Hi Dimitris,
I remember I struggled with this too, but I cannot recall if there is any tool for that. The code below is roughly what I would try. I don't have ArcGIS at hand at the moment to test it, but hopefully any glitches are only minor.
The key is that you can refer to individual bands within a raster dataset by their correct path, just like you can drill down to them in the Catalog directory tree. Usually, bands are called Band_1, Band_2, and so on. The problem is that sometimes they have different names (Layer_1, etc.) The code below deals with this by looping through whatever children the raster has and getting the correct name.
Results (individual raster bands) are stored as individual rasters in the output directory.
import arcpy, os
in_raster = r'c:\path\to\raster.tif' # input multiband raster
out_folder = r'c:\path\to\output\folder' # preferably an empty folder
desc = arcpy.Describe(in_raster)
for band in desc.children:
bandName = band.name
band_path = os.path.join(in_raster, bandName)
dest_path = os.path.join(out_folder, bandName + '.tif')
arcpy.CopyRaster_management(band_path, dest_path, "", "", "", "NONE", "NONE", "") # change parameters here
I have a feeling there might be a more elegant solution, but if you cannot find it, give this a go. Make sure you change the parameters at row 2,3, and 11, then just paste it into Python window and hit enter. And then enter again.
The code is inspired by 41145 - Add individual raster bands from a multiband raster... and Extract one band from 3 band raster
Let us know if this works for you, I'd really want to know.
Filip.