optics - Detailed form of light waves in vacuum and how to test it experimentally?

Consider a light wave in vacuum.

• Do the $\vec{B}$ and $\vec{E}$ fields have to be orthogonal to each other? Since you can add constants to a solution to Maxwell's equation it doesn't seem neccesary from theory.


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  How would one measure if the $\vec{B}$ and $\vec{E}$-vectors of a light wave are perpendicular?

  
  


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  Must it be a plane wave? How to determine that by measurement?

  
  
  


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  Must $\vec{E}$ and $\vec{B}$ be in phase? How to test this experimentally?

  
  

Edit:

A part of my question is covered in Does the direction of propagation of the natural light is perpendicular to the direction of electric and magnetic field making up natural light? but that question is closed and the answers doesn't help. However my question is more about experiment than theory, so is a different question.