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Checks that need no other code: closed forms, limits and conservation laws, the same series summed in extended precision, and independent routes through PyStratify's own physics. Each case plots PyStratify against its reference on the same axes.
a film matched to its surroundings is no film: Γ/Γ₀ = 1 everywhere
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Film Out 20 40 60 80 100 120 140 160 180 10⁻¹⁷ 10⁻¹⁶ depth in the film [nm] |Γ / Γ₀ − 1|
Source Source type Electric and magnetic dipoles
λ [nm] 600
z min [nm] 5
z max [nm] 195
z step [nm] 5
z = 0 z p d 200 nm z 100 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 200 nm z 100 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1.5 0 ∞ – 1 Film const 1.5 0 200 auto ↓ Out const 1.5 0 ∞ –
the total rate against escape + guided + absorbed
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50 100 150 200 250 300 350 400 10⁻¹ 1 10 10² 10³ height above the film [nm] Γ / Γ₀
Source Source type Electric point dipole
λ [nm] 600
z min [nm] -400
z max [nm] -5
points 30
z = 0 z p d 100 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 100 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Absorber const 0.2 3 100 auto ↓ Out const 1 0 ∞ –
the total rate against escape + guided + absorbed
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50 100 150 200 250 300 350 400 10⁻¹ 1 10 height above the film [nm] Γ / Γ₀
Source Source type Magnetic point dipole
λ [nm] 600
z min [nm] -400
z max [nm] -5
points 30
z = 0 z m d 100 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z m d 100 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Magnetic dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Absorber const 0.2 3 100 auto ↓ Out const 1 0 ∞ –
the error reported against the accuracy asked for, 18 guided modes
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0.0002 0.0004 0.0006 0.0008 0.001 10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶ 10⁻⁵ 10⁻⁴ 10⁻³ tolerance asked for error
Source Source type Electric point dipole
Offset from origin · z [nm] 400
λ [nm] 600
tolerance min 1e-08
tolerance max 0.001
points 11, log
z = 0 z p d 800 nm z 400 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 800 nm z 400 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Film const 3.5 0 800 auto ↓ Out const 1 0 ∞ –
the total rate against escape + guided, through a lossless guide
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Guide Out 20 40 60 80 100 120 140 160 180 0.2 0.4 0.6 0.8 depth in the film [nm] Γ / Γ₀
Source Source type Electric point dipole
λ [nm] 600
z min [nm] 5
z max [nm] 195
z step [nm] 5
z = 0 z p d 200 nm z 100 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 200 nm z 100 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Guide const 1.5 0 200 auto ↓ Out const 1 0 ∞ –
the emission pattern of a dipole in nothing: the free dipole's
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0 20 40 60 80 100 120 140 160 180 0 0.02 0.04 0.06 0.08 0.1 0.12 polar angle θ [°] power per solid angle
Source Source type Electric point dipole
Offset from origin · z [nm] 100
λ [nm] 600
θ min [°] 0
θ max [°] 180
θ step [°] 2
z = 0 z p d 200 nm z 100 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 200 nm z 100 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Film const 1 0 200 auto ↓ Out const 1 0 ∞ –
the Sommerfeld reference itself against the image dipole of a perfect mirror
2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 kd = 4πh/λ Γ / Γ₀
Given a perfect mirror, r s = − 1 r_s = -1 r s = − 1 r p = 1 r_p = 1 r p = 1 x = k d = 4 π h / λ x = kd = 4\pi h/\lambda x = k d = 4 πh / λ
Γ ⊥ Γ 0 = 1 + 3 ( sin x x 3 − cos x x 2 ) \frac{\Gamma_\perp}{\Gamma_0} = 1 + 3\left(\frac{\sin x}{x^3} - \frac{\cos x}{x^2}\right) Γ 0 Γ ⊥ = 1 + 3 ( x 3 sin x − x 2 cos x ) Γ ∥ Γ 0 = 1 − 3 2 ( sin x x + cos x x 2 − sin x x 3 ) \frac{\Gamma_\parallel}{\Gamma_0} = 1 - \frac{3}{2}\left(\frac{\sin x}{x} + \frac{\cos x}{x^2} - \frac{\sin x}{x^3}\right) Γ 0 Γ ∥ = 1 − 2 3 ( x sin x + x 2 cos x − x 3 sin x ) A magnetic dipole sees the mirror with the opposite sign, 2 − Γ ∥ / Γ 0 2 - \Gamma_\parallel/\Gamma_0 2 − Γ ∥ / Γ 0
decay rates against the Sommerfeld integrals, written without PyStratify
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50 100 150 200 250 300 350 400 10⁻¹ 1 10 10² height above the silver [nm] Γ / Γ₀
Source Source type Electric point dipole
λ [nm] 633
z min [nm] -400
z max [nm] -5
points 40, log
z = 0 z p d 60 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 60 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Ag const 0.056 4.28 60 auto ↓ Out const 1.52 0 ∞ –
decay rates against the Sommerfeld integrals through the guide's quasi-poles
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50 100 150 200 250 300 350 400 0.5 1 1.5 2 2.5 3 3.5 height above the film [nm] Γ / Γ₀
Source Source type Electric point dipole
λ [nm] 633
z min [nm] -400
z max [nm] -10
points 30, log
z = 0 z p d 200 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 200 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 TiO₂ const 2.3 0.001 200 auto ↓ Out const 1.52 0 ∞ –
guided power by residues against the same guide with a trace of loss
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50 100 150 200 250 300 350 400 0.5 1 1.5 2 2.5 3 3.5 height above the film [nm] Γ / Γ₀
Source Source type Electric point dipole
λ [nm] 633
z min [nm] -400
z max [nm] -10
points 30, log
z = 0 z p d 200 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 200 nm z -50 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 TiO₂ const 2.3 0 200 auto ↓ Out const 1.52 0 ∞ –
guided modes against the three-layer dispersion relation, thickness swept
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100 200 300 400 500 600 1 1.2 1.4 1.6 1.8 2 thickness [nm] n eff
Source Source type Guided modes
λ [nm] 633
d min [nm] 100
d max [nm] 600
d step [nm] 20
z = 0 z p d 500 nm z 167 nm ∥ parallel ∥ ⊥ normal ⊥ z = 0 z p d 500 nm z 167 nm ∥ parallel ∥ ⊥ normal ⊥ Thin films · Electric dipole Label Material n k Thickness [nm] Coherence ↓ In const 1 0 ∞ – 1 Slab const 2 0 100–600 auto ↓ Out const 1 0 ∞ –