Hello and thanks for your question.
There are a few different types of lasers done for glaucoma. One of them is a laser trabeculoplasty, where the drainage structure inside the eye is lasered to allow it to open up more and drain the fluid inside the eye better. Typically, the surgeon will laser one half of the drain in one eye at each session. They will check your pressure one hour afterwards because one of the most common things that can happen from this laser is a rise in pressure afterwards. Most people have a good result from this laser surgery but it is not effective in all types of glaucoma. Usually the effect only lasts 1-3 years, however. There is no known adverse long-term effects in the eye from having this surgery. That being said, there are risks of doing this surgery which include increased pressure inside the eye which may be difficult to control, damage to other structures in the eye, retinal detachment, blurry vision from retinal swelling and possible hastening of cataract formation. For most people these are uncommon to rare risks and most do well with it.
The other laser you may have done is a laser peripheral iridotomy which is where the laser is used to put a small hole in the periphery of the iris, which acts as a stop-gap, or safety valve, allowing fluid to pass from behind the pupil to in front of the pupil where the drain is. This is needed when a person has narrow angles (the areas leading to the drains) and the fluid is not draining as it should. People with narrow angles are at risk and sometimes get an acute narrow-angle glaucoma attack which causes decreased vision, a very red and very painful eye, nausea and vomiting. If the pressure is not brought down adequately within a few hours the vision can be permanently damaged from this.
The risks of doing this surgery are similar to the other laser procedure I described above. There is a possibility of pressure spike shortly after so the pressure would be checked in one hour after the procedure. Aside from the risks of the procedure, there are no known long-term adverse events to the eye or vision from having this procedure.
These lasers have different and in a way more immediate risks than drops, which for the most part are relatively safe, but they have their own set of problems. They require a daily treatment, sometimes several times per day and the side effects are usually the biggest risks which can include chronic redness, irritation, lash growth, skin hyperpigmentation, not to mention monthly costs.
As far as an initial treatment choice, they are both reasonable as long as the laser would be effective with respect to the type of glaucoma you have.
Does that make sense and does that help address your concerns?
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My opinion is solely informative and does not constitute a formal medical opinion or recommendation. For a formal medical opinion and/or recommendation you must see an eye doctor.