I've been told that adding a HO alternator will NOT fix the problem. I also have this problem and was told by many that what I need to do is check the grounds on the car and clean them up. If it still dims, then you need to install a 10 gauge wire from the neg battery terminal to the chassis. Also add a 4 gauge wire from the neg battery terminal to the transmission case. This will help ground the battery better thus eliminating the dimming of the lights.
I haven't tried it yet but I will report back after it do it. I can assure you that adding a cap will NOT help as I already have a 2 farad capacitor and it still dims. I do NOT have a cheap amp either. I'm only running a 1k watt mono block to a single JL audio 10w3.
Hope this helps.
