Emitter/Absorber Asymmetry Parameter

• Emitter/Absorber Asymmetry Parameter is a measure quantifying the unequal efficiency of emission and absorption processes in systems such as nonreciprocal photonics and gravitational-wave studies.
• It is defined through precise metrics using directional radiative coefficients, spectral imbalances (with |Δ| values up to 0.63), and retarded/advanced wave mixtures in absorber theory.
• Experimental implementations using magnetized ENZ films and bilayer metagratings validate its role in optimizing device performance and probing fundamental physical symmetries.

The emitter/absorber asymmetry parameter quantifies the unequal efficiency or balance between emission and absorption processes in physical systems. This concept is central to the study of nonreciprocal photonics, topological photonic structures, thermal radiation, and foundational electrodynamics and gravitation. The asymmetry parameter manifests in various physical contexts: as a difference in directional emission in metagratings, as a spectral imbalance in nonreciprocal thermal emitters, or as a phenomenological weight between retarded and advanced solutions in absorber theory. Rigorous definitions and theoretical frameworks are provided for each of these domains.

1. Mathematical Definitions and Physical Contexts

The emitter/absorber asymmetry parameter is instantiated in several mathematically precise forms depending on the system:

• Radiation asymmetry in photonic gratings:

The complex amplitudes of upward and downward radiated fields, $C_{\rm up}$ and $C_{\rm down}$, define the directionality parameter:

$$n = \frac{|C_{\rm up}|^2 - |C_{\rm down}|^2}{|C_{\rm up}|^2 + |C_{\rm down}|^2}$$

Complementarily, the phase difference is

$\phi = \arg[C_{\rm up}] - \arg[C_{\rm down}]$

This captures the up/down asymmetry in structured photonics (Zhuang et al., 22 Jan 2024).

• Nonreciprocal thermal radiation:

For planar films, the emissivity $e(\omega,\theta)$ and absorptivity $\alpha(\omega,\theta)$ define the asymmetry parameter

$$\Delta(\omega, \theta) = e(\omega, \theta) - \alpha(\omega, \theta)$$

In reciprocal systems, Kirchhoff’s Law enforces $\Delta = 0$; for nonreciprocal cases, $|\Delta|$ can be substantial (Liu et al., 2022).

• Wheeler–Feynman absorber theory:

The field can be decomposed as

$$F(x, t) = \alpha F_{\mathrm{ret}}(x, t) + (1-\alpha) F_{\mathrm{adv}}(x, t)$$

where $\alpha$ is the emitter/absorber asymmetry controlling the mixture of retarded and advanced waves. $\alpha=1$ corresponds to pure retarded propagation; $\alpha=\frac12$ to time-symmetric solutions (Duda, 23 Dec 2025).

2. Topological and Geometric Interpretation

In bilayer metagratings, the emitter/absorber asymmetry acquires a geometric representation via a pseudo-polarization vector: $$\mathbf{c} = \frac{1}{N}\left[(C_{\rm up} + C_{\rm down})\,\mathbf{e}_1 + (C_{\rm up} - C_{\rm down})\,\mathbf{e}_2\right]$$ where $N$ normalizes the vector. Mapping the ellipse traced by $\mathbf{c}$ to the Poincaré sphere through the Stokes parameters: $$\begin{aligned} S_1 &= \sqrt{1-n^2}\cos\phi \ S_2 &= n \ S_3 &= \sqrt{1-n^2}\sin\phi \end{aligned}$$ links the directionality and phase difference to angular coordinates, enabling topological analysis of singularities (vortices and C-points) in synthetic parameter space. The charge of these defects encodes the winding behavior of asymmetry (Zhuang et al., 22 Jan 2024).

3. Experimental Realizations and Measurement Strategies

Nonreciprocal thermal radiation (magnetized ENZ films):

• Under a magnetic field, Lorentz reciprocity is violated so that reflectance and thus emissivity/absorptivity differ for emission and absorption directions.
• Experimentally, $|\Delta|$ values up to 0.63 have been demonstrated for Berreman modes in InAs at ENZ frequencies, using angle-resolved spectroscopy at $B=1.5$ T.
• The bandwidth and magnitude of $\Delta$ are engineered by adjusting film thickness, magnetic field, grating structures, and doping profiles (Liu et al., 2022).

Wheeler–Feynman absorber asymmetry parameter ($\alpha$):

• In gravitational-wave astronomy, $\alpha$ can be estimated by comparing the fraction of GW events with/without EM counterparts, the distribution of time delays $\Delta t$, and standard-siren distance-redshift consistency.
• Indirect measures utilize pulsar timing arrays’ measurements of the stochastic gravitational-wave background to constrain $\alpha$ via spectral fits.
• Preliminary findings (from neutron star mergers) place $\alpha$ in the range 0.1–0.67 depending on the channel and modeling assumptions, with large uncertainties (Duda, 23 Dec 2025).

Topological photonics:

• The pseudo-polarization vortex and its C-point decomposition are resolved by mapping the parameters ($k_x, A_g$) and tracking the winding of directionality and phase on the Poincaré sphere.
• Absorption measurements under controlled input phases ($\delta_{\rm in}$) test predictions of arbitrarily tunable perfect absorption (Zhuang et al., 22 Jan 2024).

4. Theoretical Foundations and Implications

Photonics and Kirchhoff's Law:

• In reciprocal systems, energy conservation and reciprocity guarantee $e(\omega, \theta) = \alpha(\omega, \theta)$.
• Magnetic fields or structural asymmetry break reciprocity and permit $\Delta \neq 0$, with direct technological implications for energy conversion and signal control (Liu et al., 2022).

Wheeler–Feynman absorber theory:

• The asymmetry parameter $\alpha$ relates cosmological boundary conditions (emitter and absorber densities in past and future) to the observed time-arrow in radiation.
• $\alpha$ provides a single phenomenological parameter capturing the physical arrow of time without violating underlying time-reversal or CPT symmetry of wave equations. The Ansatz $\alpha = R/(1+R)$ links the ratio of absorber to emitter density to the fraction of retarded radiation (Duda, 23 Dec 2025).

Topological mechanisms:

• Integer and half-integer photonic vortices underpin the robust tuning of emitter/absorber asymmetry in synthetic photonic bands, providing topologically protected tunability and programmable directionality (Zhuang et al., 22 Jan 2024).

5. Key Experimental Results and Applications

System	Asymmetry Parameter Definition	Maximum Demonstrated Value
Magnetized ENZ InAs films (Liu et al., 2022)	$$\Delta(\omega,\theta) = e(\omega,\theta)-\alpha(\omega,\theta)$$	$|\Delta| > 0.6$ narrowband; $|\Delta|\sim0.45$ dual-band; $|\Delta| \geq 0.3$ broadband
Bilayer metagratings (Zhuang et al., 22 Jan 2024)	$$n = \frac{|C_{\rm up}|^2 - |C_{\rm down}|^2}{|C_{\rm up}|^2 + |C_{\rm down}|^2}$$, phase $\phi$	$n$ tunable from $-1$ to $+1$
GW/Absorber theory (Duda, 23 Dec 2025)	$\alpha$ in $$F(x,t) = \alpha F_{\rm ret} + (1-\alpha) F_{\rm adv}$$	$\alpha$ empirically in $0.1$–$0.67$ (contextual)

Practical consequences include selective thermal emission, programmable perfect absorption (CPA at arbitrary phase), energy harvesting approaching ultimate thermodynamic bounds (nonreciprocal Landsberg limits), and experimental probes of cosmological boundary conditions via gravitational radiation.

6. Broader Significance and Current Research Directions

• Photonic technology: Asymmetry measures such as $n$ and $\phi$ enable the design of metasurfaces and gratings for controlled emission, unidirectional antennas, on-chip lasers, and quantum light sources with programmable emission directionality (Zhuang et al., 22 Jan 2024).
• Energy conversion: Large $|\Delta|$ in thermal emitters enhances thermophotovoltaic and radiative cooling device performance beyond constraints set by reciprocal limits; matched absorptivities and emissivities can be fundamentally decoupled (Liu et al., 2022).
• Foundations of physics: Empirical measurement of $\alpha$ in cosmic signals may provide insight into the fundamental arrow of time and test the physical relevance of advanced waves, with astrophysical survey data offering constraints on cosmological absorber-to-emitter ratios (Duda, 23 Dec 2025).
• A plausible implication is that further increases in the tunability and robustness of asymmetry parameters will continue to drive both device engineering and the basic understanding of nonequilibrium and nonreciprocal radiation phenomena across classical and quantum domains.

7. Common Misconceptions and Limitations

• Kirchhoff’s law universality: It is often presumed that $e = \alpha$ holds in all systems. Experimentally, this is violated in nonreciprocal systems where Lorentz reciprocity does not apply and directional difference can be engineered and observed (Liu et al., 2022).
• Time-reversal invariance of field equations: Asymmetry parameters such as $\alpha$ encode boundary-condition-induced asymmetry without violation of the underlying time-reversal invariance present in the fundamental wave equations (Duda, 23 Dec 2025).
• Interpreting measured asymmetry: Observed deviations (e.g., missing EM counterparts in GW events) must be carefully corrected for selection effects before attributing the effect to a nonzero advanced-wave contribution or boundary-condition asymmetry.

The emitter/absorber asymmetry parameter serves as a central figure of merit in a wide range of advanced research areas, unifying concepts from topological photonics, nonreciprocal thermal radiation, and foundational field theory. Its quantification is essential for both the optimization of photonic devices and the probing of fundamental symmetries in physics.