This paper presents a novel method for characterization of gain spectrum of stimulated Mandelstam-Brillouin scattering (SMBS) in single-mode optical fiber. This method is based on the usage of double-frequency probing radiation. For conversion of the complex SBS spectrum from optical to the electrical field single-sideband modulation is used. Detection of double-frequency components position in the gain spectrum occurs through the amplitude modulation index of the envelope and the phase difference between envelopes of probing and passing components.

The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L f ull ∞ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory, including the gauge covariant objects like the Poisson field strength and the gauge covariant derivative of matter field. We derive the minimal set of non-vanishing ℓ-brackets and prove that they satisfy the corresponding homotopy relations. On the one hand, it provides new explicit non-trivial examples of L ∞ algebras. On the other hand, it can be useful for bootstrapping the full non-commutative gauge theory. In addition we show that the derivation properties of ℓ-brackets on L f ull ∞ with respect to the truncated product on the exterior algebra are satisfied only for the canonical non-commutativity. In general, L f ull ∞ does not have a structure of P ∞ algebra.

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