Is there a characterisation for conjugated dienes similar to cis-trans? As shown above,we know there are two configurations possible for conjugated dienes.

Are they given any special names like we have cis and trans?
This came up because while studying the Diels Alder reaction, it occured to me that maybe only the 'cis' like dienes will go through the reaction.
The current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) supports various stereodescriptors that are used to denote specific conformers, in particular concerning conjugated dienes:


  P-94.3.1.3 Stereodescriptors s-cis and s-trans
  
  The spatial arrangement of two conjugated double bonds about the intervening single bond is described as ‘s-cis’ if ‘synperiplanar’ and ‘s-trans’ if ‘antiperiplanar’. This descriptor should not be applied to other systems such as N-alkyl amides (use ‘E/Z’ or ‘sp/ap’).