Paper Tisa laser system

8/13/2019 Paper Tisa laser system

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Figure 3: Schematic overview of the Ti:Sa setup at CERN; this paper focuses on the resonator (1). Compo-nents include the Ti:Sa crystal (a), resonator mirrors (b), birefringent filter (c), etalon (d), Pockels cell (d), and the intra-cavity second harmonic generator (f). Figure taken from [ 9 ].

to focus the beam on the Ti:Sa crystal, locatedin the middle of the Z. The rightmost mirror isselected to be slightly less reflective, so the laserlight can exit there.

As can be seen in figure 3, several components

are present in the laser cavity:

• Mirrors

• Etalon

• Birefringent filter

• Pockels cell

• Second harmonic generator (SHG)

In a more recent paper [10], a second operatingmode for the Ti:Sa system was developed. Thecavity as presented in figure 3 is the broad-bandmode, while including a second etalon in the cav-ity reduces the spectral width again, which is thenarrow-band mode.

The mirrors are selected to be reflective in acertain range of frequencies, giving a first filter-ing effect. The etalon and the birefringent filterare used to narrow the width of the emission pro-

file even further. The order of magnitude for thedifferent narrowing effects can be seen in figure4. The final result of these filtering effects is themultiplication of these profiles.

Figure 4: Overview of different filtering effects. Amore recent update of the laser cavity in-cluded a second etalon [ 10 ], greatly reduc-ing the achieved line width. Figure taken

from [ 6 ].

The Pockels cell is used for Q-switching , a tech-nique where the firing of the laser is delayed. Fi-nally, the SHG doubles the frequency of the light.

All these components together form a pulsedlaser with a high power output. Details of theachieved laser can be found in table 1.

The etalon, birefringent filter, Pockels cell andSHG will be discussed in this order, roughly fol-lowing an order of simple to more complex com-ponents.

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Frequency (fundamental) 680 - 960 nmRepetition rate 1 - 15 KHz

Pump power 22 WLasing threshold 2 W

Pulse duration 40 - 60 nsOutput power 5 W (fundamental frequency)

1 W (×2)150 mW (×3 and ×4)Spectral width 10 GHz (broad-band)

1 GHz (narrow-band)

Table 1: Specifications of a typical Ti:Sa system. The data given are from measurements of the Mainz Ti:Sa system, while the spectral widths were measured at CERN. Data are taken from [ 9 , 10 ].

2.1 Etalon

An etalon is used to filter the range in frequencyspace that the laser emits, narrowing the width.The birefringent filter, as discussed further in thispaper, has the same purpose. The difference liesin the achieved width of the frequency range, witha combination of both filters giving the best re-sults. An etalon achieves the filtering effect byutilizing destructive interference.

Figure 5: Overview of optical paths in an etalon. Fig-ure taken from [ 11 ] .

As can be seen on figure 5, the light beam thatenters the etalon is reflected multiple times in theinterior of the etalon. The optical path differ-ence between two successive transmitted beams(T 1 and T 2) is given by 2n cos(θ), with n being

the refractive index of the medium. Constructiveinterference, and thus maximal transmission, isobtained when this difference is a multiple of thewavelength. This leads to the following equation

for the maximally transmitted wavelengths [5]:

λm = 2n cos(θ)

m , (1)

with m an integer.

Note that the reflected waves interfere destruc-tively for λ = λm, leading to complete transmis-sion. However, this assumes that the reflectedwaves overlap completely. Taking into accountthe finite diameter D of the laser beam gives riseto a radiation loss; the intensity of this loss isgiven by [5]

I R ≈ 2R tan(θ) I 0D

, (2)

with R the reflectivity of the surfaces of the etalonand I 0 the original intensity.

The selection of the right frequency range re-quires changing the angle of incidence on theetalon. In the setup used at CERN, this is doneby rotating the etalon using a stepping motor [9].

2.2 Birefringent filter

Figure 6: Schematic of a typical birefringent filter.Multiple birefringent crystals are spaced af-ter each other to minimize losses. Figure adapted from [ 2 ] .

The birefringent crystal is placed with its opti-

cal axis at an angle to the polarization of the laserlight. The result is that the beam is split into two:a fast and a slow component. At the end of thecrystal, the beams are combined again, resulting

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in elliptically polarized light. This will lead to dif-ferent reflection and transmission coefficients dueto the Fresnel equations, allowing a wavelengthselection. More specifically, the polarization isrotated by a phase [6]

Γ = 2π∆n

λ , (3)

with the thickness of the plate and ∆n the differ-ence in refractive index for the fast and slow com-ponent. At wavelengths where ∆n is an integermultiple of the wavelength, no effective rotationoccurs.

The Fresnel equations, derived from theMaxwell equations, describe the reflection of twotypes of polarized light on an interface:

• s polarized light, polarized perpendicular tothe plane containing the rays.

• p polarized light, polarized in the plane con-taining the rays.

The reflection amplitude for s and p polarizedlight are given by the following equations [1, 8]:

rs = n1 cos(θ1) − n2 cos(θ2)

n1 cos(θ1) + n2 cos(θ2), (4)

r p =

n2 cos(θ1) − n1 cos(θ2)

n1 cos(θ2) + n2 cos(θ1) , (5)

with n1, n2 the refractive indices, θ1 the internalreflection angle, and θ2 the propagation angle.

Figure 7: The percentage of reflectivity for both po-larizations. Figure taken from [ 1 ] .

As seen in figure 7, at a certain angle the ppolarized light is not reflected, but fully trans-mitted. The angle at which this occurs is theBrewster angle. Since the polarization of the lightat the end of the crystal depends periodically on

the wavelength, a periodic dependence in trans-mission through the filter is observed. Figure 4illustrates this effect, although only one period isplotted.

2.3 Pockels cell

A Pockels cell is a device that can modify thepolarization of light. It is made from non-centrosymmetric crystals that are sensitive to thePockels effect. Placing an electric field over suchcrystals will lead to a change of the refractive in-dex for a certain direction. By changing the elec-tric field, a proportional change of the birefrin-gence of the crystal can be induced.

The birefringence will cause a phase retardationΓ between the two mutually orthogonal polariza-tion components of the incoming beam, given by

equation 3. This retardation will cause a changeof the polarization of the light.

Except for the etalon, the components of thelaser are sensitive for the polarization of the light.Thus, it is possible to modulate the cavity lossesby controlling the polarization inside the cavity.These losses are quantified in the Q factor of theresonator, which is a measure of the damping of the oscillations and is defined as

Q = νT rt 2πI , (6)

with ν the optical frequency, I the fractionalpower loss per round trip and T rt the time of around trip [3].

By first applying a high voltage over the Pock-els cell, the polarization of the light will bechanged. This leads to high losses in the res-onator, making lasing impossible. In the mean-

time, the energy fed by the pumping laser will ac-cumulate, leading to a higher percentage of pop-ulation inversion in the Ti:Sa medium, with onlythe spontaneous emission as limit.

As the voltage on the Pockels cell is dropped,the resonator will work efficiently again, the noiseof the spontaneous emission will be amplified andtrigger the stimulated emission. This techniqueis called Q switching . The time-evolution of the

process is represented in figure 8. At time t = 0,the Q switch is activated. From that moment on,the power starts to increase, but only becomessignificant some 0.2 µs later.

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Figure 8: Time evolution of Q switching. At time t = 0 the Q switch is activated, the res-onator losses drop and the power starts toincrease exponentially. Figure taken from [ 4 ].

With this technique, one can influence whenthe cavity starts lasing. This can be importantto synchronize multiple lasers in, for instance, amulti-step ionization. First excite the electron toa higher laying energy level with a laser, and thenone can ionize the excited electrons with the sec-ond laser.

2.4 Second Harmonic Generation

The Ti:Sa-crystal has only a limited window of wavelengths, ranging from 650 to 1100 nm inwhich it can emit radiation (see figure 2). It canhappen that wavelengths outside of this windoware required, for example, to perform ResonantIonization Spectroscopy. Second Harmonic Gen-eration (SHG) can double the frequency of thefundamental laser emission light, so it can pro-duce the required wavelength.

The following explanation of the process of SHG is based on the derivation found in [7].

The process of SHG is in fact a three-wave mix-ing process, where two photons with a certain fre-quency ω annihilate to create a photon with a fre-quency 2ω. A graphical representation is given infigure 9. To keep track of the two different inci-dent photons, we will label the two componentsof the incident field with ω1 and ω2. In this case,at the end, we can assume that ω1 = ω2. Theincoming wave is thus given by

E (t) = Re{A(ω1)eiω1t + A(ω2)eiω2t}, (7)

with A(ωi) the complex amplitude of the wave.

ω1

ω2

ω3

ω1

ω2

ω3

Figure 9: Graphical representation of a three photon interaction in a nonlinear medium. Twolow-frequency photons, ω1 and ω2 anni-hilate and create a higher energetic photon ω3. This figure is taken from [ 7 ]

For a normal linear dielectric medium, a linearrelation exists between the induced polarization

P of the medium and the applied electric field E :

P = 0χ E, (8)

with 0 the permittivity of vacuum and χ the elec-tric susceptibility of the medium. The relationbetween P and E in a nonlinear medium can beapproximated by a Taylor expansion1:

P = 0(χ E + χ(2) E 2 + χ(3) E 3 + . . .). (9)

To understand second harmonic generation, it is

sufficient to look at this expansion up to secondorder. We can more conveniently write the polar-ization as P = 0χ E + P NL, with P NL = 2d E thenonlinear term and d the second-order nonlinearcoefficient. The propagation of a wave througha nonlinear medium can then, after some reduc-tions, be expressed as:

∇2 E − 1

c2∂ 2 E

∂t2 = µ0

∂ 2 P NL

∂t2 , (10)

with c the velocity of light inside the nonlin-ear medium. Because the nonlinearity is mostlysmall, it is possible to use the Born approxi-mation , an iterative process where the S ( E 0) =

µ0∂ 2 P NL∂t2

term can be seen as a source. First wecalculate this source term as a function of theincident light. The generated light can itself beseen as incident light, leading to a second step inthis iterative process by generating itself radia-tion. The source term will then be in function of the scattered field S (E 1). Because the nonlinear-

ity is in general quite low, restricting ourselves tothe first step will be a good approximation.

1The expansion of P around E = 0 is a good approximation because the typically applied fields are small in comparison

with the inter-atomic fields of the medium.

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If we now apply the Born approximation to ourproblem, we insert the incident wave (7) into thenonlinear term of the polarization, P NL = 2d E 2,and obtain that the final result contains 5 frequen-cies: 0, 2ω1, 2ω2, ω+ = ω1 +ω2 and ω

− = ω1−ω2.

Keeping in mind that the two frequencies are in

fact the same, we obtain the creation of a photonwith a frequency 2ω, and the null solution.

The two most fundamental laws of physics, con-servation of energy and momentum, still haveto be satisfied throughout this derivation. Theyare often referred as the frequency-matching andphase-matching condition:

ω + ω = (2ω)

k1 + k2 = k3. (11)

These will impose certain restrains on the cre-ation of the second harmonic. The velocities of the waves in a medium depend on the frequency,due to the dispersive nature of materials. Thismakes it possible to rewrite the last equation,ωn1 + ωn2 = 2ωn3 where ni are the refractiveindexes which are frequency dependent.

Because the medium of a second harmonic gen-

erator is a uniaxial crystal, there is an ordinary re-fractive index no, and an extraordinary refractiveindex ne. The extraordinary refractive index has,besides the dependency on the frequency, also adependency on the angle the incoming ray makes

with the optical axis. As represented in figure 10,only for a certain angle will the phase-matchingcondition (11) be fulfilled, leading to the creationof a second harmonic.

θ

ω

2ω

e

o O

p t i c

a x i

s

ne(2ω)

no(ω

)

no(2ω)

θ

ne(ω)

Figure 10: Left: The refractive index plotted in func-tion of angle for the fundamental and sec-ond harmonic. Right: Graphical repre-sentation of the incident light (red) and the generated second harmonic as an ordi-nary wave (blue). Figure taken from [ 7 ] .

3 Conclusion

The CERN Ti:Sa laser system utilizes a Z-cavity,with two possile operating modes: narrow-bandand broad-band. The output is a high-power,pulsed laser that can be used in high resolutionexperiments, since a spectral width of 1 GHz iswithin reach. The Pockels cell present can beused to delay the firing of the laser, which allows

the user to synchronize with an external event,or other laser. Using frequency doubling tech-niques allows doubling, tripling and even quadru-pling the frequency while maintaning usable laserpowers.

References

[1] RP Photonics. Fresnel Equations . URL http://www.rp-photonics.com/fresnel_equations.html.

[2] RP Photonics. Lyot Filters . URL http://www.rp-photonics.com/lyot_filters.html.[3] RP Photonics. Q factor . URL http://www.rp-photonics.com/q_factor.html.

[4] RP Photonics. Q Switching . URL http://www.rp-photonics.com/q_switching.html.

[5] W. Demtroder. Laser Spectroscopy - Basic Concepts and Instrumentation . Springer-Verlag(1981).

[6] G. Kirchmair. Frequency stabilization of a Titanium-Sapphire laser for precision spectroscopy on Calcium ions . Ph.D. thesis, Leopold Franzens University of Innsbruck (2006).

[7] B. Saleh and M. Teich. Fundamentals of Photonics . Wiley, 2nd edn. (2007).

[8] D. Griffiths. Introduction to electrodynamics . Pearson Benjamin Cummings, San Francisco(2008). ISBN 0-13-919960-8.

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http://www.rp-photonics.com/q_switching.html

http://www.rp-photonics.com/q_factor.html






[9] S. Rothe et al. A complementary laser system for ISOLDE RILIS . In: Journal of Physics:Conference Series , vol. 312, no. 5: p. 052020 (2011). ISSN 1742-6596. URL http://dx.doi.org/10.1088/1742-6596/312/5/052020.

[10] S. Rothe et al. Narrow linewidth operation of the RILIS titanium: Sapphire laser at ISOLDE/CERN . In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms , pp. 8–11 (2013). ISSN 0168583X. URL http://dx.doi.

org/10.1016/j.nimb.2013.08.058 .

[11] Wikipedia. Fabry-Perot interferometer (2013). URL http://en.wikipedia.org/wiki/Etalon.

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http://dx.doi.org/10.1088/1742-6596/312/5/052020

http://dx.doi.org/10.1088/1742-6596/312/5/052020

http://dx.doi.org/10.1088/1742-6596/312/5/052020

http://dx.doi.org/10.1016/j.nimb.2013.08.058


http://en.wikipedia.org/wiki/Etalon

http://en.wikipedia.org/wiki/Etalon



http://dx.doi.org/10.1088/1742-6596/312/5/052020

http://dx.doi.org/10.1088/1742-6596/312/5/052020

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