Now, it looks professional.
My english is far from perfection, but:
- I don't like "after having gone through your website", maybe "I visited your website and I am very....";
-"institution provides both the opportunities for research as well as the implementation of that research" -> maybe "as well as their implementation"?;
- "Today,having completed my Bachelors in Medical" : don't like having completed...
- "I aspire to get into the photonics field. Within this field, my interest lies primarily in the areas of photonic": too many "field" and "photonics". I'd rather say "into the field of photonics. In particular, my interest ...." or something like that;
- "physics and chemistry, was diversified into different fields, from electronics and the physics of semi-conductors components and
biomaterials, to optical fibers in biomedical imaging, laser technology and its applications in biomedicine, as well as simulation and modeling techniques of biomedical systems." :
different fields: .....
or "different fields, such as , , and . "
- "Added to this, I did an undergraduate project entitled Study of Fresenius Vial’s Double" : in addition... sounds better
- "As indicated earlier, my interest lies in the areas of photonic circuits and devices. I find this PhD position an..." : no need to repeat your interests. It's a new paragraph, so you can just say "I find ...." .
This is what I would suggest you to change, keep in mind I'm not a native speaker, so....