High gain photodiode amplification response time
Using a 264M feedback resistor is asking for trouble, since you will need to take great care in cleaning solder flux from your board. You would do better with







simulate this circuit &ndash; Schematic created using CircuitLab

This will give you a time constant of 1 msec, which is much more appropriate for your modulation.

As for the why of C45, you should Google "photodiode transimpedance amplifier stability". Briefly, the capacitance of the photodiode at the input to the op amp will cause the amp to start oscillating. Feedback capacitance compensates for the input capacitance. The exact relationship is beyond the scope of an answer here, but do some research.

EDIT - Since you don't know how transimpedance amps work, let me try a few numbers. Assume 10 nA out of the PD. Pushing this through the 264 M resistor will, by Ohm's Law, produce 2.64 volts. Reducing the feedback resistor to 10 M will produce 0.1 volts. Multiplying this by 26 (the gain of the second op amp) will produce 2.6 volts, which I assume will be close enough.

If you were trying for a combination of maximum sensitivity and bandwidth, the revised circuit would suffer from slightly increased noise, but this should not be a problem in your case.