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The expressions are as follows:

Any medium: alpha equals omega times [ micro epsilon prime by 2 times [ the square root of 1 plus (epsilon double prime over epsilon prime) squared minus 1 ]] to the power of one half; beta equals omega times [ micro epsilon prime by 2 times [ the square root of 1 plus (epsilon double prime over epsilon prime) squared plus 1 ]] to the power of one half; eta sub c equals the square root of micro over epsilon prime times (1 minus j epsilon double prime over epsilon prime) to the power of negative one half; u sub p equals omega over beta; lambda equals 2 pi beta equals u sub p over f

Lossless medium (sigma equals 0): alpha equals 0; beta equals omega times the square root of micro epsilon; eta sub c equals the square root of micro times epsilon; u sub p equals 1 over the square root of micro times epsilon; lambda equals u sub p over f

Low-loss medium (epsilon double prime over epsilon prime is lesser than 1): alpha equals approximately equal to omega by 2 times the square root of micro over epsilon; beta equals approximately equal to omega times the square root of micro epsilon; eta sub c equals approximately equal to the square root of micro over epsilon; u sub p equals approximately equal to 1 over the square root of micro times epsilon; lambda equals u sub p over f

Good conductor (epsilon double prime over epsilon prime is greater than 1): alpha equals approximately equal to the square root of pi f micro sigma; beta equals approximately equal to the square root of pi f micro sigma; eta sub c equals approximately equal to (1 plus j) alpha over sigma; u sub p equals approximately equal to the square root of 4 pi f over micro sigma; lambda equals approximately equal to u sub p over f

Units: alpha equals N sub p per m; beta equals rad per m; eta sub c equals ohm; u sub p equals m per s; lambda equals m