Appl Phys B (2010) 98: 383–390
DOI 10.1007/s00340-009-3801-8
Axial and conical parametric emissions from potassium atoms
under two-photon fs excitation
D. Pentaris · T. Efthimiopoulos · N. Merlemis ·
V. Vaicaitis
Received: 11 June 2009 / Revised version: 15 September 2009 / Published online: 1 November 2009
© Springer-Verlag 2009
Abstract We report on the emissions near the 5P3/2,1/2 –
4S1/2 and 4P3/2,1/2 –4S1/2 transitions of potassium atoms
which are excited by a fs laser beam. The field at the transition 5P3/2,1/2 –4S1/2 is mainly the result of a parametric
process with an axial profile when the excitation frequency
is tuned above resonance and a conical one below resonance.
Similar but not identical far-field patterns were also observed for the 4P3/2,1/2 –4S1/2 emission. No amplified spontaneous emission was observed for the fs case, in contrast to
the ns excitation for the 4P3/2,1/2 –4S1/2 transition.
PACS 42.62.Fi · 42.65.Re · 52.35.Mw
1 Introduction
In recent years a number of papers have been published
investigating the emissions from alkali atoms under twophoton excitation (see for example [1–4] and references
therein). In most of the cases the frequency of the pump
D. Pentaris () · T. Efthimiopoulos · N. Merlemis
Laser, Non linear and Quantum Optics Labs, Physics Department,
University of Patras, Patras 26500, Greece
e-mail: [email protected]
T. Efthimiopoulos
e-mail: [email protected]
D. Pentaris · V. Vaicaitis
Laser Research Center, Vilnius University, Sauletekio 10, Vilnius
10223, Lithuania
N. Merlemis
Department of Physics, Chemistry & Materials Technology,
Technological Educational Institute (TEI) of Athens,
Agiou Spiridonos st., Athens 12210, Greece
laser was tuned near an allowed two-photon transition of
the nonlinear medium in order to increase the nonlinear
susceptibility and avoid the pump depletion. However, the
pump depletion, which is closely related to the nonlinear
frequency conversion, is important only in the case of very
strong excitation of the nonlinear media. Under the twophoton resonance condition a number of nonlinear effects,
such as amplified spontaneous emission (ASE), stimulated
hyper Raman scattering (SHRS), parametric four-wave mixing (PFWM) and others, have been investigated. In the case
of exact two-photon resonance of the pump and media transitions the losses due to population transfer with subsequent
spontaneous emission and/or ionization increase considerably. On the other hand, it was observed that the closer the
external field is tuned to the corresponding atomic resonance
the stronger the atom–field interaction is and consequently
the higher is the gain. It has been shown both experimentally and theoretically that the two-photon excitation of the
3S–3P transition in sodium vapor can produce parametric internally generated coherent fields which are crucially dependent on the system parameters, such as the atomic density,
the two-photon detuning and the driving laser peak intensity [3–6]. In order to explain the coherent effects the twophoton pumping was used for the investigation of a possible
inversionless amplification in potassium atoms [7, 8]. Quantum interference between the excitation field and the different internally generated radiations plays an important role
and modifies the output intensities because of the destructive interference of the different atomic channels involved
in the interaction [3, 4, 7, 8]. The interference effect mentioned above and the reduced absorption were also realized
in the case of four-wave mixing (FWM) to generate tunable
visible and ultraviolet (UV) coherent radiation [9, 10], using
transitions to an auto-ionizing state.
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D. Pentaris et al.
It is possible, by adjusting the nonlinear parameters, such
as the two-photon detuning, the density and the laser peak
intensity, to study the mechanism of the internally generated fields. Parametric emission and wave mixing, when the
population remains in the ground state, and nonparametric
processes, when the population is redistributed between the
states, may take place. In the case of two-photon excitation
we can observe the effect of the destructive interference and
the competition of the available emission channels. In our
previous work we have investigated experimentally [7, 8]
and in a four-level simulation [11, 12] the potassium atomic
system driven by a ns duration laser pulse. We have shown
that it is possible to produce ASE generation without population inversion at the 4P3/2,1/2 –4S1/2 transition. Also, coherent emissions due to four- and six-wave mixing processes
are commonly observed during the high-power excitation of
the alkali vapors [7, 12]. The inversionless nature of some
internally generated radiations as well as their competition
with the excitation fields for specific system parameters is
a relatively new field in nonlinear optics where parametric processes appear [7–9, 11–13]. The competition between
ASE or SHRS and parametric processes can lead to suppression of the ASE or SHRS propagating fields by the parametric one radiation enabling also the transfer of the excitation
energy to other atomic transitions.
In the ns excitation the axial and the conical parts of the
internally produced radiations, as a function of the atomic
parameters, can be easily distinguished [8], despite the competitive process which can take place [14]. In [15] (see also
the references therein related to the conical emission in alkali atoms), the conical emission (CE) was observed when
a 2-ps laser beam, blue shifted from resonance, was propagating through potassium vapor. In contrast, no conical part
was visible when a 150-fs pulse had been used. This is an indication that the physical origin of CE by pulsed excitation
of the atomic vapors is still largely unknown, and further
investigation has to be done [6, 16].
In the current work we expand our previous study to the
fs duration laser pulse in order to drastically increase the
nonlinearity of the system because of the higher excitation
pulse intensity. We examine the far-field spatial profile of
the emissions at the transitions 5P3/2,1/2 –4S1/2 and 4P3/2,1/2 –
4S1/2 , respectively, for a short range of two-photon detuning
∆12 from the resonant transition. These results are compared
with the case of the ns excitation.
Fig. 1 (a) Diagram of the experimental set-up. A lens with a focal
length of 66.7 cm was used to focus the laser beam at the center
of the cell. The spectra were recorded by a digital spectrometer and
a computer. (b) Four-level configuration of the potassium atom. The
two-photon field excites the potassium atom to the state 6S1/2 . The in-
ternally generated coherent fields correspond to the transitions 6S1/2 –
5P3/2,1/2 (λ24 = 3636 nm), 5P3/2,1/2 –4S1/2 (λ41 = 404 nm) of path 1
and 6S1/2 –4P3/2,1/2 (λ23 = 694 nm), 4P3/2,1/2 –4S1/2 (λ31 = 766 nm) of
path 2, respectively. The frequencies of these coherent fields are represented as ω24 , ω41 , ω23 and ω31 , respectively
2 Experimental set-up
Our experimental set-up is shown in Fig. 1a. The atomic
medium consists of potassium atoms confined inside a
heated cylindrical stainless-steel cell. The vapor column
length in the cell was 30 cm. To keep the potassium vapor away from the cell windows we used argon buffer gas
with a pressure of approximately 10 mbar at room temperature. In order to produce strong internally generated
fields the cell temperature was kept at 300°C, which corresponds to the atomic potassium density of 5 × 1015 cm−3
Axial and conical parametric emissions from potassium atoms under two-photon fs excitation
(0.3 mbar). Subsequently, the temperature was decreased in
order to investigate the potassium density range in which
the generated field at the transition 5P3/2,1/2 –4S1/2 of the
path 1 (4S1/2 –6S1/2 –5P3/2,1/2 –4S1/2 ) was present. We used
six thermocouples to monitor the temperature along the cell.
An optical parametric generator (OPG) was pumped by a
fs Ti:sapphire laser (‘Spitfire’, Spectra Physics, Ltd), with
maximum single-pulse energy of 13 µJ and pulse duration
at FWHM of 120 fs. The beam diameter was 3 mm and it
was slightly focused into the vapor cell producing the maximum intensity of up to 0.3 TW/cm2 . A digital spectrometer
(‘Ocean Optics’ HR2000) was used to record the spectrum
of the generated radiations. In addition, appropriate interference filters centered at the wavelengths of the potassium
transitions 5P3/2,1/2 –4S1/2 (λ41 = 404 nm), 6S1/2 –4P3/2,1/2
(λ23 = 694 nm) and 4P3/2,1/2 –4S1/2 (λ31 = 766 nm) were
used to select the radiation of interest.
3 Results and discussion
Figure 1b shows the energy level diagram of the four-level
atomic configuration. The laser field with the frequency ω
(corresponding to the energy of 13736.3 cm−1 ) was used
to excite, with two photons, the atom from the ground state
4S1/2 to the state 6S1/2 . The two-photon pump was the only
external field provided to the atomic system. The coherent fields corresponding to the transitions 6S1/2 –5P3/2,1/2 ,
5P3/2,1/2 –4S1/2 of path 1 and 6S1/2 –4P3/2,1/2 , 4P3/2,1/2 –4S1/2
of path 2 were internally generated in the medium. In our
previous study [7, 8], we investigated the radiation at the
transitions 5P3/2,1/2 –4S1/2 and 4P3/2,1/2 –4S1/2 under unfocused ns excitation. It was shown that there were several
possible mechanisms that can be involved in the production
of the 404.4-nm and 404.7-nm coherent emissions from the
5P3/2,1/2 states, respectively. A parametric process was taken
place during the two-photon ns excitation for low pumping
intensity (<6 MW/cm2 ). Both axial and/or CE were observed depending on the laser two-photon detuning from
resonance. Strong indication of amplification without inversion (AWI) at the 4P3/2,1/2 –4S1/2 transition, which was
backed by a simulation study, was presented in a more recent
paper [11]. The inversionless amplification in both paths was
also predicted in a more sophisticated system by modeling
using Maxwell–Bloch equations [12].
In the following we express the two-photon detuning in
inverse wavelength units (cm−1 ), according to the formula
∆12 = δ12 /(2πc), where δ12 is the detuning in rad/s and
c is the constant velocity of light in the vacuum in cm/s.
In the current study a two-photon detuning ∆12 = (2ω −
ω6S1/2 −4S1/2 )/(2πc) was chosen to start at 191.3 cm−1
above resonance (∆12 > 0, which in wavelength units corresponds to 10 nm) and gradually varied to 186.2 cm−1 below
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resonance (∆12 < 0, which corresponds to 10 nm), while the
laser line width was 190 cm−1 (which in wavelength units
is approximately 10 nm) at FWHM. The excitation spectra
of the internally generated fields at the transitions 4P3/2,1/2 –
4S1/2 and 5P3/2,1/2 –4S1/2 were recorded at various emission
angles with respect to the pump beam axis. The unfocused
pump beam produced weak fields at the transitions of interest in the fs case; therefore, we used a slightly focusing
lens with the focal length F = 66.7 cm. We note that during
the experiment the two-photon detuning was kept relatively
close to the resonance 4S1/2 –6S1/2 in order to avoid the direct single-photon excitation of the 4S1/2 –4P3/2,1/2 transition
and also to produce reliably detectable signals at the wavelength of interest.
The Stark shift
The strong two-photon excitation field causes a dynamic
Stark shift of the ground state 4S1/2 and of the excited state
6S1/2 , respectively. This phenomenon should be taken into
account in theoretical calculations and analyzing the experimental results obtained with the fs laser pulses; therefore, in
the following we present the relative calculation.
(a) Ground state.
The frequency shift of the 4S1/2 state is given from the
formula [13]
ω4S1/2 = −
4
|µ1m |2 ε02 ω1m E(t)2 .
2
2
2
ω1m − ω2
m=3
At the laser intensities given above the maximum Stark
shift, in inverse wavelength units, is 9.5 × 10−4 cm−1 .
(b) First excited state.
In this case we have
ω6S1/2 = −
4
|µ2m |2 ε02 ω2m E(t)2 .
2
2
2
2
ω2m − ω
m=3
The maximum Stark shift in this case is 6.8 ×
10−4 cm−1 .
We note that E(t) is the electric field of the pump, ε0 is
the free-space electric permittivity and µim , with i = {1, 2},
is the matrix element [17]. We conclude that in all of the
cases above the strong excitation field causes an insignificant Stark shift of the levels involved in the interaction.
Moreover, the recorded spectra do not show any measurable
shifts from the atomic line frequencies, i.e. the emitted radiations can be observed at approximately the same wavelength
in the ns and in the fs pump cases, respectively.
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D. Pentaris et al.
Fig. 2 Excitation spectra
corresponding to the
5P3/2,1/2 –4S1/2 transition
radiation as a function of the
two-photon detuning for two
atomic densities. The maximum
was observed when the laser
was tuned above resonance at
75.9 cm−1 , which corresponds
to the axial component of the
emitted radiation. A conical
component appears when the
pump is tuned below the
resonance. We also noticed a
distinct dip on resonance, which
probably was caused by the
ionization of atoms or
population transfer and
subsequent ASE to the lower
states
3.1 Parametric generation at the 5P3/2,1/2 –4S1/2 transition
(path 1)
The excitation spectra
These results are similar but not identical to those obtained for the case of the ns excitation [8], taking into account that the broad spectrum of the laser, the intensity of the
laser and the atomic density affect the excitation spectra of
the parametric process. Finally, we note that the recorded detuning range of this radiation was almost 567 cm−1 (30 nm)
for the cell temperature range used in the experiment, which
is much broader than the ns two-photon detuning case.
The excitation spectra presented in Fig. 2 demonstrate that:
The far-field spatial distribution
(a) There is a relatively broad spectral region of the twophoton detuning in which the parametric generation
at 5P3/2,1/2 –4S1/2 takes place. This broad region is of
the same order as the spectral width of the fs laser
(190 cm−1 at FWHM).
(b) There is a distinct peak of the parametric emission below resonance, corresponding to a CE.
(c) There is a peak above resonance, at 75.9 cm−1 (which
in wavelength units is 4 nm), related to the axial component, which is well resolved at low potassium density.
(d) There is a definite minimum for zero detuning (on resonance, ∆12 = 0), which corresponds to the pump losses
either due to a two-photon resonant three-photon ionization or due to the population transfer to the 6S1/2 state
with subsequent cascade ASE. The second process is
more pronounced though for longer than fs laser pulses.
In Fig. 3a–c we present three photographs of the far-field radiation at the 5P3/2,1/2 –4S1/2 transition for a two-photon detuning of 191.3 cm−1 above, 0 cm−1 (exactly on resonance)
and 186.2 cm−1 below resonance for a potassium number
density of 5 × 1015 cm−3 . Note that for the two-photon detuning of the pump above resonance the axial profile is more
pronounced, while the CE part dominates for the negative
detuning (below resonance).
The 5P3/2,1/2 –4S1/2 coherent radiation at 404.4 nm was
observed even for a density of 1.2 × 1014 cm−3 which corresponds to 190°C. We also observed that for low atomic densities the path 1, which is associated with the 5P3/2,1/2 –4S1/2
transition, is initiated first and, when path 1 saturates, the
emission through path 2 appears for higher atomic densities.
Most probably a population redistribution take place among
In this section we present the excitation spectra and the farfield spatial distribution of the radiation at the 5P3/2,1/2 –4S1/2
transition.
Axial and conical parametric emissions from potassium atoms under two-photon fs excitation
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Fig. 3 The far-field photographs showing the spatial profile of
the radiation at 5P3/2,1/2 –4S1/2 for the two-photon detuning of
(a) 191.3 cm−1 (above resonance), (b) 0 cm−1 (on resonance) and
(c) 186.2 cm−1 (below resonance). The atomic density was 5 ×
1015 cm−3 . The laser line width was 190 cm−1 at FWHM
excited states, causing saturation of the emitted 5P3/2,1/2 –
4S1/2 radiation.
In short, the process involved could be either a parametric one, with the simultaneous emission of photons at
6S1/2 –5P3/2,1/2 and 5P3/2,1/2 –4S1/2 transitions, or a fourwave process mixing a SHRS photon to the 5P3/2,1/2 state
with two laser photons. The facts that an appropriate detector for the 6S1/2 –5P3/2,1/2 infrared field was not available and
the broad laser bandwidth make it difficult to distinguish
between the two processes. In the simulation of the ns excitation we have observed, besides the exponential region,
a linear region of the 5P3/2,1/2 –4S1/2 field as a function of
the laser intensity, which was attributed to the path-1 field
interference with the two-photon excitation [12]. In the fs
pump case the intensity is much higher than that of the ns
excitation pulses and thus the saturation due to interference
will also be present, reducing the efficiency of the generated
parametric emissions.
different atomic concentrations at ∆12 = 0 and at ∆12 =
−186.2 cm−1 , respectively. In particular, we observed two
main peaks close to 766.3 nm and 769.5 nm, respectively.
When the pump was tuned at 186.2 cm−1 below resonance,
the spectra of the emissions were broader while both lines
were almost equal in magnitude for the high atomic densities. On resonance the relative intensity of the two peaks
does not change considerably with the density change and
there is no structure of the spectra. Below resonance the relative intensity of the two peaks changes along with the structure and the overall broadening. These are the result of the
presence of the CE of a broadband fs excitation, which produces an emission that is phase matched at different angles
for the different wavelengths included in the excitation.
3.2 Parametric generation at the 4P3/2,1/2 –4S1/2 transition
(path 2)
In this section we examine the radiation at the 4P3/2,1/2 –4S1/2
transition for two different values of the two-photon detuning ∆12 . Specifically, we measured the intensity at this transition when the excitation was below resonance at ∆12 =
−186.2 cm−1 for two atomic densities. For low atomic density and a two-photon detuning of ∆12 = 191.3 cm−1 the
path 2 is inactive. In particular, we observed no signal up to
the potassium atomic density of N = 2.5 × 1015 cm−3 . This
result is similar to the one obtained in the case of the ns excitation. In both cases we registered the narrow region of twophoton detuning in which the coherent radiation 4P3/2,1/2 –
4S1/2 could be generated.
The emission spectrum
Figures 4 and 5 show the spectra of the doublet 4P3/2,1/2 –
4S1/2 taken from the central part of the emission for three
The far-field spatial profiles
In order to study further the relative importance of the conical part of the radiation in the spatial profile, we measured
the intensity of the spectral peak corresponding to the 4P3/2 –
4S1/2 transition at 766.3 nm for several observation angles
from the axis of the laser beam. In Fig. 6 we present the angular distributions of this emission for the potassium atomic
density 4.5 × 1014 cm−3 and for the two two-photon detunings (on and below resonance). On resonance the radiation
appears to have a relatively broad emission-angle distribution (Fig. 6a), while below resonance the spatial distribution
appears to have two symmetrically recorded peaks (at an angle of 5 mrad from the laser beam axis, Fig. 6b). It seems that
the beam has a filled-in conical component, which is somehow different from the ring-shaped one which was shown
in Fig. 3 for the 5P3/2,1/2 –4S1/2 transitions, since in the case
of the 4P3/2,1/2 –4S1/2 emissions the cone appears to be imperfectly shaped. This cone is in fact a broadband highly divergent beam, probably because of the very broadband laser
pulse, and as a consequence the axial part of this radiation
cannot be easily distinguished close to the two-photon resonance.
In addition, we did not observe any backward component of the emission, which could be generated due to ASE
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D. Pentaris et al.
Fig. 4 Spectra of the axial
(taken from the central part of
the emissions) internally
generated radiation at the
4P3/2 –4S1/2 (766.3 nm) and
4P1/2 –4S1/2 (769.5 nm)
transitions for the resonant
excitation conditions (zero
two-photon detuning) and three
atomic densities: (a)
4.5 × 1014 cm−3 , (b) 1.5 ×
1015 cm−3 and (c) 2.5 ×
1015 cm−3 . Note that the
radiation of the two lines seen in
the figure was also registered at
±25 mrad angle with respect to
the pump beam optical axis,
suggesting the high-divergence
filled-in conical beam profile of
the emitted radiation in addition
to the axial one
Fig. 5 Spectrum of the
radiation at the 4P3/2 –4S1/2 and
4P1/2 –4S1/2 transitions taken
along the cell axis for three
atomic densities: (a) 4.5 ×
1014 cm−3 , (b) 1.5 × 1015 cm−3
and (c) 2.5 × 1015 cm−3 , with
the two-photon excitation tuned
below resonance at 186.2 cm−1 .
In this case the spectra are
broader because more laser
wavelengths contribute to the
conical emission as part of the
total process in comparison with
the resonance case
and should be axially propagating, which means that the
forward conical radiation is a result of a parametric wave
mixing process. This is quite different from the ns excitation case [7], when axially propagating ASE was the predominant spatial component at high laser excitation intensities.
If we detune the laser well below the resonance, i.e. at
∆12 = −367.3 cm−1 (20 nm) or −578.4 cm−1 (32 nm), then
the single-photon excitation of the channel 4S1/2 –4P3/2,1/2
becomes possible, thus making the situation more complex.
In short, the path 2 produced mainly conical unidirectional
parametric radiations at 4P3/2,1/2 –4S1/2 under a broad range
Axial and conical parametric emissions from potassium atoms under two-photon fs excitation
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Fig. 6 Intensity of the emission
corresponding to the
4P3/2 –4S1/2 transition as a
function of the emission angle,
on and below resonance at
186.2 cm−1 . The intensity
distribution on resonance could
be considered as the sum of a
filled-in conical beam (as is
shown in the bottom picture for
the below-resonance case) and
an axial one with a small
misplacement of 5 mrad
of two-photon detuning (on and below resonance). These
results are different from those obtained during the experiments with the ns laser pulses, where the observation of
ASE radiation was the main indication of possible inversionless amplification [7]. In the case of the fs excitation the
broad laser spectrum introduces complications in the interpretation of the emission close to one-photon 4P3/2,1/2 –4S1/2
resonance since both axial and CE are generated at the detuning comparable to the laser spectral width.
(iii) The intensity dip on resonance of the 5P3/2,1/2 –4S1/2
field, which might be the result of two-photon resonant three-photon ionization for the fs excitation, is
not so pronounced in the unfocused ns case. In the fs
case there was no ASE detected emerging from the
5P3/2,1/2 –4S1/2 transition, since there was no backwardpropagating emission. This is similar to the result obtained from the ns excitation.
Path 2
4 Conclusions
In the current work we have studied the emissions at the
5P3/2,1/2 –4S1/2 and the 4P3/2,1/2 –4S1/2 transitions for a selected range of the two-photon fs laser detuning and compared the results with the ns laser excitation. In particular:
Path 1
(i) The emission corresponding to the transition 5P3/2,1/2 –
4S1/2 has a conical profile below resonance and on resonance there are a conical and an axial component.
Above resonance there is only an axial component.
These results are similar to the ns case [8].
(ii) The two-photon detuning from resonance for the
5P3/2,1/2 –4S1/2 field extends from 191.3 cm−1 (above
resonance) to −186.2 cm−1 (below resonance), which
is comparable to the spectral width of the fs laser. The
results also are similar to the ns case when the radiation
was detuned in a relatively wide range.
(i) In the fs case the path 2 initiates when the path 1 starts
to saturate, which is similar to the ns case. This saturation is probably also related to the population transfer
to the excited states or ionization, as confirmed by the
simulation results for the ns case.
(ii) There is no ASE, in contrast with the ns pump case,
where the axial ASE was a main feature of the spectra
at high excitation intensity [7].
(iii) In the fs case below the two-photon resonance, the
emission generated at the 4P3/2,1/2 –4S1/2 transition
shows a cone, which is broader and imperfectly shaped
in comparison with the ring-shaped one of the radiation
at the 5P3/2,1/2 –4S1/2 transition of the path 1.
Acknowledgements The authors acknowledge financial support
from: Access to Research Infrastructures activity in the Sixth Framework Programme of the E.U. (contracts RII3-CT-2003-506350, Laserlab Europe and 212025, LASERLAB EUROPE CONT.). Dionysios Pentaris acknowledges support from a Marie Curie Early Stage
Training project ATLAS (contract no. MEST-CT-2004-008048) funded
390
through the Sixth Framework Programme of the E.U. We acknowledge
the valuable assistance of all the researchers of the Vilnius University
Laserlab Center (VULC) and of its director Valdas Sirutkaitis.
Additionally, this work was supported by the Ministry of Education
and the European Union under the program EPEAEK II-Pythagoras
I-285 and also by the University of Patras under the research program
‘Karatheodoris’.
Finally, we would like to express our appreciation to academician
M.E. Movsessian of the Armenian Academy of Science for his support
in the early stages of the potassium atom–laser interaction project. The
technical and simulation assistance of Theocharis Marinos is greatly
appreciated.
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