Download A pulsed dye laser for photo-ionization of magnesium atoms

A pulsed dye laser for photo-ionization
of magnesium atoms
Master Thesis realized in March-June 2009
in the Laser Spectroscopy Division
of the Max-Planck-Institute for Quantum Optics (Garching)
by Camille Estienne,
student in the Master of Physics
at the Swiss Federal Institute of Technology (Zürich).
Supervisor in Zürich: Professor Ursula Keller
Supervisor in Garching: Doctor Thomas Udem
Aknowledgements
Thank you to Valentin Batteiger, Maximilian Hermann, Sebastian Knünz, Guido
Saatho, Mariusz Semczuk from the Ions Traps Group and to Karl Linner and
Wolfgang Simon from the workshop, for their help and advices during these four
months.
3
Contents
1 Introduction
6
2 Theory of pulsed operation of dye lasers
2.1 Laser operation from organic dye molecules . .
2.1.1 Energy levels . . . . . . . . . . . . . . .
2.1.2 Triplet state absorption . . . . . . . . .
2.2 Principle of gain switching and rate equations .
2.2.1 Principle of gain switching . . . . . . . .
2.2.2 Rate equations . . . . . . . . . . . . . .
2.2.3 Numerical study . . . . . . . . . . . . .
2.3 Resonator design . . . . . . . . . . . . . . . . .
2.3.1 Types of wavelength selective resonators
2.3.2 Choice of a resonator . . . . . . . . . . .
2.3.3 A simple model for self-seeding . . . . .
3 Experimental setup
3.1 Pump laser and pump optics . . . . . . . .
3.1.1 Pump power and pulse shape . . . .
3.1.2 Pump optics . . . . . . . . . . . . .
3.1.3 Pump beam polarization . . . . . . .
3.2 Dye solution, dye cell and circulating pump
3.2.1 Dye solution . . . . . . . . . . . . .
3.2.2 Dye cell . . . . . . . . . . . . . . . .
3.2.3 Circulating pump . . . . . . . . . . .
4 Laser resonators
4.1 Two-mirror cavity . . . . . . . .
4.2 Prisms and birefringent crystal .
4.2.1 Dispersion . . . . . . . . .
4.2.2 Spectral narrowing . . . .
4.2.3 Challenges . . . . . . . .
4.2.4 Highly birefringent crystal
4.2.5 Results . . . . . . . . . .
4.3 Littman cavity . . . . . . . . . .
4.3.1 Spectral narrowing . . . .
4.3.2 Results . . . . . . . . . .
4.4 Dual-cavity . . . . . . . . . . . .
4.4.1 Results . . . . . . . . . .
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4.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5 Second-harmonic generation and photo-ionization of magnesium atoms
55
5.1 Second-harmonic generation . . . . . .
5.1.1 Optimized confocal parameter
5.1.2 Results . . . . . . . . . . . . .
5.2 Photo-ionization of magnesium atoms
5.2.1 General remarks . . . . . . . .
5.2.2 Proof of principle . . . . . . . .
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55
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6 Conclusion
61
List of Figures
64
List of Tables
68
5
Chapter 1
Introduction
This thesis reports on the demonstration of a compact and simple laser source
for photo-ionization, to be used for ongoing [1, 2] and planned [3] Paul trap
experiments.
Ion traps are usually loaded by electron impact or by photo-ionization. Electron impact is a simple way to ionize atoms, yet it is a non selective process
(other species can be ionized and trapped with the desired ions). This problem is
avoided when a resonant multi-step photo-ionization process is used. The atoms
are rst selectively excited on resonant transitions and then ionized. Hence, only
the desired species will have a signicant ionization probability. This process
also allows for isotope selectivity, if the spectral width of resonant transition
and the line width of the exciting laser are both smaller than than the isotope
shift.
Magnesium atoms can be ionized through a two-step process using a dipole
allowed transition at 285 nm as resonant excitation step. Unfortunately, light
at 285 nm is not easily produced by simple solid state laser systems like diode
lasers, while dye lasers can easily be tuned to emit at 570 nm. Then secondharmonic generation can be used to reach the desired wavelength.
So far, a single mode continuous-wave dye laser (Coherent 699) was used for
this purpose, in combination with a resonant second-harmonic generation step.
This system is pumped by a bulky argon ion laser, it contains an elaborate resonator and a resonant enhancement cavity for frequency doubling. Furthermore,
it will be used in near future for a lithium ion trap experiment.
This thesis reports on the demonstration of a pulsed dye laser system pumped
by a compact Nd:YAG laser emitting at 532 nm. The resonator uses rhodamin
6G as ecient laser medium and contains only few frequency selective elements.
The high peak power obtainable in pulsed operation allows for ecient single pass frequency doubling without any servo-electronics. Such a pulsed dye
laser may also serve as a prototype for a photo-ionization source for a planned
beryllium ion trap experiment. Here the resonant transition at 235 nm could
be reached by second harmonic generation from a coumarin dye laser, pumped
with a solid state laser at 355 nm.
6
Chapter 2
Theory of pulsed operation of
dye lasers
2.1
Laser operation from organic dye molecules
Laser emission from organic molecules (like the one represented in Figure 2.1)
was discovered in 1966 by J. R. Lankard and P. Sorokin at IBM Thomas J.
Watson Research Center [4, 5, 6]. This discovery soon proved to be an important
step in the developement of new laser sources, because of the availability of
uorescent organic molecules covering an extremely broad spectrum, ranging
from the UV to the IR. Furthermore, each dye molecule can emit over a wide
frequency range within which the dye laser can be continuously tuned. This
feature is very important for spectroscopic studies.
Figure 2.1: Molecular structure of rhodamine 6G (from [6]).
2.1.1
Energy levels
All uorescent organic molecules resemble one another in the general arrangement of their energy levels (Figure 2.2). The ground state S0 is a singlet state
from which the molecule can be excited to the lowest excited singlet state S1 .
Transitions between singlet states are dipole allowed transitions, giving rise
7
to the strong absorption bands of uorescent organic molecules. When the
molecules decay to the ground state, uorescent light is emitted.
Each electronic level of such a big molecule (the rhodamine 6G molecule
is represented in Figure 2.1) is made of hundreds of sublevels associated with
vibrations and rotations of the whole molecule. The continuous spectrum of
uorescent radiation can span tens of nanometers.
Non radiative decay from the high vibrational sublevels to the low vibrational
sublevels is much faster than the uorescence lifetime. Furthermore, the high
vibrational sublevels of the ground state will normally be unoccupied at room
temperature. Hence, this system can be analyzed as a quasi-four-level system,
and a population inversion can be built between low-lying sublevels of the rst
excited singlet state and high-lying sublevels of the singlet ground state. This
is the basis for laser action in organic molecules.
2.1.2
Triplet state absorption
A potential problem arises from the existence of triplet states in the spectrum
of organic dye molecules [4, 5, 6]. Molecules excited to the rst singlet state can
decay, by a non-radiative process, to the lowest triplet state T1 - a metastable
state which lies below the rst excited singlet state. This process is characterized
by an intersystem crossing rate kS,T which is an important parameter for laser
action.
The accumulation of molecules in the lowest triplet state has two consequences which are detrimental to laser action. First, the population of the rst
excited singlet state is decreased, as the molecules are 'trapped' in a metastable
state, and this increases the lasing threshold. Second, molecules in the lowest triplet state are now available for absorbing radiation corresponding to
a triplet-triplet transition, like T0 → T1 in Figure 2.2. Unfortunately triplettriplet absorption bands often overlap with the uorescence band, which can
prevent laser action from occuring altogether.
One way to overcome this problem is to pump the active medium with short
pulses of radiation. If the threshold for laser action can be reached in a time
which is small compared to the inverse of the intersystem crossing rate, the
triplet state population can be kept very small. This condition will be satised
for tthreshold 1/kS,T (where tthreshold is the time during which the population
inversion rises from zero to the threshold level). For a typical value of kS,T =
107 s−1 , we need tthreshold 100 ns. This condition is easily achieved with
a pulsed pump laser delivering pulses of ≈ 10 ns. Then all triplet eects can
be neglected in a rst approximation. In the following, we assume that this
condition is satised.
8
Figure 2.2: Energy levels of a typical dye molecule (from [5]). Heavy horizontal
lines represent vibrational states. Lighter lines represent rotational states. Excitation is represented by the transition A → b. Laser emission is represented
by the transition B → a. Other transitions (absorption to higher excited singlet
states, intersystem crossing, triplet states absorption) represent losses in the
laser process.
9
2.2
Principle of gain switching and rate equations
Laser emission from organic dye molecules was discovered accidentally: Lankard
and Sorokin were actually studying stimulated Raman emission from solutions of
phtalocyanine dyes, which have a narrow absorption band near the wavelength
emitted by a ruby laser. When a pulsed ruby laser was red at a cell containing
a phtalocyanine solution, incipient laser action was observed instead of Raman
emission [6]. Thus, the rst dye laser happened to be pumped with a pulsed
laser source, a method known as gain switching.
2.2.1
Principle of gain switching
Gain switching is a convenient method for obtaining short pulses of laser radiation. A pulsed source of light is used to modulate the gain of the active medium.
During the short pump pulse duration, the population inversion in the active
medium rises very rapidly above threshold inversion for laser action. A pulse
of laser light can build up in the cavity and will quickly deplete the population
inversion. As the pump pulse has only a short duration, the laser emission will
cease after a short time, until the next pump pulse arrives.
2.2.2
Rate equations
The dynamics of gain switching can be described by a set of two coupled rate
equations (see [4, 7, 8]):
dn(t)
dt
dq(t)
dt
= W (t) − B n(t) q(t) −
= Vg B n(t) q(t) −
q(t)
tc
n(t)
τ
(2.1)
(2.2)
where n(t) is the population inversion density, q(t) is the number of photons in
the cavity, W (t) is the number of absorbed pump photons per unit time and
per unit volume, τ is the uorescence lifetime, Vg is the active volume, tc is the
photon cavity lifetime and B is the Einstein coecient for stimulated emission.
These equations can be written in a slightly dierent way if we use the
threshold condition for the onset of oscillation from [9]:
N t h νl B =
hνl
tc
(2.3)
where the term on the left represents the energy delivered to the cavity per
unit time by stimulated emission (Nt is the threshold inversion, h is the Planck
constant and νl is the lasing frequency), while the term on the right represents
the energy lost per unit time due to the nite cavity lifetime.
If we susbtitute B = 1/(Nt tc ) from Equation 2.3 in Equations 2.1 and 2.2
we obtain:
10
dn(t)
dt
dq(t)
dt
n(t) q(t) n(t)
−
N t tc
τ
n(t) q(t) q(t)
= Vg
−
N t tc
tc
= W (t) −
(2.4)
(2.5)
For simplicity, a Gaussian pulse envelope will be assumed for the pumping
pulse:
"
W (t) = Wmax exp −4 ln 2
t
t1/2
2 #
(2.6)
where t1/2 is the full width at half maximum.
2.2.3
Numerical study
Equations 2.4 and 2.5 can be solved numerically to obtain some insights on the
dynamics of gain switching.
A set of parameters corresponding to the experimental work to be presented
in the next chapter has been used: a full width at half maximum of 20 ns for
the pump pulse, a uorescence lifetime of 6 ns, a threshold population inversion
density (calculated from [9]) on the order of 1015 cm−3 and a photon cavity
lifetime of a few nanoseconds.
The behavior of this system below and above threshold is clearly represented
by the series of solutions presented in Figure 2.3. The inversion population
depletion is very fast when the laser pulse builds up. When Wmax /nT is not
too high, the output laser pulse is shorter than the pump pulse, and it shows
a steeply rising slope. This dynamic eect has been used for generating short
pulses of laser radiation [7].
Another interesting feature of gain switched oscillators is the appearance
of relaxation oscillations for certain values of the parameters. The continuous
evolution from a single-pulse regime to a regime with relaxation oscillations can
be clearly followed in the series of solutions presented in Figure 2.4.
11
Figure 2.3: Solutions of the rate equations for an increasing number of pump
photons (from left to right and from top to bottom). Cavity length: 15 cm.
Active region length: 0.5 cm. Pump pulse width: 20 ns. Blue curve : Pump
pulse. Green curve : Population inversion. Red curve : Dye laser pulse.
12
Figure 2.4: Solutions of the rate equations for decreasing photon lifetime in
terms of a decreasing cavity length (from left to right and from top to bottom).
Active region length: 0.5 cm. Pump pulse width: 2 ns. W0 /nT = 2. Blue curve :
Pump pulse. Green curve : Population inversion. Red curve : Dye laser pulse.
13
2.3
Resonator design
One of the most attractive properties of dye lasers is their tunability. The uorescence band of organic dyes spans several tens of nanometers (Figure 2.5).
Within this uorescence band, laser emission can be observed over a wavelength
range for which the probability for uorescence is high while the singlet absorption coecient is low (Figure 2.5).
If the dye concentration is increased, the absorption will also be increased,
and the maximum of the stimulated emission spectrum will be shifted towards
longer wavelengths, because the balance of gain and losses becomes more favorable at these wavelengths [4]. Hence it is possible to tune a dye laser by
changing the dye concentration or by changing the length of the active volume.
But to achieve ne tuning and spectral narrowing it is necessary to introduce
wavelength selective elements into the resonator.
Figure 2.5: Singlet state absorption and uorescence spectra of rhodamine 6G
(from [5]). Yellow line : Laser emission.
2.3.1
Types of wavelength selective resonators
The rst wavelength selective resonator for a dye laser was proposed in 1967 by
B. H. Soer and B. B. McFarland [10] who replaced one of the cavity mirrors
by a diraction grating.
Since then, dierent approaches have been widely used for wavelength selection in dye laser resonators:
• spatial wavelength separation by dispersion (using prisms) or by diraction
(using gratings);
• interferometric ltering using constructive interferences in an etalon;
• rotational dispersion by propagation of a polarized light beam in a bire-
fringent material.
14
The general idea is to modulate the balance of gain and losses within the
stimulated emission band, in order to favour lasing in the selected wavelength
interval only. For this purpose, several tuning elements can be used in the same
cavity.
2.3.2
Choice of a resonator
Two simple congurations seemed particularly attractive for our purposes.
Prisms and birefringent lter
The rst conguration consists of two plane mirrors and a series of prisms at
Brewster angle together with an anti-reection coated highly birefringent crystal
(like in [11]). This ensures minimum surface losses.
We can think of a prism followed by a broadband feedback mirror as equivalent to a mirror with a frequency-selective coating. In the same way, a series of
prisms arranged for additive dispersion is equivalent to a mirror with a highly
frequency-selective coating.
Additionally, if they are used at (or near) Brewster angle the prisms will
also have an eect on the beam polarization: the losses by reection on the
prisms surfaces will be higher for an s-polarized beam, and therefore the lasing
threshold will be lower for a p-polarized beam. The laser beam should then be
p-polarized.
A p-polarized beam will be sensitive to the eect of a birefringent crystal
which rotates the polarization direction of dierent frequency components by
dierent angles. Hence a birefringent crystal surrounded by prisms at Brewster
angle will form a birefringent lter.
Grating in grazing incidence
A second interesting conguration is a variant of the Littman cavity [13, 14]
which uses a plane mirror and a grating in grazing incidence.
When a grating is used in Littrow mount (diracted beam collinear with the
incident beam) the resolution can be much improved by using a beam expander
in the cavity. Early beam expanders consisted of a lens telescope (as in the
Haensch design [12] sketched in Figure 2.6) but they were largely replaced by
prism beam expanders. When the beam expander is inserted in the cavity, a
larger area of the grating is illuminated, and hence the resolution is improved.
Furthermore, the beam divergence is reduced, which also improves the wavelength selectivity of the cavity. Additionally, the beam expansion prevents the
grating surface from being destroyed by too high laser intensities.
It is also possible to illuminate a large area of the grating without any beam
expander in the cavity, if the grating is mounted in grazing incidence. In the
Littman conguration [13, 14], the rst order diracted beam is returned to the
grating by an additional highly reecting tuning mirror (Figure 4.3). Because of
the angular dispersion of the diracted beam, only a small wavelength range is
reected back along the direction of incidence on the mirror. This back reected
beam is diracted again by the grating and it is returned to the dye cell for
further amplication. The laser can be tuned by changing the orientation of the
15
tuning mirror. The reection from the grating (zeroeth order diracted beam)
is used to couple out the energy.
Dual-cavity
It is possible to lower the lasing threshold of a Littman-type cavity by adding a
partially reecting feedback mirror along the path of the zeroeth order diracted
beam [15, 16]. In this conguration, the wavelength selective Littman cavity
seeds the longer broadband cavity at the chosen wavelength. This mode of
operation is known as self-seeding.
In this particular case, self-seeding is achieved in a dual-cavity conguration
[15, 16]. This conguration consists of two coupled cavities (see Figure 2.8):
a long cavity formed by mirrors M1 and M3 (zeroeth order reected beam),
and a short cavity formed by mirrors M1 and M2 (rst order diracted beam).
Each cavity can lase independently. As the long cavity has no frequency selective
elements, it emits broadband laser light. The short cavity is a frequency selective
Littman cavity emitting narrow band laser light, but it is not as ecient as
the long cavity in extracting energy from the active medium. When the short
cavity seeds the long cavity, narrow band laser emission is obtained with a good
conversion eciency [15, 16].
In [15, 16] this approach was applied to a gain switched Ti:Sapphire laser.
It should be possible to apply the same method to a gain switched dye laser.
16
Figure 2.6: Cavity using a grating in Littrow mount and an intracavity telescope
for beam expansion (from [12]).
Figure 2.7: Cavity using a grating in grazing incidence (from [13]).
17
Figure 2.8: Dual-cavity conguration (from [16]).
18
2.3.3
A simple model for self-seeding
A simple model for self-seeding in a dual-cavity conguration has been proposed
by Merriam and Yin [16]. The operation of this system is analyzed in terms of
gain switching between two coupled cavities.
Assuming that the laser oscillates in a single cavity mode, the rate equation
for the number of photons in the cavity (Equation 2.2) can also be written in a
slightly dierent way:
dq(t)
q(t)
= Vg σ F n(t) −
dt
tc
(2.7)
where σ is the stimuated emission cross-section and F is the photon ux on
the transverse cross-section of the active volume Vg . The photon ux F can be
expressed in the following way:
F =
q(t) c
q(t)
=
σg tc /2
σ g lc
(2.8)
where σg is the active volume transverse cross-section, tc is the round-trip time
and lc is the cavity length. If we put Vg = σg lg (where lg is the active volume
length) and expression 2.8 for F into Equation 2.7, we obtain:
lg
dq(t)
q(t)
=
σ c q(t) n(t) −
dt
lc
tc
(2.9)
which is the form used in [16].
Following the analysis proposed by Merriam and Yin [16] we can use Equation
2.9 to dene a cavity mode gain G:
G=
1
lg
σ c n(t) −
lc
tc
(2.10)
The cavity mode gain G for one cavity can then be considered as a function of
the inversion density n(t). If we plot G as a function of n(t) we obtain a straight
line whose slope is dened by the relative gain length lg /lc and whose value for
zero inversion density depends on the value of tc . These two parameters are
characteristic of each cavity.
The laser mode gain for a Littman-type cavity and a for a long broadband
cavity are plotted in Figures 2.10 and 2.9 for dierent values of the critical
parameters.
Several important features are common to all these plots. The short Littman
cavity has a higher relative gain length and hence a steeper slope. And it has
a shorter cavity lifetime, because of the higher losses due to the relatively low
grating eciency in rst order1 . The long broadband cavity has a smaller
relative gain length but a longer cavity lifetime. With the chosen parameters,
the curves cross in the positive gain region. The mode gain for the initial
1 The
grating eciency in rst order is around 14 % in our case (measured). This gure has to be squared because the beam hits the grating twice per round-trip in a Littman
conguration
19
inversion density2 (represented by the vertical line on the right) is always higher
for the short Littman-type cavity. Hence this cavity denes the initial laser
mode that seeds the longer broadband cavity. As the inversion is depleted by
light amplication, the operating point moves to the left. At some point (the
middle vertical line) the cavity mode gain curves cross. The lasing mode can
still be amplied by the long broadband cavity, but for some inversion density
(represented by the vertical line on the left) the long cavity mode gain goes to
zero and laser emission ceases.
This simple model does not describe in detail the dynamics of mode competition in the dual-cavity, but it gives a qualitative understanding of the operation
of this system.
The series of curves represented in Figures 2.9 and 2.10 show the inuence
of two parameters: the output coupler reectivity and the broadband cavity
length. These two parameters could be varied easily in our setup.
When the output coupler reectivity is increased, the curve corresponding
to the broadband cavity (blue curve ) is translated upward (Figure 2.9). As a
consequence, the population inversion density that brings the broadband cavity
gain to zero gets lower, and the energy extraction from the gain medium is
increased.
For a constant value of the output coupler reectivity, the crossing point
is shifted towards smaller values of the inversion density when the broadband
cavity length is increased (Figure 2.10). But the point where the broadband
cavity gain reaches zero does not move signicantly in this case.
2 We
have used an initial inversion density ninitial = 5.6×1016 /cm3 corresponding to the
experimental work to be presented in the next chapter (assuming, as in [16], that the initial
inversion density is produced by the total pump energy).
20
Figure 2.9: Laser mode gain versus population inversion density for increasing
output coupler reectivity (from left to right and from top to bottom). Broadband cavity length: 31 cm. Wavelength selective cavity length: 20 cm. Grating
eciency in rst order: 14 %. Red curve : Wavelength selective cavity. Blue
curve : Broadband cavity. Vertical lines correspond (from right to left) to the
initial inversion, the gain switching inversion and the inversion for zero mode
gain.
21
Figure 2.10: Laser mode gain versus population inversion density for an increasing broadband cavity length (from left to right and from top to bottom). Output
coupler reectivity: 20 %. Wavelength selective cavity length: 20 cm. Grating
eciency in rst order: 14 %. Red curve : Wavelength selective resonator. Blue
curve : Broadband cavity. Vertical lines correspond (from right to left) to the
initial inversion, the gain switching inversion and the inversion for zero mode
gain.
22
Chapter 3
Experimental setup
3.1
3.1.1
Pump laser and pump optics
Pump power and pulse shape
The pump laser is a compact frequency doubled Q-switched diode pumped NdYAG laser (Elforlight, FQ-500-532) at 532 nm. It is triggered externally by a
TTL signal and can be operated from single shot to 20 kHz repetition rate, with
an average power of 0.6 W at 1 kHz and 2.5 W at 5 kHz. The pulse duration
varies between 15 ns and 30 ns, depending on the repetition rate (Figure 3.1
shows the pump pulse for a 100 Hz repetition rate).
The energy per pulse and the peak power increase when the repetition rate
is decreased (Figures 3.1.1 and 3.3) because this gives more time to build up
population inversion between the short pumping pulses. As the repetition rate
is decreased below 1 kHz, the pulse separation approximate the upper state
lifetime of the lasing material (≈ 1 kHz in YAG) and nally a limit is reached
for increasing the energy per pulse.
Figure 3.1: Pump pulse shape (repetition rate: 100 Hz) measured with a fast
photodiode (500 MHz bandwith) and an oscilloscope with 100 MHz bandwith.
23
Figure 3.2: Energy per pulse of the pump laser for dierent repetition rates
(calculated from measured average power and repetition rate).
Figure 3.3: Peak power of the pump laser for dierent repetition rates (from
the calculated energy per pulse and the measured pulse duration).
24
3.1.2
Pump optics
The pump beam has a diameter of approximately 2 mm. The dye is pumped
transversally (pump beam perpendicular to the output laser beam direction).
The pump beam is focused into the dye cell by one or two cylindrical lenses.
For optimum pumping we created a line focus in the dye cell by using a
telescope consisting of two cylindrical lenses (focal lengths: -30 mm and +
150 mm, distance between the lenses: 1.5 cm). The pump beam was focused to
a 20 mm long thin line, covering the whole length of the dye cell.
The optimum distance between the lenses and the dye cell is not the position
where the focus is exactly in the dye cell (Figures 3.4). When the set of two
lenses is focused exactly in the dye cell, the amount of amplied spontaneous
emission (amplication of uorescence along the direction of the active volume)
is so high that it saturates the dye medium, and the dye laser output gets very
low. This eect can be clearly seen in Figure 3.4: the output power of the dye
laser is strongly reduced when the focus is exactly in the dye cell. At the same
time the power of amplied spontaneous emission gets very high (this is not
represented in Figure 3.4). For optimum output power of the dye laser, the dye
cell has to be set slightly out of focus.
The amount of amplied spontaneous emission by the dye is also substantially reduced by removing completely the diverging lens. When only the converging lens is used, the pump light is focused to a line of approximately 0.5
mm length.
Two dierent pumping congurations were used: an horizontal pumping
conguration (represented in Figures 3.5 and 3.6) and a vertical pumping conguration (represented in Figures 3.8 and 3.7). For reasons that will become
clear in the next section, the vertical pumping conguration is advantageous.
25
Figure 3.4: Saturation of the dye medium by amplied spontaneous emission.
D: distance between the dye cell and the mount holding the two cylindrical
lenses (f = - 30 mm and f = + 150 mm).
26
3.1.3
Pump beam polarization
The pump beam is horizontally polarized. A λ/2 plate was used to rotate the
polarization. The eect of the pump beam polarization on the polarization of
the output beam from the dye laser is represented in Figures 3.5-3.7.
When the pump beam is polarized parallel to the plane containing the pump
beam and the dye laser beam, the dipole moment of the molecules are oriented
along the resonator axis. In this conguration, the molecules have to rotate
before they can radiate along the resonator axis [17]. The resulting angular
orientation distribution is isotropic, and the output beam is not polarized. But
when the pump beam is polarized perpendicular to the plane containing the
pump beam and the dye laser beam, the dipole moment of the molecule is
oriented perpendicular to the resonator axis, and the output beam is polarized
in the same direction as the pump beam.
For our purposes, an horizontally polarized beam is preferred, for higher
eciency of the grating and low losses at Brewster angle surfaces. Hence we
needed a pump laser beam polarized horizontally and perpendicular to the plane
containing the pump beam and the dye laser beam. If we want to keep the laser
resonator in an horizontal plane, this is only possible in a vertical pumping
conguration. For this purpose, the dye cell was tilted and we used a highlyreective broadband mirror set at 45o to send the focused pump beam on the
dye cell.
27
Figure 3.5: Polarization of the output beam when the pump beam is horizontally
polarized and the plane of incidence is horizontal.
Figure 3.6: Polarization of the output beam when the pump beam is vertically
polarized and the plane of incidence is horizontal.
28
Figure 3.7: Polarization of the output beam when the pump beam is horizontally
polarized and the plane of incidence is vertical.
Figure 3.8: Polarization of the output beam when the pump beam is vertically
polarized and the plane of incidence is vertical.
29
3.2
3.2.1
Dye solution, dye cell and circulating pump
Dye solution
The active medium is a solution of rhodamine 6G in ethanol. Rhodamine 6G is
a red crystalline solid with a molecular weight of 479.02 grams per mole [18]. In
ethanol, its absorption maximum is at ≈ 530 nm and its uorescence maximum
at ≈ 560 nm [18]. When pumped by the second harmonic of a Nd-YAG laser at
532 nm, it emits laser radiation tunable between 555 nm and 585 nm [18]. This
is close to the spectral region where the human eye has its maximum wavelength
sensitivity. Therefore, the color of the laser output can be clearly seen to vary
from yellow-green to orange-red.
Initially the concentration was 0.1 g/l (2.1×10−4 mol/l) as indicated in [18].
The optimum concentration for emission at 570 nm was found to be 0.15 g/l
(3.1×10−4 mol/l) from a series of measurements with concentrations varying
from 0.03 g/l (6.3×10−5 mol/l) to 0.21 g/l (4.4×10−4 mol/l). These results are
presented in Section 4.3.
3.2.2
Dye cell
The dye mixture is contained in a quartz cell with an inner length of 20 mm.
The cell is simply a rectangular parallelepiped with no wedge angle.
When the dye is illuminated by the pump beam, a strong spot is formed in
a direction perpendicular to the cell walls (Figure 3.9), even in the absence of
any additional feedback mirror. This spot should not be confused with amplied
spontaneous emission, which needs no reecting surfaces and can also be present
below threshold. Amplied spontaneous emission gives rise to a broad spot
(Figure 3.9) whose direction is xed by the active volume of the dye. Its position
can be changed by changing the position of the pump beam focus in the dye
cell, but not by tilting the cell. By contrast, the laser beam formed within the
dye cell produces a sharper spot whose position changes when the dye cell is
tilted. Hence, with their ≈ 4 % reectivity, the two parallel quartz walls already
form a two-mirror cavity. The spectrum of the laser beam formed within this
small cavity is shown in gure 3.10. It is characterized by peaks separated by ≈
1.2 nm which are probably due to the small dierence in thickness (≈ 0.1 mm)
between the two quartz walls.
A wedged cell may have eliminated this undesirable beam. For most measurements, the dye cell was simply tilted, in order to separate the desired laser
beam from the unwanted beam formed within the cavity. When the dye cell is
tilted enough, the overlap of this beam with the active volume becomes very
small and its intensity decreases, but it does not disappear completely. Hence
a signicant fraction of the available gain is taken by this unwanted beam.
30
Figure 3.9: Amplied spontaneous emission (left) and laser output formed by
the dye cell walls (right).
Figure 3.10: Spectra of the amplied spontaneous emission and of the laser
output formed by the dye cell walls.
31
3.2.3
Circulating pump
The dye is circulated by means of a small centrifugal pump. At the beginning
it produced a lot of bubbles in the dye cell. This problem was solved when the
leaks were repaired (Figure 3.11).
The pump is still a weak part ot the setup because it produces quite strong
vibrations that we could not dampen. The relatively bad performances obtained
concerning the spectral width of the laser could be due to these strong vibrations.
Figure 3.11: Repairing the circulating pump.
32
Chapter 4
Laser resonators
4.1
Two-mirror cavity
Lasing was rst observed in a simple cavity consisting of two plane mirrors: a
broadband highly reective mirror and a partially reecting mirror for output
coupling. An output coupler with 20 % reectivity was chosen from a comparison of the thresholds and slope eciencies obtained with 10 %, 20 % and 30 %
reectivity output couplers (Figure 4.1).
The threshold pump energy varies between 140 µJ and 240 µJ per pulse.
For 20 ns pulses, this corresponds to a threshold peak power comprised between
7 kW (for a 20 % output coupler) and 12 kW (for a 10 % output coupler).
The conversion eciency is ≈ 12 % for a 10 % output coupler and ≈ 22 %
for a 20 % output coupler.
33
Figure 4.1: Output power vs. pump power of a two-mirror cavity with dierent
output couplers. Horizontal pumping conguration. Repetition rate: 1 kHz.
Dye concentration: 0.1 g/l.
34
4.2
Prisms and birefringent crystal
For spectral narrowing of the dye laser output, a series of equilateral SF11 prisms
was used. Tuning is then achieved by tilting the highly reective mirror (which
is simpler than rotating the prism).
4.2.1
Dispersion
SF11 glass has a particularly high refractive index. For comparison, wavelength
dependance of SF11 and BK7 glasses are plotted in Figure 4.2. The refractive
index of SF11 glass at 570 nm is 1.79 (1.52 for BK7). As a consequence, losses
for a s-polarized beam are particularly high. The dispersion of SF11 glass is
also high, as is indicated by an Abbe number of ≈ 25 (compare to 64 for BK7
glass).
Figure 4.2: Wavelength dependence of the refractive index of SF11 glass (red
) and BK7 glass (blue curve ) calculated from Sellmeier equation.
curve
From this we can calculate the angle of incidence for minimum deviation:
imin = arcsin (sin 30o × n(570 nm)) = 63.35o
(4.1)
and the Brewster angle of incidence:
iBrewster = arctan (n(570 nm)) = 60.78o
(4.2)
The prisms are set at minimum deviation. In this conguration, the incident
and exit angles are equal, and both are close to Brewster angle. Hence the
losses are minimized for a p-polarized beam. This eect is clearly seen with
a pumping conguration which initially results in an unpolarized output beam
(like in Figures 3.5 and 3.8). The output beam becomes ≈ 90 % p-polarized
when a prism is inserted in the cavity, because the losses are strongly reduced
for this polarization.
35
4.2.2
Spectral narrowing
Let dα be the angular divergence of the laser beam in the cavity before any
prism is inserted. The single pass spectral width dλ for m prisms arranged for
additive dispersion at minimum deviation can be calculated from [19]:
dλ =
n dα
4 m tan imin | dn
dλ |
where dα is the beam divergence and
interest.
dn
dλ
(4.3)
is the dispersion at the wavelength of
Formula 4.3 was used for calculating the values given in Table 4.1 for a typical
value of the beam angular divergence of 5 mrad1 [17]. For comparison, the
calculated spectral width for a set of three BK7 prisms at minimum deviation
is 12 nm.
The measured spectral widths are narrower by a factor of ten than the calculated single pass spectral widths (Table 4.1). Indeed Formula 4.3 gives the
single pass transfer function of a series of prisms in the case of a passive cavity
with no active medium. The linewidth of the gain-switched laser is somewhat
smaller due to gain-competition.
The best results were obtained when all prisms were set on the tuning mirror
side of the dye cell.
Number
of prisms
1
2
3
Single pass
spectral width (nm)
6.6
3.3
2.2
Measured
spectral width (nm)
0.5
0.3
0.2
Table 4.1: Comparison of single-pass spectral widths (λ=570 nm,
dn
−5
(from Sellmeier equation), dα=5 mrad) and measured spectral
dλ =7.57×10
width for SF11 prisms at minimum deviation.
1 The
actual beam angular divergence has not been measured.
36
4.2.3
Challenges
Even if the measured spectral widths obtained with a series of prisms looked
quite promising, several problems were encountered with this setup.
The main problem is that the spectral width measured with a given number
of prisms can vary between large limits, for reasons which are not completely
understood. For example, the spectral width obtained with one prism at minimum deviation varied between 0.3 nm and 0.9 nm from day to day. These
variations could not be correlated clearly with changes in the setup.
Another problem concerns the resonator length. For maximum output power,
a short cavity is preferred. Hence a compact assembly of three prisms at minimum deviation was built (Figure 4.3). But this set-up cannot be used in combination with the birefringent lter (see Section 4.2.4).
Figure 4.3: Compact arrangement of three equilateral SF11 prisms at minimum
deviation.
37
4.2.4
Highly birefringent crystal
A highly birefringent anti-reection coated crystal of yttrium vanadate (YVO4 )
was inserted in the cavity containing the SF11 prisms. The crystal is 8 mm
long with an entrance surface of 5×5 mm. The optical axis is in the plane of
the entrance surface. At 570 nm the ordinary refractive index of YVO4 is 2.01
while the extraordinary refractive index is 2.24.
For the equilateral prisms used in this setup, the angle for minimum deviation is close to Brewster angle (Section 4.2.1). Hence the losses suered by the
p-polarized component of the laser beam are low, and the laser beam is mainly
p-polarized. The intensity of a p-polarized component after a 8 mm thick YVO4
crystal plate is shown in Figure 4.4. Optimum fringe contrast is achieved for an
angle φ of 45o between the optical axis and the direction of polarization.
The combination of prisms at Brewster angle and a birefringent crystal with
φ=45o should act as a birefringent lter [20] without any additional polarization
selective elements.
Figure 4.4: Intensity of a p-polarized component after a 8 mm thick YVO4
plate. The optical axis is in the plane of the plate. The angle φ between the
optical axis and the direction of polarization is 45o for the red curve, 30o for the
o
green curve and 20 for the blue curve.
Several congurations were investigated (Figures 4.5-4.8). The conguration using three prisms on a single mount was not ecient. The conguration
represented in Figure 4.8 is more ecient than the congurations represented in
Figures 4.5-4.7. In this case, there is a polarization selective element on each side
of the birefringent crystal, and both elements are on the same side of the active
medium. Hence the p-polarized component of the beam is selectively enhanced
before and after the birefringent crystal, and only this mainly p-polarized beam
is amplied by the active medium.
38
Figure 4.5: Wavelength selective resonator with one prism at minimum deviation
and a birefringent YVO4 crystal.
Figure 4.6: Wavelength selective resonator with two prisms at minimum deviation and a birefringent YVO4 crystal (two prisms on the same side of the
crystal).
39
Figure 4.7: Wavelength selective resonator with three prisms at minimum deviation and a birefringent YVO4 crystal.
Figure 4.8: Wavelength selective resonator with two prisms at minimum deviation and a birefringent YVO4 crystal (one prism on each side of the crystal).
40
4.2.5
Results
Conversion eciency
The results presented here correspond to an horizontal pumping scheme (Figure
3.6). For a two-prisms conguration like the one in Figure 4.8, the threshold
pump energy is ≈ 350 µJ per pulse (Figure 4.9). For 20 ns pulses, this corresponds to 17.5 kW threshold peak power. The conversion eciency is 3 %
only.
Spectral width
Two spectra are shown here. The rst one (Figure 4.10) was obtained in a oneprism conguration (Figure 4.5) and the second one (Figure 4.11) in a two-prism
conguration (Figure 4.8). In both cases, transmission fringes of the birefringent
lter can be resolved. They are separated by ≈ 0.14 nm as predicted from Figure
4.4. The observed width corresponds to the resolution limit of the spectrometer
(≈ 0.1 nm).
Unfortunately it has not been possible to select one of those fringes, due
to the problems encountered with the prisms. Smaller prisms could be used to
allow more round-trips in the cavity. One may also choose a smaller crystal
length since the free spectral range of the lter is not well adjusted to the
spectral width of the prism laser. Additionally, a polarizer may be included in
the cavity (as in [11]).
Figure 4.9: Output power vs. pump power for a cavity containing two SF11
prisms at minimum deviation and a 8 mm thick YVO4 plate. Repetition rate:
1 kHz. Dye concentration: 0.1 g/l.
41
Figure 4.10: Spectrum of the laser output from a cavity containing one SF11
prism at minimum deviation and a 8 mm thick YVO4 plate.
Figure 4.11: Spectrum of the laser output from a cavity containing two SF11
prisms at minimum deviation and a 8 mm thick YVO4 plate.
42
4.3
Littman cavity
In this conguration [13, 14], the resonator consists of three optical elements:
a highly reective feedback mirror, a grating in grazing incidence and a highly
reective tuning mirror (Figure 4.12).
Figure 4.12: Littman cavity.
The diraction angles are given by the grating equation:
mλ = d (sin θm − sin θi ),
(4.4)
where m denotes the diraction order, d is the grating period, θi and θm are the
incidence angle and the diraction angle of the m-th order respectively. Both
angles are measured from the axis of incidence normal to the grating surface.
The grating used in the present experiment is a 5 cm long holographic aluminum grating with 2400 groves/mm with optimized modulation depth for the
visible range (Optometrics No 5-2403). Since the grove spacing is smaller than
the wavelength only one diraction order is allowed by the grating equation. The
rst negative order is retro-reected by a at aluminum mirror which covers the
whole length of the grating.
4.3.1
Spectral narrowing
The angular dispersion of the grating is obtained by the derivative of the grating
equation with respect to λ at constant incidence angle θi :
dθm
m
=
.
dλ
d cos θm
(4.5)
In Littman conguration the grating is used in rst negative order for both
passes. Therefore the dispersion adds up to:
−1
1
1
dθm,2
=
(
+
).
dλ
d cos θm,1
cos θm,2
(4.6)
The angular dispersion in Littman conguration becomes particularly large,
since the diraction angle approaches 90◦ for the retro-reected beam.
43
4.3.2
Results
Conversion eciency
Threshold and slope eciency of a Littman cavity with horizontal pumping are
plotted in Figure 4.13. The threshold pump energy is ≈ 350 µJ per pulse. For a
20 ns pulse this corresponds to 17.5 kW threshold peak power. The conversion
eciency is 2 % only.
The inuence of dye concentration on the conversion eciency was investigated in this pumping conguration. The results are presented in Figure 4.14.
An optimum conversion eciency of 3.6 % is obtained with a concentration of
0.15 g/l (3.1×10−4 mol/l).
With a repetition rate of 1.7 kHz, the conversion eciency could be further
improved to 5.4 %. The maximum output power obtained in this conguration
is 54 mW (for a repetition rate of 1.7 kHz).
Figure 4.13: Output power vs. pump power of a Littman cavity. Horizontal
pumping conguration. Repetition rate: 1 kHz. Dye concentration: 0.1 g/l.
44
Figure 4.14: Output power vs. pump power of a Littman cavity for dierent
dye concentrations. Horizontal pumping conguration. Repetition rate: 1 kHz.
45
Threshold and slope eciency are substantially improved when a vertical
pumping conguration is used (Figure 4.15). The threshold pump energy is
≈ 300 µJ per pulse for a pump beam polarization colinear to the dye laser
beam and ≈ 280 µJ per pulse for a pump beam polarization perpendicular to
the dye laser beam. For a 20 ns pulse this corresponds to 15 kW and 14 kW
threshold peak power respectively. The conversion eciency is 9 % in the rst
case and 11 % in the second case. The maximum output power obtained in this
conguration is 110 mW (for a repetition rate of 2 kHz).
Figure 4.15: Output power vs. pump power of a Littman cavity. Vertical
pumping conguration. Repetition rate: 1 kHz. Dye concentration: 0.15 g/l.
46
Spectral width
A typical spectrum of the laser output from a Littman cavity is shown in Figure 4.16. The observed spectral width (less than 0.1 nm) corresponds to the
resolution limit of the optical spectrum analyzer.
Figure 4.16: Spectrum of the laser output from a Littman cavity.
To get a better idea of the spectral characteristics of the laser, a Fabry-Pérot
etalon was built with two partially reecting mirrors (≈ 96 % reectivity at 570
nm). This cavity has a nesse of ≈ 77(2 ).
One mirror was mounted on a translation stage. This allows a variation of
the free spectral range from 150 GHz (distance between the mirrors: 1 mm) to
6 GHz (distance between the mirrors: 2.5 cm). At 570 nm this corresponds to
a free spectral range varying between 0.2 nm and 8 pm.
For operation of the Fabry-Pérot interferometer as a spectrometer, the free
spectral range of the etalon must be larger than the signal bandwith. Assuming
a signal bandwith just below the resolution limit of the optical spectrum analyzer
(≈ 0.1 nm), this condition is satised for a distance of 1 mm between the mirrors.
For higher resolution, the distance between the mirrors can be increased, as
long as the free spectral range stays larger than the signal bandwith. When
this condition is not satised anymore, the interference fringes produced by the
Fabry-Perot interferometer get blurred.
2 For
two mirrors with the same reectivity R, the nesse F is given by:
F =
√
π R
1−R
47
(4.7)
The laser output is sent through a diverging lens (f=-50 mm) before going
through the Fabry-Pérot etalon. Interference fringes are observed on a screen
≈ 1.5 m away where their spacing and width can be measured.
A qualitative observation of the interference fringes produced by the FabryPérot etalon already gives some interesting information about the spectral features of the laser.
First of all, contrasted fringes are still observed with a 6 GHz free spectral
range (8 pm at 570 nm). Hence we can assume that the spectral width of the
laser is in the GHz range3 .
Furthermore, the spectrum does not consist of a single line, but of a series of
lines whith relative intensites varying from shot to shot. This feature has been
observed by several researchers [5, 6] and is well illustrated by a picture in [6].
These lines can be resolved in the pictures presented in Figure 4.17.
But the main problem revealed by the Fabry-Pérot etalon is the frequency
instability of the laser output (Figure 4.17). To reduce this instability, several
sources of vibrations have been investigated and controlled:
• the pump laser fan has been disconnected from the pump laser head and
installed on an anti-vibration holder;
• the pump laser power supply, which is vibrating strongly, has been re-
moved from the optical table;
• vibrations from the circulating pump have been dampen as much as pos-
sible;
• the mount for the 45o mirror in the vertical pumping conguration has
been made as compact as possible.
Nevertheless, uctuations in the frequency output of the laser are still quite
strong.
A more quantitative estimate has been obtained using the formulas derived
in [22]. The spectrum of the laser output consists of close lines which are a
few GHz broad. The eective spectral width is broadened to 5-10 GHz due to
uncontrolled sources of vibrations.
3 For isotope selective photo-ionization of magnesium, a spectral width of ≈ 1 GHz is needed
[21].
48
Figure 4.17: Interference fringes produced by the laser output of a Littman-type
cavity sent through a Fabry-Pérot etalon (Finesse: 77, Free spectral range: 100
GHz).
49
4.4
Dual-cavity
A dual-cavity is formed by adding a partially reecting mirror to a Littmantype cavity (Figure 4.18). As described in Section 2.3.2 the short frequency
selective Littman cavity can seed the long broadband cavity - a process known
as self-seeding.
The short Littman-type cavity has already been described in the preceding
section. The long broadband cavity consists of a highly reecting mirror and
an output coupler (zeroeth order reection from the grating). Output couplers
with 10 %, 20 % and 30 % reectivity were used in these experiments. Both
cavities are coupled through the grating.
Figure 4.18: Dual cavity conguration.
4.4.1
Results
Self-seeding
The self-seeding process is clearly illustrated in the spectra presented in Figure
4.19. When the tuning mirror of the Littman cavity is blocked, the long cavity
emits broadband laser light (blue curve ). When the tuning mirror is unblocked,
the broadband spectrum is replaced by a sharp spectrum (red curve ) around
the frequency dened by the short cavity. The observed width corresponds to
the resolution limit of the spectrometer (≈ 0.1 nm).
Conversion eciency
Energy extraction from the active medium is also enhanced. Figure 4.20 shows
the threshold and slope eciency for dierent values of the output coupler (for
comparison, threshold and slope eciency of the simple Littman cavity are
also plotted). As predicted by the simple model presented in 2.3.3, the output
power increases with increasing values of the output coupler reectivity (see
Figure 2.9).
For the same dye concentration and pumping conguration, the threshold
pump energy is lowered from 350 µJ (for a simple Littman cavity) to 300 µJ (for
a dual-cavity). For 20 ns pulses this corresponds to 15 kW instead of 17.5 kW
50
threshold peak power. The conversion eciency is increased from ≈ 2 % (for a
simple Littman cavity) to ≈ 6 % (for a dual-cavity with 30 % output coupler
reectivity).
It should be noted that these results were obtained with a dye concentration of
0.1 g/l, a repetition rate of 1 kHz and in an horizontal pumping conguration. It
is most probable that better results would be obtained with a dye concentration
of 0.15 g/l, a repetition rate of 2kHz and a vertical pumping conguration.
Figure 4.19: Self-seeding of a long broadband cavity by a short wavelength
selective cavity. Broadband cavity length: 31 cm. Littman cavity length: 20
cm. Blue curve : spectrum of the laser output from the broadband cavity (tuning
mirror blocked). Red curve : spectrum of the laser output from the dual cavity
(tuning mirror unblocked).
51
Figure 4.20: Output power vs. pump power of a simple Littman cavity and a
dual cavity with dierent values of the output coupler reectivity. Broadband
cavity length: 31 cm. Littman cavity length: 20 cm. Horizontal pumping
conguration. Repetition rate: 1 kHz. Dye concentration: 0.1 g/l.
52
Spectral width
The laser output from the dual-cavity has also been observed with the FabryPérot interferometer. The spectrum shows the same features as with the Littman
cavity: several lines a few GHz large and strong uctuations on the order of 510 GHz.
The lines are sharper and fewer in the dual-cavity conguration. It is possible
to select one of them by inserting an aperture or an etalon into the cavity.
But this would improve the eective spectral width only if the uncontrolled
uctuations in the frequency output could be reduced.
53
4.5
Overview
A short overview of the results obtained with dierent cavity congurations is
presented in Table 4.2.
Cavity type
Two mirror cavity
Two prisms + YVO4
Littman cavity
Dual-cavity
Conversion eciency
22 %
3%
2%
6%
Spectral width
3 nm / 2.7 THz
0.2 nm / 185 GHz
0.01 nm / 10 GHz
0.01 nm / 10 GHz
Table 4.2: Comparison of conversion eciency and spectral width for dierent cavities. Horizontal pumping conguration. Repetition rate: 1kHz. Dye
concentration: 0.1 g/l.
Remarks
Conversion eciency. In each case, the dye cell has been tilted, in order to
separate the laser beam formed by internal reections in the dye cell from the
considered laser output (see Section 3.2.2). As a consequence, the conversion
eciency is lowered.
Also, the results presented here have been obtained in an horizontal pumping
conguration, with a 1 kHz repetition rate and a dye concentration of 0.1 g/l.
These parameters can be optimized for maximum conversion eciency (see Section 4.3.2). With a vertical pumping conguration, a 1.7 kHz repetition rate
and a dye concentration of 0.15 g/l, a conversion eciency of 11 % was reached
in a Littman-type cavity. For this set of parameters, no results are available for
the other congurations.
Spectral width. In the cavity containing prisms and a highly birefringent
crystal, the spectral width is limited by the prisms (see Section 4.2.5).
In the Littman-type cavity and in the dual-cavity congurations, the spectral
width is limited by uncontrolled frequency uctuations (see Sections 4.3.2 and
4.4.1).
54
Chapter 5
Second-harmonic generation
and photo-ionization of
magnesium atoms
5.1
Second-harmonic generation
Frequency doubling of the dye laser output is achieved by single-pass conversion
in a beta barium borate (BBO) crystal. The good single-pass eciency is due
to the high peak power produced by the pulsed dye laser.
5.1.1
Optimized confocal parameter
The fundamental beam at 570 nm is focused in the BBO crystal by a converging
lens. An optimized focal length is determined in this section.
The confocal parameter is dened by (see Figure 5.1):
b = ω02
2π
λ
(5.1)
where ω0 is the beam waist and λ is the fundamental wavelength.
We use the analytical expression given in [23] for the optimized confocal
parameter b in the crystal:
bcrystal = l/
2.84 + 1.39 B 2
1 + 0.1 B + B 2
(5.2)
where the walk-o parameter B is dened by:
1
B(ρ, l, λ) = × ρ ×
2
r
2π × n(φ, 570 nm) × l
λ
(5.3)
(ρ is the walk-o angle, n(φ, 570 nm) is the refractive index at 570 nm for the
phase-matching angle φ, l is the crystal length, λ is the fundamental wavelength).
55
For a BBO crystal and an fundamental beam at 570 nm, the phase-matching
angle φ is equal to 43.3o (1 ) and the walk-o angle ρ to 4.8o (2 ). From Equations 5.2 and 5.3 we obtain the optimized confocal parameter in the crystal: bcrystal =7.2 mm. The optimized confocal parameter in air is given by:
bair = bcrystal /n(570)=4.3 mm. From Equation 5.1 we obtain: ω0 =25 µm.
By adjusting the focal length of the focusing lens, the fundamental beam can
be focused to the desired spot size ω0 . Using the expression given in [24] we nd
an optimal focal length of 14 cm if we assume a collimated beam with radius of
1.25 mm before the crystal.
Figure 5.1: Second-harmonic generation of light by a laser beam focused in a
non-linear material (from [24]).
5.1.2
Results
The output of a simple Littman-type cavity is sent into a BBO crystal (4 × 4
× 10 mm).
For the rst trials, the Littman cavity was pumped horizontally. The output beam of the dye laser was focused in the crystal with a converging lens
(f=150 mm, distance to the crystal center: 16 cm). About 100 µW of light
at 285 nm were obtained from 54 mW in the fundamental. The conversion
eciency was less than 0.2 % in this case.
1 The phase-matching angle φ (angle between the crystal axis and the direction of propagation of the beam in the crystal) is found from:
(5.4)
n(φ, 285 nm) = nord (570 nm)
where nord (570 nm) is the ordinary refractive index at 570 nm and n(φ, 285 nm) is given by:
n(φ, 285 nm) = r
cos φ
nord (285 nm)
2
1
+ n
2
sin φ
ext (285
nm)
(5.5)
(nord is the ordinary and next the extraordinary refractive index. For BBO: nord (285 nm) =
1.74 and next (285 nm) = 1.60 (from Sellmeier equations)).
2 The walk-o angle ρ is calculated from:
ρ = | arctan
n(φ, 285 nm)2
2
1
1
−
nord (285 nm)2
next (285 nm)2
56
sin (2φ) |
(5.6)
In the actual setup, the Littman cavity is pumped vertically. For optimum
focusing of the fundamental in the non-linear crystal, a second lens (f=200 mm,
distance to the crystal center: 10.5 cm) has been added added. In this conguration, about 700 µW of light at 285 nm were obtained from 180 mW in the
fundamental3 . The conversion eciency is 0.4 %.
5.2
5.2.1
Photo-ionization of magnesium atoms
General remarks
Magnesium atoms are resonantly ionized through a two-step process. The resonant excitation step is the 3 1 S0 → 3 1 P1 dipole allowed transition at 285.296 nm.
An atom in the 3 1 P1 level can be ionized by a 285 nm photon from the ionization
laser as well as by a 280 nm photon from the cooling laser4 .
The saturation intensity for the resonant transition is 4401 W/m2 , which
is easily achieved even with a cw-laser. Above saturation intensity the excited
state population appoaches 0.5 for both, pulsed and cw-excitation. Once the
resonant transition is saturated, the ionisation may be treated as a single photon
process. It should then be equally ecient for equal average power of a pulsed
and cw laser, unless saturation eects of the second step becomes signicant for
a pulsed laser source.
The natural bandwith of the 3 1 S0 → 3 1 P1 transition is 78.2 MHz and
the isotope shift between 26 Mg+ and 24 Mg+ amounts to 1.4 GHz [21]. The
magnesium atoms are evaporated from an atomic oven. The eective linewidth
due to Doppler broadening is about 3 GHz. The pulsed dye laser has the
advantage that it matches the Doppler width of the resonant transition. In
contrast, the continuous-wave dye laser used so far for photo-ionization has to
run on a single mode to generate an error signal for the resonant frequency
doubling cavity. Its spectral width is few MHz, therefore it can adress only a
small set of velocity classes. On the other hand, it is possible to arrange the
atomic beam and the photo-ionization laser perpendicular to each other, which
reduces the Doppler width. A narrow bandwidth photo-ionization laser may
then allow for isotope-selective photo-ionization. Presently, the present spectral
width of the frequency doubled pulsed dye laser is too large for this purpose.
5.2.2
Proof of principle
After a rough astigmatism compensation with a set of two cylindrical lenses,
the frequency doubled output of the pulsed dye laser was overlapped with the
cooling laser beam and directed to the linear Paul trap center. Although the
frequency had been adjusted the day before, magnesium ions could be trapped
immediately, which already indicates good long term frequency stability, despite
the aforementioned short term ucutations on the GHz level. However, dark
ions5 were also loaded, conrming the absence of isotope selectivity.
3 In this case, the laser beam formed by reection on the dye cell walls was superimposed
to the laser beam from the Littman cavity, for maximum output power. The laser output was
still smoothly tunable.
4 The ionization energy of neutral magnesium is 7.7 eV. The energy of a photon at 285 nm
is 4.3 eV. Hence 3.4 eV are needed for the second step (maximum wavelength: 364 nm).
5 Dark ions are most probably 25 Mg and 26 Mg ions.
57
Fluorescence photons from trapped Mg+ ions were collected with a f/2
imaging system attached to a single photon camera (Quantar Mepsicron II).
The imaging system is an electron multiplied CCD camera (Andor DUV ADV885 LC-VP) allowing single ion resolution. Images of the rst magnesium
ions trapped with the frequency doubled pulsed dye laser are presented in Figures 5.2 and 5.3.
58
Figure 5.2: Magnesium ions loaded in a linear Paul trap with the frequency
doubled pulsed dye laser. An increasing number of magnesium ions is trapped
after the trap potential is switched on (from left to right and from top to bottom). Intense points at the center of the picture correspond to trapped and
cooled 24 Mg ions. Dark sites within the chain correspond to 25 Mg and 26 Mg
ions, which are not adressed by the cooling laser.
59
Figure 5.3: Crystal of 24 Mg ions loaded in a linear Paul trap with the frequency
doubled pulsed dye laser.
60
Chapter 6
Conclusion
A frequency doubled pulsed dye laser has been set up for photo-ionization of
magnesium ions. Ions have been successfully loaded in a linear Paul trap with
this laser. Further investigation would be necessary in order to characterize the
loading performance of this laser and to compare it with the eciency of the
continuous-wave dye laser previously used for this purpose. The spectral width
of the pulsed dye laser could be narrowed by a better control of the circulating
pump vibrations. The eciency of second-harmonic generation has not been
optimized.
61
Bibliography
[1] M. Hermann, V. Batteiger, S. Knünz, G. Saatho, Th. Udem, T. W. Hänsch, 'Frequency metrology on single trapped ions in the weak binding limit:
The 3s1/2 -3p3/2 transition in 24 Mg+ ', Phys. Rev. Lett., 102 (2009).
[2] K. Vahala, M. Hermann, S. Knünz, V. Batteiger, G. Saatho, Th. Udem,
T. W. Hänsch, ' A phonon laser', accepted by Nature Physics.
[3] M. Hermann et al., 'Feasibility of coherent xuv spectroscopy on the 1s-2s
transition in singly ionized helium', Phys. Rev. A, 79 (2009).
[4] P. P. Sorokin, J. R. Lankard, E. C. Hammond, V. L. Moruzzi, 'Laserpumped stimulated emission from organic dyes: experimental studies and
analytical comparisons', IBM Journal, 130 (1967).
[5] B. B. Snavely, 'Flashlamp-excited organic dye lasers', Proc. IEEE, 57, 1374
(1969).
[6] P. P. Sorokin, 'Organic lasers', Sc.
Am.
, 220, 30 (1969).
[7] D. Roess, 'Giant pulse shortening by resonator transients', J.
37, 2004 (1965).
,
Appl. Phys.
[8] O. Svelto, Principles of Lasers, Second Edition, translated by D.C. Hanna,
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[9] A. L. Schawlow, C. H. Townes, 'Infrared and optical masers',
112, 1940 (1958).
,
Phys. Rev.
[10] B. H. Soer, B. B. McFarland, 'Continuously tunable, narrow-band organic
dye laser', Appl. Phys. Lett., 10, 266 (1967).
[11] H. Walther, J. L. Hall, 'Tunable dye laser with narrow spectral output',
Appl. Phys. Lett., 17, 239 (1970).
[12] T. W. Hänsch, 'Repetitively pulsed tunable dye laser for high resolution
spectroscopy', Appl. Opt., 11, 895 (1972).
[13] I. Shoshan, N. N. Danon, U. P. Oppenheim, 'Narrowband operation of a
pulsed dye laser without intracavity beam expansion', J. Appl. Phys., 48,
4495 (1977).
[14] M. G. Littman, H. J. Metcalf, 'Spectrally narrow pulsed dye laser without
beam expander', Appl. Opt., 17, 2224 (1978).
62
[15] D.-K. Ko, G. Lim, S.-H. Kim, B.-H. Cha and J. Lee, 'Self-seeding in a dualcavity-type pulse Ti:sapphire laser oscillator', Opt. Lett., 20, 710 (1995).
[16] A. J. Merriam, G. Y. Yin, 'Ecient self-seeding of a pulsed T i3+ : Al2 O3
laser', Opt. Lett., 23, 1034 (1998).
[17] F. P. Schaefer (ed.), Dye Lasers, Springer Verlag, Topics in Applied Physics,
Volume 1 (1990).
[18] U. Brackmann, Lambdachrome
, Lambda Physik (2000).
Laser Dyes
[19] F. J. Duarte, J. A. Piper, 'Generalized prism dispersion theory',
Phys., 51, 1132 (1983).
[20] J. W. Evans, 'The birefringent lter', J.
Am. J.
, 39, 229 (1949).
Opt. Soc. Am.
[21] E. J. Salumbides et al., 'Isotopically resolved calibration of the 285-nm
MgI resonance line for comparison with quasar absorptions', Mon. Not. R.
Astron. Soc., 373 (2006).
[22] K. W. Meissner, 'Interference spectroscopy',
(1941).
, 31, 405
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[23] Y. F. Chen, Y. C. Chen, 'Analytical functions for the optimization of
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63
List of Figures
2.1 Molecular structure of rhodamine 6G (from [6]). . . . . . . . . .
7
2.2 Energy levels of a typical dye molecule (from [5]). Heavy horizontal lines represent vibrational states. Lighter lines represent
rotational states. Excitation is represented by the transition A
→ b. Laser emission is represented by the transition B → a.
Other transitions (absorption to higher excited singlet states, intersystem crossing, triplet states absorption) represent losses in
the laser process. . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.3 Solutions of the rate equations for an increasing number of pump
photons (from left to right and from top to bottom). Cavity
length: 15 cm. Active region length: 0.5 cm. Pump pulse width:
20 ns. Blue curve : Pump pulse. Green curve : Population inversion. Red curve : Dye laser pulse. . . . . . . . . . . . . . . . . . . 12
2.4 Solutions of the rate equations for decreasing photon lifetime in
terms of a decreasing cavity length (from left to right and from
top to bottom). Active region length: 0.5 cm. Pump pulse width:
2 ns. W0 /nT = 2. Blue curve : Pump pulse. Green curve :
Population inversion. Red curve : Dye laser pulse. . . . . . . . . . 13
2.5 Singlet state absorption and uorescence spectra of rhodamine
6G (from [5]). Yellow line : Laser emission. . . . . . . . . . . . . 14
2.6 Cavity using a grating in Littrow mount and an intracavity telescope for beam expansion (from [12]). . . . . . . . . . . . . . . . 17
2.7 Cavity using a grating in grazing incidence (from [13]). . . . . . . 17
2.8 Dual-cavity conguration (from [16]). . . . . . . . . . . . . . . . . 18
2.9 Laser mode gain versus population inversion density for increasing output coupler reectivity (from left to right and from top to
bottom). Broadband cavity length: 31 cm. Wavelength selective
cavity length: 20 cm. Grating eciency in rst order: 14 %.
Red curve : Wavelength selective cavity. Blue curve : Broadband
cavity. Vertical lines correspond (from right to left) to the initial
inversion, the gain switching inversion and the inversion for zero
mode gain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
64
2.10 Laser mode gain versus population inversion density for an increasing broadband cavity length (from left to right and from
top to bottom). Output coupler reectivity: 20 %. Wavelength
selective cavity length: 20 cm. Grating eciency in rst order:
14 %. Red curve : Wavelength selective resonator. Blue curve :
Broadband cavity. Vertical lines correspond (from right to left)
to the initial inversion, the gain switching inversion and the inversion for zero mode gain. . . . . . . . . . . . . . . . . . . . . . 22
3.1 Pump pulse shape (repetition rate: 100 Hz) measured with a
fast photodiode (500 MHz bandwith) and an oscilloscope with
100 MHz bandwith. . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Energy per pulse of the pump laser for dierent repetition rates
(calculated from measured average power and repetition rate). .
3.3 Peak power of the pump laser for dierent repetition rates (from
the calculated energy per pulse and the measured pulse duration).
3.4 Saturation of the dye medium by amplied spontaneous emission.
D: distance between the dye cell and the mount holding the two
cylindrical lenses (f = - 30 mm and f = + 150 mm). . . . . . . .
3.5 Polarization of the output beam when the pump beam is horizontally polarized and the plane of incidence is horizontal. . . . .
3.6 Polarization of the output beam when the pump beam is vertically polarized and the plane of incidence is horizontal. . . . . . .
3.7 Polarization of the output beam when the pump beam is horizontally polarized and the plane of incidence is vertical. . . . . .
3.8 Polarization of the output beam when the pump beam is vertically polarized and the plane of incidence is vertical. . . . . . . .
3.9 Amplied spontaneous emission (left) and laser output formed
by the dye cell walls (right). . . . . . . . . . . . . . . . . . . . . .
3.10 Spectra of the amplied spontaneous emission and of the laser
output formed by the dye cell walls. . . . . . . . . . . . . . . . .
3.11 Repairing the circulating pump. . . . . . . . . . . . . . . . . . . .
4.1 Output power vs. pump power of a two-mirror cavity with different output couplers. Horizontal pumping conguration. Repetition rate: 1 kHz. Dye concentration: 0.1 g/l. . . . . . . . . . .
4.2 Wavelength dependence of the refractive index of SF11 glass (red
curve ) and BK7 glass (blue curve ) calculated from Sellmeier equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Compact arrangement of three equilateral SF11 prisms at minimum deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Intensity of a p-polarized component after a 8 mm thick YVO4
plate. The optical axis is in the plane of the plate. The angle φ
between the optical axis and the direction of polarization is 45o
for the red curve, 30o for the green curve and 20o for the blue curve.
4.5 Wavelength selective resonator with one prism at minimum deviation and a birefringent YVO4 crystal. . . . . . . . . . . . . . .
4.6 Wavelength selective resonator with two prisms at minimum deviation and a birefringent YVO4 crystal (two prisms on the same
side of the crystal). . . . . . . . . . . . . . . . . . . . . . . . . . .
65
23
24
24
26
28
28
29
29
31
31
32
34
35
37
38
39
39
4.7 Wavelength selective resonator with three prisms at minimum
deviation and a birefringent YVO4 crystal. . . . . . . . . . . . .
4.8 Wavelength selective resonator with two prisms at minimum deviation and a birefringent YVO4 crystal (one prism on each side
of the crystal). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Output power vs. pump power for a cavity containing two SF11
prisms at minimum deviation and a 8 mm thick YVO4 plate.
Repetition rate: 1 kHz. Dye concentration: 0.1 g/l. . . . . . . . .
4.10 Spectrum of the laser output from a cavity containing one SF11
prism at minimum deviation and a 8 mm thick YVO4 plate. . . .
4.11 Spectrum of the laser output from a cavity containing two SF11
prisms at minimum deviation and a 8 mm thick YVO4 plate. . .
4.12 Littman cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.13 Output power vs. pump power of a Littman cavity. Horizontal
pumping conguration. Repetition rate: 1 kHz. Dye concentration: 0.1 g/l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.14 Output power vs. pump power of a Littman cavity for dierent
dye concentrations. Horizontal pumping conguration. Repetition rate: 1 kHz. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.15 Output power vs. pump power of a Littman cavity. Vertical
pumping conguration. Repetition rate: 1 kHz. Dye concentration: 0.15 g/l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.16 Spectrum of the laser output from a Littman cavity. . . . . . . .
4.17 Interference fringes produced by the laser output of a Littmantype cavity sent through a Fabry-Pérot etalon (Finesse: 77, Free
spectral range: 100 GHz). . . . . . . . . . . . . . . . . . . . . . .
4.18 Dual cavity conguration. . . . . . . . . . . . . . . . . . . . . . .
4.19 Self-seeding of a long broadband cavity by a short wavelength
selective cavity. Broadband cavity length: 31 cm. Littman cavity
length: 20 cm. Blue curve : spectrum of the laser output from the
broadband cavity (tuning mirror blocked). Red curve : spectrum
of the laser output from the dual cavity (tuning mirror unblocked).
4.20 Output power vs. pump power of a simple Littman cavity and a
dual cavity with dierent values of the output coupler reectivity.
Broadband cavity length: 31 cm. Littman cavity length: 20 cm.
Horizontal pumping conguration. Repetition rate: 1 kHz. Dye
concentration: 0.1 g/l. . . . . . . . . . . . . . . . . . . . . . . . .
40
40
41
42
42
43
44
45
46
47
49
50
51
52
5.1 Second-harmonic generation of light by a laser beam focused in
a non-linear material (from [24]). . . . . . . . . . . . . . . . . . . 56
5.2 Magnesium ions loaded in a linear Paul trap with the frequency
doubled pulsed dye laser. An increasing number of magnesium
ions is trapped after the trap potential is switched on (from left
to right and from top to bottom). Intense points at the center of
the picture correspond to trapped and cooled 24 Mg ions. Dark
sites within the chain correspond to 25 Mg and 26 Mg ions, which
are not adressed by the cooling laser. . . . . . . . . . . . . . . . 59
5.3 Crystal of 24 Mg ions loaded in a linear Paul trap with the frequency doubled pulsed dye laser. . . . . . . . . . . . . . . . . . . 60
66
67
List of Tables
−5
4.1 Comparison of single-pass spectral widths (λ=570 nm, dn
dλ =7.57×10
(from Sellmeier equation), dα=5 mrad) and measured spectral
width for SF11 prisms at minimum deviation. . . . . . . . . . . . 36
4.2 Comparison of conversion eciency and spectral width for dierent cavities. Horizontal pumping conguration. Repetition rate:
1kHz. Dye concentration: 0.1 g/l. . . . . . . . . . . . . . . . . . . 54
68