The problem is the BPW21's self-capacitance and the op-amp's lack of gain. If the BPW21 was an ideal photodiode with zero self capacitance then the LF351's limited bandwidth of 5 MHz would still be a problem because there is very little open-loop gain at 1.5 MHz (and that's just the fundamental frequency of the squarewave you are trying to amplify as per your earlier question on this subject): -
So, you really do need an op-amp that has a significantly higher bandwidth. But, the self capacitance of the BPW21 (quoted as 48 pF) will mean that the op-amp has to drive that capacitance via the 2.2 kΩ feedback resistor and this makes it worse. At 1.5 MHz, this is an impedance of 2210 Ω. Some data sheets quote the BPW 21 having a capacitance that is much higher so you need to know what item you have bought and where it came from.
So, the op-amp is working a lot harder and the gain rises. This is your problem; a mixture of poor op-amp choice and a photodiode capacitance that is also going to ruin your square wave shape. Here's a simulation to show you the gain peaking versus photodiode capacitance (C1 below): -
And, if your BPW21 is like some of the devices you can find on the internet then the peak in the AC spectrum could be easily more than 10 dB.