GUIDED-WAVE I'H()rA(iATI()X TllK()U(iH (lYHOM A(;XKTIC MEDIA 01 1 



Fig. 9 ■ — Geometrical exploration of the solution curves. The permitted areas 

 of the X — (T plane are divided by the 0, 7, {0)t , {I)t curves into regions in which 

 G{\, a) and G{T{\), a) have like or unlike signs. Shaded regions are those of unlike 

 signs. Solution curves (shown schematically by dotted lines) must lie in regions 

 of like signs. Onlj' the first few and / curves are shown. Fig. 9(a) and (b), ro "^ 

 3.0; Fig. 9(c) and (d), ro ~ 5.0; Fig. 9(e) and (f),W2 < ?•« < j^. ; Fig. 9(g), ro < u, . 

 I p i < 1 , throughout. The horizontal dashed line marks | o- | = | o-o | . 



Polder relation is indicated, for p = 3^^, by shading. For other p-values 

 the straight portion of the boundary of the excluded region is simply 

 translated along the X-axis. 



In Fig. 9(a) the allowed region of the first quadrant is shown again, 

 together with the transforms (Ia')t, (OiOr, and (In')T of the only 

 critical curves I /, 0/ and Ib' occurring in the second quadrant for the 

 present radius. Regions in which G(\i , cr) and G(T(\i), a) have opposite 

 sign are shaded; the common signs in the remaining parts of the quadrant 

 are as indicated. (In this diagram p is taken to be %). 



From the disposition of the surfaces G(\i , a) in the region between Oi 



