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The table data are as follows:

Rectangular TE Modes.

- Tilde E sub x equals start fraction j omega micro over K squared c end fraction left parenthesis start fraction n pi over b end fraction right parenthesis H sub 0 cosine of left parenthesis start fraction m pi x over a end fraction right parenthesis Sin left parenthesis start fraction n pi y over b end fraction right parenthesis e to the power of negative start expression j beta z end expression.

- Tilde E sub y equals start fraction negative j omega micro over K squared c end fraction left parenthesis start fraction m pi over a end fraction right parenthesis H sub 0 Sin left parenthesis start fraction m pi x over a end fraction right parenthesis Sin left parenthesis start fraction n pi y over b end fraction right parenthesis e to the power of negative start expression j beta z end expression.

- Tilde E sub z equals 0.

- Tilde H sub x equals negative start fraction tilde E sub y over Z sub start expression T E end expression end fraction.

- Tilde H sub y equals start fraction tilde E sub x over Z sub start expression T E end expression end fraction.

- Tilde H sub z equals H sub 0 Cosine of left parenthesis start fraction m pi x over a end fraction right parenthesis Cosine of left parenthesis start fraction n pi y over b end fraction right parenthesis e to the power of negative start expression j beta z end expression.

- Z sub start expression T E end expression equals start fraction eta over the square root of start expression 1 minus left parenthesis f sub c over f right parenthesis squared end expression end fraction.

Rectangular T M Modes.

- Tilde E sub x equals start fraction j beta over K squared c end fraction left parenthesis start fraction m pi over a end fraction right parenthesis E sub 0 Cosine of left parenthesis start fraction m pi x over a end fraction right parenthesis Sin left parenthesis start fraction n pi y over b end fraction right parenthesis e to the power of negative start expression j beta z end expression.

- Tilde E sub y equals start fraction negative j beta over K squared c end fraction left parenthesis start fraction n pi over b end fraction right parenthesis E sub 0 Sin left parenthesis start fraction m pi x over a end fraction right parenthesis Sin left parenthesis start fraction n pi y over b end fraction right parenthesis e to the power of negative start expression j beta z end expression.

- Tilde E sub z equals E sub 0 Sin left parenthesis start fraction m pi x over a end fraction right parenthesis Sin left parenthesis start fraction n pi y over b end fraction right parenthesis e to the power of negative start expression j beta z end expression.

- Tilde H sub x equals negative start fraction tilde E sub y over Z sub start expression T M end expression end fraction.

- Tilde H sub y equals start fraction tilde E sub x over Z sub start expression T M end expression end fraction.

- Tilde H sub z equals 0.

- Z sub start expression T M end expression equals eta the square root of start expression 1 minus left parenthesis f sub c over f right parenthesis squared end expression.

Properties common to T E and T M modes.

- F sub c equals start fraction micro sub p 0 over 2 end fraction the square root of start expression left parenthesis m over a right parenthesis squared plus left parenthesis n over b right parenthesis squared end expression.

- Beta equals k the square root of start expression 1 minus left parenthesis f sub c over f right parenthesis squared end expression.

- u sub p equals start fraction omega over beta end fraction equals start fraction u sub p 0 over the square root of start expression 1 minus left parenthesis f sub c over f right parenthesis squared end expression end fraction.

Plane wave, T E M modes.

- Tilde E sub x equals E sub x 0 e to the power of negative start expression j beta z end expression.

- Tilde E sub y equals E sub y 0 e to the power of negative start expression j beta z end expression.

- Tilde E sub z equals 0.

- Tilde H sub x equals negative start fraction E sub y over eta end fraction.

- Tilde H sub y equals start fraction E sub x over eta end fraction.

- Tilde H sub z equals 0.

- Eta equals the square root of start fraction micro over epsilon end fraction.

- F sub c equals not applicable

- K equals omega the square root of start expression micro epsilon end expression.

- Mu sub p 0 equals start fraction 1 over the square root of start expression micro epsilon end expression end fraction.