Nonlinear Methods

Research in THz optoelectronic systems based on signals modulated via NLCs has seen some considerable advances in device performance, efficiencies and achiev-able output power. Under optical excitation by an ultrafast optical pulse, an NLC can undergo a change in polarisation within the volume. The NLC can re-emit an EM signal with an field strength proportional to the second derivative of the change in polarisation with respect to time, as described by:

E_{T Hz}(t) ∝ δ²P

δt² . (1.2.2.1)

The high X^[2] NL susceptibility of crystals such as ZnTe [74,75] and periodically-poled LiNbO₃ (PPLN) [76, 77] allows the optical rectification of incoming EM waves as well as difference frequency generation (DFG) within the medium to achieve THz-range signal emission. The nonlinear susceptibility of such NLCs is used to generate both high power pulsed (via rectification) THz output signals and tunable CW THz output (via DFG, discussed later). In such crystals, phase matching of the pump and generated THz waves becomes important to ensure that the generated THz wave is not interfered with destructively before it can be outcoupled to free space. If a practical degree of phase-matching can be achieved, the generated THz output power may be proportional to the square of the pump power. This may be achieved in several ways, the most predominant of which are: by engineering of the birefringence of the crystal; by quasi-phase-matching (QPM) of propagating waves within the crystal; and by waveguiding.

Schulkin et al. developed a THz spectroscopy device (including the design of the device housing) in 2008 which is based on an NLC through which the components of EM polarisation of the pulsed pump and probe signals may be evaluated, and the resultant characterised THz radiation is passed through the target to be analysed which is placed in the housing in a small removable mount [78]. The THz signal which has been modulated by the target is then passed to another NLC for detection and analysis using a coherent THz spectroscopy method which is described in more detail in Section 1.2.4.1. This device has been marketed commercially under the title of the Mini-Z [79], and is technically a compact, room-temperature source of THz radiation (with integrated detector) for use in a broad range of THz frequencies (particularly 0.01-5 THz), but this is because the device must be driven by an external pulsed pump source such as a Ti:Sapphire laser and the operating frequency is determined by the temporal pulsewidth of the external pump.

Moloney et al. recently developed a highly effective system which utilises ex-ternally pumped vertical cavity surface emitting lasers (VECSELs) as the pump sources and a PPLN crystal as the active medium [80, 81]. This was engineered with all of the aforementioned phase-control mechanisms integrated in the design of the crystal and included additional outcoupling measures at the crystal-air in-terface to further reduce losses. In this setup, several configurations are employed

Figure 1.7: Optical schematic of a high-power two-VECSEL-pumped periodically-poled LiNb03-based THz source. Reproduced from Moloney et

al., 2010.

in which the VECSELs are pumped externally and operated at slightly offset op-tical wavelengths within an external cavity which the NLC is located. Figure1.7 shows one such configuration.

DFG of the VECSEL pumps occurs within the crystal and this beating THz wave is propagated through the crystal volume, enhanced by its phase-matching properties, and is then outcoupled optically. The crystal birefringence (offset of refractive index between ordinarily and extraordinarily polarised propagating waves) is determined by the orientation of the crystal cleavage, and is chosen so to limit as far as possible the phase mismatch between the propagating ordinary and extraordinary EO signals. The crystal is periodically poled along the optical axis by applying a high electrical field across it, thereby creating opposite fer-roelectric domains which typically vary periodically every half coherence length between the optical and THz wavevectors. More sophisticated poling profiles have been developed, however, for further enhancement of wavelength-specific propagation of pump and signal wave-vectors [82]. The developers in this case have used this concept to develop a crystal with poling period(s) which corre-spond to the coherence length of both the pump and generated THz waves. This ensures that the generated nonlinear signal is not dampened by the propagat-ing pump signal, as the phase walk-off between the two signals is periodically

‘reset’ towards zero. Therefore, the amplitude of the propagating THz signal is increased quadratically as the pump is driven through each successive periodic domain. The associated patents and journal papers which were published include

a discussion on the use of poled domains which vary alternatingly in the pump beam direction through the crystal, as well as the use of tilted and aperiodic poling domains as shown in Figure 1.7(inset). Poling domains tilted at some angle Θ, which corresponds to the direction of the THz wave propagation, helps to compensate for the directional mismatch of the two propagating wavefront types. This also minimises the risk of destructive interference of the IR pump beam and the THz wave, and so the issue of divergence of the IR pump beam and subsequent reduction in the resultant THz output power is avoided. The tilt in the poling domains and the period of the poling is calculated by the following equations:

tan (Θ) = n_{T Hz}/n_IR, (1.2.2.2) Λ = λ_{T Hz}

n_IR × cos(Θ), (1.2.2.3)

where nT Hz and nIR are the refractive indices of the crystal medium for the THz and IR pump waves respectively, λ_{T Hz} is the free-space THz wavelength and Λ is the poling period. The crystal is structured so to achieve identical effective refractive indices in the nonlinear medium of both the IR pump signal and the THz generated signal, and is done so using known strip, ridge and slab waveguide structuring techniques. To reduce losses due to internal reflection at the crystal-air interface an angled extension to the emission surface is included as shown in Figure1.7(inset), which significantly improves outcoupling efficiency.

This system is perhaps the most efficient THz radiation source based on an NLC as the emission medium to date. Reported THz output power is in the milli-watt range and is potentially scalable up to the Watt-range. The THz output frequency is also tunable: it is determined by the difference frequency of the two VECSEL optical signals, which is tuned simply by rotating an etalon or coupled diffraction grating to separate or bring together the two permitted pump wave-lengths. The system is also relatively cost-effective, as high-power VECSELs and PPLN may be produced comparatively economically, and may have the dimen-sions suitable for practical, table-top use. However, the optical-THz efficiency is still rather low, with the cavity optical power being around 500 W and strict temperature control of the NLC being required, despite including dopants such as MgO for thermal stability. The THz signal tuning range is also limited by the pre-determined poling of the crystal. Additionally, the requirement for a large,

high-power pump laser system and configuration of at least one VECSEL cav-ity means the system is overall still relatively complex, bulky, and mechanically sensitive.