# Optical System Design

March 5, 2004

### Requirement

Horizontal direction

![](media/image1.wmf)=5 mm, ![](media/image2.wmf)=1 mrad, both
adjustable

Vertical direction

![](media/image3.wmf)=0.2 mm variable, ![](media/image4.wmf)\<3 mrad.

### Light source

Nd:YAG, Continuum Powerlite Precision II 8030

Pulse repetition rate 30 Hz

Pulse width 6\~8 ns

Pulse energy 650 mJ (fundamental, 1.06 μm), 150 mJ (third harmonic, 355
nm)

Linewidth 0.003 cm^-1^ (90 MHz) with injection seeded.

*λ*=355 nm,

Assuming ![](media/image5.wmf)=0.1 mrad, ![](media/image6.wmf)=1.13 mm,
![](media/image7.wmf)=11.3 m.

### Design objectives

(i) Beam parameters (waist and divergence angle)

(ii) Working distance from telescope to interaction region

(iii) Pulse intensity at the window and lenses

### I. Pre-collimation with circular lens 

Input beam parameters: *λ*=355 nm, ![](media/image8.wmf)=0.1 mrad, and
*z*=100 m,

![](media/image9.wmf)=1.13 mm, ![](media/image10.wmf)=11.3 m.

Pre-collimation lens parameters: *f*~0~=50 cm.

![](media/image11.wmf),

![](media/image12.wmf) cm, ![](media/image13.wmf)=20.03 mrad,
![](media/image14.wmf) cm,

![](media/image15.wmf)=50.25 cm.

Beam size at the plane of *z~l~*=60 cm:

![](media/image16.wmf)cm.

Beam size at the plane of *z~l~*=70 cm:

![](media/image17.wmf)cm.

## **II: Vertical beam design** 

## 

Input beam parameters:

![](media/image18.wmf) cm, ![](media/image19.wmf)=20.03 mrad,
![](media/image20.wmf) cm, *z*=10 cm.

Target beam parameters:

*λ*=355 nm, ![](media/image21.wmf)=0.2 mm, ![](media/image22.wmf) mrad,
(we assume ![](media/image23.wmf) mrad)

![](media/image24.wmf) cm, ![](media/image25.wmf)=5.02 cm.

## **Telescope design**

\(1\) *f*~1~=-50 cm (concave cylindrical lens).

![](media/image26.wmf),

![](media/image27.wmf) cm, ![](media/image28.wmf)=24.05 mrad,
![](media/image29.wmf) cm,

![](media/image30.wmf) cm.

\(2\) *f*~2~=12.5 cm (convex cylindrical lens), *d*=5 cm,
*z*~2~=*d*-*z*~1~=13.367 cm.

![](media/image31.wmf),

![](media/image32.wmf) cm, ![](media/image33.wmf)=1.67 mrad,
![](media/image34.wmf)= 4.06 cm,

![](media/image35.wmf)=192.63 cm.

\(3\) To achieve beam size 2![](media/image36.wmf)=0.4 mm, the distance
from the telescope to the interaction region will be:

![](media/image37.wmf)=181.35 cm.

Distance from the first cylindrical lens ![](media/image38.wmf)=186.35
cm.

Distance from the pre-stage lens ![](media/image39.wmf) cm.

## **III: Horizontal beam design**

Input beam parameters:

![](media/image40.wmf) cm, ![](media/image41.wmf)=20.03 mrad,
![](media/image42.wmf) cm, *z*=20 cm.

Target beam parameters:

*λ*=355 nm, ![](media/image43.wmf)=5 mm, ![](media/image44.wmf)=1 mrad,

![](media/image45.wmf)=0.0113 cm, ![](media/image46.wmf)=11.3 cm.

## **Telescope design**

\(1\) *f*~1~=-50 cm (concave cylindrical lens).

![](media/image47.wmf),

![](media/image48.wmf) cm, ![](media/image49.wmf)=28.05 mrad,
![](media/image50.wmf) cm,

![](media/image51.wmf) cm.

\(2\) *f*~2~=22.5 cm (convex cylindrical lens), *d*=9 cm,
*z*~2~=*d*-*z*~1~=23.3 cm.

![](media/image52.wmf),

![](media/image53.wmf)=0.011 cm, ![](media/image54.wmf)=1.0 mrad,
![](media/image55.wmf)= 11.3 cm,

![](media/image56.wmf)=655.1 cm.

\(3\) At ![](media/image57.wmf)cm,

![](media/image58.wmf)cm.

Distance from the first cylindrical lens ![](media/image59.wmf)=176.35
cm.

**IV: Optical pulse intensities at intersection planes**

Assume (i) the telescopes are outside of the vacuum and (ii) the
distance of the vacuum window to the light-particle interaction region
is 50 cm.

**[(1) Pre-collimation Lens]{.underline}**

Beam radius at the lens plane: *w~L0~*=1 cm,

Optical pulse intensity at the lens: ![](media/image60.wmf).

**[(2) Vertical Telescope]{.underline}**

Beam size at the first cylindrical lens:

![](media/image61.wmf),

Optical pulse intensity at the first cylindrical lens:

![](media/image62.wmf).

Beam size at the second cylindrical lens:

![](media/image63.wmf),

![](media/image64.wmf).

Optical pulse intensity at the first cylindrical lens:

> ![](media/image65.wmf).

**[(3) Horizontal Telescope]{.underline}**

Beam size at the first cylindrical lens:

![](media/image66.wmf),

![](media/image67.wmf),

Optical pulse intensity at the first cylindrical lens:

![](media/image68.wmf).

Beam size at the second cylindrical lens:

![](media/image69.wmf),

![](media/image70.wmf).

Optical pulse intensity at the first cylindrical lens:

> ![](media/image71.wmf).

**[(4) Vacuum Window]{.underline}**

Beam size at the vacuum window:

![](media/image72.wmf),

![](media/image73.wmf).

Optical pulse intensity at the vacuum window:

![](media/image74.wmf).