Achieving a uniform and intense magnetic field is critical for microsensing, yet current antenna designs struggle to balance field strength, bandwidth, and compactness. Researchers report a new planar antenna capable of generating a nearly uniform magnetic field of 1-10 Gauss across a wide frequency range of 100 MHz-100 GHz within a thin layer of material.

This design utilizes two thin, parallel metal electrodes as a spacer for a paramagnetic medium, maintaining full optical accessibility for techniques like optically detected magnetic resonance (ODMR). The antenna addresses key problems including achieving uniform fields, optimizing bandwidth, and managing power consumption, all while maintaining optical access.

Planar Antenna Design for Uniform Microwave Fields

Generating a 1-10 Gauss magnetic field with good uniformity, the design of a near-field planar antenna represents an advance in microsensing technology, addressing limitations found in both wire-based and traditional planar antenna configurations. Achieving this balance involved a two-step design process beginning with a one-dimensional model based on the telegrapher’s equation, applied to an open line with a tapered profile, to analyze impedance, bandpass, and magnetic field profile.

The antenna’s functionality relies on a carefully engineered geometry, specifically two thin parallel metal electrodes that generate a resonant magnetic field, the frequency and bandwidth of which are tunable through precise control of electrode shape, size, and thickness. Initial designs considered an open rectangular planar waveguide, but the frequencies necessary for ODMR of nitrogen-vacancy centers in diamond, around 3 GHz, would have required a 2 cm length, impractical given the typical size of commercially available diamond monocrystals.

To overcome this, the researchers focused on tapering the transmission line, a technique commonly used to match impedance characteristics, but repurposed to model the impedance, bandpass, and magnetic field profile of the near-field antenna itself. This allowed for a functional device within the constraints of available material dimensions. Analytical expressions for the generated fields and impedance were developed, enabling the design of an antenna with specific resonant frequency, impedance, and magnetic field characteristics.

Simulations were then conducted to assess antenna performance, focusing on both the average magnetic field, $B_{a} v$ , and the ratio between the maximum oscillation and the average value, ΔB/B_av, as functions of frequency. Results from these one-dimensional simulations demonstrated consistency with a resistor-inductor-capacitor (RLC) model up to two octaves above the resonance frequency, with uniformity maintained to within a few percent.

The design incorporates three distinct sections, inductive, resistive, and capacitive, each contributing to the overall current distribution and field generation. While the magnetic field exhibits some non-uniformity along the antenna profile, this is acceptable for ODMR applications where a field gradient is not detrimental. However, to achieve truly uniform fields over larger areas, the taper includes a section with nearly constant width, maximizing field consistency for precise magnetic field measurements.

A detailed map of the magnetic field intensity, calculated for an antenna dissipating 1 Watt of electric power with 15 and 100 nm thick gold electrodes at 2. 87 GHz, illustrates the achieved field distribution. The researchers designed an antenna targeting a resonant frequency of approximately 3 GHz with a bandpass of at least 30 GHz, aiming to generate a magnetic field exceeding 1 Gauss in a central region with high uniformity.

This was accomplished through a succession of exponentially tapered profiles, allowing for precise control over the antenna’s electromagnetic properties. The principles and methods developed are not limited to this specific frequency or material; they can be adapted for use with other materials like silicon carbide, available in large, thin samples, by adjusting the antenna’s size, shape, and dielectric thickness. This adaptability broadens the potential applications of the technology beyond diamond-based sensors. The ability to tailor the antenna’s characteristics opens possibilities for diverse sensing applications, notably ODMR, vector magnetometry, and radio frequency detection and spectroscopy.

Current microwire antennas, operating at 1 Watt of power and 50-ohm impedance, achieve a maximum magnetic field strength of approximately 80G, but suffer from the non-uniformity addressed by this new planar design. while existing microwire antennas have reached diameters as small as 10 μm, the need for extended field gradients to support a wide spectroscopic bandwidth presents a continuing miniaturization challenge. This planar antenna offers a pathway to overcome these limitations, providing both strong and uniform microwave fields essential for advanced microsensing and nanosensing.

Telegrapher’s Equation Models Antenna Impedance & Bandpass

This approach yielded an analytical solution defining impedance and magnetic field distribution along the antenna’s length as a function of frequency, subsequently validated through full three-dimensional simulations using COMSOL Multiphysics software. The design process begins with establishing an inductive component, transitioning into a matching section before reaching a resistive portion; a profile within this resistive section compensates for decreasing current, ensuring uniform magnetic induction intensity, and culminating in a widening, capacitive section.

This carefully constructed geometry allows for tailoring the antenna’s characteristics to specific requirements, a level of control previously difficult to achieve with conventional designs, and was further refined through detailed 3D simulations. For example, calculations demonstrate how the length of an exponentially tapered antenna resonating at 2. 87 GHz scales with the length scale Λ, and how the initial width, w_0, must be constrained to maintain a gradual taper, specifically, fulfilling the condition dw/dx<1.

The antenna, fitting within a 2 mm diameter diamond membrane, generates a nearly uniform magnetic field of 1-10 G. The magnetic field isolines deviate from vertical alignment when the antenna width is comparable to or exceeds the wavelength, Λ. The antenna’s impedance behavior exhibits two distinct regimes: a low-frequency response with a relatively constant real part and an imaginary part, and a higher-frequency regime emerging around 30 GHz when the wavelength approaches twice the antenna’s length.

“Instead of diverging at high frequencies, the impedance of the device oscillates, also reaching lower values than those typical of the first resonance frequency,” the researchers report, suggesting a potentially wider bandpass than predicted by simpler low-frequency models.

This observation is significant because it indicates the antenna’s ability to maintain performance across a broader spectrum, which is important for applications requiring wide spectroscopic bandwidth. Calculations of the antenna’s impedance across hundreds of megahertz to hundreds of gigahertz, using the one-dimensional model derived from the telegrapher’s equation, confirm this behavior, with the real and imaginary parts of the impedance plotted as a function of frequency and compared against an approximation using values of L and C. The team’s work demonstrates that the bandpass of the antenna, in relation to the magnetic field produced in its central region, may indeed be larger than initially anticipated, opening possibilities for more sensitive and versatile microsensing applications. The ability to predict and control these characteristics through analytical modeling, coupled with rigorous 3D simulation, represents an advancement in antenna design for quantum sensing and beyond.

NV Center ODMR Drives Antenna Miniaturization

New antenna geometries address this limitation, though often at the cost of field intensity; Ω-shaped wires, for example, improve uniformity over a 100μm area within a 300μm diameter coil, but generate only approximately 8 Gauss with the same power input. This trade-off between strength and uniformity presents a significant challenge for applications demanding both high sensitivity and precise spatial resolution.

The design uses a planar waveguide, a structure theoretically capable of resonating at any frequency and producing a nearly uniform transverse magnetic field in its central region, but practical limitations previously restricted its use. Researchers overcame this constraint by employing an exponentially tapered antenna, carefully scaling its length based on a parameter denoted as Λ, and controlling the initial width, w₀, to maintain a gradual taper, ensuring dw/dx remains less than 1.

For a resonant frequency of 2. 87 GHz, calculations demonstrate a relationship between equivalent gold electrode thickness and antenna length, and establish maximum permissible values for w₀. Detailed modeling reveals the antenna’s field profile is not perfectly uniform, a characteristic acceptable when a magnetic field gradient is not detrimental to the measurement; however, a section of nearly constant width within the taper is essential for applications requiring large areas of uniform field. Visualizations of the antenna’s half-profile, symmetric around the x-axis, demonstrate the geometry’s shaping, while plots of impedance against the scale Λ reveal two distinct operational regimes.

The antenna’s surface area is equivalent to that of a previous iteration, despite the miniaturization, and the design incorporates an extended ground electrode to improve low-frequency field confinement. Maps of the magnetic field intensity at the median plane between electrodes, at both the resonant frequency of 2. 87 GHz and 256 GHz, highlight the field’s behavior in different regimes.

“The scale is saturated above 10 G to show the behavior, especially in the central region,” the researchers note, emphasizing the importance of visualizing the field distribution. Comparisons of magnetic field intensity along the vertical symmetry plane and a parallel plane 150μm away reveal the antenna’s performance, demonstrating a slight improvement in uniformity with the extended ground electrode.

The team’s work extends beyond simple field calculations, enabling the design of antennas with predetermined characteristics, and opens possibilities for advanced microsensing and nanosensing of physical parameters, as well as vector magnetometry and RF frequency detection/spectroscopy. This versatility positions the antenna not merely as a physics advancement, but as a crucial component for a range of sensing applications demanding compact, high-performance magnetic field generation.

1-10 Gauss Magnetic Fields Across 100 MHz-100 GHz

The design detailed in this work addresses this trade-off, seeking to maintain strong fields while improving spatial consistency for applications like optically detected magnetic resonance (ODMR). This limitation prompted the development of a new antenna geometry designed to balance field strength and uniformity, particularly for applications where a magnetic field gradient is undesirable. The current work focuses on creating a design that maintains a nearly uniform field across a larger area, essential for accurate magnetic field measurements and wide spectroscopic bandwidth.

Simulations of the antenna, utilizing COMSOL Multiphysics software, modeled a diamond membrane positioned between electrodes as an insulating layer with a frequency-independent dielectric constant, surrounded by vacuum. Gold electrodes were simulated using two-dimensional transition boundary conditions, specifying a conductivity and a thickness of 15-100 nm, accounting for the skin depth of gold at the frequencies under investigation.

The simulations reveal a high degree of field uniformity along the z-direction, with variations in the xy-plane remaining within acceptable limits, as defined by the design parameters. This deviation, particularly noticeable at the beginning of the central section, alters the field distribution, prompting the calculation of average field strength, $B_{a} v$ , and oscillation amplitude, ΔB, within a defined rectangular region. Maps of magnetic field intensity, specifically the y-component along the xz and yz planes at a frequency of 2.87 GHz were generated through COMSOL Multiphysics simulations, visually demonstrating the field distribution between the electrodes.

These maps confirm the antenna’s ability to generate a relatively uniform magnetic field, which is important for applications demanding precise control over field characteristics. The design’s success lies in its ability to navigate the complex interplay between field strength, uniformity, and compactness, offering a promising solution for advanced sensing technologies.

The researchers emphasize the adaptability of this approach, noting that the principles and methods employed are not limited to diamond but can be extended to other materials, opening avenues for customization and optimization based on specific application requirements. The ability to tailor antenna characteristics to predetermined specifications further enhances its potential impact, enabling the development of highly specialized sensors for diverse scientific and technological challenges.

👉 More information
🗞 Near-field planar antenna for microwave excitation of paramagnetic quantum emitters
✍️ Stefano Lagomarsino and Mario Agio
🧠 DOI: http://link.aps.org/doi/10.1103/rhmf-tf2r

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