R E S E A R C H A R T I C L E
Mitigating cross-phase modulation artifacts in femtosecond
stimulated Raman scattering
Thomas Würthwein
1|
Niklas M. Lüpken
1|
Niels Irwin
1|
Carsten Fallnich
1,2,31Institute of Applied Physics, University of
Münster, Münster, Germany
2MESA+ Institute of Nanotechnology,
University of Twente, Enschede, The Netherlands
3Cells in Motion Interfaculty Centre,
Münster, Germany Correspondence
Thomas Würthwein, Institute of Applied Physics, University of Münster, Münster, Germany.
Email: t.wuerthwein@uni-muenster.de
Abstract
In contrast to spontaneous Raman scattering, coherent Raman scattering tech-niques, such as femtosecond stimulated Raman scattering (FSRS), show advan-tages for many applications. Besides an enhanced signal strength, FSRS is free of a nonresonant background but is affected by cross-phase modulation (XPM). The resulting artifacts in FSRS become relevant for high pulse intensi-ties (GW/cm2-regime) and ultrashort pulses (<2 ps), both necessary for super-resolution experiments. As the pulse duration is a crucial parameter for XPM as well as for FSRS, we present a setup in which we adjust the pulse duration across the relevant range (0.5–3 ps), in order to investigate the XPM influence on the spectra. Furthermore, we vary the peak intensity, the temporal overlap between the interacting pulses, and the nonlinear refractive index coefficient n2of the sample, showing that a trade-off between all these quantities enables
the measurement of unaffected FSRS spectra
K E Y W O R D S
artifacts, cross-phase modulation, femtosecond stimulated raman scattering, spectral distortion
1
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I N T R O D U C T I O N
Raman scattering enables chemically selective investiga-tions to study the composition of samples and, therefore, is widely used in biology and medicine.[1-3] Despite the chemical contrast, spontaneous Raman scattering suffers from a weak signal strength, which requires an extended acquisition time and limits its use in medical applica-tions.[4]In coherent Raman scattering (CRS), the interac-tion of typically two light pulses with molecular vibrations does amplify the Raman signal, but especially in coherent anti-Stokes Raman scattering (CARS), a non-resonant nonspecific background is observed, which deforms the shape of the measured signal and even covers small resonant scattering signals.[5,6] At a first
sight, stimulated Raman scattering (SRS) seems to com-bine the advantages of an amplified signal strength and a nondeformed lineshape with a background-free detection.[7-11]However, recent studies have shown that thermal lensing or thermal scattering, two-photon (two-color) absorption (TPA), and cross-phase modulation (XPM) lead to parasitic signatures on the SRS signal.[12-15] Especially, artifacts due to XPM distort the line shape of the stimulated Raman signal and become more relevant for high pulse energies and ultra-short pulse durations as used in a number of experiments.[16-20]
One example in the current research, where pulse energies in the order of hundreds of nano-joules and pulses with a duration in the femtosecond regime are needed, is the field of spatial resolution enhancement in
DOI: 10.1002/jrs.5958
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© 2020 The Authors. Journal of Raman Spectroscopy published by John Wiley & Sons Ltd
CRS,[18,20-25] to overcome the diffraction limit given by Abbe.[26]All these methods are based on depleting one of the three scattering resources: the pump photons, the Stokes photons, or the molecules in the ground state. Although the depletion of one of the resources for the Raman process shows a high potential for super-resolution microscopy, there are a few drawbacks: Besides, a complex setup with three different beams included, high pulse energies in the order of 200–300 nJ are needed,[17-20,22] which besides damaging the sample introduce unwanted effects, like XPM, disturbing the measurable spectrum.
In the recent years, experimental as well as numerical studies have been published, showing the impact of XPM
in femtosecond stimulated Raman scattering
(FSRS).[27,28]Lim et al.[27]presented a combined numeri-cal as well as experimental study about the influence of XPM, dependent on the intensity and on the molecule under investigation for a potential super-resolution microscope. They found that the SRS lineshape became more distorted for increasing pulse energies and mate-rials with a higher nonlinear refractive index. Batignani et al.[28] investigated in a setup with three pulsed laser beams the delay dependent influences of XPM in FSRS with temporal steps of 50 fs, evaluated the effect theoreti-cally, and modeled the XPM artifacts to separate them from the real Raman signal.
However, the influence of the pulse duration, as a crucial parameter for self-phase modulation (SPM) and XPM[15,29,30]was not investigated in the above mentioned experiments. In this article, we investigate in detail the impact of XPM on FSRS for different pulse durations, dif-ferent intensities, and as a function of the temporal over-lap between the two interacting light pulses. Moreover, we investigate the influence of the nonlinear refractive index of the molecules under investigation. For this pur-pose, an FSRS-setup was realized in which the pulse duration could be adjusted across the relevant range (0.5–3 ps).
2
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B A S I C S
2.1
|
Femtosecond stimulated Raman
scattering
FSRS is a broadband version of SRS,[7,8,31] such that many molecular vibrational resonances can be probed by two interacting light fields at once. In SRS typically pico-second pulses are used for sufficient spectral resolution, whereas in FSRS, the combination of broadband femto-second and narrowband picofemto-second pulses are used to stimulate several Raman resonances simultaneously. The
spectral resolution in FSRS is determined by the narrow-bandwidth picosecond pulses. Typically, the weak and broadband pulses around the wavenumberωP are called
pump pulses and the strong and narrowband light pulses at the wavernumber ωS<ωP are called Stokes pulses. If
the energy differences between the pump and the Stokes pulse spectra match the energy of vibrational resonances Ωvib=ωP− ωS, energy is transferred from the pump to
the Stokes pulses. At resonance a stimulated Raman loss (SRL) of the pump at ωP and a stimulated Raman gain
(SRG) of the Stokes atωSare measurable. In general, the
wavenumber dependent change in the intensity of the pump and Stokes pulses can be written as
ΔIPðωÞ / −NσðωÞIPðωÞISðωÞ, ð1Þ
andΔISðωÞ / NσðωÞIPðωÞISðωÞ, ð2Þ
where N is the number of scattering targets, IPand ISthe
intensity of the pump and Stokes beam, respectively, and σ the molecule-specific Raman cross-section of a certain resonance. In FSRS, the change in intensityΔIP is
typi-cally measured for all wavelengths simultaneously by means of a spectrometer, resulting in a molecule-specific spectrum. We measured the SRL on the pump and used the following definition of an FSRS spectrum to minimize thermal artifacts:
SRLðλÞ =IPðΔt,λÞ−IPðΔt + τ,λÞ
IPðΔt + τ,λÞ : ð3Þ
Thus, in our work, an FSRS spectrum is defined as the normalized difference between a spectrum of the pump pulses overlapping in time IP(Δt,λ) with the Stokes pulses
and a spectrum of the pump pulses not overlapping in time IP(Δt + τ,λ) with the Stokes pulses.
2.2
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Cross-phase modulation
High intensity laser pulses propagating in a dieletric medium will change the refractive index n via the optical Kerr-effect:
nðtÞ = n0+ n2 IðtÞ, ð4Þ
where n0is the linear refractive index and n2= 3χ(3)/4n0
the nonlinear refractive index coefficient of the mate-rial.[29] The intensity dependent refractive index n2 I
leads to a temporally varying phase shift and results accordingly in a broadening of the pulse spectrum. If sin-gle laser pulses are involved, this phenomenon is called self-phase modulation (SPM).[32-34]
In high intensity pump probe experiments, like FSRS, the refractive index n of the medium changes like-wise via the optical Kerr effect (Equation 4). As two (or more) laser pulses are involved this effect is called cross-phase modulation (XPM), where the nonlinear refractive index coefficient is given by n2= 3χ(3)/2n0 for
parallel polarized light.[35,36] Note that n2 is two times
larger for cross-coupling (XPM) than for self-action (SPM) effects.[29]
In our case, the strong Stokes pulses change the refractive index n via the intensity dependent nonlinear refractive index n2 I and, therefore, the phase of the
weak pump pulses. A phase change of the strong Stokes pulses induced by the weak pump pulses is negligible as the intensity of the pump pulses is at least two orders of magnitude lower than the intensity of the Stokes pulses. The phase is connected to the instantaneous frequency of the light via the negative derivative with regard to time.[29]Therefore, for a positive n2, the leading edge of
high intensity pulses will induce an increasing phase, resulting in a decreasing frequency (red shift). Vice versa, the trailing edge of high intensity pulses will cause a blue shift,[15,37] which both will lead to a distortion of the Raman lineshape.
As mentioned above, XPM can be observed in FSRS due to the interaction of the weak pump and the strong Stokes pulses. The impact of XPM is increased at the Raman resonances, because the third-order susceptibility χ(3)
is approximately one order of magnitude larger at molecular vibrational resonances in comparison to off-resonance conditions.[38] Accordingly, an enhanced third-order susceptibility χ(3) leads to an increased n2
and, therefore, to a stronger impact of XPM, following Equation (4).
The higher n2 at the Raman resonance is probed,
for example, in femtosecond Raman-induced Kerr effect spectroscopy (FRIKES),[39-42] where the polariza-tion retardapolariza-tion via Raman-enhanced Kerr-induced birefringence is detected as an alternative pathway to measure Raman spectra.[40,42] However, the enhanced Kerr nonlinearity does support also nonlinear effects such as XPM and SPM, which are typically unwanted in Raman spectroscopy. XPM will become of relevance in FSRS, if ultrashort (<2 ps pulse duration) and/or high intensity light pulses (GW/cm2-regime) are used.[27]
3
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E X P E R I M E N T A L D E T A I L S
For the experiments presented in this article, a home-build FSRS-setup was used, as shown in Figure 1. The setup was based on a master-oscillator power-amplifier
(MOPA) emitting pulses with a duration of 330 fs at 1,033 nm center wavelength with a repetition rate of 1 MHz. The laser pulses were split into two copies with a polarizing beam splitter (PBS). In the first arm, a supercontinuum was generated by focusing pulses with a energy of approximately 450 nJ into a 4-mm-long gadolinium vanadate crystal (GdVO4). The resulting
pulses had a duration of approximately 500 fs and span the spectral range from 600 to 1600 nm, from which the part between 750 and 1,000 nm was used as pump pulses after bandpass-filtering by a short-pass (SP1) and a long-pass filter (LP). In the second arm, a folded Fourier filter, based on a transmission grating (1,200 lines/mm), a focusing mirror (FM, f = 500 mm), and a mechanical slit, was used to adjust the spectral width and center wavelength of the pump pulses. With this spectral filter, the Stokes pulse duration could be varied in the range between 0.5 and 3 ps, which is the relevant regime for the FSRS spectra shown later. Subsequently, the pump and the Stokes pulses were overlapped spatially and temporally at a dichroic mir-ror (DM) and focused into the sample by a lens (L3, f = 25 mm). The lens L4 (f = 25 mm) collected the transmitted light and guided it to a spectrometer, after filtering out the Stokes pulses by means of a short-pass filter (SP2).
With this experimental setup, we investigated the impact of XPM in dependence of the Stokes intensity (Section 4.1), the duration of the Stokes pulses (Section 4.2), the nonlinear refractive index of the mate-rial (Section 4.2), and the temporal overlap between the pump and the Stokes pulses (Section 4.3). All dependen-cies will be investigated and described in detail in the fol-lowing sections.
F I G U R E 1 Experimental setup to measure stimulated Raman loss (SRL) with different Stokes pulse durations. Master-oscillator power-amplifier (MOPA), polarizing beam splitter (PBS), lens (L), dichroic mirror (DM), short-pass filter (SP), gadolinium vandate crystal (GdVO4), sample (S), and a Fourier filter consisting of a
grating (G), focusing mirror (FM), mirror (M), and a tuning slit [Colour figure can be viewed at wileyonlinelibrary.com]
4
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E X P E R I M E N T A L R E S U L T S
4.1
|
XPM dependence on Stokes
intensity
In this section, the influence of the Stokes intensity dependent XPM distortion is investigated. Figure 2a shows the SRL spectra of the CH-stretch vibration of liquid
acetonitrile (ACN) for different Stokes pulse intensities. The Stokes pulse duration was chosen to be 0.75 ps, leading to a spectral resolution of 37 cm−1. The SRL signal increased linearly following Equation (1) for increasing Stokes intensities and lied in the range between 2% and 10% for Stokes pulse intensities between 11 and 55 GW/cm2, respectively. Furthermore, the spectral shape stayed nearly unaffected for Stokes pulse intensities of 11 and 16 GW/cm2 (two lower curves in Figure 2a), whereas for higher Stokes pulse intensities of 40 and 55 GW/cm2(two upper curves in Figure 2a) a notable change in the peak shape became visible. This change was related to the intensity-dependent impact of XPM and became visible as a negative SRL signal, mimicking SRG, on the high wavenumber side of the Raman resonance.
To conclude, both the FSRS signal and the impact of XPM increases for higher peak intensities, resulting in a trade-off between signal strength and spectral distortion. For this purpose a Stokes pulse intensity of 16 GW/cm2 was chosen in the subsequent experiments described in Sections 4.2 and 4.3, giving a slightly distorted FSRS sig-nal of up to 6 % in ACN, which enabled the investigations on XPM induced artifacts concerning the influence of the Stokes pulse duration, the nonlinear refractive index coefficient n2of the sample, and the pump-Stokes time
delay.
4.2
|
XPM dependence on Stokes pulse
duration and nonlinear refractive index
Figure 2b,c shows the SRL spectra of ACN and of a potas-sium yttrium tungsten (KYW) crystal, respectively. ACN and KYW were chosen to have one material with low and one material with a high nonlinear refractive index, which will be of importance later in this section. In these measurements, the Stokes pulse intensity was fixed and set to 16 GW/cm2, while changing the average intensity and the Stokes pulse duration between 0.5 ps and 3 ps. For a Stokes pulse duration of 3 ps the Raman resonances of ACN and KYW showed a Lorentzian line shape with a full width at half maximum (FWHM) of approx. 16 cm−1. The shorter Stokes pulses (0.5 to 2 ps) with the associated broader spectrum, led to a broadening of the spectral Raman response. Furthermore, the spectral line shape became distorted, becoming visible through alleged SRG on the high-wavenumber side of the Raman resonance. The distortion of the lineshape can be explained by the higher gradient of the temporal profile of shorter pulses, which leads to a larger phase shift and, therefore, to a higher impact of XPM for shorter pulse durations.[29,35]The line shape distortion became visible in the CH-stretch region of ACN as well as the fingerprint region of
F I G U R E 2 (a) Stimulated Raman loss (SRL) spectra in the CH-region of liquid acetonitrile for Stokes intensities in the range between 11 GW/cm2and 55 GW/cm2; (b) and (c) show the SRL
spectra around 2940 cm−1of ACN (low n2value) and around 860
cm−1for a KYW crystal (high n2value), respectively, for Stokes
pulse durations between 0.5 ps and 3 ps at a fixed peak intensity of 16 GW/cm2and a fixed temporal delay ofΔt = 0 [Colour figure can
KYW. However, when concentrating on the SRL spectra of both materials for a Stokes pulse duration of, e.g. 1 ps, the distortion due to XPM was more pronounced in KYW, which can be explained by the higher n2of KYW
compared to ACN. ACN, as a nonaromatic molecule, has a relatively low nACN
2 = 4.1 10−17cm
2
/W (at 800 nm[43]), whereas the n2of KYW is nKYW2 =ð2:1 0:3Þ 10−15 cm
2
/ W (at 790 nm[44]) and thus is at least two orders of magni-tude larger. From this difference in n2 and with taking
Equation (4) into account the stronger distortion of the spectral line shape for materials with a higher n2can be
explained.
From the measurements presented in Figure 2b,c, one can conclude that shorter pulse durations as well as a higher n2 of the material do lead to a stronger
distortion of the SRL spectra. As the n2 of the sample
under investigation is fixed and a certain intensity is necessary to generate a sufficient FSRS signal, the pulse duration turned out as a crucial parameter influencing the impact of XPM. The Stokes pulse dura-tion should be on the one hand short enough to gen-erate sufficient FSRS signal strength, but on the other hand as long as possible in order to minimize the impact of XPM.
4.3
|
XPM dependence on Pump-Stokes
time delay for different Stokes pulse
durations
As shown in the preceding subsection, XPM is highly dependent on the pulse duration of the Stokes pulses at fixed peak intensity. Furthermore, the temporal delayΔt between the interacting pump and Stokes pulses affects the influence of XPM. In principle, XPM is an instanta-neous effect which only occurs when both pulses do over-lap in time. However, if the pump pulses arrived at the sample slightly before the Stokes pulses (Δt < 0 in Figure 3), a delayed XPM effect around the Raman reso-nances could be measured, which can be explained by
nuclear motion attributed to molecular vibrations.[14,15,27] In order to investigate the time delay dependence, SRL spectra were acquired for a constant peak intensity of 16 GW/cm2 and different time delays between the pump and the Stokes pulses for ACN (Figure 3). Please note, that different colorbars were chosen in Figure 3a–e to clearly visualize the spectral evolution. Figure 3a shows SRL spectra free of XPM artifacts for a Stokes pulse dura-tion of 3 ps and a varying temporal overlap, which is in accordance with the experimental results shown in Figure 2. The spectral resolution for Stokes pulses of 3 ps is approximately 16 cm−1. For shorter pulse durations (<2 ps), a broadening of the spectral Raman response aroundΔt = 0 became visible and increasing artifacts due to XPM showed up, mimicking SRG. Furthermore, the asymmetry with respect to the temporal delay got more and more pronounced for shorter Stokes pulse durations. Especially for pulse durations of less than 1 ps, a strong spectral modulation atΔt < 0 became visible, which can be explained by the instantaneous frequency shift induced by XPM[14,15,27,28] (red-shift for Δt < 0). For the two shorter Stokes pulses (0.5 ps and 0.75 ps), the ampli-tude of the spectral modulation was in the same order as the signal of the Raman resonance itself, which made it impossible to determine the precise spectral position of the Raman resonance (see also the extracted slices forΔt = 0 in Figure 2b,c).
The measurements with different Stokes pulse dura-tions and varying temporal delay Δt clearly show that XPM does play a major role for pulses with a duration of less than 2 ps. Furthermore, an asymmetry with respect to the temporal delay became visible, which could not be eliminated by simple time integration as suggest in previ-ous experimental studies.[15,45]In order to measure spec-tra with a reduced specspec-tral distortion induced by XPM a slightly positive temporal offset between the Stokes and the pump pulses (Δt > 0, i.e. the Stokes pulses do precede the pump pulses) should be set, which was also identified by Lim et al.[27]A study by Hoffmann et al.,[46] investigat-ing the influence of the temporal shape of the Stokes
F I G U R E 3 Measured delay dependent SRL spectra of
acetonitrile (low n2) for Stokes pulse
durations between 0.5 and 3 ps at a fixed peak intensity of 16 GW/cm2.
The Stokes pulses preceded the pump pulses forΔt > 0. Different colorbar scales were chosen to clearly visualize the spectral evolution [Colour figure can be viewed at wileyonlinelibrary.com]
pulses on the FSRS signal, underlines the presented results. In their study, the Stokes pulses were tailored by a Fabry-Pérot etalon with a matching free-spectral range and dielectric coating, resulting in ps-pulses with a steep rising and a slow trailing edge. This temporal shaping shifts the main contribution of the Stokes pulses to a pos-itive time delay in order to reduce spectral distortions. This reduction is agreement with our results; however, adjusting the available delay only by an appropriate amount is even simpler and cheaper as using an addi-tional etalon.
5
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S U M M A R Y A N D C O N C L U S I O N
In this paper, an experimental study investigating FSRS spectra for different Stokes pulse characteristics was pres-ented, as the identification of molecules using FSRS is complicated by XPM between the interacting pump and Stokes pulses. The peak intensity and the duration of the Stokes pulses, the nonlinear refractive index coefficient n2of the sample as well as the temporal overlap between
the pump and Stokes pulses were varied. It could be shown that the influence of XPM is reduced for lower Stokes pulse intensities and got negligible in our experi-ments in the regime of less than 16 GW/cm2. The investi-gations on varying the Stokes pulse duration showed FSRS spectra with less or negligible XPM artifacts for pulse durations in the regime of 2 to 3 ps. Furthermore, a sample with a larger value of n2showed a higher impact
of XPM in comparison to a sample with a lower value of n2 at a fixed peak intensity and fixed pulse duration of
the Stokes pulses.
The investigations lead to the following general con-clusions: the spectral distortion by XPM in FSRS is reduced for lower peak powers, longer pulse durations, low nonlinear refractive index materials and the Stokes pulses should slightly precede the pump pulses.
A C K N O W L E D G E M E N T
Open access funding enabled and organized by Projekt DEAL.
O R C I D
Thomas Würthwein https://orcid.org/0000-0002-3270-653X
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How to cite this article: Würthwein T,
Lüpken NM, Irwin N, Fallnich C. Mitigating cross-phase modulation artifacts in femtosecond
stimulated Raman scattering. J Raman Spectrosc. 2020;51:2265–2271.https://doi.org/10.1002/jrs.5958
