We developed  an efficient hybrid  mode expansion method to  study the
maximum tunneling current as a function of the external magnetic field
for  a  2-D  large   area   lateral   window   junction.  We  consider
inhomogeneity  in  the   critical  current  density,  which  is  taken
piecewise  constant. The  natural  modes  of  expansion in $y$ are the
linearized eigenmodes around a static solution which satisfies the 1-D
sine-Gordon equation with the  critical current  variation in $y$  and
boundary conditions determined  by the overlap  component of the  bias
current, which can be inline or overlap like. The magnetic field along
with the inline  component of  the bias  current enters  as a boundary
condition on the modal amplitudes. We obtain fastly convergent results
and even for a ratio of idle to window widths of $w_0/w = 4$ (in units
of $\lambda_J$) only  two modes  are  sufficient. A simple  scaling is
obtained for the maximum tunneling current as we vary the idle  region
width. We  also  present the  linear  electromagnetic  waveguide modes
taking  into account  the variation  normal to  the waveguide  of  the
critical current and the capacitance.