It has pleocrhoism in green and blue (3rd picture), extinction angle very close to zero but the interference colours are not seen because of the mineral's strong colour, it is found in a trachyte. Pale green-yellow mineral is biotite.
It is a common phyllosilicate Chlorite occurring as an alteration product of biotite as seen in the pictures.
Chlorite light green in color with faint pleochroism will turn indigo blue under crossed nicols.
We can see even muscovite occurring in close association with this chlorite-biotite and it seems to be secondary muscovite formed at the expense of biotite.
The fibrous habit,secondary occurrence in an alkaline rock, and (if the photos give a true representation) color are all indications that what you have is, indeed, reibeckite.
Sorry for my late replied, anyway I would like to confirm that my first thought was Amphibol ( Riebeckite) due to characteristic blue pleocrhoism, more o less I could distinguish a fibrous form, and the rock type in which it was found. I determined Riebekite found in metamorphosed riolitic lava. In my opinion, Riebekite might replaced a Na-Pyroxene.
I think the mineral is a Na-amphibole which is a product of a late-stage sodic alteration possibly by a CO2 rich fluid. This typically shows a fibrous texture and replaces the original biotite. Similar textures are seen in fenites.
It is indeed blue amphibole, not exactly riebeckite because the pleochroism is not so extreme, neither the colours so dark. The birefringence is ok for amphibole, so I'm surprised about the reference to anomalous colours. As a matter of fact, alkali amphibole might have anomalous birefringence (not the case in the picture). And, as John Coats noticed, the relationships might be indicative of fenitization. Unfortunately I have problems in downloading the image files, which precludes a closer look. Not sure I can see calcite - could you please send me the pictures as attachments, fenitization is an interesting phenomenon. What is the geological backgroud, do you have peralkaline rocks nearby?
Dear Gavril, thank you very much for your answer. There´s calcite indeed in the sample, as well as biotite. This thin section is very interesting, however it's not from my country, it´s from Galore Creek- British Columbia- Canada, there's an alkali ignoeus complex there. Nevertheless I couldn´t imagine at first that the amphibole would be secondary if there's biotite too.