Abstract:

I calculated IMMT1T QPD fundamental noise.
In the current condition, IMMT1T QPD noise should be limited by shot noise, so SNR will be improved if we increase the laser power to 10W.

Detail:

To investigate the better parameter for IMMT1T QPDs, I calculated the fundamental noise level with current parameter.
What I used for the calcuation is following documents:
QPD circuit: JGW-D1402411-v3
QPD characteristic: S5981 datasheet
OPamp characteristic: LT1114 datasheet

Total output noise of the transimpedance amplifier can be calculated as the summation of the following 5 noises:
1. Voltage noise of OP amp
2. Current noise of OP amp
3. Thermal noise of transimpedance resistance
4. Dark noise of QPD
5. Shot noise of QPD

Voltage noise of OP amp:

According to the datasheet of LT1114, maximum input voltage noise is 2.8e-8 V/rtHz above 10Hz.

Current noise of OP amp:

According to the datasheet of LT1114, maximum input voltage noise is 0.03 pA/rtHz above 10Hz.
Since curret transimpedance resistance is 20k Ohms, output voltage noise due to OP amp current noise is 0.03 pA/rtHz * 20k Ohms = 6.0e-10 V/rtHz

Thermal noise of transimpedance resistance:

The transimpedance resistance (R) is 20k Ohmas and temperature is about 300 K, so the thermal noise of the resistance is sqrt(4*k_B*T*R) = 1.8e-8 V/rtHz, where k_B and T are the Boltzman constant and absolute temperature of the resistance, respectively.

Dark current noise of QPD:

According to the datasheet of LT1114, maximum dark current (Id) of QPD is 4 nA, so the shot noise of the dark current is sqrt(2*e*Id) = 3.6e-14 A/rtHz, where e is an elementary charge.
So, the output voltage noise due to the dark current is 3.6e-14 A/rtHz * 20k Ohms = 7.2e-10 V/rtHz.

Shot noise of QPDs with the current (future) configuration:

If we use 1W (10W) input, IMMT1T trans QPD2 obtained 1W (10W) * 3000 ppm (IMMT1 transmission) * 0.1 (IMMT1T POM transmission) * 0.5 (BS before IMMT1T QPDs) = 1.5e-4 (1.5e-3) W.
According to the datasheet of LT1114, optical efficiency of the QPD is about 0.25 A/W @ 1064nm.
So, the photocurrent (Ip) of the QPD is 0.25 A/W * 1.5e-4 (1.5e-3) W = 8.75e-5 (8.75e-4) A.
Therefore, the shot noise of photocurrent is sqrt(2*e*Ip) = 3.5e-12 (1.1 e-11) A/rtHz.
Since the transimpedance resistance is 20k Ohms, output voltage due to the shot noise of photo current is 3.5e-12 (1.1e-11) A/rtHz * 20k Ohms = 6.9e-8 (2.2e-7) V/rtHz.

Summary:

Since photo current shot noise is the largest in both cases, current IMMT1T QPD noise seems to be limited by shot noise.
So, if we increase the laser power, SNR wll improve by sqrt(10).