Nonreciprocal Absorption & Emission

Updated 4 August 2025

Nonreciprocal Absorption and Emission is a phenomenon where light absorption and emission differ in direction, spectral content, and polarization due to broken time-reversal symmetry.
The topic explores the use of nonlinear excitation, synthetic gauge fields, and material anisotropies to achieve directional control in plasmonic, photonic, and atomic systems.
These principles enable innovative applications in thermal management, quantum information routing, and energy harvesting through tunable and selective optical responses.

Nonreciprocal absorption and emission describe scenarios in which the rates or characteristics of electromagnetic energy uptake (absorption) and release (emission) by a physical system differ depending on the direction, spectral content, polarization, or excitation pathway, thus violating standard reciprocity relations such as Kirchhoff’s law or Einstein’s symmetry between stimulated absorption and emission. Nonreciprocity in these optical processes is achieved by breaking time-reversal symmetry, employing nonlinear excitation, implementing synthetic gauge fields, or exploiting material anisotropies and topological effects. The resulting nonequivalence between directional absorption and emission underpins a hierarchy of fundamental physical phenomena and technologies, including tunable optical antennas, single-photon routers, thermal photon control, and novel energy-harvesting and sensing architectures.

1. Fundamental Principles of Reciprocity and Mechanisms for Breaking It

Conventional optical reciprocity stems from Lorentz reciprocity and time-reversal symmetry, dictating that absorption and emission processes are symmetric regarding direction, polarization, and frequency. This symmetry is epitomized by Kirchhoff’s law: emissivity $e(\omega, \theta, \rho) = \alpha(\omega, \theta, \rho)$ for a given frequency $\omega$ , angle $\theta$ , and polarization $\rho$ in local equilibrium. In quantum transitions, reciprocity ensures equality of stimulated absorption and emission coefficients between two states.

Nonreciprocal absorption and emission arise when time-reversal symmetry is fundamentally broken. This may be accomplished by:

Magnetic order or external magnetic fields, inducing asymmetric dielectric tensors with nonzero off-diagonal (gyrotropic or Hall) elements as in Weyl semimetals (Tsurimaki et al., 2019), magneto-optical InAs (Wu1 et al., 2021, Liu et al., 2022, Shayegan et al., 2022), and 1D magneto-optical photonic crystals (Long et al., 25 Sep 2024).
Nonlinear processes that decouple excitation and emission resonances, for example via two-photon absorption shifting plasmonic resonances versus emission in nanoantennas (Castro-Lopez et al., 2014).
Synthetic gauge fields (synthetic magnetism) or engineered dissipation in atomic systems, creating effective complex coupling terms between transitions in cyclic three- or four-level configurations (Xu et al., 2019, Xu et al., 2020, Xu et al., 2019).
The interplay of material chirality and linear anisotropy, which, when commensurate, produces direction-dependent absorption and emission of linearly polarized light even in achiral, macroscopic films (Ugras et al., 30 Jul 2025).

Mathematically, nonreciprocity manifests as $\mathbf{G}(\mathbf{r}_1, \mathbf{r}_2) \neq \mathbf{G}(\mathbf{r}_2, \mathbf{r}_1)$ for the dyadic Green’s function (photon propagator), or as $s_{12} \neq s_{21}$ for the elements of the scattering matrix, for instance in nonreciprocal scintillation (Long et al., 25 Sep 2024). In engineered photonic structures, nonreciprocal mode dispersion or resonance splitting for opposite directions underpins control over directional absorption/emission.

2. Physical Implementations: Plasmonic, Photonic, Atomic, and Material Systems

Multiple experimental platforms exemplify nonreciprocal absorption and emission:

Plasmonic Nanoantennas: Nonlinear (e.g., two-photon) absorption excites a plasmon resonance at a designated wavelength (e.g., 800 nm), but emission occurs as two-photon photoluminescence (TPPL) over a widely shifted and broadband spectrum (440–690 nm). Decoupled excitation and emission modes, modeled as orthogonal dipoles, enable tuning spatial, spectral, and polarization characteristics independently (Castro-Lopez et al., 2014).
Magneto-optical and Topological Materials: In type-I magnetic Weyl semimetals, the anomalous Hall effect produces off-diagonal dielectric tensor elements, breaking time-reversal symmetry and supporting nonreciprocal surface plasmon-polariton modes; Fermi-arc surface states further broaden response (Tsurimaki et al., 2019, Butler et al., 2023). Magneto-optical InAs films at epsilon-near-zero (ENZ) frequencies, especially when coupled to resonant photonic structures (e.g., patterned Si), exhibit very large $|\alpha-e|\,(>0.6)$ due to field-enhanced nonreciprocal modes (Wu1 et al., 2021, Liu et al., 2022, Shayegan et al., 2022).
Atomic and Circuit QED Systems: Cyclic three-level or four-level atomic schemes exploit synthetic magnetism and engineered dissipative couplings. By setting the total phase (synthetic flux) to nontrivial values, transition rates become direction-dependent, leading to pronounced asymmetry in stimulated absorption versus emission, and even complete elimination of specific spectral lines in spontaneous emission (Xu et al., 2019, Xu et al., 2019, Xu et al., 2020).
Self-assembled Cluster Films: Films synthesized from magic-size clusters of CdS, CdSe, or CdTe, with strong and comparable circular dichroism (chiral) and linear dichroism (anisotropic) responses, display nonreciprocal absorption and emission of linearly polarized light. The differential Stokes-Mueller formalism reveals that cross-terms between chiral and linear anisotropy dominate the nonreciprocal response (Ugras et al., 30 Jul 2025).

The following table summarizes representative systems and principal nonreciprocal mechanisms:

System/Platform	Symmetry Breaking Mechanism	Nonreciprocity Manifestation
Plasmonic nanoantennas	Nonlinear excitation, mode decoupling	Orthogonal excitation/emission resonances
Weyl semimetals, InAs	Magnetic order, Hall conductivity	Directional/bandwidth-tunable absorption/emission
Atomic cyclic systems	Synthetic flux, engineered loss	Directionally selective transitions, line elimination
Cluster films (CdS/Se/Te)	Chiral–linear interference	Reversible-sign linear dichroism/luminescence

3. Mathematical Formulation and Characterization

The description of nonreciprocal absorption and emission relies on careful separation of process-specific rates and directionalities:

For optical antennas, the degree of decoupling between excitation and emission is quantified by the degree of linear polarization (DoLP) and the relative strengths of orthogonal dipole moments:

$\text{DoLP} = \frac{I_\mathrm{pol,x} - I_\mathrm{pol,y}}{I_\mathrm{pol,x} + I_\mathrm{pol,y}}$

$\left(\frac{\mu_y}{\mu_x}\right) \propto \sqrt{\frac{1-\text{DoLP}}{1+\text{DoLP}}}$

allowing extraction of independently tunable emission characteristics (Castro-Lopez et al., 2014).

For atomic transition schemes, effective Hamiltonians with adjustable complex (synthetic) coupling terms $J_{ab}, J_{ba}$ receive coherent ( $\Omega$ ) and dissipative ( $-i\gamma$ ) contributions. Nonreciprocal transition is observed when, for a chosen phase $\Phi$ , $J_{ab}=0$ but $J_{ba}\neq0$ , ensuring directional selectivity in induced transitions and spontaneous emission spectra (Xu et al., 2019, Xu et al., 2020):

$\mathcal{H}_\text{eff} = (\Omega - i\gamma)|a\rangle\langle b| + (\Omega^* - i\gamma)|b\rangle\langle a|$

In thermal and photonic structures, the contrast $n=a-\epsilon$ serves as the nonreciprocity metric, where $a$ is absorptivity and $\epsilon$ is emissivity (for a specified channel), and coupled-mode theory can relate $n$ to resonance decay and coupling rates (Ghalekohneh et al., 2023):

$n = \frac{2\gamma_i (K_m^2 - d_m^2)}{(\omega - \omega_0)^2 + (\gamma_i + \gamma_r)^2}$

In fluctuational electrodynamics and polarimetry, the coherency matrix and derived Stokes parameters enable a complete description of polarization-dependent nonreciprocity:

$\mathbf{S} = \begin{pmatrix} S_0 \ S_1 \ S_2 \ S_3 \end{pmatrix} = \begin{pmatrix} \langle E_{x'}E_{x'}^*\rangle + \langle E_{y'}E_{y'}^*\rangle \ \langle E_{x'}E_{x'}^*\rangle - \langle E_{y'}E_{y'}^*\rangle \ \langle E_{x'}E_{y'}^*\rangle + \langle E_{y'}E_{x'}^*\rangle \ i(\langle E_{x'}E_{y'}^*\rangle - \langle E_{y'}E_{x'}^*\rangle) \end{pmatrix}$

Individual polarization channels can exhibit nonreciprocal behavior even as the averaged (over polarization) emissivity and absorptivity retain a generalized form of Kirchhoff’s law (Yang et al., 2022).

4. Tuning Strategies and Spectral/Spatial Engineering

Nonreciprocal absorption and emission processes are highly tunable via:

Geometrical parameter control: In plasmonic nanoantennas, emission distributions (angular, polarization, spectral) are engineered by adjusting antenna width, length, and height, thus modifying the dominant dipolar contributions (Castro-Lopez et al., 2014). In multilayer Weyl/ENZ/metal structures, the thicknesses of each layer and dielectric spacers directly set the magnitude and spectral width of nonreciprocity (Butler et al., 2023, Ghalekohneh et al., 2023).
Resonant mode engineering: Coupled cavities, particularly when supporting modes with distinct in- and out-coupling rates, allow control of both the sign and bandwidth of the contrast $n$ . Mode coupling, quality factors, and insertion of additional resonant layers (e.g., for Fabry–Perot interference) can set spectral regions of positive/negative/nonreciprocal behavior (Ghalekohneh et al., 2023).
Material and symmetry choices: Employment of magneto-optical materials with strong gyrotropy, topologically nontrivial phases (e.g., Weyl semimetals), or combination of broken inversion and time-reversal symmetries (e.g., as in magnetophotonic Fibonacci structures) enables omnidirectional and broadband nonreciprocity (Tsurimaki et al., 2019, Wu1 et al., 2021).
Synthetic phase and drive control in atomic/circuit systems: The phase of external driving fields (“synthetic flux”) is the key variable in cyclic-level schemes for gating nonreciprocal transitions and suppressing or enhancing selected emission lines (Xu et al., 2019, Xu et al., 2019, Xu et al., 2020).

5. Experimental Evidence and Characterization Techniques

Nonreciprocal absorption and emission have been quantified by:

Polarization-resolved and angular-resolved emission spectroscopy: Mapping DoLP variation, angular/Fourier plane imaging, and polarization-resolved spectra directly visualize the decoupling and orthogonality of excitation vs. emission modes in nanoantennas (Castro-Lopez et al., 2014).
Microwave and spin-wave measurements: In magnetically engineered bilayers, time- and frequency-domain nonreciprocity factors as high as $\sim$ 14 (amplitude) and $\sim$ 60 (frequency) have been measured via pulsed and frequency-resolved inductive detection of spin waves (Kwon et al., 2016).
Fourier-transform infrared and magneto-Kerr setups: Direct measurement of $|\alpha-e|$ anisotropy under moderate magnetic fields in ultrathin ENZ films confirms violations of Kirchhoff’s law beyond the single-band regime; broadband and angularly tunable contrast has been demonstrated (Liu et al., 2022).
Mueller-matrix polarimetry: Complete mapping of absorption and emission Mueller matrices, combined with sample flipping, reveals the predicted nonreciprocal signatures arising from interference of chiral and linear anisotropies (Ugras et al., 30 Jul 2025).
Spectral mapping in multilayer photonic crystals: Absorption and emission differences up to 0.9 at specific wavelengths and angles resulting from Tamm plasmon polariton localization in quasi-periodic Fibonacci structures are resolved via field mapping and spectral analysis (Wu1 et al., 2021).

6. Applications and Impact

Nonreciprocal absorption and emission enable a diversity of technologically relevant and fundamental phenomena:

Nanoscale light sources and signal transducers: By decoupling excitation and emission, nanoantennas with engineered nonreciprocity provide tailored sub-diffraction light sources, nonlinear transducers, and wavelength/polarization multiplexers (Castro-Lopez et al., 2014).
Thermal photon management and energy harvesting: Breaking Kirchhoff’s law allows for structures that strongly absorb solar/thermal radiation but emit little, surpassing intrinsic energy conversion efficiency limits (e.g., approaching Landsberg or Carnot limits in photovoltaics and thermophotovoltaics), and enables advanced heat circulators and persistent heat current devices (Tsurimaki et al., 2019, Liu et al., 2022, Ghalekohneh et al., 2023, Picardi et al., 9 May 2024).
Quantum information routing and chiral transport: In quantum networks, nonreciprocal devices based on atomic or superconducting circuit schemes act as single-photon routers, isolation elements, or photon transducers, essential for directionally controlled quantum state transfer and noise mitigation (Wang et al., 2019, Xu et al., 2019).
Directional sensing and chiral analysis: Selective elimination of emission lines in nonreciprocal multi-level systems allows enantiomeric excess determination in chiral mixtures without the need for enantiopure reference samples (Xu et al., 2019).
Magnetic and topological photonic components: Devices such as nonreciprocal isolators, circulators, or one-way scintillators (for enhanced radiation detection) are enabled by strongly gyrotropic or topological materials with nanophotonic structuring (Long et al., 25 Sep 2024).

7. Outlook and Future Directions

Emerging research seeks to advance nonreciprocal absorption and emission through (i) the development of pattern-free, polarization-independent transmission-mode architectures compatible with high-efficiency, tandem light-harvesting (Picardi et al., 9 May 2024); (ii) engineering of ever-broader bandwidth and angle tolerance by optimizing mode interference and materials platforms (Butler et al., 2023); (iii) directional and polarization-multiplexed photonic logic using scalable, solution-processed films leveraging chiral-linear interference (Ugras et al., 30 Jul 2025); and (iv) extension of fluctuational electrodynamics to multipolar, non-equilibrium, and quantum regimes incorporating full polarimetric analysis (Yang et al., 2022). Control over the sign, spectral width, and magnitude of nonreciprocal contrast at arbitrary wavelengths and angles is now possible via mode coupling, phase engineering, and symmetry design (Ghalekohneh et al., 2023, Picardi et al., 9 May 2024).

A plausible implication is that as theoretical control over synthetic magnetism, strong topological phases, and advanced polaritonic platforms improves, future devices may achieve dynamic, programmable nonreciprocity using on-chip, voltage, or field gating—facilitating integration into active photonic, quantum, and energy-harvesting circuits. The intersection of nonreciprocal photonics with quantum excitation transport, polarization-selective emission, and thermal engineering will likely establish new technological paradigms in directional information processing, sensing, and renewable energy conversion.