H* Calculations for the groovesmm required for
the Sr wavelengths to reflect from grating at ~90° *L
H* mΛ = d H sinHΑL + sinHΒL L is the general diffraction equation
for light incident at an angle Α HΒ is the diffraction angleL *L
H* We want the first order to reflect back into the beam, so take Α=Β and m=1 *L
H* Thus, we have Λ = 2d sinHΑL and Hfor our designL Α = 45° *L
H* For prototye: Rb87. 780 nm *L
N@10 ^ 6  H780  H2 * Sin@Pi  4DLLD
1813.09
H* We used 1800 gmm which turns out to
be close enough to a total reflection angle of 90° *L
N@2 * 180  Pi * ArcSin@780 * 1800  H2 * 10 ^ 6LDD
89.1754
H* 994 nm Hto be doubled to 497 nmL *L
N@10 ^ 6  H994  H2 * Sin@Pi  4DLLD
1422.75
H* What if we tried 1420 gmm? *L
N@2 * 180  Pi * ArcSin@994 * 1420  H2 * 10 ^ 6LDD
89.7787
H* Best catalog option offered by Newport is 1350 gmm *L
N@2 * 180  Pi * ArcSin@994 * 1350  H2 * 10 ^ 6LDD
84.2809
H* 922 nm Hto be doubled to 461 nmL *L
N@10 ^ 6  H922  H2 * Sin@Pi  4DLLD
1533.85
H* What if we tried 1540 gmm? *L
2
grating_calculations.nb
N@2 * 180  Pi * ArcSin@922 * 1540  H2 * 10 ^ 6LDD
90.4601
H* Best catalog option offered by Newport is 1500 gmm *L
N@2 * 180  Pi * ArcSin@922 * 1500  H2 * 10 ^ 6LDD
87.4979
H* 914 nm Hoptical lattice laserL *L
N@10 ^ 6  H914  H2 * Sin@Pi  4DLLD
1547.28
H* What if we tried 1540 gmm? *L
N@2 * 180  Pi * ArcSin@914 * 1540  H2 * 10 ^ 6LDD
89.4621
H* Best catalog option is again 1500 gmm *L
N@2 * 180  Pi * ArcSin@914 * 1500  H2 * 10 ^ 6LDD
86.5499
H* 689 nm Hsecondary trap laserNARROW linewidthL *L
N@10 ^ 6  H689  H2 * Sin@Pi  4DLLD
2052.56
H* What if we tried 2050 gmm? *L
N@2 * 180  Pi * ArcSin@689 * 2050  H2 * 10 ^ 6LDD
89.8572
H* Best catalog option is 2000 gmm *L
grating_calculations.nb
N@2 * 180  Pi * ArcSin@689 * 2000  H2 * 10 ^ 6LDD
87.102
3