"Strings which are compared are identical"
In general regular expressions are NOT used to compare identical strings (although in some specific circumstances they can do that). If you want to compare identical strings, then use the correct tool: strcmp, strncmp, strcmpi, strncmpi, strfind, contains, ismember, etc..
Regular expressions are not supposed to be identical to the parse string, they are a language that describes pattern matching. If you want to know how to write your own regular expressions, then you will have to read the documentation... and then read it again... and again... and again... (because they are not a trivial language to learn, very powerful certainly, but not trivial):
"Why the following expresseion returns empty array ?"
Because you did not write a regular expression that matches that parse string. Once you read the documentation carefully and escape the active characters, you will get the "expected" output (the start index of the matched string):
>> regexpi ('a4126643_farfield_(f=2.4)','a4126643_farfield_(f=2.4)')
ans = 
>> regexpi ('a4126643_farfield_(f=2.4)','a4126643_farfield_\(f=2\.4\)')
ans = 1
You could also escape the active characters using regexptranslate:
A strict "identical" match would also require anchors for the start and end of the text: '^...$'