Resonant Fabry-Perot cavities are commonly used in spectroscopic setups over a wide range of frequencies. The two most closely related electromagnetic domains that we will consider here for suggestions on how to extend cavity-based spectroscopic techniques into the THz range are the neighboring MW and IR regions. At infrared wavelengths, input/output coupling mirrors generally consist of dielectric stacks that are composed of multiple thin layers of materials with alternating refractive indices. These dielectric mirrors function on the principle of constructive interference, with the thickness and refractive index of the different layers chosen such that the reflected light from different layers constructively in- terfere, which allows the design of mirrors with very high reflectivity (R>0.9999) and very low loss per pass (<ppm). Due to the much longer wavelengths, this is technologically dif- ficult to achieve at THz frequencies, and no such dielectrics currently exist in this regime. Metallic mirrors, with only a small conductance loss in the surface, provide a material that is principle capable of achieving the high reflectivity required for the type of experiments discussed here. However, metallic mirrors do not transmit any radiation, thus requiring another method of coupling the radiation into and out of the cavity. At microwave fre- quencies, this problem is surmounted by coupling the radiation into the cavity using either an antenna inside the cavity, or a waveguide butted against an iris in one of the mirrors. Because the wavelengths at THz frequencies are two orders of magnitude shorter than at MW frequencies, however, these coupling methods can severely impact the quality factor of the cavity. Further, both THz strip lines and waveguides are exceedingly difficult to manufacture and have high loss.
coupling mirrors. Electric field components parallel to a thin metal wire cause the flow of electrons in the wire, turning the wire into a reflective/diffractive element. A wire- grid polarizer consists of an array of such conducting metal wires, with both the spacing between the wires, g, and the diameter of the wires, 2a, significantly less than half the wavelength: g << λ/2, 2a < g. Under these conditions, the reactive shunt impedance of the grid is significantly less than the characteristic impedance of free space, resulting in almost complete reflection of the power in the incident electric field parallel to the grid [82]. A small amount of radiation still leaks through the grid, however, giving us exactly the characteristics needed for coupling radiation in to and out of a cavity. Use of a wire- grid does affect the configuration of the cavity, as it provides a flat surface rather than the spherical mirrors used in traditional microwave confocal cavities.
The simplest configuration we attempted is shown in Figure 7.1, and consists of a semi- confocal arrangement, with the wire-grid polarizer serving as both the input and the output coupling mirror. In this case, the beam waist is positioned at the polarizer, and the distance between the polarizer and the spherical mirror, L, is equal to the effective focal length (EFL) of the mirror. This ensures that the radius of curvature of the mirror matches that of the THz field at its minimum, and gives several straightforward relationships that fix the characteristics of beam and the optics, allowing for a simple design process:
ω0 = λL π 0.5 (7.1) ω(L) =√2ω0 (7.2)
Figure 7.1: THz cavity consisting of a semi-confocal Fabry-Perot resonator. In grey is the reso- nantly enhanced THz beam. The radiation is coupled into and out of the cavity through the same wire grid polarizer and the outgoing beam is redirected towards the detector by a 50:50 beam split- ter. The accompanying spectrum can be seen in Fig. 7.3. Components of the system include: (1) THz radiation source; (2) 50:50 beam splitter, wire grid polarizer angled at 45◦ relative to the field; (3) Input coupling mirror, Microtech Instruments wire-grid polarizer, G45×10; (4) THz receiver, combined with lock-in amplifier recording in AM mode; (5) Gold spherical mirror, of Effective Focal Length, or EFL = 1200.
Figure 7.2: THz cavity consisting of an off-axis Fabry-Perot resonator. In dark grey is the reso- nantly enhanced THz beam. The radiation is coupled into and out of the cavity through two different wire-grid polarizers. This results in a mode-filtering effect by the cavity that allows only the funda- mental TEM00 modes to reach the detector, resulting in a much cleaner and simpler (transmitted)
spectrum, that can be seen in Fig. 7.4. The components of the system are: (1) THz radiation source; (2) Input coupling mirror, Microtech Instruments, G50×20; (3) Off-axis parabolic mirror, EFL = 1200; (4) Output coupling mirror, Microtech Instruments wire-grid polarizer, G45×10; (5) THz receiver, combined with lock-in amplifier in AM mode.
andλis the wavelength. Due to the gaussian nature of the beam, the diameter of the optics (in this case that of the polarizer and the spherical mirror) need to be D >4ω to ensure that diffraction losses are practically eliminated relative to other losses in the system. A 50:50 beam splitter between the radiation source and the cavity allows the redirection of the beam transmitted by the cavity to the detection system.
The second configuration we attempted is shown in Figure 7.2, and can be thought of as two semi-confocal cavities arranged at 90◦, with an off-axis parabolic mirror instead of a spherical mirror connecting the two arms. In this arrangement, the distance from one
polarizer to the mirror is still equal to the effective focal length of the mirror, but the total length of the cavity is now twice this distance. The beam waist thus changes to:
ω0 = λL 2π 0.5 (7.3)
The main reason for this arrangement versus the simple semi-confocal arrangement outlined above is that the cavity now acts essentially as a frequency selective transmitter, one in which only the fundamental cavity modes should reach the detector. In the former arrangement, since the path for direct reflection off the cavity input mirror and the emission from the cavity are the same, it can be difficult to distinguish the fundamental modes of the cavity if the power coupling reaches steady-state. Under cavity illumination with a pulsed radiation source this would not be an issue if the decay of the cavity (or molecular emission) could be monitored, but the alignment and optimization of the cavity would still be significantly impeded. Furthermore, if the cavity is used in combination with a swept CW source, simply as a method to increase the path length, the direct reflection/cavity out- coupled confusion problem would not be eliminated as the sweep-rate of the source would generally be slower than the ring down time of the cavity. Going to a configuration where the input and output coupling mirrors are separate from each other solves this problem. The second advantage of the 90◦ arrangement is that it eliminates the need for the 50:50 beam splitter that redirects the cavity emission to the detector. Since 50 % of the power is waisted on each pass through the beam splitter, only a maximum of 25 % of the source power can be recovered in the arrangement in Figure 1. In the situation arrangement shown in Figure 2, however, the maximum amount of input power that can be recovered is 50 % if the reflectivity of the input and output coupling mirrors are equal (i.e. 50 % emission from
both polarizers in steady-state). It is possible to choose a different reflectivity for the two mirrors and essentially ‘tune’ the fraction of power reaching the detector from the cavity, although such a parameter study is not pursued here.