Is the serial connection possible in a Photoelectric Sensor?

When photoelectric sensor 1 is turned on, the voltage is supplied to photoelectric sensor 2 in above figure.

At this time, inrush current I2 when the power supply of photoelectric sensor 2 is turned on flows to the output of photoelectric sensor 1. (It is about 0.5 to 1A instantaneously in charging current of capacitor.)

The output short-cut protection circuit* of a photoelectric sensor works by this inrush current I2, and the output of photoelectric sensor 1 is turned off.

As a result, the voltage is not supplied between power supplies of photoelectric sensor 2 and cannot be operated. Therefore, the serial connection cannot be connected.

*Output short-cut protection circuit:
It is the circuit that turns off output detecting the current and protects transistor, when overcurrent (above rated load current) flows to output.

Please use the serial connection by the combination with the sensor controller.