Efficient communication channel for smart contact lens with resonant magnetoquasistatic coupling

Magnetic resonant coupling is widely used for wireless power transfer in wearables but is typically employed in the strongly coupled regime, where the separation is smaller than or comparable to the device size. This work instead exploits resonant magnetoquasistatic (MQS) coupling to realize a wireless communication link between a necklace-mounted transmitter (Tx) coil and a receiver (Rx) coil embedded in a smart contact lens (SCL). A 15- cm Tx coil and an 8- mm peripheral Rx coil, operating at approximately 26.8 MHz at axial separations of ≈ 15 cm and lateral offsets ≥ 9 cm, form a weakly coupled but robust near-field channel. Finite-element simulations show only ∼ 10 dB path-loss variation across misalignments and a ∼ 5 Mbps channel capacity over 1 MHz bandwidth, sufficient for compressed 480p/15 fps video and multi-sensor telemetry. Because ocular and facial tissues have μ r ≈ 1 below 30 MHz, their presence causes negligible additional attenuation. A benchtop prototype with a 20- cm single-turn Tx coil and 1- cm four-turn Rx coil tuned near 26 MHz shows ∼ 60 dB of channel loss over necklace–eye distances and weak sensitivity to a tissue phantom, supporting the MQS-based analysis. Together, these results establish resonant MQS coupling as a viable high-data-rate communication backbone for future smart contact lenses.

The rapid rise of wearable electronics has reshaped how we consume personal and global information (Datta and Sen, 2023; Sen and Datta, 2024; Sen et al., 2023). Smart eyewear, from connected spectacles (Iqbal and Campbell, 2023; Meta, 2023) to emerging smart contact lenses (SCLs) (Yao et al., 2024), pushes that trend to its logical extreme by embedding augmented reality (AR) graphics, virtual reality (VR) content, and continuous health sensing directly in the user’s line of sight. Although today’s smart glasses have matured enough to function as true “on-the-go” computers and lightweight AR/VR headsets, they are still relatively bulky and require frequent battery recharging. SCLs promise a far more discreet alternative but introduce an even tougher challenge: every sensor, processor, and wireless transceiver must be squeezed into a mm -scale, flexible form factor that rests comfortably on the eye.

In a future where multiple on-body devices share data in real time, a wireless link to the eye must support megabit-rate throughput while incurring minimal path loss and imposing no awkward alignment constraints. These requirements become especially acute for SCLs, whose Rx coil is only a few millimeters in diameter and moves with every blink. Early smart-lens demonstrations in the 2000s showed that contact lenses can host simple electronics beyond vision correction (Xia et al., 2022). Since then, most prototypes have focused on single-channel tasks such as glucose sensing, drug delivery, or eye-tracking (Shaker et al., 2023), which typically demand only a few hundred kilobits per second and operate over short, well-aligned links.

From a communication technology standpoint, existing SCL platforms rely on three classes of wireless links: RF/near-field inductive, ultra-wideband (UWB), and optical. RF- and NFC-based inductive links are attractive for their compatibility with standard readers and relatively mature circuitry. However, they typically operate at tens to hundreds of MHz with strongly tuned resonances, leading to narrowband channels, sensitivity to lateral and angular misalignment, and non-negligible specific absorption rate (SAR) constraints in ocular tissues at higher carrier frequencies. UWB approaches offer multi-megabit data rates and robust timing-based protocols but require GHz-range operation, more complex antenna structures, and tighter regulatory limits on radiated power near the eye. Optical links (e.g., infrared or visible LEDs and photodiodes) can also support high data rates; however, they generally require line-of-sight alignment, are easily disrupted by blinking or partial occlusion, and must adhere to strict optical safety limits on corneal exposure. Recent reviews, including Yao et al. (2025), highlight that, across these modalities, achieving high throughput, low power density, and long-term ocular safety simultaneously remains a central open challenge for hydrogel-based SCL platforms.

Related work has also explored communication and powering aspects more broadly. Shaker et al. (2023) survey several communication techniques for contact lenses, while Mirzajani et al. (2022) review external, in vivo, and hybrid energy-harvesting methods. Although such techniques offer promising routes for continuous powering, their implementation in a soft, mm -scale lens remains challenging, and many demonstrated systems still require proximity to an RF energy source (Park et al., 2018). Soma et al. (1987) analyzed misalignment effects in RF coil systems for implantables, but those studies typically consider coils of comparable size and relatively short separations.

Figure 1a summarizes the distance-dependent design space for electromagnetically coupled systems. Strongly coupled systems within a few cm are standard for wireless power transfer applications and high-efficiency short-range communication. Radiative systems operate over much larger distances but at the cost of higher power consumption and more stringent antenna and regulatory constraints. Weakly coupled systems remain in the near-field regime with lower coupling strength, yet they can still support moderate power transfer or broader-band communication than tightly tuned resonant systems, enabling higher data rates (De Quinto et al., 2024). Magnetically coupled communication has been demonstrated in prior work to support increased bandwidth, continuous implantable telemetry, and improved channel capacity in weakly coupled and misaligned near-field biomedical systems (Shaw et al., 2025a; Shaw and Sen 2025; Shaw et al., 2025b).

In this work, we extend the concept of weakly coupled electromagnetic systems and explore a magnetoquasistatic (MQS) resonant link between a wearable transmitter (Tx), embedded in a necklace, and a receiver (Rx) coil integrated into an SCL. The proposed geometry pairs a 15- cm multi-turn Tx coil worn as a necklace with an 8- mm peripheral Rx coil on the lens rim. In the 20–30 MHz band, these coils remain electrically small, and the fields are predominantly magnetic. Because ocular and facial tissues have relative permeability close to that of free space (μ r ≈ 1), human tissue is largely “magnetically transparent” in this regime, and the link is primarily governed by coil geometry and relative position rather than tissue composition. Leveraging these properties, we show that a 26.8 MHz resonant necklace–lens link can sustain a ∼ 5 Mbps channel over a 1 MHz bandwidth at an axial distance of 15 cm and lateral offsets exceeding 9 cm, even under substantial misalignment between the necklace and the eye.

Compared to RF, UWB, and optical links, the proposed resonant MQS approach occupies an intermediate point in the design space: it operates at low carrier frequencies that naturally ease ocular SAR constraints, uses simple mm -scale coils compatible with hydrogel-based lenses (Yao et al., 2025), and provides a wideband, misalignment tolerant channel suitable for continuous AR/VR and sensing data streams, at the cost of being confined to the near-field regime.

While powering the contact lens remains critical to its functionality, the present study focuses exclusively on the communication challenge. We assume that the lens is equipped with either a small battery or an energy-harvesting solution (Griffith, 2022; Chatterjee et al., 2023) and leave the detailed power-delivery architecture to future work. Through detailed 3D finite-element simulations combined with careful analysis of coil sizing, placement, and orientation, we present an electromagnetic and information-theoretic proof-of-concept of the MQS channel between a necklace Tx and an SCL Rx coil.

By demonstrating a robust, high-capacity link using resonant MQS coupling with strongly misaligned coils of dissimilar dimensions, this work establishes the foundational viability of necklace–lens MQS communication and motivates future research on power-efficient transceiver integrated circuits (ICs), ocular-compatible coil fabrication, and full system co-integration for AR, VR, and health-monitoring applications.

Theoretical framework for resonant MQS coupling

Weakly coupled coil systems

An alternating current loop induces an electromotive force in a nearby conductor via its magnetic field. Its strength and the induced flux fall with coil size, separation, misalignment, and the surrounding medium. Greene’s refined near-zone model for small circular loops (Greene, 1967) and Simpson’s exact solution for any circular loop (Simpson et al., 2001) capture these dependencies, accounting for frequency, propagation delay, and finite radii. As illustrated in Figure 1b, the resulting field lines emerge perpendicular to each coil’s plane, extend axially through the center, and curve back near the conductors, even when the Tx and Rx coils are laterally offset.

For a weakly coupled pair, path loss in Equation 1 depends on the coupling factor (k) between the coils; separation distance given in Equation 2; alignment: axial (d z), lateral (d x,d y), and angular (θ); and operating frequency (ω). The properties of the coil, such as its inductance (L Tx, L Rx), quality factor (Q Tx, Q Rx), and parasitic capacitances, contribute to the coupling factor between the coils.

Greater dimensional mismatch lowers k defined in Equation 3:

Because k is determined by the mutual inductance M as in Equation 4, it ultimately depends on each coil’s self‐inductance (Waters et al., 2014). For flat spiral coils, L is given by the modified Wheeler expression (Hussain and Woo, 2021), varying with the inner/outer diameters, conductor width, and number of turns.

The arbitrarily aligned coil model of Golestani and Moghaddam (2018) provides the mutual inductance and hence the coupling coefficient for the misaligned link, in simplified form: where ϕ T x is the flux from the Tx that threads the Rx coil given by Equation 6. where S R x is the Rx coil area, and B T x = μ H T x is the Tx’s flux density. Closed-form expressions for M that incorporate coil position, angular misalignment, frequency, geometry, separation, and medium are detailed by Golestani and Moghaddam (2018).

The voltage transfer ratio between the Tx and the Rx can be calculated using Equation 6.

The total power at the Rx (P Total) is a function of Equation 7.

Factors affecting MQS coupling

Coil dimensions

The number of turns, coil radius, wire diameter, and wire spacing change the coupling coefficient between the Tx and the Rx. Similar-sized coils have higher coupling efficiency than coil systems with widely varying diameters. As the number of coil turns increases, the coupling between the coils increases, but further increases reduce efficiency due to increased parasitic capacitance between the wires. As the coil’s radius decreases, the concentration of magnetic field lines decreases, leading to lower coupling. Variations in the coil radius and the number of turns alter the inductance, series resistance, and parasitic capacitance of the inductor, thereby affecting the overall impedance and the quality factor of the circuit.

Alignment

Link efficiency peaks when coils are similar in size and perfectly coaxial. In practice, the necklace Tx tilts with the chest, while the lens-mounted Rx sits far away, fixed to the eye’s axis. These unavoidable lateral, axial, and angular offsets limit coupling. The following sections quantify how such misalignments and required coil sizes affect performance and demonstrate that the proposed MQS link retains adequate margin under typical head and body motion.

Source and load resistances

In Figure 2, R Source represents the effective internal resistance of the transmitter side, which includes the resistance of the voltage source as well as any series resistance from the transmitter coil and its driver circuitry. It governs the current supplied to the transmitter coil; hence, lowering R Source increases the coil current, strengthens the magnetic field, and increases the power transfer to the receiver, albeit at the cost of higher source power consumption. On the receiver side, R Load denotes the effective resistance of the load connected across the receiver coil after the tuning capacitor C R x. This parameter models the power-consuming device or circuit that extracts energy from the induced signal. Increasing R Load leads to a higher voltage developed across the receiver coil for a given induced current, which is advantageous for communication where a larger received voltage is desired. However, it reduces the current drawn at the receiver.

Resonant MQS coupling

Figure 2 shows the equivalent resonant MQS link. The transmitter comprises a flat spiral inductor L T x, tuned to the operating frequency by a series capacitor C T x and driven by a 1 V sinusoid V Source through a source resistor R Source that sets the coil current. The receiver uses a geometrically smaller spiral L R x with a tuning capacitor C R x chosen to satisfy Equation 8 thereby aligning both resonance peaks. The induced voltage is taken across the load resistor R Load as V R x. Additional high-frequency peaks arise from each coil’s self-resonance, where parasitic capacitance turns the spiral into a short monopole antenna.

Choice of operating frequency and MQS validity

The necklace–lens link is intentionally designed to operate in the sub-30 MHz magnetoquasistatic (MQS) regime. For the largest coil dimension (approximately 15 cm necklace diameter) and maximum necklace–eye separation (approximately 15 cm), the wavenumber‐ radius product is given by Equation 9 at 26.8 MHz, where λ ≈ 11 m in free space. Under this condition, the field remains in the reactive near field, radiation is negligible, and the coils are electrically small, so the coupling is predominantly magnetic, and standard MQS criteria are satisfied.

In practice, we first designed the Tx/Rx inductors and tuning capacitors for a target resonance of approximately 25–26 MHz. When the realized coil geometries, parasitics, and surrounding structures are included in the full-wave High-Frequency Structure Simulator (HFSS) model, the resonance of the complete link appears at 26.8 MHz. Thus, 26.8 MHz is not a uniquely optimized frequency; it is the measured resonance of our proof-of-concept implementation within the intended 20–30 MHz band. Any carrier in this sub-30 MHz range with similar coil geometry and tuning and operating well below the intrinsic self-resonance of the spirals is expected to exhibit the same qualitative behavior (near-field coupling, tissue transparency, link robustness, and SAR levels) reported in this work.

Finite-element analysis (FEA) simulation setup

A two-coil inductively coupled system is considered wherein the Tx coil is embedded in a necklace, and the Rx spiral is integrated along the rim of the contact lens, enabling a seamless experience. The coil diameters are chosen according to the necklace and contact lens dimensions. The number of turns of the coils is fixed such that maximum coupling (higher received voltage) occurs, considering the parasitic capacitance and the quality factor of the inductors.

Figure 3 illustrates the HFSS model. A cubic air domain bounds the problem, with a simplified muscle-eye phantom centered within. The simple human body model is intentionally chosen to capture the dominant electromagnetic effects of the wearer while keeping the parameter space tractable. In the MQS regime and frequency range considered here (sub-30 MHz), the coupling between the necklace and SCL coils is predominantly magnetic, and biological tissues have magnetic permeability very close to that of free space (μ r ≈ 1).

Consequently, the external magnetic field and mutual inductive coupling are only weakly perturbed by the presence or detailed composition of the body and are instead dominated by the coil geometries and their relative separation and orientation. This behavior is consistent with prior studies on inductive wireless power transfer, in which the human body is often neglected in the computation of the source magnetic field because it behaves as a poor conductor and does not significantly disturb the magnetoquasistatic field (Maity et al., 2020). In our simulations, we therefore use a homogeneous muscle phantom for the torso and layered ocular/eyelid tissues to represent the wearer, while explicitly sweeping necklace–lens separation and misalignment to account for postural variations.

A Tx flat spiral is wrapped around the neck, while a miniature Rx spiral is embedded along the contact lens rim. Each spiral is treated as an inductor port. The Tx port is driven by a 1 V, 26.8 MHz sinusoid through a series source resistor and tuning capacitor C T x; omitting C T x renders the link non-resonant. The Rx port terminates in a series tuning capacitor C R x and load resistor R Load, across which V R x is measured. The equivalent circuit diagram is shown in Figure 2, where the flat spiral coil is depicted in the form of inductors.

Human body and tissue modeling

To conform to the corneal curvature, the Rx spiral is implemented as a five-turn helical coil that wraps the contact lens rim, as seen in Figure 4); its inner radius, wire diameter, and turn spacing remain identical to the planar geometry of Figure 3b, so the change in self-inductance is negligible. The ocular phantom includes cornea, aqueous humor, lens, and vitreous humor (Zada et al., 2021). The aqueous layer is assigned the high conductivity of cerebrospinal fluid (CSF) to test worst-case magnetic absorption. An additional skin sheet is added over the coil to emulate the eyelid for the closed-eye scenario. These open- and closed-eye configurations are later used to quantify the impact of blinking and transient eyelid coverage on the resonant MQS link, allowing us to directly evaluate whether eyelid motion perturbs the channel.

In all HFSS simulations, the necklace and lens coils are modeled as copper traces with fixed cross-sections, primarily to capture the dominant electromagnetic behavior (field distribution, coupling, and link budget) using an idealized, high-conductivity material. In practice, these coils can be realized using thin-film, biocompatible, and/or encapsulated conductors (e.g., Au, Pt, parylene-packaged thin-film metals, or stretchable liquid-metal/composite traces) on soft ocular substrates, as demonstrated in prior smart contact lens and intraocular coil platforms (Mahmud et al., 2022; Kim et al., 2017; Zhang et al., 2022; Li et al., 2006; Park et al., 2018). As resonant MQS coupling is largely determined by coil geometry, inductance, and series resistance, we expect comparable channel performance when replacing copper with such flexible, ocularly compatible conductors, with only modest changes in quality factor. The necklace transmitter is tilted to match a natural hanging angle, whereas the Rx coil is normal to the eye surface; their relative orientation varies with head and body motion. This study fixes both coils at five turns and sweeps the Tx tilt to quantify its impact on the received voltage.

Communication channel analysis

Channel capacity of the resonant communication channel is evaluated with the Shannon–Hartley theorem given by Equation 10: where BW is the 3-dB bandwidth of the resonant link and SNR is the voltage signal-to-noise ratio at the receiver.

In this work, we use Equation 9 to estimate a theoretical upper bound on the information rate of the necklace–lens MQS link under the following simplifying assumptions: (i) a fixed input-referred noise floor of − 85 dBV over the considered bandwidth, (ii) noise dominated by the thermal noise of the front-end transconductor, (iii) ideal matching between the Rx coil and the receiver input with negligible implementation loss, and (iv) absence of in-band interference. The resulting capacity values should therefore be interpreted as best-case benchmarks for the channel, rather than guaranteed data rates for a particular receiver IC implementation.

The dominant noise source is the thermal noise of the front-end receiver circuit that senses the Rx coil. Its input-referred rms voltage is v n, as shown in Figure 5, evaluated at 300 K with channel length modulation factor, γ ≈ 0.67 for long-channel devices, Δ f = B W, and g m is the device transconductance. Taking − 85 dBV as a conservative design target for the input-referred noise floor, larger g m values (or a narrower bandwidth) would push the floor below − 90 dBV, as indicated by the curve in Figure 5. Table 1 summarizes the simulated link budget. As the coils’ quality factors (Q) are gradually lowered, the − 3 dB bandwidth widens, and the peak signal level drops, yet the net effect is an increase in channel capacity.

A 12 dB reduction in received signal (from − 50 dBV to − 62 dBV), combined with a fourfold bandwidth expansion (from 0.25 MHz to 1 MHz), increases the achievable data rate from 1.3 Mbps to 4.6 Mbps. Pushing to 2 MHz bandwidth yields nearly 5 Mbps data rate, which is sufficient for compressed 480p/15 fps video or multi-sensor biomedical telemetry, while still maintaining a comfortable 13 dB SNR margin above the − 85 dBV noise floor under the idealized assumptions listed above.

In practice, smart contact lens receivers operate under stringent silicon-area and power constraints, which limit the achievable transconductance g m and therefore the minimum attainable input-referred noise. For a Metal-Oxide Semiconductor (MOS) transconductor in strong inversion, the thermal voltage-noise density scales approximately as v n 2 ̄ ∝ 1 / g m, so further suppressing the noise floor requires proportionally larger g m and hence higher bias current and power consumption. For ultra-low-power, on-eye ICs operating from a sub-1 V supply and targeting sub- mW (or sub-100 μ W) power budgets, these constraints may raise the effective noise floor by several dB relative to the − 85 dBV reference used here.

Additional non-idealities, such as imperfect matching, circuit implementation losses, and in-band interference, will also degrade SNR and reduce the realizable data rate below the Shannon–Hartley limit. Nevertheless, even with a modest increase in effective noise floor, the link budgets in Table 1 indicate that multi-Mbps data rates at 10–15 cm separation remain feasible when the MQS link is combined with a carefully optimized, low-power receiver IC. A full co-optimization of the Rx architecture, biasing strategy, and link design is left for future work.

MQS versus resonant MQS coupling

Figure 6 compares the necklace-to-lens link when the Tx spiral is (i) driven directly from the source resistor (non-resonant MQS) and (ii) series-tuned with C T x so that both coils resonate at 26.8 MHz (resonant MQS). Resonance lifts the received voltage by roughly 35 dB, pushing the signal more than 30 dB above the −85 dBV front-end noise floor adopted earlier. The loaded −3 dB bandwidth of the tuned link is ≈ 250 kHz but may be broadened to 1 MHz by lowering the coil Q (for 3 dB to 4 dB extra loss), a trade-off we exploit later to achieve 4 Mbps to 5 Mbps channel capacities. Thus, capacitive tuning is essential: it recovers tens of decibels of link budget and provides bandwidth to meet high data rate AR/VR requirements.

Presence of human tissues

The coils are subjected to several media to observe the effect of body tissues on the channel response between the Tx and the Rx coils. The coils are freely suspended in the air without any human body model, then the Tx coil is wound around the head and body model made up of the muscle tissue, and the Rx coil is attached to the eye tissues, as shown in Figure 4ii. To simulate the case for closed eyes, the eyelid, made up of skin, is placed on top of the Rx coil; Figure 4iii.

Figure 7a compares frequency sweeps for four cases: non-resonant coils in air, and resonant coils in (i) free space, (ii) muscle and eye tissues, and (iii) muscle and eye tissues with an added skin layer to emulate a closed eyelid. The received voltage is virtually identical in all three resonant cases, confirming negligible tissue absorption. The vector plots in Figure 7b, taken at the 26.8 MHz resonance, show nearly overlapping magnetic field distributions. This behavior stems from the unity relative permeability of body tissues (μ r ≈ 1), which leaves the sub-30 MHz MQS field largely undisturbed (Nath et al., 2022). The tissues only weakly perturb the magnetic field, introducing a relatively small additional attenuation. This weak dependence of the magnetic coupling on the presence of torso and facial tissues supports the assumption that, at 26.8 MHz, the human body is largely magnetically transparent, and that anatomical variability mainly affects the link through changes in Tx–Rx separation and orientation rather than through strong perturbations of the H-field itself.

Physically, this behavior arises because the relative magnetic permeability of soft tissues is approximately unity (μ r ≈ 1), so the tissues neither shield nor concentrate the magnetic flux. At the same time, the tissue conductivity is not negligible at 26.8 MHz, and eddy currents can lead to ohmic loss. These conductive effects are already included in the complex permittivity tissue models used in the HFSS simulations and account for the small but finite reduction in the received voltage when tissue layers are added. The observed differences between the no-tissue, open-eye, and closed-eye cases therefore represent the net impact of both permeability (μ r ≈ 1) and conductivity (σ ≠ 0) in this frequency regime. Importantly, the negligible difference between open- and closed-eye configurations indicates that blinking and transient eyelid coverage do not significantly degrade the MQS coupling; that is, the communication channel is effectively transparent to the surrounding ocular and eyelid tissues at the chosen operating frequency.

Robustness of the proposed system

As mentioned in the previous sections, the coils would be highly misaligned in the proposed modality for enabling efficient communication in SCLs with a resonant MQS-coupled system. This work examines the feasibility of such a system and determines the maximum achievable communication channel efficiency to enable AR/VR on contact lenses. The axis of the Rx coil is always considered perpendicular to the Tx.

As the Tx coil is wound like a necklace, its orientation can vary due to body motion, and its spacing from the eye varies from one wearer to another, potentially inclining at different angles rather than remaining fixed. Similarly, the perpendicular axial distance and the lateral shift between the Tx and the Rx coil will vary across individuals depending on their body structure and dimensions. Figure 8a shows the various misalignment positions used to sweep across for checking the variation in channel capacity. xEye = 92 mm, zEye = 150 mm, and Tx angle = 40 ° are the ideal positions and orientations for the coils. Some coil positions are unrealistic for the proposed system, but they can still be used to analyze misalignment in inductively coupled systems.

Angular misalignment

The Tx inclination angle ranges from 0 ° (parallel to the ground) to 90 ° (perpendicular to the ground). While having the coil completely parallel or perpendicular to the ground is not optimal, angles within the range 20 ° to 60 ° exhibit a variation of approximately 8 dB. For a circular necklace, an angle of 40 ° has been deemed optimal across all simulations to demonstrate the feasibility of wireless power transfer between a necklace and a contact lens.

Figure 8b shows the variation of channel capacity at 26.8 MHz concerning the angular misalignment of the Tx coil. Even with a 10 dB variation in the received signal level, the channel capacity does not fall below 4.5 Mbps with the minimum bandwidth considered.

Lateral misalignment

For the lateral movement of the Rx, the channel capacity is measured in cases when the Tx coil is inclined at angles 0 ° and 40 °. Note that the theoretical bit rate remains above 4.5 Mbps as shown in Figure 8c, indicating robustness. The chosen range is 60–140 mm to show variations in human dimensions for coil coupling.

Axial misalignment

The coupling between the axially aligned coils increases as the distance between them reduces. However, the magnetic field lines tend to couple less strongly when their axes are perpendicular. In Figure 8d, all three misalignments are taken into consideration. For xEye = 0 mm (not practical), the field lines coupled eventually reduce as the distance between the coils increases, while for xEye = 92 mm, the bit rate decreases almost linearly. The variation in the Tx angle is not dominant in this plot. Hence, the channel is robust for realistic scenarios with a bit rate of over 4.5 Mbps.

Varying impedances for dual-mode operation

Source impedance, comprising the driver’s output resistance and the interconnect, sets the transmit coil current. Load impedance at the Rx determines the voltage developed across the coil for signal measurement.

Effect of source impedance

Increasing the source resistance R Source limits the current in the Tx coil, weakens the magnetic field, and lowers the induced signal at the receiver. Conversely, a smaller R Source delivers a higher V R x and thus a larger SNR. Figure 9 quantifies this trade-off at the 26.8 MHz resonance: reducing R Source from 1 k Ω to 50 Ω increases the received voltage by nearly 20 dB. The downside is higher transmitter power consumption, approximately 10 mW for a 1 V sinusoidal drive when R Source = 50 Ω. This 10 mW operating point is used as a conservative design example in this study; its implications for receiver power and link-level energy efficiency are discussed in Section 3.5, and its safety implications for ocular exposure are discussed in Section 3.6.

The Tx side of the link can be approximated by a series-resonant RLC network consisting of the necklace coil inductance L Tx, its series resistance R coil, the source resistance R s, and the tuning capacitor C Tx. Around the operating resonance ω 0 = 1 / L Tx C Tx, the input current is given by Equation 11 where V s is the source voltage. At resonance, the reactive terms cancel, and the current magnitude simplifies to Equation 12 where R eq captures any additional series resistance due to loading and matching. The loaded quality factor of the Tx resonator can then be written as Equation 13 and the corresponding − 3 dB bandwidth is approximately given by Equation 14

These expressions highlight that increasing the source resistance R s reduces the coil current at resonance (Equation 11), thereby lowering the transmitted magnetic field and received signal, while also reducing the loaded Q and widening the bandwidth. Conversely, a smaller R s increases | I Tx, res | and Q L,Tx, leading to higher peak link gain but a narrower bandwidth.

Effect of load impedance

Increasing the load resistance R Load increases the voltage across the receiver coil, thereby boosting the SNR. As shown in Figure 9, V R x increases sharply with R Load and begins to plateau once R Load exceeds approximately 200 Ω; beyond this point, additional resistance offers little further gain. Accordingly, a high R Load is chosen in the subsequent analyses to maximize voltage-mode communication performance.

Receiver power budget and link energy efficiency

The preceding sections focused on the electromagnetic link budget and the transmitter-side power required to sustain a multi-megabit channel (e.g., a conservative 10 mW operating point in Section 3.4.1). Here, a first-order estimate of the receiver side power budget on the smart contact lens and the resulting link-level energy efficiency is provided.

A minimal receiver chain on the SCL would include the lens coil and tuning network, a low-noise front-end to sense the induced voltage, a simple demodulator (e.g., non-coherent OOK/FSK), clock/data recovery, and a small digital block for framing and interfacing to local sensors. Ultra-low-power NFC and near-field receivers in the MHz to sub-GHz range typically report total power in the tens to a few hundred microwatts for Mbps -class data rates. By analogy, we assume a plausible SCL receiver power budget in the range of P Rx ≈ 50 - 200 μ W for the 4.5–5 Mbps channel considered here.

At 5 Mbps, this corresponds to a receiver energy per bit of approximately given by Equation 15 which is compatible with reported budgets for ultra-low-power short-range links. In contrast, for the conservative 10 mW transmitter power used in this study, the transmitter-side energy per bit is given as Equation 16 indicating that, at this operating point, the overall link energy efficiency is dominated by the external transmitter rather than the lens-side circuitry.

It is important to emphasize that 10 mW is an upper-bound design point chosen to demonstrate the robustness of the MQS channel under realistic misalignment and tissue-loading conditions. In practice, the average transmit power can be reduced by optimizing coil geometry and Q, impedance matching, modulation/coding, and employing duty cycling or adaptive power control that tracks the instantaneous channel gain. A full custom-IC design and detailed power optimization of the SCL receiver are beyond the scope of this work, but these back-of-the-envelope estimates show that (i) a receiver power budget in the tens to a few hundreds of microwatts on the contact lens is feasible, and (ii) the proposed MQS link can support such a receiver while leaving ample margin to reduce transmitter energy per bit in future, co-optimized implementations.

Safety considerations and SAR estimate

The necklace–lens link operates in the MQS regime at 26.8 MHz, where the coupling is predominantly magnetic, and the electric fields in tissue remain relatively weak. In this frequency range, the relative permeability of ocular and facial tissues is effectively that of free space (μ r ≈ 1), and the fields are largely reactive. As shown in Section 3.2, the presence of eye and muscle tissues, as well as an added skin layer to emulate a closed eyelid, produces a negligible change in received voltage and magnetic field distribution, indicating that only a small fraction of the transmitted power is actually dissipated in tissue. Most losses occur in the coils and matching networks rather than in the biological medium.

To provide a conservative bound on safety for the 10 mW operating point used in Section 3.4.1, we consider a worst-case scenario in which the entire 10 mW is absorbed in a 10 g tissue volume in the orbital region. In that limit, the local specific absorption rate (SAR) is estimated in Equation 17 whereas international ICNIRP/IEEE-based guidelines specify a localized SAR limit of 2 W/kg averaged over 10 g of tissue for head and torso exposure to the general public (Limits, 2019; International Commission on Non-Ionizing Radiation Protection (ICNIRP), 2020). Thus, even under this pessimistic assumption, the estimated SAR is at least a factor of two (i.e., approximately 3 dB) less than the allowable limit.

In practice, the absorbed power near the eye will be significantly smaller than 10 mW because (i) the link budget shows substantial attenuation between the necklace Tx and the SCL Rx, and (ii) the reactive near field ensures that most of the power is either stored in the field or dissipated in conductive structures rather than in tissue. The 10 mW value should therefore be interpreted as an upper-bound design point for exploring link robustness and channel capacity.

In a practical implementation, the required transmit power can be further reduced by optimizing the coil geometry, impedance-matching networks, and modulation/coding schemes, and by exploiting duty cycling or adaptive power control based on instantaneous channel conditions. A comprehensive, standards-compliant safety evaluation will be carried out in future work, using anatomically realistic eye/head phantoms and full-wave simulations to compute peak spatial-average SAR (over 1 g and 10 g) and steady-state temperature increases under long-term operation. These studies will ensure compliance with both SAR and thermal limits for ocular exposure and may further refine the allowable transmit-power envelope for continuous use of smart contact lenses.

Experimental validation

To provide experimental support for the simulation-based feasibility study, we implemented a benchtop prototype of the necklace–lens MQS link (Figure 10). The Tx coil is a single-turn loop with an outer diameter of approximately 20 cm and a conductor thickness of approximately 1.2 mm. The Rx coil is a four-turn spiral with an outer diameter of approximately 1 cm, turn spacing of 0.05 mm, and conductor thickness of approximately 0.2 mm, representing a contact-lens-scale receiver. Figures 10a,b show photographs of the setup in air and with a tissue phantom (pieces of meat) filling the space between the coils.

Both coils (Figure 10c) are tuned to resonate near 26 MHz using discrete capacitors. On the Tx side, a capacitor C Tx ≈ 100 pF is placed in series with the coil. On the Rx side, a capacitor C Rx ≈ 150 pF is placed in series with the Rx coil. As summarized schematically in Figure 10d, the Tx path consists of a function generator followed by a voltage buffer (to prevent generator loading) that drives the series combination of the Tx coil and C Tx. The Rx path consists of the Rx coil in series with C Rx and directly connected to a handheld TinySA spectrum analyzer. A 200 mV pp sinusoidal input is applied at the Tx, and the frequency is swept from 22 MHz to 30 MHz while the received spectrum is recorded at the Rx. An example measured spectrum is shown in Figure 10e, from which a 3- dB bandwidth of approximately 0.8 MHz at approximately 26 MHz is extracted.

To emulate a challenging necklace–eye configuration, the Tx coil is tilted by approximately 45 ° with respect to the horizontal plane, and the Rx coil is placed approximately 18 cm vertically above the Tx and laterally offset by roughly 5 cm. Under these strongly misaligned conditions, the measured response exhibits a clear resonance near 26 MHz, with an overall channel loss of approximately 60 dB at resonance. This is consistent with the link budgets predicted by HFSS simulations for comparable coil dimensions and misalignment and confirms that MQS-coupled communication is feasible at tens of MHz over necklace–eye scale distances, even in adverse geometries. Figure 10f plots the measured peak channel gain versus vertical separation d V for both air and tissue-phantom cases; the loss remains in the range of roughly − 56 to − 44 dB as d V increases from 18 cm to 28 cm.

To assess the impact of intervening tissue, a simple human tissue phantom was introduced between the coils, using animal meat with dielectric properties similar to those of human soft tissue at the operating frequency. When the phantom is placed between the Tx and Rx coils, the measured channel loss changes only slightly (within a few dB) across the frequency sweep and for all separations, indicating that the presence of tissue-like material has minimal effect on the magnetic coupling at 26 MHz. This observation is consistent with the magnetoquasistatic analysis and full-wave simulations presented earlier, which predict that biological tissues with μ r ≈ 1 are largely magnetically transparent and that coupling is dominated by the coil geometry and relative position/orientation. The corresponding peak received signal levels, assumed TinySA noise floor (− 94 dBm), resulting SNR, measured 3-dB bandwidth, and estimated theoretical channel capacities are summarized in Figure 10g.

These benchtop measurements are not intended as a fully integrated smart contact lens implementation, but they provide experimental evidence that supports the key claims of this work: (i) MQS coupling can sustain communication over necklace–eye distances with substantial misalignment and (ii) the presence of tissue-like material does not significantly degrade the link in the considered frequency band.

This work presents a magnetoquasistatic (MQS) resonant link for high-data-rate communication with a smart contact lens (SCL), based primarily on analytical modeling and full-wave Ansys HFSS simulations, and supported by a benchtop prototype. The proposed system pairs a 15- cm Tx coil with an 8- mm Rx coil on the lens rim, achieving a worst-case simulated link gain of approximately − 55 dB and a channel capacity of approximately 5 Mbps over a 1 MHz bandwidth. This performance is maintained in simulation while tolerating 15 cm axial gaps, 9 cm lateral shifts, and arbitrary angular misalignments. Because human tissue exhibits free-space-like permeability below 30 MHz, the simulated link metrics remain essentially unchanged when realistic head-and-neck phantoms are included, and the required transmit power is only on the order of 10 mW. Compared with prior inductive SCL links confined to coaxial, sub-5 cm separations, these results substantially extend the simulated communication envelope. A simple experimental setup with macroscopic necklace and lens scale coils, operated near 26 MHz and tested under strong misalignment and with a tissue phantom, qualitatively confirms that MQS-coupled communication is feasible at necklace–eye distances and that intervening tissue has only a modest impact on the channel loss. Together, these findings support the conclusion that, for the considered geometry and frequency range, the communication channel itself is unlikely to be the primary limiting factor for SCL-based AR/VR and sensing applications. A comparison of the proposed approach with prior work on communication to smart contact lenses is summarized in Table 2.

Looking ahead, translating this physical-layer feasibility into a deployable SCL platform will require addressing several system-level challenges. First, the Rx/Tx Application-Specific Integrated Circuits (ASICs) must be co-designed with the coils under stringent constraints on silicon area, supply voltage, and power, balancing front-end noise performance, matching, and link-layer protocols to fully exploit the demonstrated multi-Mbps channel. Second, while our simulations and initial measurements indicate that the induced fields and SAR levels are comfortably below international exposure limits for the operating conditions considered, any productization will require formal compliance testing and certification against established SAR and safety standards using standardized anatomical phantoms. Third, long-term environmental stability in the ocular environment, including exposure to tear fluid, repeated blinking, and the risk of corrosion or delamination of thin-film conductors, will necessitate careful materials selection, encapsulation, and reliability studies. These aspects are beyond the scope of the present work but constitute important directions for future research. Within this context, MQS field coupling emerges as a practical backbone for “Eyes Up, Hands Down” AR/VR overlays, continuous biomarker streaming, and gaze-based interfaces, and provides a solid physical-layer foundation for future “PC-on-the-eye” smart contact lens systems.