Electronic – practical way to create/inject some visible interference into a nearby AC mains

Microchip has a great app note on using a PIC to send and receive X10 over power lines. It is here...

http://ww1.microchip.com/downloads/en/AppNotes/00236B.pdf

Since you only want to send a single bit, you could just steal some of the ideas and simplify.

Here is their block diagram for injecting a signal onto the mains...

You could use a PIC or an AVR (like and arduino) to generate the carrier as shown, or if you want to keep it simple you could use something like a 555 or even an RC oscillator, but keep in mind that an MCU like an ATTINY only costs like $1 today and will give you a more accurate and stable frequency base (especially if driven by an Xtal), and opens up possibilities for sending more than one bit (like sending error correction with the bit to make detection more accurate).

Here is their block diagram for a detector...

...which again uses a Microchip PIC, but that could easily be replaced with an AVR or even just a relay.

I'd really urge you to read the whole app note as there is a great explanation of how the carrier interacts with the mains, when you should send it, and even how to power your circuit from the same connection to the mains using a transformer-less supply.

Yes, you can do this. However, anything called a "mains powered heater" has a time constant way longer than a power line cycle. You can still modulate the power to the heating element (resistor), but it is much easier to do this in multiples of line cycles or at most half line cycles.

I actually did this in a real product once. This product had to accurately control the temperature of a couple dozen line-driven heaters. The controller got temperature measurements from thermistors, then controlled the heaters by switching each one on or off for a 1/2 power cycles. This was done using solid state relays that only switched the outputs to a different state at each zero crossing of the AC line. Doing this reduces transients from switching, and keeps the heater power linearly proportional to the PWM value.

Instead of straight PWM where the output is turned on for some fraction of a fixed period, then off for the rest, I used a Bresenham algorithm to switch each half line cycle separately. The worst case low frequency content is still the same, but the average is better.

In this case, I had the control algorithm produce a byte representing the desired heater power. Since each PWM time slice was 1/2 power line cycle, and the PWM period was 255 slices, this period was 2.13 seconds for 60 Hz power. For 50 Hz power it would be 2.55 seconds. As long as the heater's response is significantly slower than that, this works fine. In my case, the first time constant was several minutes, so a few seconds was plenty fast enough for the PWM period.