Photon Conversion Efficiency (PCE)

• Photon Conversion Efficiency (PCE) is defined as the ratio of converted photon output to incident photons, serving as a key metric in energy and signal conversion applications.
• It relies on factors like phase matching, cavity dynamics, material properties, and device architecture to optimize nonlinear optical processes and photovoltaic performance.
• Advances in PCE modeling, measurement protocols, and material engineering drive improvements in energy harvesting, quantum photonics, and optoelectronic device efficiency.

Photon Conversion Efficiency (PCE) is a quantitative figure of merit that expresses the fraction of incident photons—typically from an optical or solar source—which are converted into useful output, such as higher-energy photons in nonlinear optics or electrical power in photovoltaic devices. PCE unifies a broad empirical and theoretical landscape spanning nonlinear wave-mixing, semiconductor photovoltaics, quantum frequency conversion, and emerging nano-optoelectronic systems. Its rigorous formulation, physical determinants, measurement protocols, and optimization pathways are crucial to both device engineering and fundamental studies of light–matter interaction.

1. Formal Definitions and General Frameworks

PCE is universally defined as the ratio of the number or flux of converted photons (or, equivalently, the extracted energy in a functional form) to the number of incident photons (or input power):

• Nonlinear Optics (Photon Number Conversion):

$$\eta_\mathrm{ext} = \frac{n_\mathrm{out}}{n_\mathrm{in}} = \gamma \, \left( \frac{\lambda_S}{\lambda_\mathrm{out}} \right) \frac{P_\mathrm{out}}{P_\mathrm{in}}$$

where $n_\mathrm{out}$ and $n_\mathrm{in}$ are output (converted) and input photon fluxes; $\gamma$ corrects for detector quantum efficiencies (Samblowski et al., 2013).

• Photovoltaics (Power Conversion Efficiency):

$$\mathrm{PCE} = \frac{J_\mathrm{sc} \cdot V_\mathrm{oc} \cdot FF}{P_\mathrm{in}}$$

with $J_\mathrm{sc}$ (short-circuit current density), $V_\mathrm{oc}$ (open-circuit voltage), $FF$ (fill factor), and $P_\mathrm{in}$ (incident power density) (Miao et al., 2012, Sachenko et al., 2017, Brenes et al., 2019, Irfan et al., 18 Jun 2025).

In more specialized quantum settings, PCE is expressed as the probability that an input single photon or Fock state is converted to a target mode after the interaction: $$\eta = \langle \psi_f | \hat n_\mathrm{target} | \psi_f \rangle$$ for state transformation under a unitary operator (e.g., sum-frequency conversion) (Donohue et al., 2014).

2. PCE in Nonlinear Frequency Conversion

2.1. Cavity-Enhanced Sum-Frequency Generation (SFG)

• High external PCE (η_ext) is achieved in χ^2 nonlinear crystals embedded in optical cavities, as demonstrated by Samblowski et al., reaching (84.4 ± 1.5)% and modeled up to 93% (Samblowski et al., 2013).
• The conversion efficiency is governed by the interplay of nonlinear coupling Γ, signal/pump input mirror reflectivities, round-trip power losses, and phase-matching conditions.
• Theoretically:

$$\eta_\mathrm{ext} = \frac{4 T_\mathrm{in}T_P (Γ\sqrt{P_P})^2} {(T_\mathrm{in}+L_S)(T_P+L_P) + 4 (Γ\sqrt{P_P})^2)^2}$$

where $T_\mathrm{in}, T_P$: mirror transmissions, $L_S, L_P$: round-trip losses, and $Γ$: effective nonlinear coupling.

2.2. Quantum Pulse and Single-Photon Regimes

• Single-photon waveform conversion via SFG can attain unit efficiency if the phasematching acceptance exceeds the spectral width of the interacting modes, the pump envelope matches the single photon, and the temporal overlap is optimized (Donohue et al., 2014).
• In photonic circuits (e.g., microring resonators), device quality factors, mode overlap, and engineered coupling determine achievable PCE, with experimental on-chip SFG conversion up to 65% at sub-mW pump powers (Chen et al., 2021).

2.3. Bragg Scattering Four-Wave Mixing (BS-FWM)

• In single-ring photonic devices, symmetry constraints limit the maximum PCE to 50%. Coupled-ring architectures enable unidirectional conversion with extinction exceeding 40 dB; with proper cavity Q-factor ratios (e.g., $Q_i/Q_c > 400$), >99% conversion is predicted and observed (1811.11741).

3. PCE in Photovoltaics and Photonic Up-/Down-Conversion

3.1. Detailed-Balance Limit and Modern Refinements

• The Shockley–Queisser (SQ) detailed-balance model sets the single-junction limit at 33% under one-sun AM1.5G, rising with concentration and photon management (Boriskina et al., 2013, Sachenko et al., 2017).
• Modern efficiency modeling introduces spectroscopically limited maximum efficiency (SLME), incorporating bandgap, absorption coefficient α(E), and finite thickness, as applied to antiperovskite compounds yielding SLME of 31.2% for AsNCa₃ (Irfan et al., 18 Jun 2025).

3.2. Device-Specific Pathways

• Chemical tuning (e.g., TFSA-doped graphene/Si) realizes PCE enhancements by increasing Schottky-barrier height and lowering series resistance, achieving jumps from 1.9% to 8.6% (Miao et al., 2012).
• Photon recycling in halide perovskites leads to measurable gains in $V_{\mathrm{MPP}}$ and fill factor, translating to ΔPCE ≈2% when nonradiative recombination rates and electroluminescence efficiency cross key thresholds (Brenes et al., 2019).
• Doping-free Janus homojunctions exploit intrinsic dipole fields and type-II alignment for PCE = 23.2%, driven by excitonic band alignment and built-in field-enhanced dissociation (Li et al., 2024).

3.3. Exceeding SQ via Thermal Up-/Down-Conversion and TEPL

• TEPL (thermally enhanced photoluminescence) and thermal-photovoltaic up-conversion utilize endothermic processes and angular/spectral selectivity to achieve theoretical PCE up to 70% at T_H~1180 K (Manor et al., 2015), and up to 73% (practical 45% for Si) under spectral/angle-restrictive hybrid up-converter designs (Boriskina et al., 2013).

4. Determining and Measuring PCE: Protocols and Influencing Factors

4.1. Methods of Measurement

• Nonlinear optics: Direct photon counting at signal and output, power calibration, depletion analysis for cavity-based frequency conversion (Samblowski et al., 2013).
• Photovoltaics: Extraction from J–V curves under AM1.5G/AM1.5D, EQE integration, and, in high-precision studies, correction for fill factor, shunt/series resistance, and quantum yield (Miao et al., 2012, Sachenko et al., 2017).
• Quantum/few-photon domain: Unitary probability amplitudes from interacting states, state tomography for fidelity, power-normalized emission (Donohue et al., 2014, Niu et al., 2016).

4.2. Limiting and Enhancing Factors

System/Device	Limiting Mechanisms	Enhancement Strategies
SFG Cavities (Samblowski et al., 2013)	Round-trip losses, mode mismatch, phase detuning	AR coating, cavity impedance matching, thermal stabilization
Photovoltaics	Nonradiative recombination, parasitic absorption, surface recombination, series resistance	Surface passivation, photon recycling, light-trapping, advanced contact/passivation (Hossain et al., 2023)
BS-FWM Microrings	Symmetric conversion (single-ring)	Coupled rings for unidirectionality, high Q_i/Q_c
TEPL/TPV Up-Converters	Sub-bandgap thermalization, entropy	Spectral/angle selectivity, endothermic PL, optimized absorber–cell bandgap matching

5. Theoretical and Computational Modeling of PCE

• Nonlinear conversion processes are modeled by coupled-wave or master equations, including cavity dynamics and quantum unitary evolution (Samblowski et al., 2013, Donohue et al., 2014).
• Photovoltaic device PCE is modeled with drift-diffusion and recombination kinetics (e.g., J–V curves with ideality factor n), detailed-balance (SQ), absorption modeling (Yablonovitch/Tiedje), and band-structure calculations via DFT for emergent materials (Kalaiselvi, 14 Jan 2025, Irfan et al., 18 Jun 2025).
• Data-driven predictive tools, as in organic photovoltaics, leverage graph neural networks and language descriptors to predict PCE from molecular structure in low-data regimes (Nguyen et al., 2024).

6. Applications and Technological Impact Across Domains

• Quantum Information: High-PCE single-photon wave-mixing enables spectral tuning and entanglement-preserving transduction essential for hybrid quantum networks and detectors (Donohue et al., 2014, Chen et al., 2021, 1811.11741).
• Advanced Photovoltaics: New material platforms (2D Janus semiconductors, antiperovskites, perovskite/Si multijunction stacks) depend on accurate modeling and realization of high theoretical PCE, pushing practical devices toward—and in some architectures, beyond—the SQ limit (Kalaiselvi, 14 Jan 2025, Irfan et al., 18 Jun 2025, Boriskina et al., 2013).
• Thermally-Driven Hybrids: TEPL and hybrid TPV platforms offer PCE far in excess of conventional single-junction limits, contingent on spectral management and minimized entropy generation (Manor et al., 2015, Boriskina et al., 2013).
• Photonic Chips: On-chip nonlinear PCE, via microrings or adiabatically-tuned resonators, enables scalable, highly integrated quantum and classical photonic systems (Chen et al., 2021, Preble et al., 2012).

7. Outlook: Fundamental and Practical Implications

The pursuit of high photon conversion efficiency is central to progress in energy harvesting, quantum photonics, and optoelectronic integration. State-of-the-art experiments and models underscore the criticality of loss management, phase and mode matching, and nanostructural/material optimization. Engineered quantum coherence and nonlinear dynamical control can, in principle, push efficiency at maximum power beyond classical thermodynamic limits, as formalized in quantum-dot converters surpassing the Curzon–Ahlborn bound (Su et al., 2016). A unifying theme is that, across domains, the maximization of PCE is synonymous with the optimization of photon management, spectral and spatial coherence, and entropy minimization.

High-efficiency PCE now serves as both a stringent test of fundamental light–matter physics—probing the limits of coherence, entanglement, and nonlinearity—and as a practical benchmark for next-generation optoelectronic device engineering.