I disagree with you, Serge:
In all of your circuits, of course the IR diode is foward-biased, with its anode shown connected to +9V, +4.5V or +5V, and the cathode connected through a resistor to negative or ground. The diode is shown conducting forward current, all the time.
Please check your working circuits and you will find that the IR diode is connected in reverse. For example, in your 3rd circuit, the anode of the IR diode is shown connected to +5V. Since its cathode connects to ground through a resistor, then you must measure about +4.3V at the inputs of the logic gates without IR radiation, since the diode will be forward-biased. But when you measure it, I think that you will actually measure about 0V, since the diode is actually reversed and will not be conducting. I do agree that the 9V battery and resistor in the 1st and 2nd circuits and the +5V and resistor in the 3rd circuit will convert DC to AC during modulated IR radiation, but only if the IR diode is reverse-biased.
Again, I ask what is the function of the rectifier diode and why is it forward biased? Are you using the voltage divider that includes the rectifier simply to bias-up the input of the schmitt trigger and therefore make it more sensitive to low-level signals? If so, then the rectifier is not needed.