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I know that laser wavelength depends on four important properties:

  • Bandgap of its material
  • Gain spectrum
  • Length of cavity
  • Size of a quantum well, if we talk about the quantum well laser

But it's a bit hard to wrap my head around the the interplay of those four factors. Is there some final formula for that?

For example, the wavelength emitted by the semiconductor is determined by the bandgap. But if said semiconductor is placed inside of quantum well, the wavelength decreases (because energy increases, due to electron confinement).

The emitted wavelength is not perfectly corresponding to the bandgap, because of thermal excitations, which spread the electron energies.

Then there's gain spectrum. A bunch of wavelengths will get amplified in the cavity. Some of them a lot, some just a little bit.

And in the end there's cavity length, that will allow for resonance of only those wavelengths that create a standing wave in said cavity. There can be many wavelengths that fulfill that condition (cavity length equal to integer number of half-wavelengths).

So in the end, let's say that I want to make a laser of x nanometers wavelength. How do I choose the correct parameters? How is that even possible to make a mono-chromatic laser, with so many interplaying parameters?

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  • $\begingroup$ Those are the same issues with design of any laser, so I'm not sure exactly how to answer. $\endgroup$
    – Jon Custer
    Jun 8, 2020 at 20:01
  • $\begingroup$ @JonCuster maybe answer with a reasoning that goes inside of laser designer's head, when he/she is tasked with making a laser of certain wavelength? "Step by step guide to a laser of your desires". Also: not every laser can include quantum well. $\endgroup$
    – user46147
    Jun 8, 2020 at 20:04

2 Answers 2

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Like any laser, the lasing happens when the modes of the cavity overlap the gain spectrum.

In your list, the cavity length is the main factor affecting the cavity modes. You might also add the waveguide material index of refraction, and the phase shift of the reflectors (which is engineerable in a DFB or DBR laser) to this list.

The material bandgap and the QW geometry mainly affect the gain spectrum. I wouldn't consider the gain spectrum a separate factor. You can engineer the bandgap by changing the semiconductor material. There are a couple of systems where two or three semiconductors can be alloyed to control the bandgap while retaining the same lattice constant (so keeping them lattice-matched to an appropriate substrate). For example, AlAs and GaAs can for the most part be alloyed in arbitrary proportions (but too high an AlAs content results in an indirect gap material) to get bandgaps corresponding to various wavelengths in the 700-850 nm range. And InAs, GaAs, InP, and GaP can be alloyed in various proportions to get wavelengths in the 850 - 1600 nm range (again I didn't go look up the actual limits).

Here's a diagram that shows common III-V semiconductor alloys and how their lattice constant and band gap vary with alloy composition:

enter image description here

You can also play with strain (deliberately mismatching the lattice constant of the QW material with the surrounding material) to further adjust the gain spectrum.

Generally, as with other laser types, the gain spectrum will be relatively wide, and the cavity modes will pick out a particular wavelength within the gain spectrum to actually laser. So first find a material system and QW geometry that lets you produce reasonable gain at the wavelength you want. Then design a cavity that picks out exactly that wavelength.

This isn't my day job, so you'll probably find I've oversimplified things considerably, and you may run into "engineering challenges" trying to achieve some of the possible combinations.

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The previous answers appear to miss one important design aspect. Note that a typical HeNe laser for example has a length of several tens of centimeters, and emits light around 633 nm, containing up to 8 longitudinal modes, each with a slightly different wavelength corresponding to a different integer number of wavelengths fitting into the length of the cavity (the space between mirrors). The range of lasing wavelengths is determined by the gain spectrum of the HeNe medium, while the specific wavelengths emitted are determined by the condition that an integral number of wavelengths must fit into the cavity.

When the cavity is very short and has a high Q, changing that integral number by 1 can result in a large change in wavelength. If the gain spectrum is relatively narrow, only one such wavelength (longitudinal mode) can fit into the cavity and still fall within the gain spectrum. In that case, the laser will emit a single wavelength rather than a mix of wavelengths.

Alternatively, an etalon can be put inside the cavity. This is basically a secondary "cavity" consisting of a flat glass plate. The etalon is essentially a "comb filter" that causes losses except for very specific wavelengths. When the etalon is adjusted to make one of its low-loss wavelengths coincide with the wavelength of one of the longitudinal modes of the main cavity, the laser emits only that one wavelength.

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  • $\begingroup$ I learnt some about HeNe lasers, I guess similar constraints apply to semiconductor lasers too? $\endgroup$
    – boyfarrell
    Jun 9, 2020 at 19:05
  • $\begingroup$ Yes, the same applies to all lasers. $\endgroup$
    – S. McGrew
    Jun 9, 2020 at 19:24

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