40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  PSL  Not logged in ELOG logo
Entry  Mon Jul 29 22:30:34 2013, tara, Notes, optic, coating optimization for AlGaAs multilayer1.JPGmultilayer2.JPGopt1_2013_07_29.pngnb_opt1_2013_07_29.pngT1200003_refcav.png
    Reply  Wed Jul 31 00:31:39 2013, tara, Notes, optic, coating optimization for AlGaAs 
       Reply  Fri Aug 9 17:58:01 2013, tara, Notes, optic, coating optimization for AlGaAs TOoptimized_2013_08_09.pngTOoptimized_2013_08_09.figTO_opt_200ppm_layer.pngTO_opt_200ppm_layer.fig2013_08_09_TOopt_200ppm.mat
          Reply  Tue Aug 27 16:11:26 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis 8x
             Reply  Wed Aug 28 21:21:38 2013, tara, Notes, optic, GWINC for TO calculation: recap 
             Reply  Sun Sep 1 18:38:37 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis 7x
                Reply  Mon Sep 2 18:31:46 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis 
                   Reply  Wed Sep 18 21:55:11 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis opt_coatings.mat
                      Reply  Thu Sep 19 20:38:17 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis power_vs_mirror_size.png
                Reply  Fri Sep 20 19:26:45 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis error_check_params.pngerror_check_params.figerror_thick_params_compare.pngerror_thick_params_compare.fig
                   Reply  Fri Sep 20 21:19:29 2013, Matt A., Notes, optic, coating optimization for AlGaAs:error analysis 
                   Reply  Sat Sep 21 23:49:29 2013, rana, Notes, optic, coating optimization for AlGaAs:error analysis 
                      Reply  Sun Sep 22 00:27:09 2013, some random goon, Notes, optic, coating optimization for AlGaAs:error analysis 
                         Reply  Mon Sep 23 18:07:22 2013, rana, Notes, optic, coating optimization for AlGaAs:error analysis 
                            Reply  Mon Sep 23 18:50:05 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis compare_indices.pngcompare_indices.figcompare_indices.png
                               Reply  Thu Sep 26 23:25:40 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis  8x
                                  Reply  Thu Oct 3 10:34:32 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis  
                                     Reply  Thu Oct 10 01:59:24 2013, tara, Notes, optic, coating optimization for AlGaAs:error analysis  
                                        Reply  Fri Oct 11 15:23:54 2013, tara, Notes, optic, coating optimization for AlGaAs:electric field in coating layer 6x
                                           Reply  Mon Oct 14 21:02:00 2013, tara, Notes, optic, coating optimization for AlGaAs:variation in x 
                                           Reply  Sun Oct 27 20:12:25 2013, tara, Notes, optic, photothermal noise in AlGaAs Int_cotings.pngInt_cotings.fig
                                              Reply  Wed Dec 18 21:05:28 2013, tara, Notes, optic, photothermal noise in AlGaAs: thickness resolution 8x
                                                 Reply  Sat May 17 22:01:28 2014, tara, Notes, optic, Coating TO opt for Adv LIGO: ETM 7x
                                                    Reply  Sun May 18 10:45:42 2014, tara, Notes, optic, Coating TO opt for Adv LIGO dOpt_ITM1.pngdOpt_ITM1.figAdvLIGO_AlGaAs.pngAdvLIGO_AlGaAs.fig
                                           Reply  Sat Jun 20 10:14:50 2015, Evan, Notes, optic, coating optimization for AlGaAs:electric field in coating layer Efieldtrans.pdf
Message ID: 1365     Entry time: Fri Oct 11 15:23:54 2013     In reply to: 1363     Reply to this: 1367   1374   1550
Author: tara 
Type: Notes 
Category: optic 
Subject: coating optimization for AlGaAs:electric field in coating layer 

Electric field in coating layer is calculated. This will be used in loss calculation in AlGaAs coatings.

 

  • In each coating layer, there are two E waves, transmitted and reflected  waves. The two interfere and become an effective field.
  • The averaged electric field will depend only on the transmitted beam inside each layer, see the calculation.
  • The effective transmissivity can be calculated, for coatings with N layers between air and substrate, there will be an N+1 vector representing the effective transmission, called tbar in the code. This tbar(n) is the transmissivity in the nth layer, similar to rbar in Evans etal calculation.
  • The ratio of E field/ E input in nth layer will be tbar(1)*tbar(2)*...tbar(n)
  •  |E field/ E input |^2 of the final transmitted beam is the transmission of the coatings.  The numbers from this calculation agrees to the calculation from before.

==supplementary information==

1) average E field in layer is the transmitted E field in the layer.

avgE.jpg

 I attached a short matlab file for a simulation of the combined field. Ein in each layer will be the transmitted beam through the layers. For a value of r close to 1, we get a standing wave. Try changing the value of r in test_refl.m to see the effect

 

2) Calculation for the transmitted field in each layer

transE.jpg

I borrow the notation from Evns etal paper (rbar), the calculation code multidiel_rt.m is attached below. Note: the final transmission calculated in the code is the transmission from the coating to the substrate. To calculate the transmission to the air, multiply the last transmission by 2*n_sub/(n_sub + n_air) which is the transmission from sub to air. Since the thickness of the substrate is not known with the exact number, it will not be exact to the transmision calculated in GWINC or Matt A's code (which do not take the sub-air surface into account), but they will be close, because the reflected beam in the last interface will be small compare to those in the coatings.

 

==result==

Efield.png

The penetration of E field for QWL and different optimized coatings are shown here. The transmissions in the legend are calculated from MattA./GWINC and the values in the parenthesis are calculated from multidiel_rt.m which include the effect from the substrate-air surface. This makes the values in the parenthesis smaller (as more is reflected back and less is transmitted).

Attachment 3: test_refl.m.zip  735 Bytes  Uploaded Sun Oct 13 02:55:44 2013
Attachment 4: multidiel_rt.m.zip  1 kB  Uploaded Sun Oct 13 02:56:02 2013
Attachment 6: Efield.fig  14 kB  Uploaded Sun Oct 13 03:53:01 2013
ELOG V3.1.3-