The peak THz field is seen to saturate for both bulk and porous InP. At low excitation fluences, however, the peak radiated field from the porous sample proves to be one order of magnitude larger than that inherent to bulk InP.
Figure 4.23: Peak detected THz field as a function of fluence for porous (filled circles) and bulk (filled squares) InP samples.
It is difficult to determine the origin of the increase in conversion efficiency from optical to far infrared between porous and bulk InP without knowing the exact contributions from the various processes to the radiated THz field. However, for InP it is known that at low excitation fluence the photo-carrier acceleration in the surface depletion field dominates (at room temperature) , whereas bulk optical rectification and photocarrier diffusion dominate at higher fluences, with the crossover in mechanisms occurring at fluences between 0.1-10 J/cm2 .
In order to find out which process is being actually enhanced, Reid et al measured the THz emission from the bulk and porous sample as a function of the azimuthal angle. The samples were irradiated with an incident flux of approximately in a p-pol in p-pol out polarization geometry (p-p geometry). The azimuthal dependence of the THz field is shown in Figure 4.24. A change in polarity in the emitted electric field is observed from both samples as a function of the azimuthal angle. As one can see from Figure 4.24, the peak detected field from the bulk sample is approximately 1.6 V/cm, while the peak detected field from the porous membrane is in excess of 7.0 V/cm.
Reid et al repeated the experiments in the p-s geometry. For emission resulting from photo-carrier effects in bulk InP, the generated transient current is oriented perpendicular to the surface, and cannot radiate an s-polarized wave , and will therefore not contribute to the THz radiation for a p-s geometry. In the porous sample, where exists the possibility of lateral photo-currents, s-polarized THz radiation may be generated, however, the emission would be expected to be angularly independent. The results for s-polarized THz radiation from the porous sample are plotted, along with the data for the p-polarized THz emission, in Figure 4.25.
One can see that the s-polarized THz field is non-zero, and has a two-fold rotational symmetry associated with a second-order nonlinear response. Also, there does not exist an angularly-independent contribution to the s-polarized THz field at levels greater than 10 %, indicating that the s-polarized THz emission is primarily due to optical rectification. Taking the ratio of the square of the peak detected s-polarized THz signals from porous relative to bulk InP gives a power ratio of nearly 100. The power enhancement factor is therefore attributed to the portion of the THz wave radiated by the process of optical rectification.
Figure 4.24: Azimuthal dependence of the p-polarized THz field amplitude in reflection from the porous (squares) and bulk (circles) InP (100) samples under p-polarized excitation. Solid lines are qualitative fits to the data reflecting azimuthal dependence.
To test this assertion, the reflectance of SHG radiation from the porous membrane relative to the bulk sample was examined using a variable aperture technique, where it was determined that 90 % of the reflected radiation was diffusely reflected.
Assuming that the porous InP surface is a Lambertian surface, it was estimated by the authors that only 0.86 % of the total reflected SHG radiation has been collected and detected in their experiments. Correcting the measurement for scattering fraction gives a measured power ratio of SHG radiation from the porous membrane relative to the bulk sample of 33. Concerning the s-polarized SHG, it was observed that the ratio of power in the SHG beam from porous, relative to bulk was 0.48. Again, correcting for the scattering losses, an estimated enhancement factor for the p-s geometry of 56 was calculated. This qualitatively agrees with the observation that a higher conversion efficiency results from the porous network in the p-s as compared to the p-p geometry for THz emission.
As in the case of GaP, the observed enhancement is believed to be a result of local field enhancement within the porous network. The power in the SHG or THz radiation scales as the input pump intensity squared, such that the output scales as the input electric field strength to the fourth power. Therefore a volumetric averaged field strength in the porous network would only have to be approximately (30)1/4=2.3 times larger than in the bulk in order to explain the results presented by Reid et al. Local field enhancement is conceptually similar to focussing a pump beam to achieve higher conversion efficiencies.
At this point it is worth noting that an increased effective interaction length of the fundamental and SH or THz radiation may exist due to scattering, which would also lead to an enhancement [102, 103]. However, it is expected that this effect is minor in comparison to local field enhancement for the following reasons. First, the absorption in InP of the second harmonic beam is strong enough (escape depth at 400 nm in InP is approximately 18 nm), that even if there were substantial scattering of the pump beam, the effective interaction length with the SH radiation is limited by the escape depth of the 400 nm light, which is much less than the optical absorption depth of the fundamental beam (800 nm). For the case of THz emission, there is virtually no scattering of the THz radiation as the wavelength in this case is much larger than the characteristic sizes of the porous membrane entities. Given that the enhancement factors are qualitatively similar for THz and SHG, it seems likely that the same process governs both emissions.