1. Gaps in Light Guides H.O. Meyer, Indiana University meyer1@indiana.edu HOM, 2/8/8, nEDM

2. uniform, isotropic light source p θ z distance to z axis ray propagation in a cylinder p and θ constant under wall reflection From now on: Cylinder radius = 2.5 cm Space is either acrylic (n=1.49) or vacuum angle with z axis HOM, 2/8/8, nEDM Phase Space: p, θ + two more numbers (e.g. coordinates of a wall reflection point)

3. uniform, isotropic light source p θ z distance to z axis ray propagation in a cylinder emitted (100%) 55% propagate 25% exit planar end surface having crossed the gap angle with z axis HOM, 2/8/8, nEDM

4. geometric gap loss w 4.2% loss per mm 1.6% loss per mm vacuum gap gap filled with acrylic HOM, 2/8/8, nEDM

5. the gap depopulates the phase space selectively two gaps in series w w 1 st gap 2 nd gap HOM, 2/8/8, nEDM 1 st gap2 nd gap less loss!

6. fraction of rays exiting Fraction of exiting rays that cross 1cm gap combined: no net gain! light guides with non-planar ends HOM, 2/8/8, nEDM

7. PM make the view port a lens R lens = ∞R lens = 5 cm PM The lens does focus, but because it also increases the total gap width, there is HOM, 2/8/8, nEDM no net gain!

8. Fresnel losses n i /n t = 1.49n i /n t = 1/1.49 normal incidence HOM, 2/8/8, nEDM

9. how a single-layer coating affects reflectance ¼ λ coating with n = 1.38 (MgF 2 ) n = 1.22 (?) reflectance wavelength (nm)angle of incidence (deg) no coating TPB emission HOM, 2/8/8, nEDM

10. ideal coating does not exist HOM, 2/8/8, nEDM

11. actual Fresnel reflection losses w vacuum gap gap filled with acrylic >40% loss!

12. ● use light guide with normal, planar end face ● use plane-parallel view port, as thin as possible ● get light guide and PM as close to the view port as possible ● apply commercial custom coating with a 440 nm design wavelength to all surfaces (light guide, view port and the PM) Example: 5 mm thick view port with a 1 mm gap on both sides: ● the geometric loss is 16 %. ● the reflection loss (4 untreated surfaces) is ~40 %; coating on all surfaces will lower this to 5 – 10 % ● overall loss of well-designed gap: 20 -30 %. summary (recommendation) HOM, 2/8/8, nEDM