Light as a Vibrational Mixture: From Dilute Superposition to Photonic Phase Transitions

We develop a systematic analogy between the behavior of light and that of chemical mixtures, going beyond the standard pedagogical comparison (white light = "mixture of colors"). The analogy is organized around five regimes of increasing interaction strength — dilution, concentration, separation, saturation, and coagulation — each of which has a precise photonic counterpart in established physics. The five regimes: Dilution → Linear superposition of electromagnetic waves (ideal solution, non-interacting components) Concentration → Nonlinear optics: Kerr effect, second-harmonic generation, four-wave mixing (non-ideal solution, effective photon-photon interactions) Separation → Prisms, diffraction gratings, Fabry-Pérot cavities (chromatography, selective precipitation) Saturation → Planck blackbody spectrum (saturated solution at thermodynamic equilibrium) Coagulation → Bose-Einstein condensation of photons, optical solitons (precipitation, crystallization) The central thesis: linear superposition is the dilute limit of a richer vibrational interaction, not its fundamental description — exactly as Raoult's law is the dilute limit of thermodynamics, not a fundamental law of nature. The vibrations are always potentially coupled; they appear independent only when the coupling is negligible. This is a conceptual paper. No new experimental results or calculations are presented. We organize known physics into a unified interpretive framework connecting phenomena usually discussed in separate chapters: nonlinear optics, cavity QED, blackbody radiation, and photon condensation. The analogy's limitations (interference has no chemical counterpart, quantum statistics vs. distinguishability, reversibility) are explicitly documented. The paper raises a natural open question: what organizing principles determine which vibrational mixtures are stable? In chemistry, the answer is thermodynamics (free energy minimization). In optics, the analogous question connects to fundamental problems in cavity QED and photonic condensed matter.