Amplitude Modulation in Coherent Photonic Cores

• Amplitude modulation in coherent photonic cores is the process of encoding electrical or optical signals into controlled light intensity variations while maintaining phase coherence.
• It employs architectures such as Mach–Zehnder interferometers, ring modulators, photonic crystal cavities, and quantum-dot devices to achieve high-speed modulation with low energy consumption and minimal chirp.
• The technology supports scalable, monolithic integration for optical computing and communications, with key performance metrics including bandwidth, extinction ratio, energy efficiency, and AM–PM crosstalk management.

Amplitude modulation (AM) in coherent photonic cores enables controlled variation of optical field intensity while retaining precise phase relationships, a requirement for advanced optical computing, communications, and signal processing. The landscape spans guided-wave modulators, quantum-dot devices, photonic-crystal and ring-resonator circuits, distributed architectures leveraging injection-locked lasers, and emerging non-Hermitian temporal designs. This article reviews the foundational principles, dominant device categories, theoretical frameworks, operational metrics, and system-level integration strategies central to amplitude modulation in coherent photonic cores.

1. Physical Principles of Amplitude Modulation in Coherent Photonic Cores

Coherent photonic cores manipulate both amplitude and phase of optical carriers to realize linear operations—such as matrix–vector products and dot products—entirely on chip. Amplitude modulation within these environments entails converting or encoding an external electrical or optical signal into the intensity envelope of the light field, while ensuring that the coherence properties are retained for downstream interference-based logic, multiplexing, or demodulation.

Underlying all amplitude modulators is a physical mechanism—electro-optic, all-optical, or cavity-resonant—that transduces an input perturbation (voltage, field, pump, or wave collision) into modulation of the photon number (amplitude) and often, through amplitude–phase coupling, the optical phase. Preserving controlled and predictable relationships between amplitude, phase, and spectral characteristics is essential for error-free operation in coherent-processing tasks (Gao et al., 15 Apr 2026, Geravand et al., 2024, Kari et al., 15 Feb 2025, Larocque et al., 2023).

2. Device Architectures and Modulation Mechanisms

2.1 Electro-Optic Mach-Zehnder and Ring Modulators

Classical amplitude modulation in integrated photonics is implemented via Mach–Zehnder interferometers (MZIs) equipped with single- or dual-drive phase modulators (PMs), as well as by ring-resonator modulators (MRMs). In both, the amplitude at the output is controlled by the relative phase across arms, itself a function of the applied drive:

• MZI modulators exploit constructive/destructive interference through push–pull operation, enabling pure amplitude modulation with minimal chirp and independent bias of sideband content (Capmany et al., 2011).
• Microring modulators provide compactness and resonant enhancement but exhibit strong dynamic AM–PM coupling due to their Lorentzian response; embedding rings in a push–pull (ring-assisted) MZM cancels phase excursions (“chirp”) and yields true amplitude-only modulation (Geravand et al., 2024).

Device Platform	Key Mechanism	Typical Performance
Silicon MZI/PM	Plasma-dispersion effect	Sub-pJ/bit, >40 GHz BW
MRM (Si/SiN)	Resonant enhancement	~10 fJ/bit, OMA peaking

2.2 Resonant Photonic Cavities

Recent advances leverage sub-wavelength resonators—such as Gires–Tournois etalons and photonic crystal (PhC) cavities—on platforms like TFLN for amplitude modulation:

• Gires–Tournois-based MZIs enhance the phase shift per volt, reducing modulator footprint while sustaining moderate- to high bandwidths (e.g., 29 GHz with <1 dB loss) (Kari et al., 15 Feb 2025).
• Fabry–Perot–enhanced Michelson IQ modulators using PhC cavities in TFLN realize arbitrary amplitude and phase control (IQ modulation) with GHz-scale bandwidth and CMOS drive voltage compatibility, at scale and with low energy per bit (≈26 fJ/bit) (Larocque et al., 2023).

2.3 Direct Quantum-Amplitude and Heterodyne Devices

Quantum-dot ridge waveguides serve as platforms for resonant AM and phase modulation at the few-photon (attojoule) level, with amplitude swing and bandwidth set by homogeneous linewidth and spin relaxation rates (Moody et al., 2016).

2.4 Distributed and Non-Hermitian Schemes

Distributed amplitude modulation can be achieved through optical injection locking (OIL) in remote lasers, enabling direct optical–optical copying, stripping, or tailoring of amplitude-encoded signals, crucial for scalable, real-time distributed computing (Gao et al., 15 Apr 2026).

Additionally, ultrafast AM can be accomplished using time-interfaces (non-Hermitian temporal boundaries), where counter-propagating coherent pulses interfere at an imposed temporal discontinuity, carving or amplifying selected temporal components based on relative amplitude and phase (Galiffi et al., 2022).

3. Theoretical Modelling of Amplitude Modulation Dynamics

3.1 Semiconductor Laser Rate Equations and Injection Locking

The interaction of remote and injected optical fields under OIL is modeled by rate equations for the slowly varying complex field $E(t) = A(t) e^{i\phi(t)}$ and carrier density $N(t)$:

$$\frac{dE}{dt} = \frac{1}{2}(1 + i\alpha) G[N, |E|^2] E + \kappa E_{\text{inj}}(t)$$

$$\frac{dN}{dt} = R_p - \frac{N}{\tau_n} - g[N, |E|^2] |E|^2$$

where $\alpha$ is the linewidth enhancement factor, $\kappa$ is the injection coupling, and $E_{\text{inj}}$ encodes the amplitude- and phase-modulated seed (Gao et al., 15 Apr 2026). AM–PM transfer functions $H_{\text{AM}\to\text{AM}}(\Omega)$, $H_{\text{AM}\to\text{PM}}(\Omega)$, etc., are evaluated numerically.

3.2 Coupled-Mode and Quantum Theories

• For MZIs and ring modulators, time-domain and frequency-domain transfer functions relate drive to amplitude response, incorporating chirp and bandwidth limitations due to photon lifetime, coupling, and electrical parasitics (Geravand et al., 2024).
• Quantum mechanical formalisms describe the system via unitary evolutions of field operators across beam splitters and phase modulators, enabling analysis of multi-photon states, sideband structure, and multicarrier operation (Capmany et al., 2011).

3.3 Resonant Topological Approaches

Topological synthesis constrains the pole–zero structure of the scattering matrix to trace an Apollonius circle in complex frequency, enabling $2\pi$ phase sweeps at constant amplitude and fully suppressing AM–PM conversion (Krasnok, 24 Dec 2025).

$N(t)$0

with $N(t)$1 as zero and pole frequencies.

4. Performance Metrics and Limits

Principal performance figures for amplitude modulation in coherent photonic cores include:

• Bandwidth: Determined by cavity photon lifetime $N(t)$2, carrier/electronic response (RC-limited), and device geometry. Silicon and TFLN devices exceed 20–40 GHz; quantum-dot devices limited by T2 to ~1 GHz (Geravand et al., 2024, Kari et al., 15 Feb 2025, Moody et al., 2016).
• Modulation Depth and Extinction Ratio: Deep AM is achieved via careful interferometric biasing, resonant enhancement, or impedance engineering; observed ERs >30 dB for PhC IQ modulators; up to 16% modulation depth for single-quantum-dot devices (Larocque et al., 2023, Moody et al., 2016).
• Energy Consumption: Ranges from aJ/bit (quantum dot) to sub-10 fJ/bit (MRM/MRA-MZM), with capacitance, drive voltage, and device length as key determinants; PhC devices demonstrate CMOS-level Vπ with minimum drive and footprint (Geravand et al., 2024, Larocque et al., 2023).
• AM–PM Crosstalk (Chirp): Strong in resonant and semiconductor-laser-based schemes; minimized by push–pull or topological approaches (Geravand et al., 2024, Krasnok, 24 Dec 2025).

Device Type	Bandwidth (GHz)	ER (dB)	Vπ (V)	Energy/bit (fJ)	Reference
Ring-Assisted MZM (Si)	>35–60	>25	~1–2	~10	(Geravand et al., 2024)
Gires–Tournois MZI (TFLN)	4.4–29	~6	~40	500–1000	(Kari et al., 15 Feb 2025)
PhC Michelson (TFLN)	~1.5	>30	~1.2	~26	(Larocque et al., 2023)
Quantum dot ridge	~1	~1.8	—	<1 (estimated)	(Moody et al., 2016)

5. Stability, Scalability, and System Integration

• Stability Under Deep Modulation and Mismatched Conditions: In OIL-driven topologies, high injection ratio $N(t)$3 broadens frequency locking but enhances AM–PM cross-leakage and relaxation-oscillation features, whereas low $N(t)$4 restricts locking but ensures greater amplitude/phase orthogonality and computational fidelity (Gao et al., 15 Apr 2026).
• Cascadability and Arrayed Integration: PhC IQ modulators and overcoupled ring arrays support monolithic integration and operation at high channel densities (tens to hundreds per mm^2) for WDM/SDM photonic cores (Larocque et al., 2023, Geravand et al., 2024, Kari et al., 15 Feb 2025).
• Thermal and Electrical Engineering: Resonance alignment (thermal tuning, closed-loop feedback), deep electrical integration (co-packaged or on-chip electronics), and minimization of parasitics are essential for robust system-level performance (Geravand et al., 2024, Kari et al., 15 Feb 2025).

6. Advanced and Nonclassical Amplitude Modulation Scenarios

• Time-Interface (TI) AM: Ultrafast broadband AM without spatial modulators is enabled via non-Hermitian temporal boundaries; the relative phase and amplitude of counterpropagating signals colliding at the TI select for constructive enhancement (amplification) or destructive suppression (erasure), with modulation bandwidth constrained only by the index-switching mechanism, potentially extending to THz (Galiffi et al., 2022).
• Quantum and Few-Photon AM: Quantum-dot systems demonstrate AM and phase control with single-digit photon occupation per emitter, extending coherent photonic core capabilities into the quantum regime and neuromorphic computation (Moody et al., 2016).

7. Design Trade-Offs and Practical Considerations

Performance in amplitude-modulated coherent photonic cores is subject to complex trade-offs:

• Higher Q and stronger resonance yield greater modulation depth but narrower optical and electrical bandwidth, increased chirp, and increased sensitivity to detuning and fabrication tolerances.
• Minimizing AM–PM crosstalk is key for high-fidelity coherent processing, achieved via topological design, push–pull biasing, or low injection locking ratios.
• System scaling favors architectures with independent amplitude/phase control, low-power bias, and monolithic cascades; resonance alignment and thermal crosstalk must be actively managed in dense integrated systems (Geravand et al., 2024, Kari et al., 15 Feb 2025, Larocque et al., 2023, Krasnok, 24 Dec 2025, Gao et al., 15 Apr 2026).

Emerging paradigms—including non-Hermitian wave control, quantum-coherent AM, and topological synthetic design—are expected to further advance the stability, bandwidth, and energy efficiency of amplitude modulation in future coherent photonic cores.