Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, in analogy with the quantum Bose-Einstein condensation. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the non-equilibrium formation of nonlinear coherent structures (solitons, vortices...), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that, in opposition to quantum Bose-Einstein condensation, the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the demonstration of a coherent phenomenon of self-organization that is exclusively driven by the statistical equilibrium properties of classical light waves.
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