🔬 applied physics

Demonstration of a planar multimodal periodic filter at THz frequencies

This paper presents the theory, design, and experimental validation of a planar multimodal periodic band-stop filter fabricated on a silicon nitride substrate, which operates at a center frequency of 0.8 THz and offers flexible design and potential for active control through its unique multimode configuration.

Original authors: Ali Dehghanian, Mohsen Haghighat, Thomas Darcie, Levi Smith

Published 2026-03-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ali Dehghanian, Mohsen Haghighat, Thomas Darcie, Levi Smith

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to listen to a specific radio station, but the airwaves are filled with static and other channels bleeding through. To hear your favorite song clearly, you need a filter that blocks out the noise while letting your desired frequency pass.

This paper is about building a very special, ultra-fast "noise-canceling" filter, but instead of for radio waves, it works with Terahertz (THz) waves. These waves are like the "missing link" between microwaves (used in your Wi-Fi) and light (used in fiber optics). They are incredibly fast and hold a lot of information, making them the future of super-speedy wireless communication and super-sensitive medical sensors.

Here is the story of how the researchers built this filter, explained simply:

1. The Problem: The "Goldilocks" Zone is Hard to Reach

Building devices for THz waves is tricky. It's like trying to build a house out of sand; the waves are so fast and the components so tiny that standard tools don't work well.

The Challenge: Most electronic testing equipment is too big, too expensive, or simply can't handle these super-fast frequencies.
The Solution: Instead of using giant, clunky machines, the team used lasers and ultra-thin films. Think of it like using a high-speed camera (a femtosecond laser) to take a snapshot of the wave as it zips through the device, rather than trying to catch it with a net.

2. The Design: A "Train" of Alternating Tracks

The filter itself is a flat, planar structure (like a circuit board) made of a very thin sheet of silicon nitride (only 1 micrometer thick—about 1/50th the width of a human hair).

Imagine a train track that switches back and forth between two different types of rails:

Track A (CPS): A standard two-wire track.
Track B (CPW): A three-wire track that has a "secret" mode of operation.

Usually, engineers try to suppress the "secret" mode on the three-wire track because it causes interference. But this team decided to embrace the secret. They realized that by alternating between the two-wire track and the "secret mode" of the three-wire track, they could create a unique rhythm.

The Analogy:
Think of the signal as a runner.

When the runner hits the two-wire track, they run at a normal pace.
When they hit the three-wire track, they switch to a "ghost mode" (the odd-mode) that changes their speed slightly.
By alternating these tracks perfectly, the runner gets confused at a specific speed (0.8 THz). They can't keep going, so they bounce back. This creates a stopband—a wall that blocks that specific frequency.

3. The "Multimodal" Magic

The coolest part of this paper is the "Multimodal" aspect.

Standard Filters: Usually, a filter is like a one-way street. It lets one thing through and blocks another.
This Filter: It's like a shapeshifter. Because the three-wire track has two different "modes" (ways the electricity can flow), the researchers can change the rules of the game.
- Mode 1 (The Experiment): They set it up to block a specific frequency (a Band-Stop filter). This is like putting a roadblock on a highway to stop traffic at 60 mph.
- Mode 2 (The Appendix): They showed that if you add a tiny electrical "short circuit" (a bridge) between the wires, the filter flips! It stops blocking and starts only letting that specific frequency through (a Band-Pass filter). It's like turning the roadblock into a VIP entrance that only lets 60 mph traffic through.

4. The Experiment: Did it Work?

The team built the device on a tiny, suspended membrane (like a trampoline made of silicon nitride) to prevent energy loss. They fired a laser pulse at it and watched how the wave traveled.

The Result: The filter worked almost exactly as predicted. It successfully blocked the 0.8 THz frequency (the "stopband") while letting other frequencies pass.
The Match: The math (theory), the computer models (simulation), and the real-world laser test (experiment) all lined up perfectly. It was like building a bridge based on a blueprint, and when they opened it, the cars drove across exactly as the engineers predicted.

Why Does This Matter?

This isn't just about blocking a frequency; it's about control and flexibility.

Future 6G/7G Internet: As we move toward ultra-fast wireless networks, we need filters that can be tiny, fast, and tunable. This design is a blueprint for that.
Smart Sensors: In medical or security sensing, being able to tune a filter to detect a specific chemical or material is crucial.
Active Control: Because this filter uses "modes," we could potentially add tiny electronic switches (diodes) to it later. This would allow us to change the filter's behavior in real-time, like turning a volume knob on a radio, but for light-speed data.

In a nutshell: The researchers built a tiny, ultra-fast traffic cop for light-speed waves. They found a clever way to use the "hidden gears" of the waveguide to create a filter that not only blocks noise but can be reconfigured to become a VIP gatekeeper, all while using lasers instead of heavy machinery to test it.

1. Problem Statement

Terahertz (THz) communication and sensing applications require effective signal processing components, specifically band-stop filters, to enhance dynamic range and detect analytes. However, designing and characterizing these devices at THz frequencies presents significant challenges:

Instrumentation Limitations: Standard Vector Network Analyzers (VNAs) used for microwave frequencies cannot operate directly at THz. While extension modules exist, they are costly, band-limited, and require complex mode conversion (rectangular waveguide to planar) that introduces losses and alignment issues.
Substrate Losses: Uniplanar waveguides on standard substrates suffer from significant radiation losses at THz frequencies due to substrate modes.
Design Rigidity: Traditional periodic filters often rely on single-mode operation, limiting design flexibility and the potential for active reconfigurability.

2. Methodology

The authors propose a novel planar multimodal periodic band-stop filter and a specialized experimental characterization method.

A. Device Design & Theory

Topology: The filter consists of alternating sections of Coplanar Stripline (CPS) and the odd-mode of a Finite-Ground Plane Coplanar Waveguide (FGPCPW, referred to as CPW).
Multimodal Approach: Unlike standard filters that suppress the "parasitic" odd-mode of the CPW, this design intentionally utilizes the CPW odd-mode ( $CPW_o$ ) to couple with the CPS mode. This multimodal interaction creates the periodic filtering effect.
Substrate: To minimize radiation loss and dispersion, the device is fabricated on an ultra-thin 1 µm Silicon Nitride (SiN) membrane, mechanically suspended by a 500 µm Silicon frame.
Theoretical Modeling:
- ABCD Matrices: The periodic structure is modeled by cascading ABCD matrices of unit cells (composed of $\lambda/4$ CPS and $\lambda/2$ $CPW_o$ sections).
- Impedance Calculation: Characteristic impedances ( $Z_{CPS}$ and $Z_{CPW_o}$ ) are derived using quasi-static expressions and refined via full-wave simulations (ANSYS HFSS).
- Key Equations: The center frequency ( $f_c$ ) is determined by the grating period ( $\Lambda$ ), while the fractional bandwidth is controlled by the ratio of the characteristic impedances of the two line types.

B. Fabrication

Materials: Gold (Au) conductors (200 nm thick) on a 1 µm SiN substrate.
Process: Utilized UV lithography and Electron-Beam Physical Vapor Deposition (EBPVD). The Si substrate was selectively etched using KOH to create the suspended membrane.
Integration: Low-Temperature Gallium Arsenide (LT-GaAs) Photoconductive Switches (PCS) were fabricated using an epitaxial lift-off method and bonded to the circuit using Van der Waals bonding for signal generation and detection.

C. Experimental Characterization

Technique: Instead of a VNA, the authors used a modified THz Time-Domain Spectroscopy (THz-TDS) system.
Setup: A femtosecond laser (80 fs pulse, 80 MHz) drives a DC-biased LT-GaAs PCS to generate sub-picosecond current pulses. The signal traverses the filter and is detected by a receiver PCS using lock-in amplification.
Data Processing: The transient time-domain signal is converted to the frequency domain via Discrete Fourier Transform (DFT). Results are normalized against a reference structure ( $W_m = 0$ ) and corrected for the inherent frequency roll-off of the transient source.

3. Key Contributions

Multimodal Periodic Filter Topology: Demonstrated a new filter architecture that exploits the coupling between CPS and the CPW odd-mode, enabling flexible design and potential active control (e.g., via diodes or phase shifters).
Proof-of-Concept at 0.8 THz: Successfully designed, simulated, and fabricated a band-stop filter with a center frequency of 0.8 THz and a bandwidth of 0.07 THz (theoretical) / 0.1 THz (experimental).
Alternative Characterization Method: Validated a cost-effective, high-accuracy method for characterizing uniplanar THz devices using photoconductive switches, bypassing the need for expensive waveguide-based VNA extension modules.
Reconfigurability Demonstration: Theoretical proof (Appendix A) showing that by manipulating the even-mode excitation (via short circuits), the same physical structure can be converted from a band-stop to a band-pass filter, highlighting the versatility of the multimodal approach.

4. Results

Simulation vs. Theory: The ABCD matrix model provided a good first-order approximation of the filter response. Full-wave simulations (HFSS) revealed additional losses (1–6 dB) due to conductor loss and diffractive grating radiation, which the ABCD model did not capture.
Experimental Performance:
- Center Frequency: The experimental stopband centered at 0.8 THz, matching the design target.
- Bandwidth: The measured bandwidth was approximately 0.1 THz, slightly wider than the theoretical 0.07 THz, attributed to manufacturing tolerances.
- Rejection: With 20 unit cells ( $N=20$ ), the filter achieved a stopband rejection of 15–20 dB.
- Agreement: After correcting for the source's frequency roll-off, the experimental spectral response showed excellent agreement with full-wave simulations regarding center frequency and bandwidth.
Loss Mechanisms: Insertion loss below the stopband was ~1 dB (conductor loss), while loss above the stopband increased to 4–6 dB due to diffractive grating radiation.

5. Significance

This work represents a significant step forward in THz integrated circuit design by:

Enabling Active Control: The multimodal nature of the filter opens the door for reconfigurable devices (e.g., tunable filters) by integrating active elements like diodes, which is difficult with standard single-mode periodic structures.
Cost-Effective Testing: It validates a methodology for characterizing planar THz devices without relying on prohibitively expensive waveguide-based instrumentation, making THz research more accessible.
Scalability: The theoretical framework and design equations are scalable to higher frequencies, providing a blueprint for future THz communication and sensing systems.
Substrate Engineering: It reinforces the necessity of ultra-thin, suspended substrates to mitigate radiation losses in uniplanar THz components.