COUPLED ■\VAVK TJIHOUV AM) W A VKi; f 1 1)1'; Al'l'LICATIOXS ()()5 



A simplified example will illustrate the application of these relations. 

 Suppose the coupling function 4>(x) is constant in the inter\-al —L/2 to 

 L/2 and zero for other values of x. Then the discrimination function is, 

 from (4) 



Uniform Coupling Discrimination = . (5) 



sni 6 



Let us further assume, in the hypothetical example, that line 2 (Fig. 2) 

 is a single-mode line having a guide wavelength X2 equal to 1 .2X0 , and 

 that line 1 is the three-mode line ha\'ing guide wavelengths Xi , Xo , and 

 X3 equal to l.lXo , 1.2Xo , and 1.3Xo respective^. Assume the coupUng 

 length L equals 20Xo . For equal coupling to all modes in a differential 

 unit of length, the relative current waves travelling in the forward direc- 

 tion in the three modes of line 1 are obtained from (4). For the ratio of 

 the Xo forward current to the Xi forward current, 



for which (5) gives a discrimination of about 13.5 db. For the ratio of 

 the X2 forward current to the X3 forward current 



corresponding to a discrimination of about 14 db. For the I'atio of the Xo 

 forward current to the X2 backward current, 



corresponding to a discrimination of about 43 dl). The backward currents 

 in modes Xi and X3 can similarly be verified to be very small compared to 

 the forward-travelling X2 current. 



Thus, directivity and mode purity in a simplified case have been shown 

 to be of the desired form. 



It may be noted that the denominator of (4) is the Fourier ti'ansform 

 of the coupling function (f)(x). Since the numerator of (4) is independent 

 of 6, the discrimination is maximized by minimizing the denominator. 

 An analogous prol)lem exists in the time versus frequency domain rela- 

 tions, and experience with the latter can be used to predict the discrim- 

 inations to be expected using various coupling distributions. 



In the simple example cited al)ove, a length of coupling interval of 

 20X0 yielded a discrimination l^etween the desired versus imdesired for- 



