🔬 optics

Incoherence-assisted mode excitation in non-Hermitian resonant systems

This paper introduces and experimentally demonstrates a robust, passive method for selectively exciting topological edge states in non-Hermitian photonic systems using incoherent light, thereby eliminating the need for the precise phase control typically required by coherent excitation schemes.

Original authors: Amin Hashemi, Vinzenz Zimmermann, Armando Perez-Leija, Andrea Blanco-Redondo

Published 2026-04-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Amin Hashemi, Vinzenz Zimmermann, Armando Perez-Leija, Andrea Blanco-Redondo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Tuning a Radio Without the Knob

Imagine you have a very complex, high-tech radio with many different stations playing at once. In a normal world (what physicists call a "Hermitian" system), if you want to listen to just one specific station, you simply turn the dial until the frequency matches. The static fades, and you hear your song clearly.

But in the world of Non-Hermitian systems (which are more realistic because they involve energy loss, like a radio signal fading over distance), things get messy. Even if you tune to the right frequency, the signal doesn't just play one song; it plays a jumbled mix of many stations because the "static" (energy loss) is always interfering.

To get just one song in these messy systems, scientists usually try to use Coherent Light. Think of this like a choir where every singer must hit the exact same note at the exact same time with perfect precision. If one singer is slightly off-key or late, the whole harmony breaks, and you get noise instead of music. This requires expensive, complex equipment to keep everyone perfectly synchronized.

This paper introduces a new trick: "Incoherent Excitation."
Instead of trying to get the choir to sing in perfect unison, the researchers say: "Let's just let everyone sing randomly, but loud enough, and see what happens."

Surprisingly, they found that by using random, uncoordinated light (incoherent light), they could actually isolate the specific "song" (or mode) they wanted better than if they tried to force a perfect, coordinated signal that wasn't quite perfect.

The Experiment: The Ring of Resonators

To prove this, the team built a physical model using seven tiny glass rings (microring resonators) connected in a line.

The Setup: Imagine seven children holding hands in a circle, passing a ball (light) between them.
The Goal: They wanted to get the ball to stay mostly with the first child (the "Edge State"), which is a special, protected position in this chain.
The Problem: Because the children are tired (energy loss), the ball naturally leaks out or gets passed to the wrong kids. If you try to throw the ball to the first and third child at the same time, you have to throw them with perfect timing and angle. If your timing is off by a fraction of a second, the ball ends up everywhere.

The Solution: The "Random Throw" Strategy

The researchers tried two methods to get the ball to the right place:

The Coherent Method (The Precise Throw):
They tried to throw the ball to the first and third child with a specific, calculated timing (phase).
- Result: If they got the timing perfectly right, it worked great. But if they were even slightly off (due to temperature changes or vibrations), the ball went everywhere. It was fragile and hard to maintain.
The Incoherent Method (The Random Throw):
They threw the ball to the first and third child, but they let the timing and angle change randomly every time they threw it. They did this thousands of times and averaged the results.
- Result: Even though every single throw was "messy," the average result showed the ball staying exactly where they wanted it!

Why Does This Work? (The Analogy)

Think of it like trying to fill a bucket with a leaky hose.

Coherent approach: You try to aim the hose perfectly into the bucket. If you slip, the water misses.
Incoherent approach: You spray water everywhere randomly. But because the bucket is in a specific spot, and the "leak" (loss) affects the other spots differently, the water that stays in the bucket over time naturally settles into the shape of the bucket. The randomness actually helps cancel out the "noise" of the other modes, leaving the desired state standing out.

The "Mismatch Index" (How Good Are We?)

The scientists created a score called the Mismatch Index to measure how well they isolated the target mode.

High Score: The ball is all over the place (Bad).
Low Score: The ball is exactly where it should be (Good).

When they used the "perfect" coherent throw but made a tiny mistake, the score was bad. When they used the "random" incoherent throw, the score was consistently good, even without any fancy equipment to stabilize the timing.

Why This Matters

This discovery is a game-changer for Photonics (the science of using light for technology) and Quantum Computing.

Simplicity: You don't need expensive, complex lasers that require perfect synchronization. You can use cheaper, simpler light sources.
Robustness: The system works even if the environment is noisy, hot, or vibrating. It's "passive," meaning it just works without needing constant adjustment.
Real-World Application: This makes it much easier to build devices like ultra-sensitive sensors or secure communication networks that rely on these special "topological" states of light.

In a Nutshell

The paper shows that in complex, lossy systems, perfection isn't always the goal. Sometimes, embracing a little bit of randomness (incoherence) is actually the most reliable way to get exactly what you want. It's like finding your way through a foggy forest: instead of trying to walk a perfectly straight line (which is hard when you can't see), you just keep walking in a general direction, and eventually, you arrive at your destination more reliably than if you tried to be perfect and got lost.

1. Problem Statement

Selective excitation of specific modes in non-Hermitian resonant systems (systems that exchange energy with their environment, exhibiting gain or loss) is a significant challenge in photonics.

The Core Issue: In Hermitian (lossless) systems, a single mode can be selectively excited by tuning the input frequency to the mode's eigenfrequency. However, in non-Hermitian systems, modes possess non-zero decay rates (finite linewidths). Consequently, a real-frequency input field typically excites a linear superposition of multiple modes rather than a single target mode.
Limitations of Existing Solutions:
- Gain/Loss Engineering: Requires active platforms and precise integration of gain to counteract decay, which is often impractical in passive photonic systems.
- Complex-Frequency Excitation: Requires inputs with negative imaginary frequency components (exponential decay in time), necessitating ultrafast amplitude modulation and precise system knowledge.
- Coherent Multi-port Excitation: While using multiple input ports can enhance mode overlap, it requires precise phase control (phase-locking) between ports. In realistic experimental settings, thermal fluctuations, fiber length variations, and mechanical vibrations cause phase drift, making stable phase control difficult and degrading excitation efficiency.

2. Methodology

The authors propose and experimentally demonstrate a strategy using incoherent multi-port excitation to selectively excite modes without the need for precise phase stabilization.

Theoretical Framework:
- The system is modeled using Temporal Coupled Mode Theory (TCMT) and stochastic differential equations.
- Key Condition: The method relies on the hierarchy of time scales: $\tau_s < \tau_c < \tau_d$ $τ_{s} < τ_{c} < τ_{d}$ .
  - $\tau_s$ : System relaxation time (time to reach steady state).
  - $\tau_c$ : Coherence time of the input (time over which phases remain constant).
  - $\tau_d$ : Detector response time.
- Mechanism: If the input coherence time is longer than the system's relaxation time ( $\tau_c > \tau_s$ ), the system reaches a quasi-steady state for each specific realization of the random input phases. If the detector integration time is longer than the coherence time ( $\tau_d > \tau_c$ ), the measured output is an ensemble average of these steady states.
- Mathematical Formulation: The system state under incoherent excitation is treated as a mixed state described by a frequency-domain density matrix (coherence matrix) $\tilde{\rho}(\omega) = \hat{G}(\omega)\hat{\Gamma}\tilde{\rho}_s(\omega)\hat{\Gamma}^\dagger\hat{G}^\dagger(\omega)$ , where $\hat{G}$ is the Green's operator and $\tilde{\rho}_s$ characterizes the statistical properties of the incoherent input.
Experimental Platform:
- Device: A programmable silicon photonic chip featuring a chain of seven coupled microring resonators.
- Model: A non-Hermitian Su-Schrieffer-Heeger (SSH) model with staggered losses ( $L_1 = 0.03$ GHz, $L_2 = 0.22$ GHz) to create a topological edge state.
- Parameters: Quality factor $Q \approx 4 \times 10^4$ , intrinsic loss $l_0 = 0.56$ GHz.
- Excitation: Two input ports were used to excite specific rings (e.g., rings #1 and #3 for the edge state).
- Incoherence Generation: Instead of a physical broadband source, incoherence was simulated experimentally by averaging the results of 50 coherent excitations with randomly varying relative phases between the two input ports. This mimics the statistical effect of a true incoherent source.

3. Key Contributions

Novel Excitation Strategy: Introduction of "incoherence-assisted" excitation, which eliminates the need for complex phase-locking hardware while maintaining high mode selectivity.
Robustness to Phase Noise: Demonstration that incoherent excitation is inherently robust against phase fluctuations. Unlike coherent excitation, where a slight phase error can drastically reduce efficiency, incoherent excitation averages over all phase configurations, yielding a consistently high overlap with the target mode.
Experimental Validation: Successful experimental realization of the topological edge state in a non-Hermitian SSH model using a passive silicon photonic platform.
Disorder Resilience: Demonstration that the method preserves the topological protection of the edge state even in the presence of coupling disorder (random fluctuations in coupling coefficients).

4. Key Results

Edge State Excitation (Rings #1 & #3):
- Coherent Case: When the relative phase was optimized ( $\Delta\phi = \pi$ ), the mismatch index (a metric for deviation from the target mode) was low. However, with a suboptimal phase ( $\Delta\phi = 0.15\pi$ ), the mismatch index spiked ( $\eta \approx 1.07$ ), indicating poor selectivity. The average mismatch for random coherent phases was $\bar{\eta}_{coh} = 0.44$ .
- Incoherent Case: The incoherent excitation yielded a mismatch index of $\eta_{incoh} \approx 0.26$ (experimentally $0.30$). This represents a 60% improvement over the phase-averaged coherent case and is comparable to the best-case coherent scenario, but achieved without any phase tuning.
Challenging Excitation (Rings #3 & #4):
- When exciting rings with significant overlap with multiple modes, coherent excitation became highly sensitive to phase. A non-optimal phase ( $\Delta\phi = 3\pi/2$ ) resulted in a high mismatch ( $\eta \approx 0.99$ ).
- Incoherent excitation maintained a significantly lower mismatch ( $\eta \approx 0.58$ ), demonstrating superior selectivity in complex scenarios.
Disorder Robustness: Under 500 realizations of coupling disorder ( $\sigma = 0.1 \times t$ ), the incoherent excitation of the edge state maintained a mean mismatch index of $\langle \eta \rangle \approx 0.276$ with very low standard deviation, confirming statistical stability.
Bulk Mode Excitation: The method was also successfully applied to excite bulk modes, showing that incoherent excitation generally outperforms random-phase coherent excitation.

5. Significance

Practical Viability: This approach provides a "passive" and robust tool for mode selection in non-Hermitian systems, removing the stringent requirement for active phase stabilization which is often a bottleneck in integrated photonics.
Broad Applicability: The technique is applicable to various platforms (lasers, sensors, quantum optics) and is particularly valuable for systems where implementing optical gain is impractical.
Topological Photonics: It broadens the scope of non-Hermitian topological photonics by enabling the reliable preparation of topological states (like edge modes) in realistic, noisy environments.
Fundamental Insight: The work bridges the gap between deterministic transient dynamics (governed by coherent excitation) and statistical ensemble averages, showing that incoherence can be a resource rather than a limitation for mode control.

In conclusion, the paper establishes that incoherent light, often viewed as a source of noise, can be harnessed as a robust mechanism for selective mode excitation in non-Hermitian resonators, offering a practical alternative to complex coherent control schemes.