A lot of mystique is attached to the omelet pan. Many cooks require a certain kind or weight of pan, some swearing that it must be steel, or cast iron, or aluminum, or coated with a nonstick surface. And more than one professional we know insists that the pan used for omelets must never be washed.
In our experience, however, the size of the pan is the only critical factor. For a 2- or 3-egg omelet, sufficient for 1 portion, we recommend a 5- to 6-inch skillet. Small pans give a thick and often undercooked omelet, while too large a pan gives a thin omelet that is easily overcooked.