Abstract: Shaped near-infrared (NIR) femtosecond pulses are usedfor the first time to control the generation of coherent deep-ultraviolet(UV) radiation in an atomic resonance-mediated (2+1) three-photonexcitation. The broadband excitation coherently involves pathways that areon resonance with the intermediate resonance state as well as pathwaysthat are near resonance with it. Experimental and theoretical results arepresented for phase controlling the total emitted UV yield in atomic sodium.Depending on the NIR spectrum of the excitation pulse, the coherent UVemission is either predominantly due to a single excited real state that isaccessed resonantly or due to a manifold of virtual states. The former leadsto a narrowband UV emission, while the latter leads to a broadband UVradiation. Basic phase control is exercised in both cases, with excellentagreement between experiments and calculations. The tunability is over anorder-of-magnitude UV-yield range.
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”Measurements of collisional dephasing of 3s-4s Na coherent superpositions by femtosecond four-wave mixing.”
Following from their coherent broadband nature, femtosecond pulses allow to control quan-tum systems in unique ways that cannot be achieved otherwise [1-8]. The corresponding con-trol utilizes the fact that the transition probability to a given state results from the interferencesamong all the initial-to-final quantum pathways leading to this state that are photo-induced bythe broad coherent spectrum of the pulse. By spectrally shaping the femtosecond pulse [9,10],i.e., manipulating the amplitude, phase, and/or polarization of its different frequency compo-nents, one can manipulate these interferences and control transition probabilities and state pop-ulations.
Over the past decade, among the processes over which such femtosecond coherent controlhas been demonstrated to be very effective are multiphoton processes in atoms and molecules[8,11-33]. The multiphoton processes, which have been rationally controlled based on the iden-tification of the excitation pathways and their interference mechanism, include non-resonantand resonance-mediated processes of two-photon absorption [8,11-17], three-photon absorp-tion [8,18-21] and Raman transitions [22,23] as well as the process of coherent anti-stokesRaman scattering (CARS) [24-28]. In the context of the present work, an important aspect ofthe CARS process is the fact that, as opposed to the other processes, it leads to the (directed)emission of stimulated coherent radiation in new frequencies (other than the ones of the ex-citing femtosecond pulse). Beyond the fundamental scientific interest in quantum control ofmatter by light, controlling multiphoton processes is of importance for applications of nonlin-ear spectroscopy and microscopy. Additionally, the control over directed emission of coherentradiation is also of technological significance for standoff detection of materials [34,35].
Here, we study and demonstrate for the first time femtosecond coherent control over thegeneration of coherent deep-ultraviolet (UV) radiation in an atomic resonance-mediated (2+1)three-photon excitation. The excitation is induced by phase shaped near-infrared (NIR) fem-tosecond pulse. The overall process can be viewed as an atomic resonance-mediated (2+1)third-harmonic generation process. The UV radiation is emitted due to the build-up of a tran-sient polarization between the excited and ground states of the system. Depending on the exci-tation pulse spectrum, the coherent UV emission is either predominantly due to a single excitedreal state that is accessed resonantly or due to a manifold of virtual states. The former leadsto a narrowband UV emission, while the latter leads to a broadband UV radiation. The in-tensity and phase of each emitted UV frequency ωUV results from the interferences betweenall the three-photon excitation pathways that lead to a total excitation energy of ω UV . Fol-lowing from the broad coherent spectrum of the excitation pulse, these three-photon pathwaysinclude pathways that are on resonance with the intermediate resonance state as well as path-ways that are near resonance with it. The resonance-mediated nature of the excitation provides a
#103465 - $15.00 USD Received 3 Nov 2008; revised 4 Dec 2008; accepted 7 Dec 2008; published 16 Dec 2008
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3s
4s
7p
r4p5p
8p
6p
3p
g0 0
jv states
UV
Rv
12800 12850 12900 12950 130000.0
0.2
0.4
0.6
0.8
1.0
Spe
ctra
l Int
ensi
ty [a
rb.u
]
NIR frequency [cm-1]
Fig. 1. The generation of coherent broadband UV radiation via resonance-mediated (2+1)three-photon excitation in Na. Several sets of three-photon pathways that are on resonance(δ = 0) or near resonance (δ �= 0) with the intermediate state |r〉 ≡ 4s are shown. The insetshows the two NIR excitation pulse spectra with (thick gray line) and without (thin blackline) a resonant access to |vR〉 ≡ 7p.
much higher degree of control over the emitted UV radiation as compared to a completely non-resonant excitation. The present work utilizes previous works on femtosecond coherent controlof resonance-mediated (2+1) three-photon absorption [18-20], also extending them from a caseof a single real final state to a case of a continuous manifold of multiple (virtual) final states.Resonance-mediated three-photon excitation in atomic vapors has actually been employed verysuccessfully in the past for efficient and tunable generation of short-wavelength radiation, how-ever it has been used only for generating narrowband (nanosecond or picosecond) UV andVUV coherent radiation by narrowband NIR and VIS excitation (for example, see [36-46]);The present broadband nature of the excitation introduces a completely new dimension to theprocess.
Consider the atomic resonance-mediated (2+1) UV generation process, induced by a NIRfemtosecond pulse, depicted in Fig. 1. It involves an initial ground state |g〉 and an excitedstate |r〉 that are of one symmetry, and a manifold of excited states
∣∣v j
⟩
that are of anothersymmetry. The NIR excitation pulse spectrum is such that all the |g〉 − ∣
∣v j⟩
and |r〉 − ∣∣v j
⟩
couplings are non-resonant, except for the |r〉− |vR〉 coupling that, according to the consideredcase, is either resonant or non-resonant. Additionally, the excitation spectrum contains half the|r〉 − |g〉 transition frequency (ωr,g/2). Hence, the irradiation with the NIR broadband pulseleads to a resonance-mediated three-photon excitation from |g〉 to a broad continuous range offinal energies followed by a stimulated de-excitation back to |g〉 emitting a coherent broadbandUV radiation. In the time domain picture, the UV emission results from a time-dependent dipolemoment induced by the NIR pulse. This dipole moment is given by:
μ(t) = ∑j∑j′
a j(t)∗a j′(t)μ j, j′eiω j, j′ t , (1)
where a j(t) is the amplitude of any atomic eigenstate | j〉, μ j, j′ and ω j, j′ are the transition dipolemoment and transition frequency between states | j〉 and | j ′〉, respectively.
#103465 - $15.00 USD Received 3 Nov 2008; revised 4 Dec 2008; accepted 7 Dec 2008; published 16 Dec 2008
(C) 2008 OSA 22 December 2008 / Vol. 16, No. 26 / OPTICS EXPRESS 21741
Within the framework of a 3rd order time-dependent perturbation theory, this temporal dipolemoment is given by:
μ (3)(t) = ∑j∑j′
a(3)j (t)∗a(0)
j′ (t)μ j, j′eiω j, j′ t +a(2)
j (t)∗a(1)j′ (t)μ j, j′e
iω j, j′ t + c.c., (2)
where a(n)j (t) is the nth-order correction to the amplitude of the state | j〉 given by:
a(n)j (t) = − 1
ih ∑j′
μ j, j′∫ t
−∞a(n−1)
j′ (t ′)E(t ′)eiω j, j′ t dt ′, (3)
with E(t) being the temporal electric field of the NIR excitation pulse and the zero-order cor-
rections being a(0)j = δ j,g, i.e., the system lies initially at the ground state. Eq. (1) can be trans-
formed to the frequency-domain to give the emitted spectral UV field:
where ℘ is the principal value of Cauchy and E(ω) is the (NIR) spectral field of the excitationpulse. It is given by E(ω)≡ |E(ω)|exp [iΦ(ω)], with |E(ω)| and Φ(ω) being, respectively, thespectral amplitude and phase at frequency ω . For the (not shaped) transform-limited (TL) pulse,which is the shortest pulse for a given spectrum |E(ω)|, Φ(ω) = 0 for any ω . The quantity μ 2
r,g
is the |g〉→|r〉 effective non-resonant two-photon excitation coupling, while D (UV )R (ωUV ) and
D(UV )nonR stand, respectively, for the |r〉→|vR〉→|g〉 coupling via |vR〉 and for the |r〉→∣
∣v j⟩→|g〉
coupling via all the other v j states. They are given by
D(UV )R (ωUV ) =
μg,vR μvR,r
ωvR,g −ωUV + iΓvR
, (9)
D(UV )nonR =
∞
∑v j �=vR
μg,v j μv j ,r
ωv j ,g − (ωr,g + ω0)=
∞
∑v j �=vR
μg,v j μv j ,r
ωv j ,r −ω0, (10)
where Γvr is the linewidth of |vR〉. The spectral intensity emitted at a UV frequency ωUV isIUV (ωUV ) ∝ |EUV (ωUV )|2. The total UV yield is YUV =
∫ ∞−∞ IUV (ωUV )dωUV .
As illustrated in Fig. 1, Eqs. (4)-(8) reflect the fact that the (complex) spectral field EUV (ωUV )at each emitted UV frequency ωUV results from the interferences between all the three-photonpathways starting from |g〉 and reaching the final excitation energy that corresponds to ω UV .Each such pathway is either on resonance or near resonance with the intermediate state |r〉,having a corresponding detuning δ . It involves a non-resonant absorption of two photons with atwo-photon transition frequency ω r,g−δ and the absorption of a third complementary photon offrequency ωUV −(ωr,g−δ ). The term A(2+1)on−res(ωUV ) [Eq. (6)] interferes all the on-resonantpathways (δ = 0), while the term A(2+1)near−res(ωUV ) [Eq. (7)] interferes all the near-resonantpathways (δ �= 0) with a 1/δ amplitude weighting. Hence, in general, each emitted UV fre-quency, ωUV , acquires its own amplitude and phase depending on the complex spectral field of
#103465 - $15.00 USD Received 3 Nov 2008; revised 4 Dec 2008; accepted 7 Dec 2008; published 16 Dec 2008
(C) 2008 OSA 22 December 2008 / Vol. 16, No. 26 / OPTICS EXPRESS 21742
the NIR excitation pulse, E(ω). One should note that, due to the resonance-mediated nature ofthe (2+1) excitation, this applies also for an excitation with a transform-limited NIR pulse dueto the interference between the on- and near-resonant pathways.
When the excitation pulse spectrum allows resonant access to the |vR〉 state by three-photonpathways, the emitted UV spectrum contains the corresponding frequency ω UV = ωvR,g. Since
the coupling component D(UV )R (ωUV ) [Eq. (9)] associated with |vR〉 has a narrow response
around ωUV = ωvR,g, with a magnitude that is much larger than the magnitude of the other
coupling component D(UV )nonR [Eq. (10)] associated with all the other
∣∣v j
⟩
states, the emitted UVspectrum consists of a dominant narrowband part centered around ω vR,g that is superimposedon a broadband part of much smaller magnitude. The corresponding total UV yield is thenproportional to the spectral intensity at ωvR,g, i.e., YUV ∝ IUV (ωvR,g) ∝ |A(2+1)(ωvR,g)|2. Thisis actually proportional to the population excited to |vR〉 by the femtosecond pulse [18,19].When there is no resonant access to |vR〉, i.e. A(2+1)(ωUV ) is zero for ωUV around ωvR,g, the
D(UV )R (ωUV ) coupling is effectively of non-resonant nature and becomes effectively indepen-
dent of the emitted ωUV , similar to D(UV )nonR . The UV emission spectrum is then broadband with
no narrowband component.The above excitation scheme is physically realized here with atomic sodium (Na) (see Fig. 1),
having the 3s ground state as |g〉, the 4s state as |r〉, and the manifold of p-states as∣∣v j
⟩
with7p as |vR〉. The transition frequency ωr,g ≡ ω4s,3s = 25740 cm−1 corresponds to two 777-nmphotons and the frequency ωvR,r ≡ ω7p,4s = 12801 cm−1 corresponds to a 781.2-nm photon.The sodium interacts with phase-shaped linearly-polarized femtosecond pulses having a NIRspectrum centered around 777 nm with ∼5-nm (FWHM) bandwidth (∼180-fs TL duration).The pulse energy is 10 μJ and the peak intensity of the TL pulse is about 10 10 W/cm2 (thefocused beam radius is 0.25 mm). Experimentally, atomic sodium vapor of 3.7×10 17 cm−3
density in a heated cell at 900 K with 10-Torr Ar buffer gas is irradiated with such NIR laserpulses, after they undergo shaping in an optical setup incorporating a pixelated liquid-crystalspatial light phase modulator [9,10]. The effective spectral shaping resolution is 2.05 cm −1 perpixel. Following the interaction with the NIR pulse, the coherent UV radiation emitted in thepropagation direction of the NIR beam is measured using a UV-spectrometer coupled to a time-gated camera system. The corresponding overall UV spectral resolution is 35 cm −1 (0.23 nm),with 5.8-cm−1 spectral width of each camera pixel.
As a first control work on resonance-mediated (2+1) generation of coherent UV radiation, wehave chosen to demonstrate here phase control over the total emitted UV yield YUV with shapedpulses having simple spectral phase patterns Φ(ω) of a spectral π-step at variable position ω step.As previously shown, this group of spectral phases is highly effective in controlling two-photonabsorption [11-17] and resonance-mediated (2+1) three-photon absorption [18-21]. The phasecontrol over the UV yield is studied in two cases: when the excitation spectrum allows accessto the 7p state (via various three-photon pathways) and when it does not (see above). The latteris implemented by blocking the low-frequency end of the excitation pulse spectrum. The cor-responding excitation spectra for both cases are shown in Fig. 1(inset). The corresponding UVspectra for the above two cases, measured with the TL excitation pulse having the appropriatespectrum, are shown in Figs. 2(a2) and 2(b2). As seen and explained above, an access to the7p state leads to a UV spectrum that is dominated by a strong narrowband component locatedaround ωUV = ω7p,3s=38541 cm−1 (259.46 nm) with a measured width equal to the UV spec-tral resolution [Fig. 2(a2)], and when the access to the 7p state is blocked the UV spectrum ispurely broadband [Fig. 2(b2)]. Here, it is measured to be of 130±6 cm −1 bandwidth (FWHM)around 38679±3 cm−1 (258.54 nm).
The experimental (circles) and theoretical (lines) results for controlling the total UV yield
#103465 - $15.00 USD Received 3 Nov 2008; revised 4 Dec 2008; accepted 7 Dec 2008; published 16 Dec 2008
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12750 12800 12850 12900 129500.0
0.5
1.0
Position of the NIR phase step [cm-1]
(b1)
Tota
l UV
yie
ld [a
rb.u
]
(a1)
12750 12800 12850 12900 129500.0
0.5
1.0
1.5
2.0
2.5 Experiment Calculations
Tota
l UV
yiel
d [a
rb.u
]
Position of the NIR phase step [cm-1]
38550 38700 388500.0
0.2
0.4
0.6
0.8
1.0
UV frequency [cm-1]
(b2)
Spe
ctra
l Int
esity
[arb
.u]
UV frequency [cm-1]
38550 38700 388500.0
0.2
0.4
0.6
0.8
1.0
Spe
ctra
l Int
esity
[arb
.u.]
UV frequency [cm-1]
7p,3s
(a2)
Fig. 2. Experimental (circles) and theoretical (solid lines) results for the total UV yieldgenerated by shaped NIR pulses with spectral π phase step, when the excitation pulsespectrum (a1) allows and (b1) blocks the resonant access to 7p (see Fig. 1). The UV yieldis shown as a function of the position of the NIR π phase step. The traces are normalizedby the yield generated by the corresponding transform-limited (TL) pulse. The UV spectragenerated by the NIR TL pulses in the two cases are shown in panels (a2) and (b2).
YUV with shaped femtosecond pulses having π-step spectral phase pattern for the cases of the 7pstate being accessible or inaccessible are presented in Figs. 2(a1) and 2(b1), respectively. Eachtrace is normalized by YUV induced by the corresponding TL pulse. The theoretical results arecalculated numerically using Eqs.(4)-(10), using a grid with a bin size equal to the experimentalshaping resolution. As can be seen, there is an excellent agreement between the experimentaland theoretical results, confirming our theoretical description and understanding.
Consider first the case when 7p is resonantly accessed. As explained above, the total yieldYUV in this case is proportional to the population excited to the 7p state P7p. Indeed, theTL-normalized trace shown in Fig. 2(a1) for YUV reproduces the one measured for P7p withsimilar NIR excitation [18,19]. The total UV yield is experimentally controlled from 3% toabout 200% of the yield induced by the TL pulse. The strong enhancement occurs whenωstep = ω7p,4s=12801 cm−1. As previously identified for the resonance-mediated three-photonabsorption [18,19], it originates from a change in the nature of the interferences betweenthe positively-detuned (δ>0) and negatively-detuned (δ<0) near-resonant 3s-7p three-photonpathways. With the TL pulse they are destructive, while with a π-step at ω7p,4s they are con-structive. The physical reason for this proportionality between YUV and P7p is the coherentsuperposition of the 3s and 7p states that is created by the excitation and survives also afterthe pulse is over, leading to a long-lived time-dependent dipole moment. This dipole momentinduces the UV emission at frequency ω7p,3s. The decay of this 3s-7p UV emission is, on onehand, due to the inhomogeneous Doppler broadening (free induction decay [47]) and, on theother hand, due to the dephasing of the 3s-7p coherent superposition following collisions withthe Ar buffer gas. Based on previous collisional dephasing measurements conducted for variousexcited states of Na other than the 7p state [48-50], we conclude that under our experimentalconditions the decay of the UV radiation is dominated by the inhomogeneous Doppler broad-ening, with an estimated decay time of tens of picoseconds. Hence, in this case, the overallresult is an ultrashort UV pulse of small integrated energy, followed by a very long quasi-
#103465 - $15.00 USD Received 3 Nov 2008; revised 4 Dec 2008; accepted 7 Dec 2008; published 16 Dec 2008
(C) 2008 OSA 22 December 2008 / Vol. 16, No. 26 / OPTICS EXPRESS 21744
monochromatic radiation at ω7p,3s with large integrated energy.In the other case when the 7p is inaccessible [Fig. 2(b1)] the total UV yield YUV is not dom-
inated by any single frequency. Similar to the above enhancement with ω step = ω7p,4s whenthe 7p is accessed, a π-step at a position ωstep enhances here the UV amplitude at frequen-cies around ωUV = ωstep + ω4s,3s, while it affects the amplitudes of other frequencies in acomplicated way (leading to attenuation or enhancement) according to the above theoreticaldescription. Thus, no enhancement of the total UV yield YUV beyond the TL level is observedin Fig. 2(b1) for any ωstep. The corresponding control is from about 10% to 100% of the UVyield induced by the TL pulse. Under our experimental conditions, the integrated energy of thebroadband UV emission is about 1% of the NIR pulse energy for a TL excitation.
In summary, we have studied and demonstrated for the first time basic phase control overthe resonance-mediated (2+1) generation of coherent UV radiation by shaped NIR femtosec-ond pulses. Depending on the NIR excitation spectrum, the coherent UV emission is eitherpredominantly due to a single excited real state that is accessed resonantly or due to a man-ifold of virtual states. The former leads to a narrowband UV emission, while the latter leadsto a broadband UV radiation. Controlling the directed emission of short-wavelength coherentradiation is important for nonlinear spectroscopy and microscopy as well as for standoff detec-tion of materials. The presented scheme can generally be extended to the vacuum-ultraviolet(VUV) spectral range by changing the excitation pulse spectrum to the visible (VIS) range andchoosing an atomic system whose state energies fit the resonance-mediated (2+1) VIS exci-tation. Then, further development of the scheme can be a basis for the production of shapedfemtosecond pulses in the VUV range where no current pulse shaping technique [9,10] is ap-plicable. This will greatly extend the variety of molecules to be coherently controlled as mostof the molecular electronic transitions are in the UV and VUV spectral range.
This research was supported by The Israel Science Foundation (Grant No. 127/02), by TheJames Franck Program in Laser Matter Interaction and by The Technion’s President Fund.
#103465 - $15.00 USD Received 3 Nov 2008; revised 4 Dec 2008; accepted 7 Dec 2008; published 16 Dec 2008
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