I changed the LC tank circuit, inductor to 470uH. These are the old inductors in elec shop. I couldn't understand why my resonant frequency shifted from 2.1Mhz to 1.63MHz. First I took it as some drift in pockel cell capacitance. But, then I tried to find the specs of the inductor. (It's bad!!)

The self resonance frequency of the inductor is 2.4Mhz. It's literally near my resonant freq. I was not expecting it to be this low. If we use such inductor near their self resonant freq, all forms of parasitic capacitance will affect my circuit. This explains also why my circuit could only achieve half of the desined modulation. The radial leaded inductor stored in elec shop are not good for RF applications. Being so close to self resonance freq can lead to degraded quality factor as well.

I found specs of some from coilcraft, and their self resonance freq is 210Mhz. Some inductor like this will solve the issue. There are some chip based inductors in elec shop, I will check their specs. 

Fig 1 is the circuit currently. The opamp used is EL2099CT. 

File 2 is datasheet of 470uH from elec shop.