A different way to think about loss
In conventional wave physics, loss is usually treated as something to minimize.it weakens signals, lowers efficiency and shortens propagation distance. In an open photonic system, however, loss is also part of the complex eigenfrequency of a mode. Its real part determines where a mode sits in frequency and how it disperses, while its imaginary part determines how quickly that mode decays. This means that two waves can share the same real frequency yet survive for very different lengths of time.
In conventional wave physics, loss is usually something to minimize. In open photonic systems, however, loss is part of the complex eigenfrequency: the real part determines dispersion, while the imaginary part determines how fast a mode decays. Two waves can therefore share the same real frequency yet survive for very different lengths of time.
This idea motivates a shift from conventional band engineering toward lifetime engineering. While Bloch bands and equifrequency contours determine which propagation channels are available, non-Hermitian physics adds another degree of freedom: how long those channels survive.
Nonreciprocal dynamic degeneracy splitting
Dynamic degeneracy splitting, or DDS, captures this lifetime difference at a fixed excitation frequency. States on the same equifrequency contour can remain degenerate in real frequency while acquiring different decay rates.
A team led by Yihao Yang and Hongsheng Chen at Zhejiang University, together with collaborators from the National University of Defense Technology and Beijing Institute of Technology, has now demonstrated nonreciprocal DDS in a gyromagnetic photonic crystal. In this regime, counter-propagating channels at the same real frequency can have unequal lifetimes.
The effect was created through sequential symmetry breaking. A static magnetic field breaks time-reversal symmetry, while a displaced ceramic pillar reshapes the coupling between guided and rotating p-like modes, producing an anisotropic hyperbolic-like dispersion. Microwave absorbers then introduce non-Hermiticity. Because different modes overlap differently with the lossy regions, local material loss is converted into a momentum-dependent decay rate, forming an asymmetric lifetime landscape.
The source chooses the momentum; lifetime chooses the direction
The researchers translated this lifetime asymmetry into directional transport using a phased array of dipole sources. The source determines which Bloch momentum is excited, while nonreciprocal DDS determines how far that channel can propagate.
In simulations and microwave near-field measurements, long-lived bulk modes propagated across the sample, whereas the counter-propagating short-lived modes decayed rapidly. Fourier-space measurements confirmed that the directional response followed the momentum-dependent lifetime distribution rather than a boundary-state mechanism.
Dispersion draws the path; lifetime decides what survives
The same mechanism was extended to directional imaging. Hyperbolic-like bulk dispersion provides the negative refraction needed to form a focus, while lifetime asymmetry suppresses reflected and counter-propagating components.
At 7.8 GHz, the forward configuration produced a clear focal spot with an experimentally measured full width at half maximum of about 0.81 wavelengths. In the reverse direction, no comparable focus formed because the relevant bulk channels decayed much more strongly. The reported forward and backward imaging efficiencies were 0.495 and 0.026, respectively, with an isolation ratio of up to 4.8 dB.
Unlike reflection-suppressed negative refraction based on three-dimensional Weyl surface states, the filtering mechanism here operates through the bulk states of a two-dimensional photonic crystal.
Toward complex-band dynamical engineering
The central advance is therefore not simply to add more loss in one direction, but to structure loss in momentum space so that dissipation acts as a channel-selection rule. Conventional dispersion engineering asks which routes are allowed; nonreciprocal DDS adds a second question: which of those routes survive long enough to carry energy?
This points toward a broader framework of complex-band dynamical engineering, in which the real and imaginary parts of a photonic band structure are designed together. The concept may be extended to other lattice geometries, multiband systems and synthetic dimensions, with potential applications in mode-selective transport, nonreciprocal frequency conversion and frequency-domain routing.
Research team
Mingyu Tong and Yuze Hu are co-first authors of the study. Hongsheng Chen and Yihao Yang are the corresponding authors. The work involved researchers from Zhejiang University, the National University of Defense Technology, Beijing Institute of Technology and collaborating institutes.
Science Bulletin
Experimental study