Polarizing Transforming Reflector (PTR)

• 1: Theory of Operation
• 2: Installation
• 3: Maintenance
• 4: References

1 - Theory of Operation

The PTR was first described in the literature by Howard et al. operating at a frequency of 28 GHz. Despite its low insertion loss, the PTR has only been used in QO systens for high-field EPR/DNP spectroscopy in some rare instances.

Theory

Wire Grids

Before discussing the PTR in more detail, we will briefly review some fundamental properties of wire grid polarizers.

Free-standing wire grid polarizers made from cylindrical metallic wires either transmit or reflect electromagnetic radiation depending on the orientation (polarization) of the incident E field vector with respect to the grid wire orientation. For cylindrical wires with wire radius \(d\) and wire separation distance \(S\) with \(d \ll S\), the frequency dependent transmission coefficient for an electric field vector oriented parallel to the wire grid can be calculated using the Jones Matrix formalism. The corresponding reflection and transmission matrices are:

$$ C_{R} = \begin{pmatrix} -\cos^{2}{\theta} & -\cos{\theta} \sin{\theta} \\ \cos{\theta} \sin{\theta} & \sin^{2}{\theta} \end{pmatrix} $$

and

$$ C_{T} = \begin{pmatrix} \sin^{2}{\theta} & -\cos{\theta} \sin{\theta} \\ -\cos{\theta} \sin{\theta} & \cos^{2}{\theta} \end{pmatrix}. $$

This only correct if the grid orientation to be perpendicular to the propagation direction of the beam (\(\theta^{ \prime} = 0^{\circ}\)). However, if the purpose of the grid is to clean up the polarization of the microwave beam, the resulting reflected microwave power should be directed away form the source and not directly reflected back. This can be achieved by orienting the grid at an angle of \(\theta^{\prime} = 45^{\circ}\). In this case determining the reflection and transmission coefficients is less intuitive. This is summarized in the following figure (Figure 1).

If the grid is oriented perpendicular to the beam propagation direction (\(\theta^{ \prime} = 0^{\circ}\)) the free-standing wire grid needs to be rotated by (\(\theta = 45^{\circ}\)) to transmit 50 % of the power (see Figure 1A). On the other hand, if the grid is oriented at an angle (\(\theta^{ \prime} = 45^{\circ}\)) the wire grid needs to be rotated by (\(\theta = 54.7^{\circ}\)) to transmit 50 % of the power and reflect 50 % of the power (see Figure 1B). For more details check out Paul Goldsmith’s book Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (chapter 8.6.2, page 210).

The power transmission and reflection for a variable grid is shown in Figure 2. By rotating the grid and varying the angle \(\theta\) from 0º to 90º the beam can be continuously attenuated. Depending on the quality of the grid this attenuation can reach values of - 30 dB or lower.

Polarization Transforming Reflector (PTR)

The PTR consists of two principle components: 1) A free-standing wire grid and 2) A flat metal reflector. The free-standing wire grid is made from metallic wires having a diameter of d and separated by a distance of S (see figure below). Directly located behind the grid is a flat mirror. A schematic of the PTR is shown in Figure 2 (left).

By changing t, the distance between the flat mirror and the wire grid polarizer of the PTR it is possible to change the polarization state of e.g. a linearly polarized Gaussian incident beam to from linear to circular clockwise and counter-clockwise polarization (Figure 2, right).

How it works

Assuming the gird/mirror pair of the PTR is oriented at angle \(\theta = 45^{\circ}\) with respect to the propagation direction of the incident beam and a grid wire orientation of (\(\theta^{ \prime} = 54.7^{\circ}\)) half of the power of the incident beam will be reflected by the wire grid at point A (see Figure 2, left). The remaining portion of the beam will travel through the grid and be reflected by the flat mirror surface at point B (see Figure 2, left).

Depending upon the distance t between the wire grid and the flat mirror surface, the portion of the beam transmitted by the wire grid will have to travel an additional distance ABC (see Figure 2, left) and will accumulate a phase difference \(\rho\) with respect to the portion of the beam taht is reflected by the wire grid at point A (see Figure 2, left).

For the incoming beam, having a wavelength of \(\lambda \), propagating at an incident angle \(\theta = 45^{\circ}\) and a grid–mirror separation of t, the optical path difference P to travel the additional distance is:

$$ P = AB + BC \\ P = 2t \cos(\theta^{\prime}). $$

The phase difference \(\rho\) between orthogonal components is given by

$$ \rho = 4 \pi t \cos(\theta^{\prime} \lambda), $$

and the separation distance between orthogonal components \(\Delta\) (beam walk-off, Figure 2 right) is given by

$$ \Delta = 2t \sin(\theta^{\prime}). $$

By changing the distance t, it is possible to change the phase difference between the two beam components and therefore to change the polarization of the e-field of the reflected beam, e.g., from linear to circular or arbitrary linear polarization orthogonal to the propagation axis, with respect to the reflected beam. Choosing the correct distance t, an incident linearly polarized THz beam can therefore be transformed into a beam with a phase difference given by \(\rho\) with respect to the orthogonal polarization. This property enables transformation of, e.g., linear polarization to circular polarization, similar to a quarter-lambda waveplate.

2 - Installation

The PTR is compatible with the Bridge12 bread-board for quasi-optical instrumentation. The bread-board is based on a 2.5 in. by 2.5 in. grid. It is commonly referred to as a 1 1/2 - 3 - 1 1/2 optic. This means, make sure that there are 2 empty cube positions between two refocusing mirrors.

Installation

To install the PTR:

1. Slide the dowel pin into the clearance hole of the bread board
2. Orient the PTR
3. Lock the PTR position by fastening the 1/2-40 socket head screw

Optimizing the Position

The PTR, as all Bridge12 QO elements only have one degree of freedom (rotation about the dowl pin) to optimize the insertion loss or overall transmission loss of a QO system. To minimize transmission losses:

1. Loosen the 1/4-20 socket head screw. Do not remove the screw from the bread board
2. Monitor the transmitted power
3. Rotate the PTR while maximizing the transmitted power

Adapters

The PTR is fully compatible with the Bridge12 QO bread board design. Bridge12 offers adapter plates if you are using a different bread board design. Please contact us at info@bridge12.com for more information.

3 - Maintenance

The Bridge12 PTR is completely maintenance free. If you experience any problems please contact Bridge12 at support@bridge12.com.

4 - References

The PTR is not a new device and has been described throughout the scientific literature. Some major references are:

• Howard, J., W. A. Peebles, and N. C. Luhmann. “The Use of Polarization Transforming Reflectors for Far-Infrared and Millimeter Waves.” International Journal of Infrared and Millimeter Waves 7 (October 1, 1986): 1591–1603. https://doi.org/10.1007/bf01010760.
• Earle, Keith A., Dmitriy S. Tipikin, and Jack H. Freed. “Far-Infrared Electron-Paramagnetic-Resonance Spectrometer Utilizing a Quasioptical Reflection Bridge.” Review of Scientific Instruments 67 (1996): 2502–13.
• Amer, N., W. C. Hurlbut, B. J. Norton, Yun-Shik Lee, and T. B. Norris. “Generation of Terahertz Pulses with Arbitrary Elliptical Polarization.” Applied Physics Letters 87, no. 22 (November 28, 2005): 221111. https://doi.org/10.1063/1.2138351.
• Chuss, David T., Edward J. Wollack, Ross Henry, Howard Hui, Aaron J. Juarez, Megan Krejny, S. Harvey Moseley, and Giles Novak. “Properties of a Variable-Delay Polarization Modulator.” Applied Optics 51, no. 2 (January 10, 2012): 197. https://doi.org/10.1364/AO.51.000197.

However, when characterizing the PTR developed by Bridge12 Technologies, Inc. we realized that the PTR can also be used as an Universal Polarizer. This properties hasn’t been reported before and was first described in:

• Chen, Jeson, and Thorsten Maly. “Compact, Tunable Polarization Transforming Reflector for Quasi-Optical Devices Used in Terahertz Science.” Review of Scientific Instruments 93, no. 1 (January 1, 2022): 013102. https://doi.org/10.1063/5.0036292.

If you are using a PTR manufactured by Bridge12, please consider referencing the above publication.

Initial results were presented at the 2018 ENC Conference as a poster contribution by Jeson Chen.