The way to do this is use a crystal oscillator and divide the frequency down to 38 Khz at a very small duty cycle.
You can then safely pulse maybe an Amp or so through the LED if the duty cycle is made short enough.
That takes care of the transmitter.
The receiver needs to be very precisely tuned to the exact same 38 Khz pulsing transmitter frequency, and you can do that with either synchronous digital sampling, or analog techniques.
By only being sensitive to the exact 38 Khz transmitter switching frequency, it will eliminate all ambient lighting interference and noise problems, and you can use really high gain in the receiver.
It then works exactly like a tuned narrow band radio receiver, but working at infrared.
There is nothing new or revolutionary about any of this, some commercial intruder beam alarm systems work on this narrow band tuned reception principle to span very long ranges day or night.
The secret is accurate timing at both ends. If you want an operating bandwidth of maybe only a few Hz, your frequencies need to be that accurate at both ends, and only a quartz crystal oscillator will give you that.