  Two-dimensional (2D) resonant gratings enable dual angular tunability by
controlling the plane of incidence (POI) under linear polarization. If the POI
is set to be perpendicular to the electric field vector (s-polarization or
transverse electric (TE) polarization), an excited TE mode provides spectral
tuning. The orthogonally propagating TM mode is robust in angle. Conversely, if
the POI is set for p-polarization, an ex-cited TM mode provides the tuning.
Detailed explanations of the underlying physical processes are set forth by
decomposing the 2D lattice into equivalent 1D gratings using second-order
effective-medium theory (EMT). This is shown to work extremely well even for a
strongly modulated lattice with refractive-index contrast of 3. With proper
design and corresponding experiments, a widely tunable notch filter covering
longwave infrared bands is demonstrated. Experimentally varying the incidence
angle up to 16 degree, a notch channel in TM polarization tunes across a band
exceeding 0.5 um with the TE channel remaining at a constant wavelength. The
interesting appearance of a resonance channel originating in diagonally
propagating leaky modes is briefly examined. The analysis and experiments
presented will be useful for realizing diverse 2D tunable filters while
furnishing methodology for detailed understanding of the attendant near fields
and mode structure.
