Near Total Faraday Rotation in 2DEGs

• Near Total Faraday Rotation is the phenomenon where the polarization plane rotates nearly 90° in a single pass through a high-mobility 2DEG system.
• It leverages inertial electron dynamics and classical Hall conductivity under low magnetic fields to yield an 82° rotation with minimal dissipative losses.
• Engineered electromagnetic mode coupling via waveguide and conducting iris configurations enables tunable, nearly lossless non-reciprocal optical response.

Near total Faraday rotation refers to the regime where the polarization plane of electromagnetic radiation is rotated by an angle approaching or reaching 90° (π/2 radians) upon a single traversal through a material or structured environment. This phenomenon represents an extreme limit of magneto-optical rotation, achieved when the interplay between electronic transport, electromagnetic coupling, and material geometry is optimally configured, such that nearly all input linear polarization is converted to a perpendicular direction without significant loss. In the context of high-mobility two-dimensional electron gases (2DEGs), recent research demonstrates that this regime can be realized via the classical Hall effect in the inertial, collisionless transport regime, leveraging electromagnetic mode engineering to access and sustain this near-ideal non-reciprocal optical response (Suresh et al., 6 Sep 2025).

1. Physical Principles and Regime of Operation

Achievement of near total Faraday rotation in a 2DEG system is governed by the interplay between:

• High carrier mobility and the inertial response: A 2DEG with ultrahigh mobility (μ ≈ 7×10⁶ cm²/V·s) supports a charge carrier scattering time τ such that ωτ ≫ 1 at GHz frequencies. In this limit (the "inertial, collisionless regime"), the electron dynamics are dominated by the reactive (displacement) current rather than the Ohmic conduction current, virtually eliminating dissipative losses.
• Classical Hall conductivity dominance: In the presence of a perpendicular magnetic field (B < 200 mT), the off-diagonal (σ_xy) term in the Drude conductivity tensor becomes significant:

$$\hat{\sigma} = \frac{\sigma_0}{(1 - i\omega\tau)^2 + (\omega_c\tau)^2} \begin{pmatrix} 1 - i\omega\tau & -\omega_c\tau \ \omega_c\tau & 1 - i\omega\tau \end{pmatrix}$$

where ω is the angular frequency, ω_c is the cyclotron frequency, and σ_0 is the zero-field conductivity.

• Weak radiative (capacitive) coupling: The environment, engineered by embedding the 2DEG in a hollow waveguide with a conducting iris, provides a geometrically controlled capacitive coupling. This configuration permits strong interaction with the electromagnetic field without excessive radiative damping or Ohmic absorption.

The net effect is that Faraday rotation, defined as the angle θ_F by which the polarization is rotated, is drastically enhanced. In the optimal regime (Suresh et al., 6 Sep 2025),

$$\tan\theta_F = \frac{\gamma Z \sigma_{xy}}{K + Z \sigma_{xx}}$$

Here, Z is the mode impedance, K is a coupling parameter, and γ quantifies the iris–mode transverse coupling. When $|\sigma_{xy}|\gg|\sigma_{xx}|$ and K is small (weak coupling), $\theta_F$ can approach π/2.

2. Experimental Realization and Observables

In the demonstration reported in (Suresh et al., 6 Sep 2025), near-total Faraday rotation (θ_F ≈ 1.43 rad or 82°) was measured for microwaves (9.2–11.2 GHz) traversing an ultra-high-mobility GaAs/AlGaAs 2DEG (50 nm thickness) at B-fields around 30 mT. The crucial parameters and setup include:

• Verdet constant: An extraordinary Verdet constant $V = 9.5 \times 10^8$ rad·T⁻¹·m⁻¹, exceeding other materials in the microwave and optical domains by one or more orders of magnitude.
• Single-pass geometry: The rotation was achieved on a single pass, indicating that the effect is not a result of multi-reflection buildup (as in resonators), but intrinsic to the Hall-driven response of the 2DEG within its electromagnetic environment.
• Iris/waveguide mode control: The conducting iris's size and the waveguide’s TE₁₁ doublet offer a means to realize the detuning and impedance-matched coupling conditions necessary for sustaining this effect away from absorption maxima.

The measured rotation is determined directly by the ratio of cross- and co-polarized microwave transmission amplitudes, $\tan \theta_F = S_{\perp} / S_{\parallel}$.

3. Mechanism of Enhanced and Tunable Rotation

The key mechanism enabling near-total rotation is the decoupling of Faraday rotation resonance from the cyclotron resonance (CR):

• Detuning from cyclotron resonance: In the inertial regime (ωτ≫1), the Faraday rotation maximizes not exactly at the CR field $B_c = m^*\omega / e$, but at a higher “pole” field $|B_0| = |1+\alpha|^{1/2}B_c$, where α quantifies the electromagnetic (EM) mode coupling strength.
• Suppression of dissipation: At this detuned field, the imaginary part of the complex pole in σ+ or σ- approaches zero, signifying that the resonance is no longer constrained by Ohmic losses, and the Faraday angle diverges towards π/2.
• Reactivity-dominated conductivity: For circular polarization, the inertial regime yields

$$\sigma_{\pm} = \sigma_{xx} \pm i \sigma_{xy} = \frac{\sigma_0}{i(\omega \pm \omega_c)\tau}$$

indicating absorptive (real) parts are negligible near the Faraday maximum.

Therefore, the engineered electromagnetic environment (waveguide, iris, and sample mounting) and the dynamical transport properties of the 2DEG can be finely tuned so that total Faraday rotation is achievable in the absence of strong absorption or reflection.

4. Comparison with Other Material Systems and Regimes

The reported near-total Faraday rotation stands in stark contrast to the typical results for other systems:

Material/System	Typical Verdet Constant [rad·T⁻¹·m⁻¹]	Max Rotation (Single Pass)	Regime	Reference
2DEG (GaAs/AlGaAs)	$9.5 \times 10^8$	82°	GHz, low B	(Suresh et al., 6 Sep 2025)
Graphene (THz)	$\sim 10^7$	0.15 rad (~9°)	THz, high B	(Ubrig et al., 2013)
WSe₂ monolayer	$\sim 10^7$ (optical)	<π/4 per pass	optical	[quoted in 2509]
YIG/Ferrite	$\sim 10^3 - 10^6$	<π/2 (multi-pass)	GHz/optical	historical

The achievement is enabled by the combination of ultrahigh mobility, inertial regime operation (ωτ≫1), and optimized EM boundary conditions, none of which are simultaneously present in the other systems.

5. Implications for Non-Reciprocal Device Engineering

Faraday rotation at the π/2 limit is the basis for ideal non-reciprocal optical elements: a plane of polarization rotated by 90° cannot be reversed by retracing the optical path, thus isolating input and output directions. The key implications and potential applications include:

• Ideal isolators/circulators: Devices built around such 2DEG structures can exhibit perfect non-reciprocity for linear polarizations, with low insertion loss due to suppressed dissipation in the inertial regime.
• Frequency/scalability prospects: The physical mechanism is not constrained to GHz frequencies—analogous engineering of mode coupling and collisionless transport in other frequency domains or with other high-mobility systems (e.g., Dirac materials, topological insulators) could achieve similar outcomes.
• Dynamic reconfigurability: Carrier density, scattering time, and magnetic field (even at low fields) can be tuned to modulate the rotation, enabling dynamic control crucial for next-generation magneto-optical and photonic circuits.

6. Limitations and Prospects for Further Optimization

• Material constraints: The exceptional performance relies on maintaining extremely high mobility. Disorder, impurity scattering, or finite temperature effects that reduce τ can rapidly degrade the inertial regime.
• Coupling configuration: The use of a weakly coupled iris is essential for suppressing radiative losses. Stronger coupling or mismatched geometries would lower the maximum attainable rotation.
• Extension to other systems: While the microwave demonstration is compelling, realization in other spectral regions would require either similar high-mobility 2DEGs or new material platforms with analogous dynamical and coupling characteristics.

7. Summary Table: Regime, Key Metrics, and Formulae

Regime	Expression for Faraday Rotation	Key Criterion	Rotation Limit
Drude (ωτ ≪ 1)	$\theta_F \sim VBL$	Dominant Ohmic loss	Small (order degrees)
Inertial, collisionless (ωτ≫1)	$$\tan \theta_F = (\gamma Z \sigma_{xy})/(K + Z \sigma_{xx})$$	Displacement current	Up to π/2 (90°) per pass
Resonant (B = B*)	$\sigma_{+} = \sigma_0/[i(\omega+\omega_c)\tau]$	Detuned from CR	Lossless total rotation

• Near total Faraday rotation in 2DEG: (Suresh et al., 6 Sep 2025)
• Fabry–Perot enhanced rotation in graphene: (Ubrig et al., 2013)

This state-of-the-art realization of near-total Faraday rotation demonstrates that classical Hall physics, when interfaced with engineered electromagnetic environments and with ultraclean transport, can outperform all previously known intrinsic and extrinsic magneto-optical platforms for the purpose of non-reciprocal device engineering, with broad implications across microwave, THz, and potentially optical photonic technologies.