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Finite width of the analog event horizon is determined by the nonlinearitylength in the Kerr nonlinear optical system, which is discussed here, or by thehealing length in Bose-Einstein condensates. The various eigen modes offluctuations are found in the immediate vicinity of the event horizon and thescattering matrix due to the finite width horizon is calculated to within theleading order correction in the nonlinearity length. The Hawking radiation isfound to be that of a grey body with the emissivity larger than one. Aprocedure of paraxial quantization of the fluctuation field is discussed andits connection to the conventional quantization of the electromagnetic field isdemonstrated.

Finite width of the sonic event horizon and grey body Hawking radiation