The invention relates to novel transparent glasses, vitroceramics, and transparent or translucent ceramics containing, in relation to the total composition of the glass, vitroceramic, or ceramic, at least 60 wt % of a composition having the following formula (I): (M1O)x(M2O)y(M3)2O3)z(Al2O3)100−x−y−z (I), where M1 is an element selected from among Ba and/or Sr, M2 is an element selected from among Mg or Ca, x and y are numbers such that 30≦x+y≦80, y is between 0% and 10% of x, M3 is an element selected from among B, Ga, or In, and z is a number between 0% and 10% of (100−x−y). The invention also relates to the method for manufacturing said compositions and to the uses of said compositions in the field of optics.