HFSS15: Formula Summary for HFSS Floquet Modes

• Planar array lattice is specified by lattice vectors a and b.

• Lattice angle a defined by a * b = abcosa

• Unit cell area A

• Global material is lossless, isotropic, and homogeneous, and specified by real e_r and m_r.

• Frequency is specified in the form of free-space wave number where f is frequency and c is the speed of light in a vacuum.

• Local coordinate system (LCS) unit vectors and are related to lattice vectors by:

(1)

(2)

(3)

where

Unit vector denotes scan direction. In the global coordinate system (GCS) the components of are given by (sinq_scosf_s, sinq_ssinqf_s, cosq_s) where scan angles q_s and f_s are specified as spherical angles in the GCS.

(4)

(5)

(6)

If

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(29)

If k_Z = 0, use the preceding formulas with k_Z = a where 0 < a <<1 is a small constant.

If k_C = 0

(30)

(31)

(32)

(33)

(35)