1. Rough surface reflections
Gregory Hart
Steve Turley
BYU XUV

2. Why do we care? Astronomy Computers Microscopy He Photolithography
imaging
BYU XUV

3. XUV
1-100 nm
Low reflectance
𝑛≈1
𝜅≈1 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑣𝑒
BYU XUV

4. BYU XUV

5. The Equations
𝐸 𝑧 𝑖𝑛𝑐𝑙 𝑥,𝑦 = 𝐾 𝑡 𝑥,𝑦 −𝑖 𝑘 1 𝜂 𝐽 𝑧 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 1 𝑟 𝑑 𝑠 ′ + 𝜕 𝜕𝑥 𝑦 ∙ 𝑡 𝑥 ′ , 𝑦 ′ 𝐾 𝑡 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 1 𝑟 𝑑 𝑠 ′ − 𝜕 𝜕𝑦 𝑥 ∙ 𝑡 𝑥 ′ , 𝑦 ′ 𝐾 𝑡 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 1 𝑟 𝑑 𝑠 ′
0= 𝐾 𝑡 𝑥,𝑦 −𝑖 𝑘 2 𝜂 𝐽 𝑧 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 2 𝑟 𝑑 𝑠 ′ + 𝜕 𝜕𝑥 𝑦 ∙ 𝑡 𝑥 ′ , 𝑦 ′ 𝐾 𝑡 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 2 𝑟 𝑑 𝑠 ′ 𝑦 ∙ 𝑡 𝑥 ′ , 𝑦 ′ 𝐾 𝑡 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 2 𝑟 𝑑 𝑠 ′ − 𝜕 𝜕𝑦 𝑥 ∙ 𝑡 𝑥 ′ , 𝑦 ′ 𝐾 𝑡 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 2 𝑟 𝑑 𝑠 ′ 𝑥 ∙ 𝑡 𝑥 ′ , 𝑦 ′ 𝐾 𝑡 𝑥 ′ , 𝑦 ′ 𝑖 4 𝐻 𝑘 2 𝑟 𝑑 𝑠 ′
𝛻∙( 𝜖 0 E)= 𝜌 𝑒 𝛻∙( 𝜇 0 𝐇)= 𝜌 𝑚 𝛻×𝐄=𝑖ω 𝜇 0 𝐇−𝑲 𝛻×𝐇=−𝑖ω ϵ 0 𝐄+𝑱 𝛻 2 + 𝑘 2 𝐄=0 𝛻 2 − 𝑘 2 𝐁=0
Assumption time dependence is harmonic, mu = mu0, epsilon is a scalar. S polarized makes it a scalar problem in z.
BYU XUV

6. Numerically
𝐸= 1 2 𝐾 𝑡 + 𝑖𝑗 𝑀 𝑖𝑗 1 𝐽 𝑧 𝑖 + 𝑖𝑗 𝑁 𝑖𝑗 1 𝐾 𝑡 0=− 1 2 𝐾 𝑡 + 𝑖 𝑀 𝑖 2 𝐽 𝑧 𝑖 + 𝑖 𝑁 2 𝐾 𝑡 𝑀 𝑖𝑗 𝜔 = 𝑘 𝜔 𝜂 𝜔 4 𝑐 𝑖 𝑆 𝑖 𝐻 0 1 𝑘 𝜔 𝑟 𝑖𝑗 𝑁 𝑖𝑗 𝜔 = 𝑖 𝑘 𝜔 4 𝑐 𝑖 𝑆 𝑖 𝐻 1 1 ( 𝑘 𝜔 𝑟 𝑖𝑗 ) 𝑟 𝑖𝑗 [ cos 𝜃 𝑖 ′ 𝑦 𝑗 − 𝑦 𝑖 ′ − sin 𝜃 𝑖 ′ 𝑥 𝑗 − 𝑥 𝑖 ′ ]
𝐸 0 = ( 𝑁 1 ) 𝑀 1 (− 𝑁 2 ) 𝑀 𝐾 𝐽
BYU XUV

7. Test
.Smooth surface incident at 20°
BYU XUV

8. Test
.Cylindical surface incident at 20°
BYU XUV

9. Correlation
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10. Discussion The program works for simple cases
Found single processor limits
Random roughnesses have same overall effect
2D surface
Parallel processing
BYU XUV

11. Acknowledgement Steve Turley Jed Johnson Fulton Supercomputing Lab
BYU Physics and Astronomy
BYU XUV