Direct discrimination of structured light by humans

Abstract

<jats:p>We predict and experimentally verify an entoptic phenomenon through which humans are able to perceive and discriminate optical spin–orbit states. Direct perception and discrimination of these particular states of light with polarization-coupled spatial modes is possible through the observation of distinct profiles induced by the interaction between polarization topologies and the radially symmetric dichroic elements that are centered on the foveola in the macula of the human eye. A psychophysical study was conducted where optical states with a superposition of right and left circular polarization coupled to two different orbital angular momentum (OAM) values (<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:msub><m:mrow><m:mi>ℓ</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub></m:math></jats:inline-formula>and<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:msub><m:mrow><m:mi>ℓ</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub></m:math></jats:inline-formula>) were directed onto the retina of participants. The number of azimuthal fringes that a human sees when viewing the spin–orbit states is shown to be equal to the number (N) of radial lines in the corresponding polarization profile of the beam, where<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mi>N</m:mi><m:mo>=</m:mo><m:mo>|</m:mo><m:mrow><m:mo>(</m:mo><m:mrow><m:msub><m:mrow><m:mi>ℓ</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo>−</m:mo><m:msub><m:mrow><m:mi>ℓ</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msub></m:mrow><m:mo>)</m:mo></m:mrow><m:mo>−</m:mo><m:mn>2</m:mn><m:mo>|</m:mo></m:math></jats:inline-formula>. The participants were able to correctly discriminate between two states carrying OAM<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mo>=</m:mo><m:mn>7</m:mn></m:math></jats:inline-formula>and differentiated by<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mi>N</m:mi><m:mo>=</m:mo><m:mn>5</m:mn></m:math></jats:inline-formula>and<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mi>N</m:mi><m:mo>=</m:mo><m:mn>9</m:mn></m:math></jats:inline-formula>, with an average success probability of 77.6% (average sensitivity<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:msup><m:mrow><m:mi>d</m:mi></m:mrow><m:mrow><m:mo>′</m:mo></m:mrow></m:msup><m:mo>=</m:mo><m:mn>1.7</m:mn></m:math></jats:inline-formula>,<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mi>t</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>9</m:mn></m:mrow><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mn>5.9</m:mn></m:math></jats:inline-formula>,<jats:inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mi>p</m:mi><m:mo>=</m:mo><m:mn>2</m:mn><m:mo>×</m:mo><m:mn>1</m:mn><m:msup><m:mrow><m:mn>0</m:mn></m:mrow><m:mrow><m:mo>−</m:mo><m:mn>4</m:mn></m:mrow></m:msup></m:math></jats:inline-formula>). These results enable methods of robustly characterizing the structure of the macula, probing retina signaling pathways, and conducting experiments with human detectors and optical states with nonseparable modes.</jats:p>

Human psychophysical discrimination of spatially dependant Pancharatnam–Berry phases in optical spin-orbit states

“…( b ) Relationship between performance of common participants between Ref. 33 and the current study. Performance in the previous study was strongly predictive of performance in the current study.…”

“…Correspondingly, in Ref. 33 an induced phase shift caused the entoptic profile to rotate. In the presented study we consider an alternative method of observation utilizing stationary beams.…”

“… 33 extended the applications to visual science which sees a growing interest in integrating human detectors with recent technological advances 34 – 38 . It was shown that humans are able to perceive and discriminate spin-orbit states through entoptic images that arise from the interaction between the 2D polarization topologies of these beams and the radially symmetric dichroic elements in the macula of the human eye 33 . As shown in Fig.…”

“…Ref. 33 employed refractive elements to generate OAM = 7 and couple it to different polarization states to induce and azimuthal fringes. Here we consider spin-orbit states prepared through devices that manipulate geometric phases.…”

Engineering photonic angular momentum with structured light: a review

“…For differentiation purposes, we will refer to these two as longitudinal SAM and OAM. [16][17][18][19][20][21][22][23][24][25][26] Under situations that involve strong focusing or evanescent waves, the situation can change dramatically, and AM with a component that is orthogonal to the propagation direction can be generated, which will be referred to as transverse AM. The transverse AM of light has gained increasing attention because of its unique physical characteristics.…”