Image rotation about the axis of view via skew lenses and special relativity

Abstract We propose a configuration of skew ideal lenses that provide a stigmatic image of the scene with a magnification +1, rotated around an axis of view. The design of the proposed skew-lens system is inspired by the theory of special relativity, namely the Wigner rotation, when noncollinear Lorentz transformations are combined. The angle of image rotation φ can be set arbitrarily within a range <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mi>π</mml:mi> <mml:mo>,</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> except for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mi>π</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . Provided that an experimental realization is achievable, the Wigner rotator introduced here, may serve as a foundation for biomedical applications, for example, in the treatment of cyclotropia. Our work reveals previously unappreciated imaging properties of skew-lens combinations and aims to escalate the research in fabrication of metalenses as the closest real-life realizations of ideal thin lenses.