Analysis of the Single Tapered Mode Coupler

853 854 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1955 ficient vary with distance along the lines. Strictly speaking, the concept of normal modes is not applicable to non-uniform coupled lines, but if the phase constant difference and the coupling coefficient vary slowly enough with distance, it is useful to introduce the idea of "quasi-normal modes." A quasi-normal mode is a field configuration at a given point in the lines when the line parameters vary slowly compared with the local beat wave length. It differs only slightly from the field configuration of a normal mode that would have existed at the same point if the line parameters were constant at their local values. Since the line parameters vary, the quasi-normal modes are actually tapered, so that the same quasi-normal mode may correspond to all the power in line 1 at the beginning of the coupler and practically all the power in line 2 at the end. The quasi-normal modes in non-uniform lines are coupled, but the coupling is small if the variation of line parameters is gradual. Hence directional couplers may be made in which essentially all the power remains in one of the quasi-normal modes while passing from one line to the other. Such couplers will be called single tapered mode couplers. A study will be made of the restrictions that must be placed on the phase constant difference and the coupling coefficient variation in order that power transfer may be effected between two lines in a single tapered mode coupler. It is found that the phase constant difference and the coupling coefficient must vary slowly compared with the local beat wave length.