wave with the SPP is highly dependent on the thickness of the dielectric sublayer in both the Kretschmann and Otto configuration [@Zeller1; @Zeller2; @Zeller3]. Shadrivov [*et al.*]{} have studied the GH shift in the Otto configuration with the metal sublayer substituted by a left-handed metamaterial [@Shadrivov]. A large GH shift with beam splitting was observed, and the energy transfer between the right- and left-handed materials was demonstrated by numerical simulations. There also exist studies to enhance the GH shift using various hybrid structures containing sublayers of graphene, MoS$_2$ or cytop [@Xiang1; @Xiang2; @Xiang3]. Recently, much progress has been made on obtaining a tunable GH shift in the prism-coupling system, by applying an external voltage to a graphene sublayer and other heterostructures [@Farmani1; @Farmani2; @Farmani3; @Xiang4]. Kim [*et al.*]{} have studied the GH shift of incident $p$ waves in the Otto configuration containing a nonlinear dielectric layer and shown that its magnitude can be as large as several hundred times of the wavelength at the incident angles where the SPPs are excited [@Kim3]. Furthermore, they have shown that the sign and the size of the GH shift can change very sensitively as the nonlinearity parameter varies.

In this paper, we study 