Vinay,
Your experiments confirm the pen and paper analysis I did when you mentioned light funnels in this group a long time ago. The light cone ends up having lots of internal reflections and turns away lots of light. The CPC is the ideal version of what you are thinking. looking into a CPC from inside the collection angle, the walls are all black (or whatever color the target is). From outside that angle the walls look shiney.
Looking into your light cone from where you expect light to be coming from (ie, your eye is the sun), you could see how much of the reflector surface is blacked by the reflection of the target. That shows you what areas of the reflector are actively engaged when your eye is replaced by the sun. That will tell you better than a simulation would because this design is very inefficent and not very sensitive to varations.
A simulation will tell you that the angle of a ray becomes rapidly more shallow with secondary and tertiary reflections, and with multiple reflections the ray is turned back and shot out of the cone. (I dont have those original notes with me right now). with sides at 45 degrees, all light is rejected from the cone. at 60 degrees, light coming straight in can bounce once, but a second bounce and its on its way out again.
Thats with light coming straight in. With light coming in at some angle (due to the sun having some size, and much more due to imperfect tracking), the performance is much worse.
If you make the cone too long, then the extra length is not doing anything because any light that hits the sides thee will bounce several times and escape.
So, you make the sides steeper, and rays can sustain more bounces before they are rejected, but the entrance becomes narrower. adding length doesn't fix this.
http://books.google.com/books?id=MliJHWwTnVQC&lpg=PP1&dq=nonimaging%20optics&pg=PA49#v=onepage&q=&f=false
A 2d version would be easy to model, the 3d would require writing new geometry, which I wont do. The 2d CPC is an ideal concentrator, but its 3d version is actually less than ideal. I bet the 3d light cone rejects more light than the 2d also.
I will model a CPC using two or three flat sections rather than an continuous curve and see how that goes.