# Controlling output light power by constructive/destructive interference

• Mayan Fung
In summary, a Mach-Zehnder modulator splits an input light into two, and can alter the refractive index of one of the two arms to induce a phase difference between the split lights, which can be recombined into one output light signal.
Mayan Fung
In optical communications, one of the modulation methods is to control the optical power (Simplest case, for example, bright = bit 1, dim = bit 0). I learned that we can achieve this by a Mach-Zehnder modulator (MZ modulator).

Simply speaking, the principle of MZ modulator is to split the input light into two, traveling in two waveguides. By applying a voltage across one of the two arms, we can alter the refractive index of it and thus inducing a phase difference between the two split lights. Then, when they are combined as one output light signal, if they constructively interfere, then the output power is maximum (bit 1). Otherwise, if they destructively interfere, then the output power is minimum (bit 0).

It sounds good till here. Yet, I am puzzled about energy conservation. Let's say we split the input light into two with the same amplitude. When they combined with destructive interference, there is no light. How come we have optical power input but no power output?

The two point sources are combined so as to get cancellation in one direction.
There will be other directions in which the energy is summed.

Baluncore said:
The two point sources are combined so as to get cancellation in one direction.
There will be other directions in which the energy is summed.

But in the above schematic, seems that there is only one output direction. Can the light escape the wavelength?

Chan Pok Fung said:
But in the above schematic, seems that there is only one output direction.
The diagram is symbolic.
It is not shown how light is split into two channels.
It is not shown how light is recombined into one line.

sophiecentaur
Baluncore said:
The diagram is symbolic.
It is not shown how light is split into two channels.
It is not shown how light is recombined into one line.
One possibility is to split and combine with half silvered mirrors. The diagram of a beam splitter is on this Wiki page. There are two input ports and two output ports. When combining your two beams, one port will let through the sum and the other will let through the difference resultants. You 'just' need to get the path lengths right to achieve that.

I see your points. That makes sense if there are two outputs. Thanks

## 1. What is constructive and destructive interference?

Constructive interference occurs when two or more waves of the same frequency combine and their amplitudes add together, resulting in a larger amplitude. Destructive interference, on the other hand, occurs when two waves of the same frequency combine and their amplitudes cancel each other out, resulting in a smaller or zero amplitude.

## 2. How can constructive and destructive interference be used to control output light power?

By carefully manipulating the path length and phase difference of two or more light waves, constructive and destructive interference can be achieved. This can be used to either amplify or cancel out certain frequencies of light, thus controlling the output light power.

## 3. What is the principle behind controlling output light power by interference?

The principle is based on the superposition of waves, where the amplitude of the resulting wave is the sum of the individual wave amplitudes. By adjusting the phase and path length of the waves, their amplitudes can be manipulated to either add up or cancel out, resulting in controlled output light power.

## 4. What are some applications of controlling output light power by interference?

This technique is commonly used in devices such as lasers, interferometers, and optical filters. It is also used in various optical communication systems, as well as in spectroscopy and microscopy.

## 5. Are there any limitations to controlling output light power by interference?

Yes, there are limitations such as the coherence of the light source and the stability of the setup. The interference pattern can also be affected by external factors such as temperature and vibrations. Additionally, the technique is only effective for controlling output light power within a certain range of frequencies.

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