A Broad-Band Dual-Polarization All-Metal Dichroic Filter for Cryogenic Applications in Sub-THz Range

In this article, we report on the design and characterization of an all-metal, wideband single-layer dichroic filter operating at nonnormal beam incidence. The dichroic filter consists of a perforated metal plate with an angular offset of the perforated channels equal to the beam incidence angle onto the dichroic surface. The fabricated filter is characterized using a specially designed quasi-optical test system. The filter demonstrates 96% transmission of the incoming electromagnetic (EM) radiation averaged in the signal band about 37–50 GHz for both polarizations while simultaneously achieving a rejection better than 20 dB for frequencies lower than 26 GHz at the designed beam incidence of 13°. The cross-polarization level for each polarization is better than 30 dB in the passband. The experimental results of the transmission measurements are in very good agreement with EM simulations confirming the feasibility and benefits of our proposed design concept even at THz frequencies. The simulations of the dichroic scaled version demonstrate that, for instance, it can be employed in the event horizon telescope project, where 230 and 345 GHz receiver channels could be operating simultaneously.


I. INTRODUCTION
M ULTIBAND receiving systems have gained significant popularity as a solution for instrumentation in environmental sciences and radio astronomy [1].In such systems, the receiver channels run simultaneously while the receivers' spatial pointing is aligned.The use of broadband frequency receivers offers several advantages.In continuum observations, increasing the instantaneous bandwidth directly enhances the power of the received signal.For spectral line observations, a wider instantaneous frequency band enables quicker spectral line surveys or simultaneous observations of astronomically important CO lines, such as J = 2→1 and J = 3→2 transitions at 230 and 345 GHz [2].Moreover, multifrequency receiver systems allow simultaneous calibration of the different receiver bands, leading to an improved cross-correlation of the measured lines' intensities compared to individual observations of the same spectral lines.Additionally, such multifrequency systems can utilize the lower frequency band to calibrate with better accuracy, removing atmospheric noise contributions and introducing phase corrections for higher frequency bands in interferometric observations, as exemplified by the atacama large millimeter array (ALMA) [3], and millimeter wavelength very large baseline interferometry (mm-VLBI) [4], which includes event horizon telescope (EHT) [5].For instance, the ALMA band 3 channel observing a water maser at a frequency around 86 GHz is used to measure and calibrate out the atmospheric phase contribution for each antenna of the interferometer, while the actual observations occur using the higher frequency channels.In the receiver described in [4], all separate frequency channels are co-aligned on the sky, enabling an accurate accounting of atmospheric noise and phase contributions, thereby significantly improving the observation quality.
One possible implementation of a multiband receiver system relies on duplexing and filtering techniques using waveguide technology, as presented in [2].However, the inclusion of diplexers and filters between the feed and the receivers, along with the associated signal (RF) transmission loss, inevitably contributes to an increased system noise.Moreover, these systems often have limitations on the frequency coverage of the available receiver bands due to the constraints of waveguide single-mode operation.
In cases where different receiver channels cannot share the same waveguide due to significant differences in operating frequencies, optical frequency-selective components could be employed, particularly dichroic filters.These components specifically suited for mm and THz frequencies [6], have gained significant attention recently, as they are frequency selective and have low transmission loss.The dichroic filters integrated as part of tertiary optics enable the combination of at most two receiver channels by reflecting the lower frequency band while transmitting the higher frequency band, therefore acting as a high-pass filter.A comprehensive review on the possible designs and constraints of single-layer and multi-layer dichroic filters can be found in [6].
In this article, our focus is to explore the feasibility of using a single-layer, all-metal dichroic plate with high-pass filter functionality, similar to the approach presented in [7] and [8].The primary objective of this article is to develop, validate the design, and test a prototype of such a dichroic filter.The use of an all-metal design offers the advantages of employing the dichroic filter at cryogenic temperatures, thereby minimizing system noise contributions through the improved metal conductivity and the reduced RF insertion loss, as well as reducing issues with outgassing and thermal contraction causing delamination.
For design and prototyping, we have selected the Q-band frequencies of 35-55 GHz, with a filter transmission exceeding 90% in the 37-51 GHz range and RF damping of at least 20 dB at 26 GHz.The relatively low frequency of this technology demonstrator offers the advantage of being compatible with the conventional CNC milling or similar machining techniques.Additionally, this dichroic filter can be directly utilized for the multi-band VLBI receiver system, currently under development for the Onsala Space Observatory (OSO) 20 m antenna.Nevertheless, the results of our work are also directly applicable and scalable to projects, such as EHT [5], where the co-alignment of 230 and 345 GHz receiver channels on the sky and dual-polarization performance are required for simultaneous observations.
In our design, we emphasize minimizing the deterioration of the frequency properties at nonnormal angles of incidence (AOI) for the signal beam, as well as minimizing the crosspolarization.These considerations ensure the symmetry of the dichroic polarization response and facilitate the design of the tertiary optics.Potentially, to achieve the desired functionality at sub-THz frequencies and overcome the challenges in manufacturing small-sized all-metal components, we established microfabrication techniques, which can be employed as described in [9].

II. BACKGROUND AND DESIGN CONCEPT
For the analysis of the dichroic filter, we consider it as a singlelayer metal plate with symmetrical discontinuities in the form of perforated apertures located at n = ±t/2, where t is the thickness of the plate as depicted in Fig. 1.
The plate is assumed to be illuminated by a plane wave at AOI, θ, from the direction of z = Ý.In the current design, the angular offset of the apertures matches the AOI, θ, as shown in Fig. 1.The original problem may be decomposed into symmetric and antisymmetric wave excitations, which correspond to open and short circuit scenarios, respectively, at z = 0.The sum of the resulting fields can then be calculated [10].On the incident side of the plate (e.g., n = t/2), the electromagnetic (EM) fields are expressed as a set of Floquet modes [11].
The hollow structures inside the metal plate behave as waveguides, and the fields inside those could be considered in terms of conventional waveguide modes.The cut-off frequency values of the waveguide modes depend on the specific geometry of the apertures, such as their dimensions and shape.On the transmitted side (e.g., n = -t/2), the dichroic acts as an array of waveguide apertures.Each aperture, or cell reradiates the EM waves, which are expanded again into the set of Floquet modes.The transverse aperture fields on both sides of the plate, along with the reflection and transmission coefficients could then be calculated as described in [10].
The frequency response of the dichroic filter is obtained by matching the Floquet and waveguide modes.As previously mentioned, the cut-off frequency of waveguide modes inside the unit cells, f c1 , establishes the lower end of the dichroic passband.At frequencies below this cut-off, the dichroic filter behaves as a plane reflector, with the reflection coefficient increasing as the frequency decreases.In the simplified case of circular apertures with a diameter d, the passband occurs above the cut-off frequency of the dominant TE 11 mode in the circular waveguide, which can be calculated as in [11] where c is the speed of light in free space.To optimize the frequency response of our design, we proposed a more advanced cell aperture geometry with a "snow-flake" cross section shape and an hexagonal periodic pattern for the dichroic layout with the initial dimension a of the desired hexagonal aperture, as shown with dot lines in Fig. 1.It has been demonstrated that if a regular hexagon with a side length a and a circle with diameter d have nearly the same cross-sectional area, the cut-off frequencies of the first ten modes of waveguides with such geometry can be considered equal with an error of less than 3% [13].Therefore, the cut-off frequency of the dominant mode in the hexagonal waveguide and the dichroic plate can be approximated as To achieve a cut-off frequency ƒ c1 of 34 GHz, the value of a can be approximated as 2.84 mm using (2).
As mentioned earlier, the dichroic filter acts as an aperture array.The aperture pitch s (see Fig. 1) determines the diffraction limit, f c2 .At frequencies higher than f c2 , when the wavelength of the incident wave is shorter than the aperture spacing values, the insertion loss of the filter increases drastically.This occurs because a portion of the power is diffracted into the first side lobe [14].In the case of an equilateral triangular lattice with spacing s between the holes, this diffraction frequency can be expressed as where c is the speed of light in free space.However, this diffraction into the first lobe above f c2 from ( 3) is estimated only in the case of a normal incident and zero angle of the apertures slant [7].
A nonnormal beam incidence, θ ࣔ 0, has a significant impact on the dichroic filters, reducing the bandwidth of the passband.This effect is known as the angular degradation.The filtering behavior of the dichroic plates with zero angle of the apertures slant at different θ values was studied in [7] by calculating the lowest Rayleigh frequency of Floquet harmonic.This frequency provides the highest limit of the filter passband and demonstrates a reduction of the passband.
However, in the current design, the slant angle of apertures is not zero and is the same as θ (see Fig. 1).Therefore, the axis of the beam that comes from the z-direction will always be coaxial to the waveguide apertures in the dichroic plate.Thereby, (3) could be complemented with the empirical correction factor F(θ) introduced from our simulations, as   we performed HFSS three-dimensional EM simulation of the dichroic filter as the periodic structure with the "snow-flake" shape apertures illustrated in Fig. 1(e).In this simulation, we estimated the diffraction limit normalized to f c2 (θ = 0) as a function of θ (the beam axis is kept coaxial with the axis of the waveguide).More simulation results will be discussed in Section III.
In practice, the undesirable effect of the angular degradation can be reduced, for instance, by changing the apertures' shape, or the use of multilayer dichroic filters [15].However, the multilayer filters can have performance issues during cryogenic operation and require the implementation of cold filters and restricted apertures [15].From (3) or (4), the diffraction limit increases with a denser perforation of the dichroic plate, which poses a challenge when designing the dichroic filter for specific purposes.
Fig. 3 depicts the conceptual optical layout for the OSO multiband receiver similar to [7].The dichroic plate is considered to be a three port device that spatially separates the beams for the receiver bands.Both dichroic filters (DF1 and DF2, in Fig. 3) have to be tilted to a certain angle to produce an off-axis reflection for the lower-frequency part of the RF band.However, the situation is different for the transmitted beam, as an angular degradation of the spectral properties appears to be unavoidable.As an alternative solution to multi-layer dichroic filters, in this article, we proposed a novel design concept based on tilting the waveguide inside the plate, as shown in Fig. 1.It should also be mentioned that special attention is required when a specific polarization state is aimed to be maintained in the transmission or reflection.The rotation angle, α, around axis n, in the dichroic plane [see Fig. 1(a)], is expected to produce an effect, similar to θ, resulting in a detrimental effect for the waveguide propagation modes and, consequently, reducing the passband and generating cross-polarization [15].
Furthermore, there is a trade-off between the thickness of the dichroic plate and the desired passband.The thickness of the plate determines the length responsible for the attenuation of the waves inside each waveguide perforation for the evanescent mode.A thicker plate provides a steeper cut-off slope just below the transmitted band.However, it could introduce undesired ripples in the band of interest and additional insertion loss [7].
To summarize, in order to enhance the filter passband and minimize the angular deterioration we propose a novel design of the dichroic with tilted perforations in the metal plate in combination with a customized geometry of the cell aperture.

III. SIMULATIONS RESULTS
The frequency response of a dichroic filter is determined by geometrical parameters of the cell aperture (i.e., its shape and size), spacing between the cells, the thickness of the metal plate, and the tilt of the waveguide apertures (equals θ).Once we estimated the initial aperture dimensions and the spacing, a and s, we performed a tuning of the performance of the dichroic filter using Ansys HFSS.Fig. 4(a) and (b) shows the simulated transmission as a function of frequency at different θ values, representing POL0 and POL1 polarizations, respectively.In the simulations, the perforation's tilt angle in the metal plate follows θ.Therefore, at the incident radiation wave vector will always be coaxial to the waveguide apertures.It is observed that as θ increases, the passband where the transmission exceeds 90% becomes narrower.A value of θ = 13°was considered acceptable for the proposed optical layout (see Fig. 3), ensuring a fractional bandwidth of over 30%.
It is worth noting that the reflected and transmitted bands for the proposed design are not separated very sharply.The frequency gap between 30 and 37 GHz with transmission values of 10% and 90%, respectively, are shown in Fig. 4(a).This gap imposes certain operational limitations in the reflected bands.As mentioned in Section II, this cut-off slope could be made steeper using a thicker plate, nonetheless, it would introduce ripples in the response.
When the incident beam is normal to the dichroic plate and θ = 0, the simulated passband for both polarizations is maximal and reaches 65 GHz.The estimation of the diffraction cut-off frequency f c2 at θ = 0 from (4) gives 64.5 GHz for the actual spacing distance between apertures of 5.37 mm.At other AOI values, the passband for each polarization becomes narrower due to the angular degradation.
The narrower passband observed for POL1 corresponds to different curves of F(θ), for the presented polarizations in Fig. 2.This effect could likely be attributed to the collinearity of the rotating θ-axis for POL1.As illustrated in Fig. 1(e), the apertures are projected over the front face of the dichroic filter, orthogonal to the waveguide axis, and the plane of the incident beam is shifted in phase.That causes changes in the shape of apertures and, consequently, the length of pitch s.Those result in a narrower dichroic passband, e.g., slight increase of f c1 and a more noticeable decrease of f c2 [see Fig. 4(b)].Fig. 5 demonstrates the simulated cross-polarization characteristic as a function of frequency at different AOI values.From the simulations, the cross-polarization sequence shows a negligible effect on the performances.Therefore, in Fig. 5 the only case represented is when POL0 was excited and POL1 was detected.
Notably, at all the presented AOI values, the leakage of the undesired polarization remains exceptionally low, consistently staying well below the threshold value of −30 dB, and denoted Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The prototype of the dichroic filter was manufactured from a 7.11 mm thick aluminum alloy plate as shown in Fig. 6.The detailed view of the "snow-flake" hexagonal cell unit is depicted in the insert of Fig. 6.After the optimization process new values for a = 2.89 mm and s = 5.37 mm were found.A fillet radius, r, of the hexagon's corners, and the parameter, δ [see Fig. 1(b)] appeared to be 0.65 and 0.046 mm, respectively.

IV. EXPERIMENTAL SETUP
To accurately measure the spectral performance of the fabricated dichroic filter, we designed and built a quasi-optical system that provides a plane-wave-like beam at the position where the tested dichroic is installed.The setup consists of four ellipsoidal mirrors with horn antennas at the transmitting and receiving sides.The layout of the measurement setup, visualizing the propagated beams, is illustrated in Fig. 7(a).
Additionally, a photograph of the measurement system is displayed in Fig. 7(b).The conical horn antennas with smooth spline-profile walls were optimized for the Q-band frequency range.The horns are connected to a 67 GHz vector network analyzer via a series of circular-to-rectangular and rectangularto-coaxial adapters.One horn plays the role of the transmitter (Tx in Fig. 7) while the other serves as the receiver (Rx in Fig. 7).During the measurements, the dichroic filter, referred to as a device under test (DUT) in Fig. 7, was positioned in the path of the collimated beam between the M2 and M3 mirrors, practically at the beam waist position, as illustrated in Fig. 7

(b).
To prevent any parasitic reflections, the area outside of four times the beam diameter at the dichroic plate is shielded with an absorber.Moreover, polarization grids have been incorporated into the optical system to minimize cross-polarization levels.
The incident angle θ m represents the apparent angle between the beam axis, indicated by a red arrow in Fig. 7(a), and the normal direction to the metal plate n, marked with a dark gray arrow in Fig. 7(a).
Careful consideration was given to the design of the optical components used in the measurement setup in Gaussian optics approximation.The mirror aperture sizes were determined to be four times the width of the propagating beam (4w o ) ensuring that the spillover loss remained below 0.1%.Furthermore, the ellipsoidal mirrors and their positions were optimized to maintain a frequency-independent optical system.The optical train was specifically calculated for a frequency of 42.5 GHz using the methodology described in [16].Polarization grids in front of the horns were employed to ensure the quality of cross-polarization measurements.
To calibrate out the impact of the measurement setup and ensure accurate characterization of the dichroic filter, a measurement with the presence of the dichroic and without it [but with an absorber limiting the opening, as shown in Fig. 7(b)] was performed.The measurements were repeated for both polarizations by rotating both horns and grids by 90°.

V. MEASUREMENTS RESULTS AND DISCUSSION
In order to validate the performances of the designed dichroic filter, we conducted a comparison between the simulated transmission and the measured values at θ m = 13°.This angle corresponds to the nominal value of θ = 13°at which the perforations in the dichroic metal plate were tilted from the normal direction as illustrated in Fig. 7(a) (marked in blue color).
The comparison was carried out for both polarization states, POL0 and POL1 as depicted in Fig. 8(a) and (b), respectively.It is evident from the figures that the measurement results closely align with the simulated transmission data exhibiting a fractional bandwidth of at least 30%.The measured low and high edges of the filter (defined as 90% transmission) passband match well with simulations with an accuracy of about 0.5 GHz.The simulated transmission at θ = 13±0.5°demonstratesa deviation of less than 2% of the passband.This negligible deviation clearly indicates that the dichroic design is tolerant to a practical angular position accuracy of the dichroic plate, up to approximately one degree.Clearly, as an optical component, the dichroic should be placed with higher accuracy.
It is important to acknowledge that our simulations did not take into account the roughness of the metal plate surface and the perforation walls.This simplification underestimates losses and may explain the discrepancy observed in the shape of the transmission dips around 53 GHz for POL0 and 52 GHz for POL1 between the measured data and the simulations.Nevertheless, we have a very good agreement between the measurements and simulations within the dichroic RF band.The measured cross-polarization leakage remains better than 32dB across the entire passband for both polarizations, fully satisfying the practical design requirements.During the cross-polarization measurements, the dichroic apertures symmetry axis is always oriented vertically and aligned with the E-field direction of POL1 (see Fig. 1).We rotated correspondingly the horn and grids at the receiver side (Rx in Fig. 7).There is a noticeable difference between the measured data and simulated values of the cross-polarization.This disparity can be attributed to several reasons.The Ansys HFSS simulation model relied on perfect manufacturing and exact mathematical symmetry.Moreover, certain limitations in the experimental setup should be noted.One is specifically related to the alignment of the horns and the polarization grids over an optical path spanning, approximately two meters long.Additionally, the cross-polarization Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.characteristic of the smooth-wall conical horns utilized in the measurements affects their accuracy.
In order to verify the accuracy of our model, we performed the measurements of the fabricated dichroic with manufactured aperture tilt of θ = 13°at different values of θ m = θ±Δθ, where Δθ was set to ±2°and ±5°[see Fig. 7(a)].In the HFSS simulations AOI was kept always at 13°and Δθ values were an angle between the waveguide walls axis and the incident wave axis.
The simulated transmission closely matched the measured results for both polarizations at all four values θ m varied in the experiments.In Fig. 9 we depict a comparison between the measured transmission and the corresponding simulated values for POL0 and POL1 at Δθ = ±2°, respectively.The measurement results proved the feasibility of the dichroic filter design with desirable frequency and polarization performance.
By scaling the dimensions with a factor of 0.11, a suitable dichroic filter could be constructed with the transmission exceeding 90% in the band around 345 GHz and lower than −30 dB at frequencies below 230 GHz.Therefore, this filter could be employed to spatially separate beams of 230 and 345 GHz receiver channels for EHT with minimal contributions to the receiver noise.Fig. 10 demonstrates the simulated RF performance of such a dichroic filter at the AOI of 13°.
Nonetheless, given the smaller values of a and s (as small as 500 μm) along with less than 1 mm thickness of the plate and the wider bandwidth of, such a dichroic filter, it will demand an advanced fabrication method combining conventional CNC machining with the all-metal micromachining method described in [9].However, even with the fabrication accuracies provided by the micromachining method, the tolerance analysis should be addressed and the measured performances achieved in the Q-band are very challenging to preserve at higher signal frequencies.

VI. CONCLUSION
We have successfully designed and characterized a dichroic filter with desired RF and polarization performance.The perforation of the metallic plate has been designed and fabricated with an offset angle that corresponds to the AOI, θ = 13°of the incoming beam.In such a design, the tilted perforation compensates for the projected shape of the aperture when the dichroic plate is tilted, thereby minimizing the impact on the RF properties in the passband.With our design, we have achieved a dichroic fractional bandwidth of 30% with transmission better than 90% at any frequencies within the dichroic filter passband and 96% on average.The cross-polarization level better than 32 dB over the whole passband was achieved.We demonstrated an excellent match between the simulated and measured performance.The all-metal dichroic design is fully compatible with cryogenic operation.
The presented design is also scalable to higher frequencies and could be employed as a cold dichroic filter for providing simultaneous operation at higher frequencies, for instance, the EHT 230 and 345 GHz receiver channels.For applications suitable for millimeter and THz frequencies, the filter could be fabricated using a well-established micromachining technique.

Fig. 1 .
Fig. 1.Geometry of the designed perforated plate.(a) Top view from n direction.(b) Detailed top view A of the dichroic aperture from n direction, the hexagon's corners and shape are modified with radius r and parameter δ.(c) and (d) Side view of the dichroic plate.(e) Detailed side view B of the single dichroic aperture.The incident wave illuminates the dichroic plate with the angular offset of the apertures θ from the direction of z = Ý.Parameter a is a side length of the initial hexagonal aperture marked with a red color dot line.The top view is taken from the n-direction.The splitting plane is normal to the axis of the waveguide aperture wall.

Fig. 4 .
Fig. 4. Simulated transmission of the designed dichroic filter as a function of the frequency at various values of AOI.(a) For horizontally (E H ) oriented E-field (POL0).(b) For vertically (E V ) oriented E-field (POL1).The frequency ranges with transmission exceeding 90% at the design value of θ = 13°, are indicated by the hatched areas.This transmission level is indicated by a gray dashed line.

Fig. 5 .
Fig. 5. Simulated cross-polarization characteristic between POL0 and POL1 of the designed dichroic filter as a function of the frequency at various values of AOI.POL0 is excited and POL1 was detected.The threshold for crosspolarization, set at −30 dB, is indicated here by a grey dashed line.The hatched area indicates the frequency ranges with transmission exceeding 90% at the design value of θ = 13°for POL0 corresponding to Fig. 4(a).

Fig. 6 .
Fig. 6.Manufactured dichroic filter.The insert provides a close-up view of a single perforation cell, highlighting the details of its structure.

Fig. 7 .
Fig. 7. Designed optical system for the characterizing the dichroic filter.(a) Schematic layout of the optical assembly, the grey-shaded volume represents the calculated quasi-optical beam indicating the path of the beam within the system.(b) Photograph of the measurement setup.The following components are marked: DUT-the dichroic filter; M1-M4-ellipsoidal l focusing mirrors; PG-polarization grids; Tx and Rx-transmitting and receiving conical horns, respectively; and Abs-absorber material.

Fig. 8 .
Fig. 8. Simulated and measured performance of the designed dichroic filter at nominal θ = θ m = 13°.(a) For horizontally (E H ) oriented E-field (POL0).(b) For vertically (E V ) oriented E-field (POL1).The hatched area in the graph indicates the frequency range with transmission exceeding 90%, which is marked with a grey dashed line.Black solid and blue dotted lines show simulated values of the transmission (left Y-axis), and cross-polarization values in the logarithmic dB scale (right Y-axis), respectively.Similarly, dash lines with red circles and green up-triangles depict the measurement data of the transmission and crosspolarization values in the logarithmic dB scale (right Y-axis), correspondingly.

Fig. 9 .
Fig. 9. Simulated and measurement results of the dichroic filter at nominal θ = 13°and Δθ = ±2 degrees.(a) For horizontally (E H ) oriented E-field (POL0).(b) For vertically (E V ) oriented E-field (POL1).The black solid and blue dotted lines depict the simulation results at θ m = 11°and 15°, respectively.The dash lines accompanied by red circles (at θ m = 11°) and green up-triangles (at θ m = 15°) represent the measured transmission data of the dichroic plate.The hatched area in the graph indicates the frequency range with measured transmission exceeding 90%, which is marked with a gray dashed line at θ m = θ = 13°from Fig. 8.

Fig. 10 .
Fig. 10.Scaled simulated dichroic passband performances around 345 GHz and stop band at 230 GHz at θ = 13°.Solid red and dotted black lines depict transmission values for POL0 and POL1, respectively (applied to the left Y-axis).Dotted lines with blue circles and green up-triangles illustrate the cross-polarization characteristic of the dichroic filter for POL0 and POL1, respectively (applied to the right Y-axis).The hatched areas in the graph indicate 8GHz wide EHT bands of interest around 230 and 345 GHz.