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## PhotonicsRT: Wave Propagation in Multilayer Structures

The tool calculates the reflection, transmission and absorption of light passing through a lamellar structure with uniform isotropic layers.

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#### Abstract

**PhotonicsRT: Wave Propagation in Multilayer Structures**calculates the electromagnetic field for a plane wave incident at an arbitrary incident angle on a multilayer material stack using the T-matrix approach. The outputs of the tool are real and imaginary part of reflection coefficient (r), real and imaginary part of transmission coefficient (t), reflectance (R), transmittance (T) and absorption (A).

r = E_{r} ⁄ E_{i}

t = E_{t} ⁄ E_{i}

where E_{i} is the incident electric field amplitude, E_{r} is the reflected electric field amplitude and E_{t} is the transmitted electric field amplitude.
(Note that the same definitions are used for both TE mode and TM mode.)

The values of R, T and A are calculated by the following equations,

R = |r|^{2}

T = |t|^{2} × n_{sub} ⁄ n_{sup}

A = 1 - R - T

where n_{sup} is the refractive index of the substrate and n_{sup} is the refractive index of the superstrate.

User defines the following parameters:

- Polarization of incident waves
- Incident angle of the waves
- Wavelength range
- Material at the front (source) side
- Multilayer structure (material and thickness for each layer)
- Material at the back (shade) side

The material parameters used in this tool are permittivity and permeability. For permittivity, the same interpolation method and sources are used as
**PhotonicsDB: Optical Constants**.

For permeability, all the values are fixed to unity.

Related tools:

PhotonicsSHA-2D: Modeling of Single-Period Multilayer Optical Gratings and Metamaterials Hyperlens Design Solver Hyperlens Layer Designer PhotonicsDB: Optical Constants#### Powered by

**PhotonicsRT: Wave Propagation in Multilayer Sturactures** is built on a MATLAB script developed in collaboration by Drs. Uday Chettiar and Alex Kildishev.
Learn more about nanophotonics and plasmonics from **Professor Shalaev's research webpage**.

#### Credits

**Development**

*S. Ishii*... Developed and tested the tool (user interface and integrated simulation engine)*U. Chettiar and A. Kildishev*... Developed the core simulation engine*M. Thoreson and X. Ni*... Developed the tutorial and performed overall testing*A. Kildishev*... Led the development effort

**Support**

*D. Kearney and G. Klimeck*... Provided Rappture and nanoHUB.org support*U. Chettiar*... Performed the initial prototyping

#### References

*Electromagnetic Theory*, J. A. Stratton, McGraw-Hill Book Company (1941).

*Principles of Optics - Electromagnetic theory of propagation, interference and diffraction of light*, M. Born and E. Wolf, Cambridge University Press (2001).

*Negative refractive index in optics of metal-dielectric composites*, A.V. Kildishev, W. Cai, U. K. Chettiar, H-K. Yuan, A.K. Sarychev, V.P. Drachev, and V.M. Shalaev, J. Opt. Soc. Am. B, Vol.23, No.3 423-433 (2006).

*Handbook of Optical Constants of Solids*, Edward D. Palik (Ed.), Academic Press (1997).

*Optical Constants of the Noble Metals*, P. B. Johnson and R. W. Christy, Physical Review B Vol.6 n.12 (1972).

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