In this paper, the magic wavelength of the 87Sr optical lattice clock is determined by a method that bypasses the need for lattice trap depth modulation. Instead, it relies on an additional AC Stark shift generated by a dipole beam operating near the frequency of the lattice light and oriented perpendicular to the optical lattice. The magic wavelength is inferred by measuring the AC Stark shift induced by the dipole beam as a function of its power under various frequency detunings. The effect of the dipole beam on the external states of the cold ensemble is evaluated through comparative analysis of the radial and axial sideband spectra, both with and without the dipole beam. Variations in density shift resulting from changes in external states are evaluated using comprehensive numerical calculations. By avoiding trap depth modulation, this method effectively suppresses the influence of the density shift, thereby offering a promising avenue for accurately determining the magic wavelength.
