Universal multiport interferometer

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The overview of the first important point, as it appears in the following sections, may be given in this short paragraph.

The overview of the second important point, as it appears in the following sections, may be given in this short paragraph.

This section should be used to catch the reader's attention and encourage them to read the following sections.

Formal definition of topic or description of problem

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$P=|\psi _{1}+\psi _{2}|^{2}=|\psi _{1}|^{2}+|\psi _{2}|^{2}+\psi _{1}\psi _{2}^{*}+\psi _{1}^{*}\psi _{2}$

Let ${\textstyle P_{1}=|\psi _{1}|^{2}}$ and ${\textstyle P_{2}=|\psi _{2}|^{2}}$, then the following holds,

$P=P_{1}+P_{2}+2{\sqrt {P_{1}P_{2}}}\cos {\left[\arg {(\psi _{1}\psi _{2}^{*})}\right]}$.

Motivation

Main theorem supporting the topic

Here is a formal theorem that supports the main topic defined in the previous section. If the main topic of the article is the theorem itself, then this would likely be moved to the previous section.

The compression ratio for the three-lens spaceplate is defined as,

$R={\frac {d_{eff}}{d}}={\frac {f_{ext}}{2f_{mid}}}-1$,

where $f_{ext}$ is the focal length of the external lenses and $f_{mid}$ is the focal length of the middle lens.

Corollary to the main theorem

Here is a supporting statement that is easily deduced from the main theorem and may help motivate the main topic of this article.

The ideal spaceplate phase is given by,

$\varphi _{SP}(k_{x},k_{y},d_{eff})=d_{eff}(|{\textbf {k}}|^{2}-k_{x}^{2}-k_{y}^{2})^{1/2}$.

Rainbow dove surface hologram used as a security feature on most visa cards.

Another perspective

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Properties

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Property 1:

• Definition or equation describing property 1.
• Example supporting property 1.
• Reference to formal proof.

Property 2:

• Definition or equation describing property 2.
• Example supporting property 2.
• Reference to formal proof.

History

Important background story

If there is an intriguing story behind the main topic or problem, the article will likely reference it in a history section. If the main topic is experimental in itself, this section may be combined with the following section on experimental evidence.

Experimental evidence

Experiment 1

Overview

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An interferometer typically used for demonstration purposes in educational settings.

Setup

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The interferometer is seen in the image on the right.

Results

Here are the results of experiment 1.

Experiment 2

Overview

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Setup

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Results

Here are the results of experiment 2.

Applications

Real-world application 1

The interior of LIGO at Hanford, Washington.

The interior of LIGO is seen in the image on the right.

Real-world application 2

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Real-world application 3

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See also

• Fourier optics
• Holography
• Quantum information

Further reading

• Savoia, S., Castaldi, G., & Galdi, V. (2013). Optical nonlocality in multilayered hyperbolic metamaterials based on Thue-Morse superlattices. Physical Review B - Condensed Matter and Materials Physics, 87(23). https://doi.org/10.1103/PhysRevB.87.235116
• Zhou, Y., Zheng, H., Kravchenko, I. I., & Valentine, J. (2020). Flat optics for image differentiation. Nature Photonics, 14(5), 316–323. https://doi.org/10.1038/s41566-020-0591-3
• Pagé, J. T. R., Reshef, O., Boyd, R. W., & Lundeen, J. S. (2022). Designing high-performance propagation-compressing spaceplates using thin-film multilayer stacks. Optics Express, 30(2), 2197. https://doi.org/10.1364/oe.443067