We demonstrate the first electronically switchable Bragg structure for THz frequencies. The structure works as stop-band filter and as mirror. It exhibits the 60 GHz broad stop-band around 300 GHz which can be removed by reorienting liquid crystal molecules in an external electric field. Our first proof-of-principle experiments agree very well with transfer matrix calculations.
©2009 Optical Society of America
Terahertz (THz) waves attracted a lot of attention over the past years due to a number of possible applications ranging from basic research [1, 2, 3, 4] to industrial quality control  and security applications . In these application fields THz spectroscopy and THz imaging systems stand at the focus of current interest. Moreover, short-range communication via THz waves is a promising market  as it is expected that future indoor communication systems will work at several hundred gigahertz and will be capable of transmitting several tens of Gb/s. In particular the frequency window around 300 GHz is of interest as it provides sufficient bandwidth and is free of water vapor absorption lines .
Such THz systems and a mature THz technology in general require not only efficient, inexpensive, and compact terahertz sources and detectors but also passive components to guide and manipulate THz waves. Such passive devices include terahertz mirrors [8, 9, 10], filters [11, 12], and modulators [13, 14]. A very promising class of THz devices are those which contain liquid crystals (LC). Yet, up to now only a few LC based devices working in the millimeter wave/THz range have been presented. Most of them are magnetically controlled phase-shifters , switches  and filters . More compact are electrically controlled phase shifters [18, 19] and modulators .
In this paper we present the world’s first LC-based switchable dielectric Bragg structure for THz frequencies. The structures design frequency is 300 GHz. It represents a switchable stop-band filter as well as a switchable mirror.
Our structure is based on the concept of a multilayer dielectric mirror. The standard design of a dielectric mirror consists of pairs of λ/4 layers made of materials with low nL and high nH refractive indexes . Dielectric mirrors show a reflection band around the design wavelength. The reflectivity and spectral width of this band depends on the number of pairs and the difference in the refractive indices. Therefore, contrary to simple metal mirrors this approach allows for tailoring the reflection properties. The reflectivity increases with a number of layers and a value of nearly 100% can be reached. Note, that such a structure is likewise a stop-band filter.
Here, we propose a switchable Bragg structure which contains liquid crystals as high refractive index layer. The refractive index of LC molecules can be switched between its ordinary no and extraordinary ne value in the presence of an electric field. This results in a change of the transmission/ reflection properties of the multilayer structure.
The Bragg structure is designed to have its stop or reflection band, respectively, around 300 GHz. Twelve layers of polypropylene (PP) foil with a thickness of 161 μm and a refractive index of nPP=1.51+i0.003 are stacked together with 158 μm thick spacers in between. The entire staple is clamped together in a holder. See Fig. 1(a). for a schematic drawing of the cell. The liquid crystal 7CB fills the entire residual volume of the cell, in particular the room provided by the spacers. The refractive index of 7CB can be switched between no=1.61+i0.028 and ne=1.73+i0.016 for 7CB molecules in extraordinary and ordinary orientation, respectively . The 7CB material parameters are determined using a standard THz TDS setup. The imaginary part of the complex refractive index indicates the losses in the material. The side, top and bottom walls of the cell are made of quartz glass covered with a thin ITO layer and act as electrodes providing an electric field to orient the molecules of 7CB. The front and back windows are made from PP foil glued to the holder. Figure 1(b). shows a photograph of the device.
As the materials parameters and the thickness of the layers are known the expected reflection and transmission properties of the structure can be calculated using the transfer matrix method . Figure 2(a). shows the simulated power reflection coefficient for both cases when the biasing field is applied to vertical and horizontal electrodes, respectively. The performed simulations take into account the absorption coefficients of 7CB and PP foil. Therefore the sum of reflection and transmission coefficients is less than unity. For the 7CB molecules in the extraordinary orientation the multilayer structure generates the reflection band around 300 GHz with the power reflection coefficient of 45%. Note, that for the best performance the outer layers of the dielectric mirror should be made of the material with the higher refractive index. In our case, due to physical limitations, the outer layers are made of PP foil which is the lower index material. Therefore, the simulated maximum reflection coefficient is smaller than that of a hypothetical mirror with outer layers made of 7CB molecules. Such a mirror could reach the reflectivity of 80% with the PP foil, LC, and spacer foil available. Losses originate mainly from absorption of 7CB and insufficient number of layers. With ideal, non-absorbing material one could theoretically reach 94% and >99% for 12 and 19 PP layers, respectively. For the ordinary molecular orientation the reflection coefficient does not exhibit any significant reflection bands and reaches values of about 5% over the entire spectrum.
Figure 2(b). shows the simulated transmission coefficients of the investigated dielectric mirror. As expected, the structure shows a significant stop-band in the ”on-state”. Note, that due to a higher absorption of 7CB in its ordinary orientation, the simulated transmission coefficient of the structure in ”off-state” is significantly smaller than that of a LC mirror with 7CB in extraordinary orientation.
The above presented simulations were based on the assumption that in a central part of the cell LC molecules are aligned along electric field lines which are parallel (or perpendicular) to the electric vector of incident THz wave. This is the case if the electric field is strong enough to fully align the LC molecules (this point is discussed further below in section 4) and if the electric field vectors are perpendicular to the electrodes under bias. To clarify the latter point we simulate the electric field distribution in the cell using commercially available software based on finite element analysis (COMSOL Multiphysics). Figure 3 shows the simulation results when bias is applied to side electrodes and the top and bottom electrodes have floating potential. According to the simulation the electric field is homogeneously distributed between the electrodes apart from small areas close to the corners of the cell. Due to the symmetry of the sample cell the electric field distribution will be analogous when electric potential is applied to top and bottom electrodes.
4. Experimental demonstration
The switchable Bragg structure is characterized by THz time domain spectroscopy in transmission geometry. By applying an electric field of 41 kV/m chopped at 1 kHz the LC molecules are being re-oriented according to the electric field lines. The applied electric field is well above the threshold value of 10kV/m  and the molecules in the central part of the mirror are assumed to be fully aligned along the E-field lines. Therefore, the refractive index experienced by the incident THz wave can be switched between its ordinary and extraordinary values of no=1.61+i0.028 and ne=1.73+i0.016, respectively. All measurements of the LC-based mirror are performed at 28.5°C, at which the 7CB crystal has a high switchable birefringence.
Figure 4 shows a comparison of the measured relative power transmission (to the air reference) and the simulation results in the ”on” (a) and ”off” state (b), respectively. The experimentally measured transmission of the mirror in the on-state shows excellent agreement with the simulation results. One can easily observe that the transmission through the mirror around 300 GHz is clearly reduced, due to the generated reflection band. The measured transmission spectra are more uniform than the simulated spectrum with periodic pattern. We attribute this to the finite time window, which does not cover the first reflection from the outer walls of the investigated Bragg structure (see [22, 23] for a detailed discussion of this effect). Moreover, the generated stop-band and its higher harmonics are somewhat less strong then the calculated ones. The differences could arise from small thickness fluctuations of the liquid crystal layer and the PP foil used, or even from small air bubbles in the structure (see e.g. ). The second, more significant effect arises from the multilayer nature of the presented mirror. As described by  there is always a competition between the molecular orientation imposed by the wall structure and the external electric field at the LC-PP foil boundaries. This effect known as Freedericksz transition causes that close to the LC-PP foil interfaces there is a smooth rather than step-like transition of the LC’s molecular orientation which results in a smooth transition in the refractive index profile. We note, the somewhat reduced transmission at frequencies below 250 GHz. It originates from the beam clipping at the apertures of the mirror cell. For higher frequencies the measured and simulated transmission spectra agree very well in off-state too.
Since switching with liquid crystals is slow our device does not represent a modulator but rather an on-off-switch. For our device the switching time is on the order of hundreds milliseconds.
In conclusion, we have demonstrated the first electronically switchable Bragg structure for THz frequencies. Switching is accomplished by reorienting liquid crystal molecules in an external electric field. The structure works as stop-band filter and as mirror. It exhibits a 60 GHz broad stop-band around 300 GHz which can be removed if the structure is switched to the off-state. Our first proof-of-principle experiments agree very well with simulations. In the future we plan to improve the performance of the Bragg structure, in particular its reflectivity, by optimizing the layers structure regarding thickness, refractive index, lower absorption and higher birefringence. As discussed in  the properties of LCs may strongly vary with temperature. Hence, temperature changes could affect the performance of the Bragg-structure. For practical applications one might turn to nematic mixtures of LCs which are less sensitive to temperature changes and can also hold a higher birefringence.
We acknowledge useful discussions with D. Turchinovich in the early stage of this work.
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