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Comment:
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= Mode matching optical system of Green Lock System = = Mode matching optical system for ALS at the side of PR2 and SR2 =
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<<TableOfContents(3)>> Last modified : 2017/09/04

Under investigation : Which is the better of the 2 lens or 3 lens

<<TableOfContents(4)>>

------

== Target beam parameter ==

=== For Y-arm ===

||<|2>Mirror||<:-2>q-parameter||<:-2>waist radius [mm]||<:-2>beam radius [mm]||
||<:>q,,x,,||<:>q,,y,,||<:>W0,,x,,||<:>W0,,y,,||<:>W,,x,,||<:>W,,y,,||
||SR2 (AR-surface)||1.141658 + 0.026444i||1.145729 + 0.026587i||0.066919||0.067099||2.889797||2.892313||
||SR2 (HR-surface)||1.485931 + 0.040023i||1.488242 + 0.040171i||0.082325||0.082478||3.057628||3.056716||
||SR3 (Input)||12.597431 + 0.040023i||12.599742 + 0.040171i||0.082325||0.082478||25.912697||25.869453||
||BS (HR-surface)||-1020.981427 + 292.656219i||-1017.458984 + 291.640312i||7.039791||7.027562||25.548554||25.504674||
||ITMY (HR-surface)||<-2>-1500 + 774.596669i||<-2>11.452985||<-2>24.961202||
||ETMY (HR-surface)||<-2> 1500 + 774.596669i||<-2>11.452985||<-2>24.961202||

=== For X-arm ===

||<|2>Mirror||<:-2>q-parameter||<:-2>waist radius [mm]||<:-2>beam radius [mm]||
||<:>q,,x,,||<:>q,,y,,||<:>W0,,x,,||<:>W0,,y,,||<:>W,,x,,||<:>W,,y,,||
||PR2 (AR-surface)||1.180362 + 0.026317i||1.182840 + 0.026422i||0.066757||0.066891||2.994930||2.995218||
||PR2 (HR-surface)||1.530937 + 0.039779i||1.533251 + 0.039928i||0.082075||0.082228||3.159778||3.158651||
||PR3 (Input)||12.597037 + 0.039779i||12.599351 + 0.039928i||0.082075||0.082228||25.991009||25.947268||
||BS (HR-surface)||-1024.352551 + 292.664734i||-1020.788880 + 291.640312i||7.039893||7.027562||25.626199||25.581817||
||ITMX (HR-surface)||<-2>-1500 + 774.596669i||<-2>11.452985||<-2>24.961202||
||ETMX (HR-surface)||<-2> 1500 + 774.596669i||<-2>11.452985||<-2>24.961202||

------

== Mode matching optical system ==

||Conditions||

 * The waist radius of the transmitted beam from the fiber = 350um (measured)

 * Optical path length from AR-surface of SR2/PR2 to the optical table ~ 2m

 * Assume CVI lenses
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== Target beam parameter ==

=== X-axis ===

||<|2>Mirror||<:-2>q-parameter||<:-2>waist radius [mm]||<:-2>beam radius [mm]||
||<:>q,,x,,||<:>q,,y,,||<:>W0,,x,,||<:>W0,,y,,||<:>W,,x,,||<:>W,,y,,||
||PR2 (AR-surface)||1.179513 + 0.026317i||1.181989 + 0.026422i||0.066757||0.066891||2.992774||2.993064||
||PR2 (HR-surface)||1.530937 + 0.039779i||1.533251 + 0.039928i||0.082075||0.082228||3.159777||3.158650||
||PR3 (Input)||12.597037 + 0.039779i||12.599351 + 0.039928i||0.082075||0.082228||25.991002||25.947259||
||BS (HR-surface)||-1024.352272 + 292.664734i||-1020.788469 + 291.640312i||7.039893||7.027562||25.626193||25.581808||
||ITMX (HR-surface)||<-2>-1500 + 774.596669i||<-2>11.452985||<-2>24.961202||
||ETMX (HR-surface)||<-2> 1500 + 774.596669i||<-2>11.452985||<-2>24.961202||


=== Y-axis ===

||<|2>Mirror||<:-2>q-parameter||<:-2>waist radius [mm]||<:-2>beam radius [mm]||
||<:>q,,x,,||<:>q,,y,,||<:>W0,,x,,||<:>W0,,y,,||<:>W,,x,,||<:>W,,y,,||
||SR2 (AR-surface)||1.141436 + 0.026444i||1.145506 + 0.026587i||0.066919||0.067099||2.889234||2.891750||
||SR2 (HR-surface)||1.485931 + 0.040023i||1.488242 + 0.040171i||0.082325||0.082478||3.057627||3.056715||
||SR3 (Input)||12.597431 + 0.040024i||12.599742 + 0.040171i||0.082325||0.082478||25.912690||25.869443||
||BS (HR-surface)||-1017.395806 + 291.640196i||-1017.396204 + 291.640312i||7.027560||7.027562||25.503215||25.503220||
||ITMY (HR-surface)||<-2>-1500 + 774.596669i||<-2>11.452985||<-2>24.961202||
||ETMY (HR-surface)||<-2> 1500 + 774.596669i||<-2>11.452985||<-2>24.961202||

-----

== Mode matching optical system ==

__'''Conditions'''__

・ Waist radius of the beam from the fiber coupler = 350um (measured)

・ Optical path length from AR-surface of SR2/PR2 to the optical table ~ 2m

・ Assume CVI lenses

----
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{{attachment:GreenModeMatch_y_lens_170823.png|Mode matching optical system (back of SR2)|width="600"}} ==== Pattern A (2 lenses) ====
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==== Simulation of beam parameters using above optical system with FINESSE ==== {{attachment:GreenModeMatch_Y_2lens_170903.png|Mode matching optical system (back of SR2)|width="600"}}
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||L1 (Input)||<-2>0.095 + 0.723393i||<-2>0.350||<-2>0.353005||
||L1 (Output)||<-2>-0.108744 + 0.016016i||<-2>0.520787||<-2>0.357411||
||L2 (Input)||<-2>0.759744 + 0.016016i||<-2>0.520787||<-2>2.470960||
||L2 (Output)||<-2>-0.699938 + 36.041929i||<-2>2.470500||<-2>2.470966||
||L3 (Input)||<-2>1.324938 + 36.041929i||<-2>2.470500||<-2>2.472169||
||L3 (Output)||<-2>-0.973537 + 0.026516i||<-2>0.670087||<-2>2.461182||
||SR2 (AR)||<-2>1.143463 + 0.026516i||<-2>0.670087||<-2>2.890476||
||ITMy (HR)||-1463.290098 + 730.177686i||-1537.778046 + 823.090006i||11.119753||11.806048||24.904507||25.018072||
||ETMy (HR)||1536.709902 + 730.177686i||1462.221956 + 823.090006i||11.119753||11.806048||25.909775||24.068022||		 ||L1 (Input)||<-2>0.220 + 0.723393i||<-2>0.350||<-2>0.365828||
||L1 (Output)||<-2>-0.108344 + 0.015935i||<-2>0.051947||<-2>0.356989||
||L2 (Input)||<-2>0.759858 + 0.016086i||<-2>0.051947||<-2>2.199920||
||L2 (Output)||<-2>-0.865307 + 0.026488i||<-2>0.066974||<-2>2.188928||
||SR2 (AR)||<-2>1.143693 + 0.026488i||<-2>0.066974||<-2>2.892571||
||SR2 (HR)||1.489013 + 0.040119i||1.485169 + 0.039991i||0.082425||0.082292||3.060270||3.057282||
||ITMy (HR)||-1463.753784 + 729.531387i||-1538.350364 + 822.405327i||11.114831||11.801137||24.917463||25.031092||
||ETMy (HR)||1536.246216 + 729.531387i||1461.649636 + 822.405327i||11.114831||11.801137||25.910643||24.066063||

{{attachment:BeamRadius_FC_ITMY_2lens_170903.png|Y-axis Beam radius|width="800"}}
{{attachment:BeamRadius_FC_ETMY_2lens_170903.png|Y-axis Beam radius|width="800"}}

----

==== Pattern B (3 lenses) ====

{{attachment:GreenModeMatch_y_3lens_170903.png|Mode matching optical system (back of SR2)|width="600"}}

||<|2>Mirror||<-2>q-parameter||<-2>Waist radius [mm]||<-2>Beam radius [mm]||
||qx||qy||W0x||W0y||Wx||Wy||
||Fiber coupler||<-2>0 + 0.723393i||<-2>0.350||<-2>0.350||
||L1 (Input)||<-2>0.089 + 0.723393i||<-2>0.350||<-2>0.352639||
||L1 (Output)||<-2>0.108858 + 0.016086i||<-2>0.052192||<-2>0.357035||
||L2 (Input)||<-2>0.759858 + 0.016086i||<-2>0.052192||<-2>2.465986||
||L2 (Output)||<-2>0.434746 + 35.905184i||<-2>2.465809||<-2>2.465990||
||L3 (Input)||<-2>1.019746 + 35.905184i||<-2>2.465809||<-2>2.466803||
||L3 (Output)||<-2>-0.973312 + 0.026619i||<-2>0.067139||<-2>2.455838||
||SR2 (AR)||<-2>1.143688 + 0.026619i||<-2>0.067139||<-2>2.885427||
||SR2 (HR)||1.489002 + 0.040318i||1.485159 + 0.040189i||0.082629||0.082496||3.052712||3.049731||
||ITMy (HR)||-1461.017819 + 731.892574i||-1535.118889 + 824.885592i||11.132804||11.818919||24.856063||24.969411||
||ETMy (HR)||1538.982181 + 731.892574i||1464.881111 + 824.885592i||11.132804||11.818919||25.921818||24.087634||

{{attachment:BeamRadius_FC_ITMY_3lens_170903.png|Y-axis Beam radius|width="800"}}
{{attachment:BeamRadius_FC_ETMY_3lens_170903.png|Y-axis Beam radius|width="800"}}
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== Beam radius from the fiber coupler to arm cavity == === Back of PR2 ===
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{{attachment:BeamRadius_FC_ITMY_3lens_170830.png|Y-axis Beam radius|width="800"}}
{{attachment:BeamRadius_FC_ETMY_3lens_170830.png|Y-axis Beam radius|width="800"}}

------

== Lens displacement ==

=== For Y-arm ===

==== Pattern A (2 lenses) ====

[[attachment:GreenModeMatch_2lens_170904.pdf]]

----

==== Pattern B (3 lenses) ====

[[attachment:GreenModeMatch_3lens_170904.pdf]]


-----


=== For X-arm ===

Mode matching optical system for ALS at the side of PR2 and SR2

Last modified : 2017/09/04

Under investigation : Which is the better of the 2 lens or 3 lens

Contents

  1. Mode matching optical system for ALS at the side of PR2 and SR2
    1. Target beam parameter
      1. For Y-arm
      2. For X-arm
    2. Mode matching optical system
      1. Back of SR2
        1. Pattern A (2 lenses)
        2. Pattern B (3 lenses)
      2. Back of PR2
    3. Lens displacement
      1. For Y-arm
        1. Pattern A (2 lenses)
        2. Pattern B (3 lenses)
      2. For X-arm

Target beam parameter

For Y-arm

Mirror

q-parameter

waist radius [mm]

beam radius [mm]

qx

qy

W0x

W0y

Wx

Wy

SR2 (AR-surface)

1.141658 + 0.026444i

1.145729 + 0.026587i

0.066919

0.067099

2.889797

2.892313

SR2 (HR-surface)

1.485931 + 0.040023i

1.488242 + 0.040171i

0.082325

0.082478

3.057628

3.056716

SR3 (Input)

12.597431 + 0.040023i

12.599742 + 0.040171i

0.082325

0.082478

25.912697

25.869453

BS (HR-surface)

-1020.981427 + 292.656219i

-1017.458984 + 291.640312i

7.039791

7.027562

25.548554

25.504674

ITMY (HR-surface)

-1500 + 774.596669i

11.452985

24.961202

ETMY (HR-surface)

1500 + 774.596669i

11.452985

24.961202

For X-arm

Mirror

q-parameter

waist radius [mm]

beam radius [mm]

qx

qy

W0x

W0y

Wx

Wy

PR2 (AR-surface)

1.180362 + 0.026317i

1.182840 + 0.026422i

0.066757

0.066891

2.994930

2.995218

PR2 (HR-surface)

1.530937 + 0.039779i

1.533251 + 0.039928i

0.082075

0.082228

3.159778

3.158651

PR3 (Input)

12.597037 + 0.039779i

12.599351 + 0.039928i

0.082075

0.082228

25.991009

25.947268

BS (HR-surface)

-1024.352551 + 292.664734i

-1020.788880 + 291.640312i

7.039893

7.027562

25.626199

25.581817

ITMX (HR-surface)

-1500 + 774.596669i

11.452985

24.961202

ETMX (HR-surface)

1500 + 774.596669i

11.452985

24.961202

Mode matching optical system

Conditions
  • The waist radius of the transmitted beam from the fiber = 350um (measured)
  • Optical path length from AR-surface of SR2/PR2 to the optical table ~ 2m
  • Assume CVI lenses

Back of SR2

Pattern A (2 lenses)

Mode matching optical system (back of SR2)

Mirror

q-parameter

Waist radius [mm]

Beam radius [mm]

qx

qy

W0x

W0y

Wx

Wy

Fiber coupler

0 + 0.723393i

0.350

0.350

L1 (Input)

0.220 + 0.723393i

0.350

0.365828

L1 (Output)

-0.108344 + 0.015935i

0.051947

0.356989

L2 (Input)

0.759858 + 0.016086i

0.051947

2.199920

L2 (Output)

-0.865307 + 0.026488i

0.066974

2.188928

SR2 (AR)

1.143693 + 0.026488i

0.066974

2.892571

SR2 (HR)

1.489013 + 0.040119i

1.485169 + 0.039991i

0.082425

0.082292

3.060270

3.057282

ITMy (HR)

-1463.753784 + 729.531387i

-1538.350364 + 822.405327i

11.114831

11.801137

24.917463

25.031092

ETMy (HR)

1536.246216 + 729.531387i

1461.649636 + 822.405327i

11.114831

11.801137

25.910643

24.066063

Y-axis Beam radius Y-axis Beam radius

Pattern B (3 lenses)

Mode matching optical system (back of SR2)

Mirror

q-parameter

Waist radius [mm]

Beam radius [mm]

qx

qy

W0x

W0y

Wx

Wy

Fiber coupler

0 + 0.723393i

0.350

0.350

L1 (Input)

0.089 + 0.723393i

0.350

0.352639

L1 (Output)

0.108858 + 0.016086i

0.052192

0.357035

L2 (Input)

0.759858 + 0.016086i

0.052192

2.465986

L2 (Output)

0.434746 + 35.905184i

2.465809

2.465990

L3 (Input)

1.019746 + 35.905184i

2.465809

2.466803

L3 (Output)

-0.973312 + 0.026619i

0.067139

2.455838

SR2 (AR)

1.143688 + 0.026619i

0.067139

2.885427

SR2 (HR)

1.489002 + 0.040318i

1.485159 + 0.040189i

0.082629

0.082496

3.052712

3.049731

ITMy (HR)

-1461.017819 + 731.892574i

-1535.118889 + 824.885592i

11.132804

11.818919

24.856063

24.969411

ETMy (HR)

1538.982181 + 731.892574i

1464.881111 + 824.885592i

11.132804

11.818919

25.921818

24.087634

Y-axis Beam radius Y-axis Beam radius

Back of PR2

Lens displacement

For Y-arm

Pattern A (2 lenses)

GreenModeMatch_2lens_170904.pdf

Pattern B (3 lenses)

GreenModeMatch_3lens_170904.pdf

For X-arm

ModeMatch (last edited 2018-03-27 09:54:33 by KazuyaYokogawa)