By definition, a molecule is considered aromatic when in its constitution there is at least one derivative of benzene, ie, a cyclic structure with 6 vertices (all carbon atoms!), and 3 double bonds (in fact, as I said in other posts, they are not 3 double bonds, but 6 partially double bonds, with bond order of 1.5). Therefore, when, in a molecule, there is at least one such structure, the molecule is considered aromatic.
Probably some of you may be questioning yourself why to use the concept of "aromatic". In fact, most of the substances we know that have flavour (e.g., cinnamon or clove), have their aroma exactly due to the presence of molecules containing aromatic rings, in this particular case, cinnamaldehyde and eugenol, respectively. It is the delocalized electron cloud of the derivatives of benzene rings that give the fragrance to these (and many other!) molecules, and hence the chemical definition of aromatic is clearly related to the "physiological" setting of aromatic.
Let us return to amino... there are 3 that contain a derivative of the benzene ring on its side chain and are, therefore, referred to as aromatic amino acids:
Phenylalanine - the name itself explains the composition of this amino acid. In a previous post I talked about the nonpolar amino acids with aliphatic side chains, among whom was alanine (this post). Phenylalanine is no more than an alanine with a phenyl group, ie with a benzene ring. Since it only has carbon and hydrogen in its side chain, it is a nonpolar chain.
Tyrosine - this aminoacid is a hydroxylated phenylalanine. In fact, it only differs from phenylalanine because it presents a hydroxyl group on the aromatic ring, more precisely on a diametrically opposed carbon to the alpha carbon position. This hydroxyl group gives it some polarity, with the resulting side chain being therefore amphipathic.
Tryptophan – it is the amino acid with the more complex side chain comprising two cyclic structures: one is a benzene derivative, another is a heterocycle (ring composed of 2 different atoms, carbon and nitrogen in this case). These two fused rings form a functional group called indol group, which is amphipathic, since the nitrogen confers some polarity. Tryptophan is very important from a biological standpoint, because in addition to being used in the production of proteins, it is also the precursor of many important molecules, such as, for example, serotonin.
The tyrosine and tryptophan have an important characteristic, which is that of absorbing ultraviolet radiation. Due to this, the proteins having these amino acids (almost all!) present the ability to absorb UV light. In fact, phenylalanine also absorbs UV radiation, but in much smaller amount than the other aromatic amino acids, because the chemical modifications of the benzene ring (hydroxyl group in the case of tyrosine, and embedding the indole group in the case of tryptophan) significantly increase the UV absorptive capacity of aromatic rings.