We propose an optimal minimum sidelobe modal beamforming approach based on the spherical harmonics decomposition for spherical sensor arrays, which provide the ability of three-dimensional broad-band beampattern synthesis. The spherical harmonics domain array processing problem is expressed with a matrix formulation. The weight vector design problem is written as a multiply constrained problem, so that the resulting beamformer can provide a suitable trade-off among mutually conflicting beamforming objectives, such as the lowest sidelobe level, beamwidth, multi-null steering, robustness and so on. The multiply constrained problem is formulated as a convex form of second-order cone programming which is computationally tractable. The main advantage of this method over classical element-space array processing approaches is that the frequency dependent components can be pre-decoupled and removed from angular depe-ndent spherical harmonics, so the same beampattern could be used over a frequency range with a single set of array weights, and the complexity of broad-band beamforming optimization algorithms can be reduced.