For engraving, like cutting, we need opaque acrylic. Not only is it opaque, but it is darker in color. White and blue are about the same, no.
Anyway, what can you do with opaque acrylic? Just like wood, you can carve on it, shallow or deep, etch it without masking material, and of course cut it. Unlike wood, engraving on acrylic will not give you a deep black or dark brown finish, but the same color or white version as your acrylic.
Run the cut pass test to determine the combination that cuts the material most quickly and cleanly. Both types can be found in the files section of the group I uploaded. By reading the associated post for each test file, you'll see a video on how to use the test in the first comment.
On a basic level, the faster you go, the less depth you gain. Power is the opposite, the greater the power, the greater the depth. This should give you an idea of what to expect in the test results.
Acrylic for laser engraving sheets usually have protective layers on both sides and are usually made of paper, but sometimes plastic. Some people keep it and pick the rest from their project. Everything the laser touches should evaporate, which makes this a viable option, but I find it tedious to pick after the fact, and sometimes the melted parts don't want to come out of small details. For this reason, I habitually remove paper unless it's just for cutting.
Like the paper/no paper issue, using air assist is often a matter of personal taste or project requirements. When working with wood, ideally set the air assist to low output to prevent smoke and particulates from collecting on/in the conical assist nozzle, and on the laser lens. Higher air volume or pressure during engraving can have a faded effect on engraving, which is often a less attractive result.
Acrylic responds differently to air assist when cutting. What you get is not a faster/more efficient cut, but a slower cut. But it's not all bad. On close inspection of cutting acrylic, cuts with air assist tend to be cleaner and have less warping or blistering in the surrounding area.
When engraving, air assist tends to result in a more whitish appearance. Without air assist, the color is closer to the original, but material warping/blistering may be noticeable.
Can you make photos on opaque acrylic with a laser engraver? Yes, of course. You just don't need to use a masking material like tempera. The light touch of the best laser engraver for acrylic whitening the surface is perfect for taking pictures.
In some ways, opaque acrylic is easier to work with than wood because its properties are so consistent and the surface is so smooth. This removes many of the frustrations of working with organic materials.
Just because we're talking about engraving on acrylic doesn't mean you're going to be bothered by the natural look acrylic offers. Quite the opposite. It is suitable for multi-layer paint work such as used with tile and canvas. Laser foil is a particularly good match, and the smooth surface of acrylic is great for bonding.
Because acrylic can be carved out like wood and can become a little sticky when touched by a laser beam, powder coating media works well, as does mica. For all of the above combinations, the same technique used for wood works for acrylic, just the power and speed vary.
Obviously, you can do a lot with acrylic other than just cut out the earring shape. It's not particularly difficult to work with, and in some ways easier to manage than wood. The key to a successful acrylic engraving is the setup section at the top.
A small test will give you a lot of information that you can then use for any number of projects. Pure acrylic, acrylic plus one or more other media, surface color, depth, you name it. Don't limit your creativity or product line. Explore, experiment and grow your own business.