Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

PERFORMANCE STUDY OF FOUR MIRROR LASER RESONATOR
FOR 6 m MINIMUM BEAM SIZE USING GREEN LASER OSCILLATOR
Arpit Rawankar #A,B), Junji Urakawa A,B), Hirotaka Shimizu B),
Nobuhiro Terunuma A,B) ,Yosuke Honda B)
A)

Department of Accelerator Science, School of High Energy Accelerator Science, Graduate
University for Advanced Studies, Shonan International Village, Hayama, Miura, Kanagawa , JapanB)
High Energy Accelerator Research Organization [KEK], 1-1 Oho, Tsukuba, Ibaraki , JapanAbstract
The Accelerator Test Facility (ATF) was constructed at KEK to study low emittance beam physics and to develop thetechnologies associated with it. In ATF damping ring, electron beam size is measured with laser wire system based on
Compton scattering. A new four mirror laser wire system is developed for this purpose. This system has many
advantages over two mirror laser wire system. Four mirror resonator reduces the sensitivity towards misalignment ascompare to two mirror resonator. Measured Finesse of resonator is more than 4000. Optical cavity has enhancement
factor of 1900. Inside ATF damping ring, electron beam has very small size of 10in vertical direction. To measureelectron beam profile, very thin laser beam size is needed. Laser waist size, around 6
in sagittal plane is achieved in
between two concave mirrors. Special type of mirror alignment scheme is used to make a compact four mirror opticalcavity. Laser resonator is designed to work in vacuum environment with a complex mirror holder design .We report theperformance studies of such four mirror resonator using 532 nm CW laser oscillator in this research.

1.

Introduction

Production and handling of low emittance beam isimportant technology for linear colliders. For thisdamping ring generates low emittance beam by radiation
damping process. The Accelerator Test Facility (ATF) in
KEK is a test accelerator to examine the technicalpossibility in generating the low-emittance beam required
for linear colliders. The damping ring has two arc sections
and two straight sections [1]. In the damping ring at ATF,
vertical beam size is less than 10 m. For emittancemeasurement, we are developing a new type of beamprofile monitor which works on the principle of Compton
scattering between electron and laser light. A thin andintense laser beam is produced by exciting a Fabry-Perot
optical cavity and it is scanned across the electron beam
in perpendicular direction as shown in Figure 1.

When electron beam crosses the laser, some of theelectrons interact with laser light and emit energetic
photons in the forward direction via the Compton
scattering process. A detector placed downstream of thecollision point measures the flux of the scattered photons.
By scanning the position of laser beam and counting thenumber of scattered photons, a projected beam size isobtained. Such type of optical resonator system is called
laser wire. Laser wire is one of such a technique tomeasure a small electron beam size. In particular, if bothelectron and laser beam are assumed to have Gaussian
profiles with widthand, the observed profile isalso gaussian with width 𝑜𝑏𝑠 expressed by(1)
σ2obs = σ2lw + σ2e
We used a four mirror Fabry-Perot optical cavity toproduce laser wire. It enhances the effective laser powerand improves the intensity of the signal. The geometricalproperties of laser beam are completely defined byboundary conditions formed with two concave mirrors
and two plane mirrors [2, 3]. The minimum beam waist is
obtained in between two concave mirrors. The two
concave mirrors of same curvature are used in compact
resonator. Electron beam interacts with laser pulse atminimum beam waist position, which is called interaction
point (IP).

Figure 1: KEK-ATF Damping Ring

Aspect ratio of resonator is important parameter toachieve small beam waist. Aspect ratio of resonator isdefined as ratio of side by side plane and concave mirror- 760 -

Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

distance (d) to distance between two concave mirrors (L).
The Aspect ratio
for four mirror optical resonator isgiven as [2]⁄ .
=(2)
To achieve very small minimum beam waist, aspect ratioof cavity is kept constant and cavity length is reduced.

2. Design of compact resonator
2.1 Design values and mirror alignment scheme
The optical cavity assembly consists of four mirrors,
mirror holder system and cyilindrical spacers which
define length of cavity. In order to have precision control
over cavity length , both plane mirror holders were
supported by a piezo actuator through a disk type plate
spring. Hollow piezo actuators are used for laser beam topass through them [4]. Four mirror optical cavity isdesigned for 532 nm wavlength. Distance between
concave-concave mirror is kept at 102.8 mm and distance
between plane-plane mirror is kept at 103.2 mm. A
complex mirror alignment scheme as hown in Figure 2 isused to keep side by side distance between plane andconcave mirror to 29.2 mm. All mirrors used in cavity
design are of 1 inch diameter. The radius of curvature fortwo concave mirror is 101.81 mm.

Figure 3: Beam waist variation with mirror curvature
2.2 Beam Evolution inside resonator
Figure 4 shows the evolution of beam size in both sagittal
and tangential plane along longitudinal distance inside
four mirror resonator. The beam size is squeezed in
between concave mirrors. Large value of beam waist isobtained at the interface of concave mirrors. Smaller
beam size in between two concave mirrors depends on thedivergence of beam inside resonator. If beam waist at theinterface of concave mirror is large then we get smaller
value of beam waist in between two concave mirrors. The
beam size is almost constant in both planes while
prapogating through free space region formed among
concave-plane-plane-concave mirrors. Beam size at thesurface of concave mirrors and plane mirrors are greaterthan 1.2 mm in sagittal plane , and greater than 0.3 mm intangential plane.

Figure 2. Cavity assemply and its mounting.
Figure 3 shows beam waist variation with radius ofcurvature of concave mirror. Horizontal axis indicatesradius of curvature of concave mirror in mm and verticalaxis shows beam size in mm. To get the minimum beam
size in one plane i.e. sagittal plane in this case, we choose
values of curvature of cavity mirrors close to the length ofresonator. In order to obtain minium beam waist in thisconfiguration we keep optical cavity at marginally stablecondition and choose value of mirror curvature very close
to distance between two concave mirrors. We choose themirror curvature value as 101.81 mm.

Figure 4: Beam evolution inside four mirror optical cavity
2.3 System Setup
We utilized a diode-pumped solid state laser withwavelength of 𝜆=532 nm (Light-Wave Series 142). Thislaser employs the Non-Planer Ring–Oscillator (NPRO)
technique to realize ultra-low line width (10kHz/msec).
Its output power is 300mW. Two type of lens system isused to make the laser beam match to themode ofthe cavity. Spherical lens system consists of two spherical- 761 -Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

lenses is used to make laser beam divergence free andwell collimated. Another lens system consists ofcylindrical lenses is placed to make ratio of sagittal beam
size to tangential beam size equal to 3.Thus we can obtain
good coupling efficiency from laser output and matching
section. The measured coupling efficiency for this setup ismeasured as 35 %. Photo-diodes are used to monitor
transmitted light intensity. To observe the excitation ofvarious modes of the cavity, the cavity length was swept
repeatedly by the piezo actuator. The piezo actuator isdriven by a sinusoidal wave through a high voltage
amplifier. In order to reduce some higher order modes,
matching lens section is tuned. Figure 5 shows diagram ofsystem setup.

Finesse is measured experimentally by finding the ratio ofFree Spectral range (FSR) to width of resonance at half
maximum ( ) of Airy function. FSR is distance betweenpeaks of two consecutive 0th order modes

Figure 6: Transmitted laser signal
In Figure 6, the yellow waveform shows the voltage of
piezo actuator, which means cavity length expansion. The
red wave form shows the signal from photo diodedetecting the cavity transmitted laser power.
⁄Experimental Finesse =(6)Experimental Finesse is obtained as 4126.6 230 and
Enhancement Factor () is calculated as 1900
3.2 Waist Measurement by Transverse Mode Difference

Figure 5: Total system setup

3. Parameters of Four Mirror Resonator
3.1 Finesse
Sharpness of the resonance width is represented by thecavity finesse (F), it is defined from the reflectance of thefour mirrors of optical cavity as [5, 8]=(3), wherebyis effective reflectivity of resonator defined
=√

2(4).

Design reflectivity (R1 and R2) of plane mirrors are 99.9%
and 99.99%. Reflectivities of both concave mirrors (R3and R4) are 99.99 %. Total Finesse (F) of compact
resonator is given by [2]
=√√

(5)

The Guoy phase is defined by the order of the transversemode (m+n) and the beam waist ( ) [10, 11]. The
distance between two modes of one-order difference isdefined by beam waist. When cavity length was swept
while monitoring the resonation by the cavity
transmission intensity, some peaks of the resonances wereobserved. Each resonance peak corresponds to some orderof modes. There are two 1st order modes representing twovalues of Guoy phase corresponding to sagittal andtangential plane. In order to calculate minimum beam
waist of resonator based on mode difference method,
distance between plane–plane and concave–concave
mirrors are changed while keeping the total length ofpulsed resonator constant.
Guoy phase can also be represented by ray transfer matrixof resonator for one round trip. Eigen values of a nondegenerate matrix are complex [12] and are given by
= 2=
(7)

=

Theoretical finesse of resonator is 4831.3- 762 -√(2)(8)

Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

Where phase angle
is round trip Guoy phase ofresonator. Figure 7 shows the theoretical variation of
Guoy phase in sagittal and tangential plane with mirror
separation. Since the dimensions of laser resonator are
fixed, we measured the Guoy phase value at minimum
beam waist position and calculated the corresponding
waist size.

is the Rayleigh length. In the case of z
divergence angle can be approximated as [7]:
== 𝜆⁄

( )

, the(9)The minimum beam waist measured using divergence
method in sagittal plane ( 𝑠 ) is 6.9 1 m and intangential plane ( ) is 20.14 2 m.

4. Analysis
Following Table 1 describes various parameters forcompact four mirror laser resonator.
Table 1: Parameters for four mirror resonator
Parameter

Value

Length103.2 mm

Side by side distance29.2 mmFinesse4126.6 230

Enhancement Factor

1900

Min. beam waist ( 𝑠Figure 7: Variation of Guoy phase with mirror sepration
Minimum beam waist measured using transverse mode
difference method in sagittal plane ( 𝑠 ) is 5.9 1.5 m
and in tangential plane ( ) is 16.02 2.5 .
3.2 Waist Measurement by Divergence Method:)

6.9 1 m , 20.14

2 m.

We test the optical cavity using CW green laser and findthat very high finesse can be achieved with very small
beam waist in vertical direction. The results of beam
waist measurement using Guoy phase difference methodand divergence method are comparable. It is found thatminimum beam waist of compact resonator has very highsensitivity towards any change in cavity length. Four
mirror resonator has less sensitivity for misalignment
compared to two mirror resonator. We carefully selectlength and mirror curvature parameters, so that beam
waist around 6
can be achieved.

5. Conclusion

Figure 8: Minimum beam waist measurement using
divergence method
The output laser profile is measured as an extension of thecavity resonating mode, so the waist size of laser beam
inside optical cavity can be determined by measuring theoutput profile by scanning the pin hole photo diode, bothin horizontal plane and vertical plane as shown in Figure
8. The output laser size at the distance z from the focal
point is represented by ( ) = √ + ( ⁄ )2 , where

Compact four mirror laser wire system will make use of
pulsed green laser to scan electron beam profile insidedamping ring. Electron beam can be measured in vertical,
horizontal and longitudinal direction in very short time ascompare to CW laser wire system [13]. The laser cavity
already is tested with 714 MHz IR mode locked laser
oscillator. With IR pulsed laser oscillator, minimum beam
waist of 12
is measured [2]. Thus same optical cavity
design gives around 6
minimum beam waist using
CW green laser oscillator. We developed a system, which
amplifies laser pulse of 714 MHz IR laser oscillator with
Yb doped photonic crystal fiber to high value. After
amplification of pulsed IR laser, a non-linear crystal isused for 2nd harmonics generation. Thus we can obtainpulsed green laser which has 714 M Hz repetition rate.
This pulsed green laser can provide effective photon andelectron collision. High Finesse and small beam size aremost important characteristics of compact four mirror
resonator.

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Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan)

Acknowledgement
This research has been supported by Quantum beamtechnology program of Japanese Ministry of Education,Culture, Sports, Science and Technology (MEXT).

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