Vol. 14
Latest Volume
All Volumes
PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2010-04-15
Efficient 4x4 Propagation Matrix Method Using a Fourth-Order Symplectic Integrator for the Optics of One-Dimensional Continuous Inhomogeneous Materials
By
Progress In Electromagnetics Research Letters, Vol. 14, 1-9, 2010
Abstract
Understanding the propagation of light in continuous inhomogeneous materials is important to design optical structures and devices. To have accurately numerical calculations Berreman's 4×4 propagation matrix method is generally used, and layer approximation, i.e., the whole one-dimensional continuous inhomogeneous material is divided into many small homogeneous layers, is assumed. However, this layer approximation is only correct up to the second-order of the layer thickness. To efficiently solve Berreman's first-order differential equation, a simple fourth-order symplectic integrator is presented. The efficiency of the fourth-order symplectic integrator was studied for a cholesteric liquid crystal. Numerical results of reflectance spectra show that the fourth-order symplectic integrator is highly efficient in contrast to the extensively used fast 4×4 propagation matrix.
Citation
Zhao Lu, "Efficient 4x4 Propagation Matrix Method Using a Fourth-Order Symplectic Integrator for the Optics of One-Dimensional Continuous Inhomogeneous Materials," Progress In Electromagnetics Research Letters, Vol. 14, 1-9, 2010.
doi:10.2528/PIERL10031501
References

1. Berreman, D. W., "Optics in stratified and anisotropic media: 4×4 matrix formulation," J. Opt. Soc. Am., Vol. 62, 502-510, 1972.
doi:10.1364/JOSA.62.000502

2. Abdulhalim, I., "Analytic propagation matrix method for linear optics of arbitrary biaxial layered media," J. Opt. A: Pure Appl. Opt., Vol. 1, 646-653, 1999.
doi:10.1088/1464-4258/1/5/311

3. Lu, Z., "Accurate and efficient calculation of light propagation in one-dimensional inhomogeneous anisotropic media through extrapolation ," J. Opt. Soc. Am. A, Vol. 24, 236-242, 2007.
doi:10.1364/JOSAA.24.000236

4. Wohler, H., G. Hass, M. Fritsch, and D. A. Mlynski, "Faster 4×4 matrix method for uniaxial inhomogeneous media," J. Opt. Soc. Am. A, Vol. 5, 1554-1557, 1988.
doi:10.1364/JOSAA.5.001554

5. Hawkeye, M. M. and M. J. Brett, "Narrow bandpass optical filters fabricated with one-dimensionally periodic inhomogeneous thin films," J. Appl. Phys., Vol. 100, 044322, 2006.
doi:10.1063/1.2335397

6. Brett, M. J., M, and M. Hawkeye, "New materials at a glance," Science, Vol. 319, 1192-1193, 2008.
doi:10.1126/science.1153910

7. Suzuki, M., Quantum Monte Carlo Methods in Condensed Matter Physics, World Scientific Pub Co Inc, 1994.

8. Shankar, R., Principles of Quantum Mechanics, 2nd Ed., Springer, 1994.

9. Chin, S. A., "Symplectic integrators from composite operator factorizations ," Phys. Lett. A, Vol. 226, 344-348, 1997.
doi:10.1016/S0375-9601(97)00003-0

10. Chin, S. A. and D. W. Kidwell, "Higher-order force gradient symplectic algorithms," Phys. Rev. E, Vol. 62, 8746-8752, 2000.
doi:10.1103/PhysRevE.62.8746

11. Chin, S. A. and C. R. Chen, "Gradient symplectic algorithms for solving the SchrÄodinger equation with time-dependent potentials," J. Chem. Phys., Vol. 117, 1409-1415, 2002.
doi:10.1063/1.1485725

12. Nehring, J., "Light propagation and reflection by absorbing cholesteric layers," J. Chem. Phys., Vol. 75, 4326-4337, 1981.
doi:10.1063/1.442639

13. Lu, Z., "Accurate calculation of reflectance spectra for thick one-dimensional inhomogeneous optical structures and media: Stable propagation matrix method," Opt. Lett., Vol. 33, 1948-1950, 2008.
doi:10.1364/OL.33.001948