Linearly polarized light is a special case of elliptically polarized light.  If the light is linearly polarized, then the two components oscillate in phase,  for example Ex = E0xexp(i(kz - ωt)), Ey = E0yexp(i(kz - ωt)), φ = 0.  The direction of E and the direction of propagation define a plane.  The electric vector traces out a straight line.  For example, E = Ei = E0xexp(i(kz - ωt))i.

“The large-scale structured areas and surfaces endowed with high aspect ratio morphology at the microscale, fabricated with the holographic approach that we have developed here, could even extend the range of applications of our shape-shifting surfaces beyond photonics to biology and general surface engineering,” Oscurato added.

Elliptically polarizedlight

“First, the entire fabrication process can be completed in a standard laboratory environment without the need for specialized facilities, expensive equipment, and additional multi-step processes,” explained Ambrosio.

“The most surprising aspect of this research is the effectiveness and the simplicity of the optical surface erasing that underlies our shape-shifting optical elements,” Oscurato said. “Although we were aware of the potential of the azobenzene-containing materials for this unique task, the large number and the quality of the erase and rewrite cycles that can actually be achieved by precisely tuning the experimental parameters was unexpected.

The creation of diffraction gratings and planar optics requires tailoring the surface morphology on the same spatial scales of light wavelength, which is currently done by lithography  —  the transfer of a pattern to a surface (or “substrate”) using a radiation source, such as a beam of light or electrons, and a subsequent chemical or physical selective surface engraving (or “etching”) process.

It is hard to imagine a world without light, and fittingly for such an important aspect of the Universe, scientists have found a remarkably wide range of applications for electromagnetic radiation. The manipulation of light, whether visible to our eyes or not, is used in mundane everyday functions like operating TVs as well as out-of-this-world applications, like assessing the chemical properties of distant stars.

How light interacts with an optical element depends on its three-dimensional shape and the nature of the material it is made of. In some cases, the way light passes through a component, such as a lens, can be completely controlled within ultra-thin devices — the concept underlying “planar optics.”

Elliptical polarization equation derivation

“Our system can project holographic light patterns with the geometry of the desired component directly onto the polymer surface, thereby directly fabricating the operating planar optical component,” Oscurato said. “By updating in time, the projected holograms, the morphology and the functionality of the device is updated accordingly, resulting in unprecedented shapeshifting diffractive elements.”

A diffraction grating is made of periodically spaced grooves that, when light shines through it, produce at a distance a line of light dots along a direction perpendicular to the grating grooves. Deceptively simple in nature, diffraction gratings represent the first example of structuring light utilizing an engineered manipulation of the phase of light — a property inherently associated with the wave nature of the light.

The figure below shows the trace of the field vector Ex = E0exp(i(kz - ωt)), Ey = E0exp(i(kz - ωt + φ)) in a plane perpendicular to the z-axis when looking towards the source.  (E0x = E0y = E0)

Their special lithographic environment is based on computer-generated holography — a technique that allows a light wave to be recorded and later reconstructed to create a 3D image.

“This aspect makes the results of our work even more relevant for emerging technological applications that require both miniaturized and fully reprogrammable optical components.”

“Many practical applications can take advantage of the compact, lightweight, and reprogrammable nature of our shapeshifting diffractive elements,” Ambrosio said.

The two beams within the birefringent crystal are referred to as the ordinary and extraordinary ray, respectively.  The polarization of the extraordinary ray lies in the plane containing the direction of propagation and the optic axis, and the polarization of the ordinary ray is perpendicular to this plane.

“The result of our research is the shapeshifting diffractive optical elements, which are fully operating micro-structured surfaces directly fabricated on a photo-responsive material film,” said Stefano Oscurato, head of the research group in Naples and co-corresponding author of the paper. “The morphology of our polymeric surfaces can be changed in real-time to provide different optical functionalities on-demand.”

In a paper published by Laser & Photonics Reviews, researchers at the University of Naples Federico II and the Instituto Italiano di Tecnologia (IIT) document the creation of diffractive optical elements with tuneable properties that could overcome the limitations of the standard lithographic methods currently used to fabricate planar optical components.

Circularlypolarizedlight

In other devices the changes in direction of propagation between the two rays is used to separate the incoming beam into two orthogonally polarized beams as in the Wollaston and Thompson beam-splitting prisms.

The team’s system can project grey-scale (black and white) spatially-structured intensity distributions of light onto the surface of a photo-responsive film.

This dramatically reduces the resources and the costs associated with the fabrication of advanced planar optical devices while also avoiding the waste of hazardous materials typically involved in standard lithography. “Second, our shapeshifting diffractive devices are fully reprogrammable by light, which is impossible for optical components fabricated by other methods,” he continued.

Circular polarization

“Shapeshifting diffractive optical elements are planar and reconfigurable optical components, designed as designed as micro-patterned surfaces with sub-micron thickness and low weight,” added his colleague, Antonio Ambrosio, principal investigator of Vectorial Nano-Imaging, the research line at IIT in Milan and co-corresponding author of the paper.

If a beam of linearly polarized monochromatic light enters a birefringent crystal along a direction not parallel to the optical axis of the crystal, the beam will may be divided into two separate beams.  Each will be polarized at right angles to the other, and they will travel in different directions.  The intensity of the original beam will be divided between the two new beams in a manner which depends on the original orientation of the electric field vector with respect to the crystal.  The ratio or the intensities of the two orthogonally polarized beams can have any value.

The electric field vector E can always be resolved into two perpendicular components.  The light is elliptically polarized, then the two components have a constant phase difference, and the tip of the electric field vector traces out an ellipse in the plane perpendicular to the direction of propagation.

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The problem with current etching methods is that once the process has been completed, the morphology of the lithographed surface is set. That results in “static” optical devices with a functionality forever defined by its manufacture and no room for tunability.

Ambrosio added that there are two major breakthroughs associated with the team’s method over current fabrication methods.

The extraordinary ray violates both Snell’s Law and the Law of Reflection.  It is not necessarily confined to the plane of incidence.  Its speed changes with direction.  The index of refraction for the extraordinary ray is a continuous function of direction.  The index of refraction for the ordinary ray is independent of direction.  When the ordinary index of refraction is plotted against wavelength, the dispersion curve for the ordinary ray is a single unique curve.  The dispersion curve for the extraordinary ray is a family of curves with different curves for different directions.  A ray normally incident on a birefringent crystalline surface will be divided into two rays at the boundary, unless it is in a special polarization state or unless the crystalline surface is perpendicular to an optic axis.  The extraordinary ray will deviate from the incident direction while the ordinary ray will not.  The ordinary ray index n0 and the most extreme extraordinary ray index ne are together known as the principal indices of refraction of the material.  The direction of the lesser index is called the fast axis because light polarized in that direction has the higher speed.

Elliptically polarizedlight equation

They reversibly inscribe this film in a single lithographic step with the surface morphology of multiple reconfigurable diffractive elements, including gratings with variable periodicity and orientation and varifocal diffractive lenses.

Elliptically polarizedexamples

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The surface structures are sometimes implemented on the nanoscale, making their function less obvious and their fabrication more challenging than standard optical components. In addition to “flat lenses”, planar optics include polarizers, color filters, and diffraction gratings.

A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

A quarter-wave plate δ = π/2 can be used to convert linearly polarized light to circularly polarized light.  The incident linearly polarized light must be oriented at 45o to the wave plate's axes.  A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

Reference: S. L. Oscurato, et al., Shapeshifting Diffractive Optical Devices, Laser & Photonics Reviews, (2023). DOI: 10.1002/lpor.202100514

Elliptically polarizedformula

The authors explained that future work from the team will mainly be focused on achieving more complex optical functionalities for the team’s shape-shifting surfaces to meet the demands of emerging miniaturized optical technology. An example of this technology are holographic projectors developed and demonstrated by the same team in separate recent research.

Elliptical polarization example

Oscurato explained that to create their shapeshifting diffractive optical elements and to obtain unprecedented capabilities for a planar optical device, the team developed a maskless photolithography scheme to fully exploit the capabilities of the direct fabrication of dynamically structured surfaces.

The key to these operations, no matter how complex, are optical components, such as lenses found in eye glasses, smartphones, cameras, telescopes, and a host of other technologies.

When the sun is at a low angle in the sky, the sunlight reflecting off the surface of water is nearly 100% horizontally polarized because the angle of incidence is close to the Brewster angle.  Glare-reducing sunglasses are coated with a polarizer with a vertical transmission axis and therefore block the reflected light.

In the Glan-Taylor polarizing prism shown on the right the rejected (ordinary) ray is absorbed by black mounting material in the prism housing.

Potential applications include optical systems that currently must operate with different diffraction gratings and even cameras that zoom by moving one or two lenses. The system could also assist microscopes used to track moving elements, something currently done mechanically.

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