visible light communication data reception
First, what do you mean by "modulate"? AM? FM? What bandwidth? 

Second, you need faster op amps. The LM358 at 200 kHz is running right at the raggedy edge. And a 200 kHz high-pass with a 358 is madness. Furthermore, assuming a single-pole high-pass at 200 kHz means that you are losing 50% of your signal - check out the details of high-pass operation. Finally, if you have a high-pass at 200 kHz, why do you have a notch filter at 100 Hz? It makes no sense. The fact that your TIA never levels out at either top or bottom is proof positive that it (in combination with the photodiode) is too slow. And the asymmetric rise/fall waveforms are a strong indicator that you are saturating, probably at the zero level.

Third, I'll bet you're running the LM358 in your TIA single-supply. Don't. It doesn't work all that well at zero output. You must either a) go dual-supply, or b) run a virtual ground. Are you using photoconductive or photovoltaic mode? If the former, what is your bias supply?

Fourth, if you're running photovoltaic, this is not a good choice of sensor. It has a big area (10 x 10 mm), which is gigantic by most standards. This makes it sensitive, but it also makes it slow. The data sheet gives the 0V rise time as 2 usec. This is probably the rise time from 10% to 90% of final value. At 200 kHz, each phase is only 2.5 usec, so you can see that you are (once again) on the raggedy edge. You must go with photoconductive, and the need for a bias supply once again says you should be running dual-supply. And if you use a photoconductive mode, be aware that the diode capacitance (160 pF at 10 volts bias) means that you will need to have a decent feedback capacitor to ensure stability. And this, in turn will limit TIA bandwidth, so be careful. 

TL;DR - Not enough information to provide an answer, just questions. Please edit and use the schematic tool (the button with the diode and resistor), or just hit ctrl-m. Provide schematics of your circuit.

I suggest you try running your LED at 1 KHz and see what your waveforms, particularly the TIA output, look like when the op amp is operating within its proper range.