If you are interested in seeing how the aria fits with Shakespeare's poetry, you can view a literal translation of the opera at The Aria Database. Although the poetry may not be Shakespearean, the beauty of the music and the sound of the human singing voice magnificently represents the emotion of the play and adds a layer of richness to the experience of Shakespeare's work.
For further study into the ways in which Shakespeare's work has been adapted into musical form, Arthur Graham -- professor emeritus at Kentucky University School of Music -- taught a class at the university titled: Shakespeare in Opera, Ballet, Orchestral Music, and Song: An Introduction to Music Inspired by the Bard. His book by the same name was published by Edwin Mellen Press, Ltd. in 1997.
Graham provides a detailed study of both Shakespeare plays Macbeth and Romeo and Juliet and their relationship to the various musical works inspired by them including the Gounod "Romeo and Juliet" and Verdi's "Macbeth" being offered by the Metropolitan Opera on simulcast this year. Graham also includes discussion of Verdi's "Otello" in his book. "Otello" is also being offered at the Met this season, although not on simulcast.
You can investigate Graham's work for yourself on Google Books. Page 45-46 gives a poetic translation of the "ah, leve toi soleil" aria.
In his book, Graham also gives a short discussion of Shakespeare's use of music in the plays. On page 200, Graham says:
In the plays he (Shakespeare) mentions several instruments with understanding of the mechanics of their performance, he puns on musical topics, frequently uses music as metaphor, and employs music in songs, dance, and for dramatic purposes. These give evidence of better than superficial knowledge of the art.
Yes, I would agree -- Shakespeare evinces a much better than superficial knowledge of the art of music. On page 199, Graham gives examples of Elizabethan musical culture, all relating to Elizabeth's court. And what does Graham have to say about the Stratfordian's deep knowledge and appreciation for the art of music?
Again, on page 200, "Shakespeare's middle-class upbringing would have included much contact with music in church, at home, and elsewhere."
Of course, there is no documentation of any such thing, but we are used to supposition in Stratfordian biography. That "elsewhere" is a particularly neat (and pointless) touch. And how much is "much contact"?
"Middle class" upbringing? What does that mean? There is no "middle class" as we think of it in Elizabethan England. There are some non-aristocrats who are beginning to get very rich, but the Shakspers of Stratford are not among them. Music in the home? This is not the Nineteenth Century -- there are no pianos in every parlor. Shakespeare's knowledge and deep understanding of music is yet another example of the Stratfordian's "genius". I'll bet he performed surgery with his bare hands, too!
I have no doubt that Graham is a man of depth and knowledge, and I find his book interesting and useful. But over and over, men of understanding twist the work to fit a shadow and I only wish they would begin to look for real substance.
On page 106, Graham says of the source of Shakespeare's Othello:
Giraldi Cinthio's Hecatommithi, published in Venice in 1566, provides the inspiration for Othello. We do not know whether Shakespeare read the story in the original Italian, in the French translation (1584), or in a now lost English translation. A knowledge of Italian was not unusual for educated Elizabethans.
This guy from Stratford, not only was he a "genius", he had all the polish of an aristocrat!
I don't think there is any conspiracy regarding the Shakespeare authorship -- I just think they got it wrong and it would be a lot more interesting to get it right.