But here are some references you can download to get you started. Check out George Augspurger's "Sound System Design Reference Manual." Chapter 3 is about directionality, and it touches on the subject of narrowing directivity. Polar plots are used to illustrate coverage at various frequencies. Also see the AES paper called "Improvements in Monitor Loudspeaker Systems," by David Smith, Don Keele and John Eargle. It discusses directivity as well.