Third-order nonlinear femtosecond optical gating through highly scattering media Ma mouna Bocoum Institut Langevin ESPCI Paris Universit e PSL CNRS 75005 Paris France

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Third-order nonlinear femtosecond optical gating through highly scattering media

Ma¨ımouna Bocoum∗

Institut Langevin, ESPCI Paris, Universit´e PSL, CNRS, 75005 Paris, France

Zhao Cheng,†Jaismeen Kaur,‡and Rodrigo Lopez-Martens§

Laboratoire d’Optique Appliqu´ee, CNRS, Ecole Polytechnique, ENSTA Paris,

Institut Polytechnique de Paris, 181 chemin de la Huni`ere et des Joncherettes, 91120, Palaiseau, France

(Dated: October 25, 2022)

Discriminating between ballistic and diﬀuse components of light propagating through highly scat-

tering media is not only important for imaging purposes but also for investigating the fundamental

diﬀusion properties of the medium itself. Massively developed to this end over the past 20 years,

nonlinear temporal gating remains limited to ∼10−10 transmission factors. Here, we report non-

linear time gated measurements of highly scattered femtosecond pulses with transmission factors as

low as ≈10−12 . Our approach is based on third-order nonlinear cross-correlation of femtosecond

pulses, a standard diagnostic used in high-power laser science, applied for the ﬁrst time to the study

of fundamental light scattering properties.

When an ultrashort light pulse propagates through a

scattering medium, its intensity undergoes an exponen-

tial decrease with ballistic propagation quantiﬁed by the

scattering coeﬃcient µs. Simultaneously, a slower dif-

fused component of light rises, withholding additional

information about the medium. In a transmission conﬁg-

uration, temporal gating of the ballistic component may

be exploited for shadow imaging [1] or to simply extract

of µsfrom the attenuation e−µsLfactor [2, 3], where

Lis the length of the medium. In the highly scatter-

ing regime, where propagation is described by a diﬀu-

sion equation [4], ﬁtting the temporal shape of either the

transmitted of reﬂected light at longer times (ps) pro-

vides a measure of the diﬀusion coeﬃcient D=ve/(3µ0

s),

where veis the energy velocity [5] and µ0

sthe inverse of

the transport mean free path [4]. Measuring both µsand

µ0

sis crutial to fully characterize a scattering media as

they are related by the relation µ0

s=µs(1−g), where gis

the anisotropy which quantiﬁes the directionality of the

scattering process. Although direct measurements of µ0

often rely on the use of coherent back-scattering (CBS)

techniques [6, 7] or photonic Ohm-law static transmis-

sion [8], time gating methods may also be applied to the

characterization of biological samples or scattering phan-

toms whenever the value of veis known [9, 10]. The

main advantage of temporal gating over CBS is its sen-

sitivity to Dover time as opposed to µ0

sonly, hence the

additional information it provides about the spatial or

spectral behavior of the scatterers inside the medium. In

the early 2000s, temporal gating was for instance used to

demonstrate the transition from diﬀuse to localized prop-

agation states when µ0

s∼λ−1[11], where λdesignates

the wavelength of the scattered light. Although this in-

terpretation has since been subject to debate and most

∗maimouna.bocoum@espci.fr

†zhao.cheng@ensta-paris.fr

‡jaismeen.kaur@ensta-paris.fr

§rodrigo.lopez-martens@ensta-paris.fr

likely attributable to ﬂuorescence [12], temporal gating

remains a powerful experimental tool for exploring devi-

ations from classical diﬀusion behavior and their link to

the mesoscopic topology of the scattering medium [13–

16].

We often undermine how crucial the choice of tem-

poral detection method is relative to the application or

sample properties. Coherent gating either in the tem-

poral [17, 18] or spectral domains [15, 19] has been ex-

tensively used to probe the temporal dynamics of mul-

tiply scattered light. The measured quantity however is

not the averaged diﬀused intensity by the medium but

rather its temporal (Green function) [18] or spectral re-

sponse (transfer function) [15, 19] for one realization of

disorder. Probing the diﬀusion properties of a given scat-

tering medium therefore requires averaging over multi-

ple realizations of disorder [1, 15, 20]. In addition, the

bandwidth of the measured transfer function is limited

by that of the illumination source [20], and the maxi-

mum measurable time window either by the excursion of

the delay stage used for temporal measurements or by

the resolution of the spectrometer in the case of spectral

measurements. This limitation is extremely problematic

because non-classical propagation behavior such as local-

isation eﬀects [21–23] are expected for very long delays

and low transmission factors. To circumvent this exper-

imental diﬃculty, one must rely on incoherent temporal

detection that is sensitive to the intensity of the scattered

light.

Historically, such time-resolved experiments were

based on streak camera gating [24–27], but the linear

dynamic range of digital sensors makes it inadequate

for temporal acquisitions with log-variation in time.

Single-photon counting detectors oﬀer excellent sen-

sitivity but feature limited temporal resolution, such

that temporal traces have only been reported in the

nanosecond range [9, 11]. In a transmission measurement

where the spreading of the incident pulse scales with the

Thouless time τl=L2/D [28], the scope of investigation

is therefore restricted to highly scattering phantoms

arXiv:2210.13165v1 [physics.optics] 24 Oct 2022

such as solid powders [11, 29], unresembling biological

tissues or diluted phantoms, unless the measurement

is performed in (less precise) semi-inﬁnite reﬂection

conﬁguration [9, 30].

The 1990s witnessed the emergence of nonlinear tem-

poral gating techniques with femtosecond laser pulses [2,

3, 31–33], combining both high temporal resolution and

high dynamic detection range. Although techniques such

as second harmonic generation (SHG) gating [33] or opti-

cal Kerr gating (OKG) [2, 3, 31] are very eﬃcient to probe

complex media, the lowest transmission factor reported is

∼10−10 [2, 34], which is still too high for characterizing

fat emulsions in transmission. In this work, we show how

third-harmonic generation (THG), a standard technique

in high-power laser science with sensitivities of ∼10−12

or higher, can be used to characterize a highly scattering

slab in transmission. Although comparable sensitivities

have been reported using state-or-the-art setups based

on optical parametric ampliﬁcation or even SHG in one

case [35, 36] could in principle reach similar sensitivities,

our approach oﬀers immediate access to this record level

of sensitivity using almost the highest dynamic range ac-

cessible today, all this using a commercially available de-

vice that anybody can buy and operate. We illustrate

this by performing the ﬁrst simultaneous measurement

of both the scattering coeﬃcient, µs, and reduced scat-

tering coeﬃcient, µ0

s, of a fat emulsion in a transmission

geometry.

THG cross-correlators were originally developed to di-

agnose unwanted pedestals, pre-pulses or ampliﬁed spon-

taneous emission (ASE) on the picosecond-to-nanosecond

timescale surrounding the peak of ultra-intense fem-

tosecond laser pulses [37–40], and can reach up to

1013 dynamic range in the near-IR (NIR) spectral re-

gion [39, 41, 42]. In our experiment, we use a commercial

all-reﬂective third-order cross-correlator (Tundra, Ultra-

fast Innovations GmbH) featuring 1012 dynamic detec-

tion range. A schematic representation of the cross-

correlator setup is shown in Fig 1(c). S-polarized 30fs

input pulses, centered at 790 nm, with 400 µJ energy,

are sent into the device at 1 kHz repetition rate. Each

pulse is separated into a probe and a gate pulse with a

5-95%-beamsplitter. The 20 µJ probe pulse of ≈5 mm

in diameter is attenuated using variable calibrated reﬂec-

tivity mirrors (RA in Figure 1) so as to keep the PMT

response linear. The pulse is then sent through the scat-

tering medium, located in between two long-range delay

lines, while the gate pulse undergoes type I SHG in a

BBO crystal to generate a P-polarized SHG gate pulse

centered at 2ω, where ωis the central laser frequency.

The SHG gate pulse is ﬁltered out from the residual

NIR pulse using dichroic mirrors, converted back to S-

polarization with a periscope and mixed with the time-

delayed S-component of the scattered pulse in a type I

THG crystal to generate the cross-correlation signal at

3ω. The cross-correlation trace is obtained by recording

the spatio-spectrally ﬁltered 3ωsignal with a solar blind

FIG. 1. (a) THG cross-correlation measurement of the in-

put NIR laser pulse proﬁle, normalized to its peak inten-

sity. (ASE: Ampliﬁed Spontaneous Emission);(b) calculated

square-root of the measured temporal NIR pulse proﬁle (c)

THG cross-correlator setup. M1,M2,M3,M4: Silver mirrors.

BS: beamsplitter. RA: reﬂective attenuator set. DM: dichro¨ıc

mirror. P: Periscope SHG: Second Harmonic generation crys-

tal. THG: Third harmonic generation crystal. SM: Spherical

focusing mirror. Retro-reﬂectors are mounted on two high-

stability delay stages. PMT: Photo-multiplier tube

photo-multiplier tube (PMT) as a function of delay be-

tween scattered and gate pulses, with a maximum delay

of up to ±2 ns and ∼100 fs temporal resolution at best.

Each data point is an average of 100 consecutive shots

recorded in 100 fs time steps, except for the range span-

ning from -10 ps to +10 ps, where data are recorded in

10 fs time steps. A typical cross-correlation trace of the

(unscattered) input laser pulse is shown in Figure 1(a)

over a 350 ps time window around the pulse peak. A de-

tection noise ﬂoor of ∼10−12 can indeed be measured by

blocking the ωprobe arm at early times in the trace. The

key to noise reduction in THG cross-correlators is the

very low level of self-generated signal leaking from either

arms of the optical setup into the 3ωdetector [38, 41].

To demonstrate the potential of a ∼10−12 sensitiv-

ity for the detection of diﬀused light, we characterized

the scattering properties of a commercial intralipid-10%

emulsion used in previous scattering experiments [43].

Fat emulsions are extensively used as light scattering

models or as phantoms for biological applications [43, 44].

The reason is an accessible price, low absorption (µa

µs), scalability of scattering properties with dilution, and

the spherical shape of the fat droplets, which makes them

easy to model using Mie theory. Despite this, measuring

their scattering properties remains a challenge and diﬀer-

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Third-ordernonlinearfemtosecondopticalgatingthroughhighlyscatteringmediaMamounaBocoumInstitutLangevin,ESPCIParis,UniversitePSL,CNRS,75005Paris,FranceZhaoCheng,yJaismeenKaur,zandRodrigoLopez-MartensxLaboratoired'OptiqueAppliquee,CNRS,EcolePolytechnique,ENSTAParis,InstitutPolytechniquedeParis,181...

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Third-order nonlinear femtosecond optical gating through highly scattering media Ma mouna Bocoum Institut Langevin ESPCI Paris Universit e PSL CNRS 75005 Paris France

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