Vage Karakhanyan

Clément Eustache
email: clement.eustache@femto-st.fr

Yannick Lefier
email: yannick.lefier@gmail.com

Thierry Grosjean
email: thierry.grosjean@univ-fcomte.fr

Inverse Faraday effect from the orbital angular momentum of light

It is usually admitted that the inverse Faraday effect (IFE) originates from the spin angular momentum (SAM) of light. In this paper, we evidence that part of the IFE in a metal is induced by the orbital angular momentum (OAM) of light. On the basis of a hydrodynamic model of the conduction electron gas, we describe the dependence of the IFE on the spin and orbital angular momenta as well as spin-orbit interaction in a non-paraxial light beam. We also numerically quantify the relative contributions of the SAM and OAM of light to the IFE in a thin gold film illuminated by different focused beams carrying SAM and/or OAM. The OAM of light provides a new degree of freedom in the control of the IFE and resulting optomagnetic field, thus potentially impacting various research fields including all-optical magnetization switching and spin-wave excitation.

I. INTRODUCTION

Light is known to possess polarization and spatial degrees of freedom, manifested by its linear momentum as well as spin and orbital angular momenta [1]. Remarkably, the spin angular momentum (SAM) of light can be transferred to electrons in matter, a phenomenon which refers to as the inverse Faraday effect (IFE) [2][3][4]. The inverse Faraday effect (IFE) has attracted much attention for its ability to generate light-induced magnetization, thereby opening the prospect of an ultrafast magnetic data storage [5][6][7][8] and a non-contact excitation of spinwaves [9][10][11][12][13]. Plasmonic nanostructures have recently been investigated to locally enhance and control the IFE in non-magnetic metals [14][15][16][17][18][START_REF] Lefier | Etudes du couplage spin-orbite en nanophotonique. applications à l'excitation unidirectionnelle de modes plasmoniques guidés et à la génération d'optoaimants nanométriques contrôlables par l'état de polarisation de la lumière[END_REF][START_REF] Nadarajah | [END_REF][21][22][23][24] and in hybrid structures including magnetic materials [25][26][27][28][29][30].

So far, the orbital counterpart of the spin-based IFE has been hardly addressed. To our knowledge, an optomagnetism induced by the OAM of light has not been reported yet. As a first evidence of the interaction of magnetism and OAM of light, Sirenko et al showed a vortex beam dichroism in a magnetized material at THz frequencies [31]. Note that an OAM-dependent IFE has been evidenced in the case of a paraxial vortex light beam propagating in a plasma [32]. More generally, the transfer of optical OAM to matter has been shown to create a torque in absorbing micro-particles [33][34][35][36] and inorganic ionic nanofilms [37], forces and torque in a dielectric medium [38,39], as well as spin and charge transport in topological insulators [40]. The OAM of light can also be coupled to the total angular momentum of an electron vortex beam [41]. The OAM of light and its combination to the optical SAM holds promise of new opportunities and strategies in tailoring optomagnetic effects [42].

In this paper, we provide a spin and orbital angular momentum representation of the IFE in a metal. In the case of axisymmetrical optical systems (including vortex beams), we analytically show the role of the SAM and OAM of light, as well as spin-orbit interaction (SOI), in the generation of an opto-induced magnetization. We find that the SAM contributes to the IFE only in nonparaxial optical beams (carrying noticeable longitudinal light fields), whereas the OAM has a non negligible contribution even in the paraxial optical regime. Finally, we numerically quantify the spin and orbital parts of the IFE in a thin gold film under illumination with different focused beams carrying SAM and/or OAM. We numerically confirm the importance of the SOI of light in the IFE and resulting optomagnetic field, which manifests via SAM-to-OAM or OAM-to-SAM conversions at focus.

II. MODEL DESCRIPTION

In a hydrodynamic approach, the conduction electron dynamics in a metal can be described from the Euler's equation [43,44]:

m e ∂v ∂t +m e (v•∇)v = - m e τ v+eE+µ 0 ev×H-m e β 2 n ∇n.
(1) where m e , n, τ and v are the effective mass, the conduction electron fluid density, the collision time and velocity of the conduction electrons, respectively. E and H are the applied electric and magnetic optical fields. The last term in Eq. ( 1) is due to the electron gas pressure, with β proportional to the Fermi velocity v F . µ 0 and e are the permeability of free space and the elementary charge, respectively. E(r, t), H(r, t), v(r, t), n(r, t) are time and space dependent variables. n and j satisfy the continuity equation:

∇ • j = -e ∂n ∂t , (2)
where j = nev = ∂P/∂t is the current density and P is the polarization density vector. Eq. ( 2) can be rewritten as:

n(r, t) = n 0 - 1 e ∇ • P, (3)
where n 0 is the background, equilibrium charge density in the absence of any applied fields.

Assuming that the time variation of the conduction electron fluid density is relatively small (i.e., ṅ << n), the ratio ṅ/n may be expanded in powers of 1/(n 0 e):

ṅ(r, t) n(r, t) = - 1 n 0 e ∇ • Ṗ 1 - 1 n 0 e ∇ • P -1 ≈ - 1 n 0 e ∇ • Ṗ 1 + 1 n 0 e ∇ • P . (4)
Thus, we have:

ṅ(r, t) n(r, t) ≈ - 1 n 0 e ∇ • Ṗ - 1 n 2 0 e 2 (∇ • P)(∇ • Ṗ).
(

) 5
By applying the above-described assumptions in Eq. ( 1), we find [44,45]:

∂j ∂t + j τ = e 2 n 0 m e E -eβ 2 ∇n - e m e (∇ • P) E+ + µ 0 e m e j × H - 1 en 0 [(∇ • j) j + (j • ∇)j] (6)
.

III. TIME HARMONIC REGIME

In the time harmonic (i.e., monochromatic) regime, the electric and magnetic optical fields become E = E ω (r)e -iωt +c.c and H = H ω (r)e -iωt +c.c, where ω is the angular frequency, t is time, c.c is the complex conjugate. To predict both the linear and nonlinear responses of the metal, we solve Eq. ( 6) using a perturbation approach. To this end, the current density j is written as:

j = (j ω e -iωt + c.c) + j NL . (7)
j ω and j NL are the linear and nonlinear contributions to the current density, respectively. In the following, we focus on the nonlinear optical process defined by the drift current density j d = j NL where the operator denotes time averaging. j d originates from an optical rectification process [46]. Because j NL is small as compared to j ω , the perturbation method turns Eq (6) into the following couple of equations:.

j ω = γ ω E ω -eβ 2 ∇n, (8)
j d = - τ n 0 e Re γ 0 i ωτ (∇ • j ω )E * ω + (∇ • j ω ) j * ω + +(j ω • ∇)j * ω -µ 0 γ 0 j ω × H * ω , (9)
where

γ ω = γ 0 1 -iωτ , (10)
and

γ 0 = n 0 e 2 τ m e , (11)
are the linear (i.e., dynamic) and DC conductivities, respectively. This system of equations describes both the linear and nonlinear (rectification) responses of a material to an optical field. It can be numerically solved using for instance the two-fluid plasma model solver [47]. However, these solvers require high computational power and are time consuming.

IV. INVERSE FARADAY EFFECT

Assuming that the optical response of a metal is mainly driven by its conduction electrons, the IFE can be described by the orbital magnetization defined as:

M = 1 2V V LdV, (12)
where:

L = r × j d , (13)
is the opto-induced local orbital angular momentum in the conduction electron gas. In that case, the IFE directly depends on the opto-induced drift current density in the metal.

A. IFE in the metal bulk

The last terms of Eqs. ( 1) and ( 8) both describe nonlocal effects in the metal. In the case of smooth and slowly varying charge densities n, it is possible to neglect nonlocal effects (i.e., considering β → 0) and take into account only the local response [45]. This local response approximation simplifies the resolution of Eqs. ( 8) and (9) [21,48]. It is however only valid within the metal bulk. The extension of the local approximation method to metal surfaces will be addressed in section IV B.

In the framework of a local response approximation, Eqs. ( 8) and (9) become:

j ω = γ ω E ω , (14)
and

j d = - τ n 0 e Re i ωτ (∇ • j ω )j * ω + (j ω • ∇)j * ω - µ 0 γ 0 τ j ω × H * ω , (15)
respectively. Using the following vector identity:

(j ω • ∇)j * ω = j ω • ∇j * ω -j ω × (∇ × j * ω ), = j ω • ∇j * ω + iωµ 0 γ * j ω × H * ω , (16)
Eq. ( 15) becomes:

j d = - τ n 0 e 1 ωτ Im (∇ • j ω )j * ω + + Re j ω • ∇j * ω - µ 0 |γ ω | 2 τ Re E ω × H * ω . (17)
When the spatial variation of γ ω are small enough to be neglected, Eq. ( 17) reads:

j d = - |γ ω | 2 n 0 e 1 ω Im (∇ • E ω )E * ω + + τ Re E ω • ∇E * ω -µ 0 Re E ω × H * ω . (18)
Using vector identities and Maxwell's equations, Eq. ( 18) can be rewritten as:

j d = |γ ω | 2 n 0 eω - τ ω 2 ∇ |E ω | 2 + Im [E * ω • ∇E ω ] + 1 2 ∇ × Im[E * ω × E ω ] (19)
According to Refs. [49,50], the last two terms of Eq. ( 19) represent the orbital and spin parts of the timeaveraged Poynting vector Π = Re [E ω × H * ω ], respectively. We have:

Π = Π orb + Π spn , (20)
where [49,[51][52][53]. The opto-induced drift current density in the metal bulk becomes:

Π orb = Im [E * ω • ∇E ω ] and Π spn = ∇×S. Vec- tor S = Im[E * ω × E ω ] is proportional to the SAM density of light
j d = j ig d + j orb d + j spn d , (21)
where,

j ig d = - τ |γ ω | 2 2n 0 e ∇|E ω | 2 , (22)
j orb d = |γ ω | 2 n 0 eω Π orb , (23)
j spn d = |γ ω | 2 2n 0 eω Π spn = |γ ω | 2 2n 0 eω ∇ × S. (24)
The opto-induced drift current density thus combines three source terms (Eq. ( 21)). Term j ig d is linked to the so-called intensity-gradient force [54,55] that is central in optical tweezing applications [56]. The other two source terms are related to the orbital and spin parts of the Poynting vector.

In the monochromatic regime, the linear momentum of light is proportional to the time averaged Poynting vector [49,51]. Eqs. ( 23) and ( 24) thus describe momentum transfer from light to the conduction electrons in a metal, leading to an optical drag effect [57]. Π orb and Π spn are thus proportional to the canonical (orbital) and spin momentum densities of light, respectively. When vector-multiplied by r, the source terms of Eqs ( 23) and (24) give the orbital and spin contributions to the angular momentum L of the conduction electron gas, respectively [49,50]. The local angular momentum (Eq. ( 13)) and resulting orbital magnetization (Eq. ( 12)) of the conduction electrons then read:

L = r × j ig d + r × j orb d + r × j spn d , (25)
and

M = M ig + M orb + M spn , (26)
respectively. M ig , M orb and M spn are the intensitygradient, spin and orbital contributions to the IFE, respectively. We have M id = 1/(2V ) V r × j id d dV , where "id" stands for "ig", "orb" and "spn". Therefore, the IFE does not solely originate from the SAM of light. Eq. (26) shows that part of the IFE in the metal bulk relies on the transfer of OAM from a light beam to the conduction electron gas of a metal. It appears from Eqs. ( 23) and ( 26) that the orbital part of the IFE relies on an axissymmetrical optical drag effect induced and controlled by the OAM of light.

B. IFE at metal surfaces

As previously stated, the local approximation approach used to analytically solve Eqs. ( 8) and ( 9) is only valid within the metal bulk. To overcome ambiguities of this simplified model at metal interfaces (where strong variations of the electron fluid density occur), an analytical method has been proposed to describe opto-induced surface currents [23,24,45,[58][59][60]. This method brings a non-local correction to the local response approximation at metal surfaces.

The idea is to define a thin metal layer beneath interfaces, whose thickness matches Thomas-Fermi length (λ T F 0.1 nm for noble metals). This layer is considered to be a "surface layer", where the electron gas pressure and the spatial variations of the conductivity are not negligible. Out of this layer, in the metal bulk, the local model applies (β → 0). Within the interface layer, the component j T ω of the linear current density that is locally parallel to the surface preserves whereas the normal component j N ω decays to zero. This additional boundary condition on j N ω , which is required to solve the nonlocal problem, is attributed to a neglected electron "spill-out" at interfaces [45].

We define ρ as the spatial coordinate normal to the surfaces so that the metal bulk is located at ρ < 0 and the surface layer corresponds to 0 < ρ < λ T F . In that case, we have in the surface layer j T ω (ρ) ≈ j T ω (0 -) and

j N ω = j N ω (0 -)σ(ρ)
, where σ is a decaying function defined by [45]. σ is the derivative with respect to ρ. The σ(ρ) function has the following useful properties:

λ T F 0 σ (ρ)dρ = -1
λ T F 0 σ(ρ) m σ (ρ)dρ = - 1 m + 1 , (27)
λ T F 0 σ(ρ) m dρ = 0. (28)
This non-local correction is applied by redefining the linear conductivity of the metal as a tensor. The linear current density (cf. Eq. ( 14)) then becomes:

j ω =   γ ω 0 0 0 γ ω 0 0 0 γ ω σ(ρ)     E T 1 E T 2 E N   (29)
where E T 1 , E T 2 and E N are the vector components of the optical electric field that are transverse and normal to the interfaces. Finally, the opto-induced drift current density at metal surfaces is deduced by replacing j ω in Eq. ( 17) by its expression given in Eq. ( 29).

V. IFE IN AXISYMMETRICAL OPTICAL SYSTEMS

We now focus on axisymmetrical optical systems where both the metal structure and light intensity are axially symmetric. In that case, the IFE mainly involves a magnetization oriented along the symmetry axis [21,23,48]. The azimuthal component [j d ] ξ of the drift current density (in the cylindrical coordinates (r, ξ, z)) then becomes the main contributor to the IFE (see Eqs. ( 12) and ( 13)).

Since ∇ ξ |E ω | 2 =0 in light beams showing axissymmetrical intensity, j ig d has no contribution to the IFE in axis-symmetrical optical systems (i.e., [j ig d ] ξ = 0). Only the orbital and spin parts of the opto-induced drift current density are now involved (cf. Eqs. ( 23) and ( 24), respectively). The angular momentum of the conduction electron gas now reads:

L = r × j orb d + r × j spn d , = |γ ω | 2 n 0 eω r × Π orb + r × Π spn . (30)
In the following, we consider the incoming light to be a Laguerre-Gauss vortex beam described by a polarization helicity s (-1 ≤ s ≤ 1) and a topological charge l [61-63], respectively. Laguerre-Gauss beams fulfill the cylindrical symmetry condition required to cancel the contribution of the intensity-gradient source term j ig d .

A. IFE in the metal bulk

From Eq. ( 19), we find that the azimuthal component of the drift current density within the metal bulk reads:

[j d ] bulk ξ = κ l + s r |E ω | 2 - 2 r S z + κ ∂S r ∂z - ∂S ξ ∂r (31) = j orb d bulk ξ + [j spn d ] bulk ξ , (32)
where κ = |γ ω | 2 /(n 0 eω). S r , S ξ , S z are the components of the SAM density S of light in cylindrical coordinates. We have

S r = Im[E * ξ E z ], S ξ = Im[E * z E r ] and S z = Im[E * r E ξ ].
The first term of Eq. ( 31), namely:

j orb d bulk ξ = κ l + s r |E ω | 2 - 2 r S z (33) = κ r l|E ω | 2 + s|E ω | 2 -2S z (34)
refers to the azimuthal component of j orb d (cf. Eq. ( 23)). This part of the opto-induced drift current density evidences the contribution to the IFE of the OAM of the light within the metal.

The second term of Eq. ( 31):

[j spn d ] bulk ξ = κ ∂S r ∂z - ∂S ξ ∂r . ( 35
)
describes the spin part of the IFE. Therefore, in an axis-symmetrical optical problem, our model suggests that the IFE in the metal bulk relies on both the SAM and OAM of light. From Eq. ( 34), the OAM manifests itself via the topological charge l of the incoming vortex beam and as an intermediate between the SAM of light and the OAM of the electron gas, via optical SOI (see section V C).

B. IFE at metal surfaces

In the following, we consider the opto-induced drift current density at the surfaces perpendicular to (0z). We thus have ρ = ±z, where ρ is defined in section (IV B). From section (IV B) and Eqs. (33) and (35), the orbital and spin parts of the azimuthal drift current density at metal surfaces read:

j orb d surf ξ = κ l + s r |E | 2 - 2 r S z (0 -) , (36)
and

[j spn d ] surf ξ = κ ∂σ(ρ)S r (0 -) ∂ρ - ∂σ(ρ)S ξ (0 -) ∂r , (37)
respectively. We have

|E | 2 = E r (0 -)E * r (0 -) + E ξ (0 -)E * ξ (0 -).
The definition of the optical electric field within the surface layer follows that of the linear current density (see section IV B). We have

E T ω (ρ) ≈ E T ω (0 -) and E N ω (ρ) = E N ω (0 -)σ(ρ)
. We now define i s ξ as the linear density of the surface current. We have:

i s ξ = λ T F 0 [j spn d ] surf ξ + j orb d surf ξ dρ (38)
Using Eqs. ( 27) and (28), we find:

i s ξ = κ l + s r |E | 2 λ T F - 2λ T F r S z (0 -) -S r (0 -) . ( 39
)
The terms containing λ T F being negligible, we finally obtain:

i s ξ -κS r (0 -), (40)
where S r (0

-) = Im[E * ξ (0 -)E z (0 -)].
At metal surfaces, the IFE is mainly driven by the radial component of the SAM of light.

C. Paraxial approximation, spin-orbit interaction

In the paraxial approximation, the optical field is considered to be purely transverse (E z = 0) and the SAM of light reduces to S z = s/2|E ω | 2 (S r = S ξ = 0) [51]. In that case, the second term (in brackets) of Eq. ( 34) vanishes, leading to:

j orb d bulk ξ = κ r l|E ω | 2 . ( 41
)
The second term of Eq. ( 34) thus analytically describes the spin-dependence of the OAM of light in nonparaxial beams, by virtue of SOI (SAM-to-OAM conversion) [64,65]. We will numerically see in section VI that SOI (OAM-to-SAM conversion) is also inherent in the spin part of the IFE (cf. Eq. ( 35)).

The spin part of the IFE being dependent on S ρ and S ξ (see Eqs. (35) and ( 40)), the contribution of the SAM of light to the IFE vanishes in the paraxial optical regime. According to our model, the IFE induced by paraxial optical beams is solely driven by the OAM of light, which manifests via the topological charge l.

Such a property is consistent with the fact that in the paraxial approximation, the orbital momentum of light (proportional to Π orb ; at the origin of the OAM) is the only observable contribution to the optical momentum [49,51]. The orbital momentum is here proportional to the wave vector of the optical field and is solely responsible for energy transport [49]. The spin momentum (proportional to Π spn ; at the origin of the SAM) represents a solenoidal current, which does not contribute to energy transport [49,51]. In paraxial approximation, the spin momentum has no observable contribution to the IFE in a metal.

VI. OPTOMAGNETISM IN A THIN GOLD LAYER

To estimate the relative contributions of the SAM and OAM in the IFE and resulting optomagnetic field, we simulate the optomagnetic response of a thin gold film under illumination with single focused light beams carrying SAM and/or OAM.

A. Design and theory

The configuration under study is shown in Fig. 1. A 20-nm thick gold layer lies on a semi-infinite glass substrate. An incoming vortex beam of topological charge l, polarization helicity s, and of Gaussian or Laguerre-Gaussian profile is focused onto the backside of the gold film, in the substrate. The 1/e width of the beam waist coincides with the pupil diameter of the microscope objective. Operating in the immersion regime, the objective shows a numerical aperture N A of 1.3. On the basis of the theory established by Richards and Wolf [66,[START_REF] Novotny | Principles of nano-optics[END_REF], the optical electric field at focus can be written as:

E(r, ξ, z) = - ik 1 f exp[-ik 1 f ] 2π 1 √ n 1 × θ M 0 cos 1 2 (θ) sin(θ)F (θ) 2π 0 e(θ, ψ, z) exp [iαr cos(ψ -ξ)] dθdψ, (42)
where (r, ξ, z) are cylindrical coordinates, f is the focal length of the microscope objective, θ and ψ are directional angles and α is a function of θ. We have θ M = arcsin(N A/n 1 ), where n 1 is the refractive index of the substrate. The (0z)-axis matches the symmetry axis of the microscope objective and is perpendicular to the metal surfaces (see Fig. 1).

Vector e(θ, ψ, z) takes the form:

e(θ, ψ, z) = exp[ilψ]   E s t s (z) sin ψ -E p t r p (z) cos θ cos ψ -E s t s (z) cos ψ -E p t r p (z) cos θ sin ψ E p t z p (z) sin θ   (43
) For circular polarization (s = ±1), we have:

E s = -is( √ 2/2) exp[isψ], (44)
E p = -( √ 2/2) exp[isψ], (45)
The apodization function at the exit pupil plane of the microscope objective reads:

F (θ) = 2 w 0 Z 0 P 0 π|l|! √ 2f sin θ w 0 |l| exp -f 2 sin 2 θ w 2 0 , (46) with
:

w 0 = f sin θ M , if l=0, (47)
w 0 = f sin θ M (2|l|) 1 2 , if |l| ≥1. (48)
P 0 and w 0 are the power and 1/e width of the incoming beam and 0 is the vacuum impedance. In the case of a radially-polarized vector vortex beams of the first order (l = 1, s = 0), the optical field at focus is defined by:

E p = 1, E s = 0, ( 49
)
and we assume the Gaussian apodization function at the pupil plane given by Eq. ( 46) for l=0.

For all the above-described vortex beams, the optical magnetic field is calculated by replacing e(r, ξ, z) by h(r, ξ, z) = k × e(r, ξ, z)/ωµ 0 in Eq. (42).

Predicting the IFE in a metallic structure requires the calculation of the optical field inside the metal (see Eqs. ( 19) and ( 40)). In the basic configuration treated here, the optical field in the metal layer is described by coefficients t s , t r p and t z p under the form

C + exp[iw 2 z] + C -exp[-iw 2 z]
where w 2 is the component of the wave vector normal to the surfaces (i.e., along (0z)). Coefficients C + and C -, which are obtained by applying boundary conditions of the optical fields onto the film interfaces, can be found for instance in Ref. [START_REF] Born | Principles of optics: electromagnetic theory of propagation, interference and diffraction of light[END_REF]. The dispersion properties of gold at λ=800nm are defined by the Drude model with ε r = -24.76 + 0.88i and γ 0 = 1.5718 • 10 7 S.m -1 . From the calculated optical field in the metal, we anticipate the distribution of opticallyinduced drift current density using the formalism detailed in section V.

B. OAM and SAM-driven optomagnetism

In the following, we consider four different light beams carrying SAM or OAM, or a combination of SAM and OAM. We examine the circularly polarized beam (l = 0, s = 1), the radially polarized vortex beam (l = 1, s = 0) leading for instance to optical skyrmions [START_REF] Du | [END_REF], and two circularly polarized vortex beams of opposite topological charges (l = ±1, s = 1) [70,71]. The incoming light waves are characterized by a maximum intensity of 10 12 W.cm -2 at focus and a wavelength (λ) of 800 nm. The waist of the incident beam coincides with the pupil plane of the microscope objective. Its 1/e-width matches the pupil diameter.

Fig. 2 shows cross-sections of the bulk and surface currents generated in the metal film under illumination with the above-described light beams. The drift currents are calculated by numerically integrating the azimuthal components of the bulk and surface current densities (cf. Eqs. (31) and (40), respectively ) over areas of 0.1×0.1 nm 2 . The optomagnetic fields originating from the SAM and OAM-driven loops of drift current are represented in Fig. 3 together with the overall optomagnetic field.

SOI [72] is known to tailor the helicity of focused light. As an example, in the focal region of a circularly polarized beam, the SAM is partly converted into OAM [71]. A reciprocal OAM-to-SAM conversion occurs at 37) is used to calculate the surface currents as it is assumed to be solely driven by the SAM of light (cf. Table I). Currents in the metal bulk are represented along the longitudinal (x0z)-plane (see (e)) and are decomposed in their (e-h) spin and (i-l) orbital parts (cf. Eqs. ( 35) and ( 33), respectively). The overall bulk current combining spin and orbital contributions is shown as well in (m-p) (cf. Eq. ( 32)). The color code used to represent these out-of-plane currents is defined in (e). All currents are given in nA.

the focus of vector vortex beams [START_REF] Du | [END_REF]73]. An immediate consequence of the SOI of light on the IFE is that opto-induced drift currents show both orbital and spin components even when the incoming beam solely carries SAM or OAM. We see from Figs. 2(e) and 2(i) for the circularly polarized beam (carrying SAM) and Figs. 2(f) and 2(j) for the radially polarized vortex beam (carrying OAM) that in the metal bulk both the orbital and spin parts of the drift currents are non negligible. The SAM dependence of the orbital part is analytically evidenced in Eqs. (33) and (36), whereas the OAM dependence of the spin part is contained in the spatial derivatives of Eqs. (35) and (37). As anticipated in Eq. ( 40), the orbital part of the drift current at metal surfaces is negligible. This property is numerically verified in Table I using Eq. (39).

The effect of the SOI in the IFE is also visible in the case of circularly polarized vortex beams (carrying both SAM and OAM; cf. the two last columns of Fig. 2). By comparing Figs. 2(c) and 2(d), and Figs. 2(k) and 2(l), we see that the spin part of the drift current in the metal bulk and at metal surfaces is reversed and shows a different morphology when the sign of the topological charge l (i.e. the OAM) of the incoming beam is flipped while the polarization helicity s (i.e., the SAM) remains unchanged.

To quantify the relative contributions of the SAM and OAM of light to the IFE, we consider coefficients β spn and β orb , respectively, defined as:

β spn = µ spn z µ spn z + µ orb z , (50)
β orb = µ orb z µ spn z + µ orb z . (51)
µ spn z and µ orb z are the z-component of vectors µ spn and µ orb defined as being derived from the spin and orbital parts of the opto-induced magnetization (M spn and M orb , respectively).

We first focus on the ability of the SAM and OAM of light to create local orbital angular momentum in the electron gas (e-OAM), i.e., to move conduction electrons in the form of drift current loops. To this end, we define

µ id = 1 2V V r × |j id d |dV, (52)
with

|j id d | = |[j id d ] surf | + |[j id d ] bulk |, "
id" stands for "orb" or "spn". Here, µ z = µ spn z + µ orb z quantifies the total amount of opto-induced e-OAM. We thus avoid angular momentum compensation effects that could be induced by current loops of opposite handedness to focus on how much of the total opto-induced e-OAM comes from the SAM and OAM of light.

From these considerations, it appears that the OAM of light is the main source of e-OAM in the metal bulk for three of the four helicities of the incoming light (see Table I). In contrast, the SAM of light is the main contributor to e-OAM at metal surfaces (calculated from Eq. ( 39)), which confirms the simplification made in Eq. (40). Table I also shows that the overall e-OAM (combining surface and bulk contributions) is mainly driven by the SAM of light. The existence of a non-negligible OAM-driven magnetization (SAM-driven magnetization, respectively) for an incoming beam solely carrying SAM (OAM, respectively) highlights the crucial role of the SOI of light in the IFE. In the case of the radially polarized vortex beam solely carrying OAM (l = 1, s = 0), the contribution of the SAM to the total generated e-OAM is even three times as high as the contribution of the OAM. OAM-to-SAM conversion in such a beam has already been evidenced in Ref [START_REF] Du | [END_REF], leading to the concept of an optical skyrmion. When the incoming beam carries both OAM and SAM (l = ±1 and s = 1), the OAM and SAM contributions to the overall e-OAM are almost balanced. We now study the observable magnetization associated to the IFE. µ is then defined as the amplitude of the magnetization.:

µ id = |M| = 1 2V V r × j id d dV , (53)
"id" stands for "orb" or "spn". The e-OAM compensation effects induced by current loops of opposite handedness are now taken into account. We see for instance by comparing Figs. 2 (b-d) and 2 (j-l)) that the SAMdriven drift currents at metal surfaces and bulk can be of opposite handedness.

The SAM and OAM contributions to the overall IFE (combining surface and bulk contributions) are given in Table II. We find that except for an incoming circularly polarized beam (l = 0, s = 1), the contribution of the OAM of light dominates the IFE. The spin part of the IFE undergoes compensation effects due to surface and bulk currents of opposite handedness, which reduces the resulting optomagnetization. The SAM of light thus induces a larger amount of e-OAM, but due to compensation effects between surfaces and bulk contributions (electrons move in opposite directions), the SAM of light can be less efficient than its orbital counterpart to generate an observable magnetization. This surface-to-bulk compensation effect can be almost perfect, leading to a near zero contribution of the SAM to the IFE (as observed from Tables I and II with the radially polarized vortex beam (l = 1, s = 0)). The resulting optomagnetic field is calculated from the drift currents shown in Fig. 2 using Biot and Savart law. We show in Fig. 3 the optomagnetic field generated from the spin and orbital parts of the drift currents (Figs. 3(a-d) and 3(e-h), respectively) as well as the overall magnetic field combining these two parts (Figs. 3(i-l)). Figs. 3(i-l) reveal that the distribution of the overall optomagnetic field strongly depends on the OAM of the incoming beam. When l = 1 and s = 1, the optomagnetic field forms a ring-like pattern and points upward at the center of the light beam (Fig. 3(k)). The amplitude of the static magnetic field reaches 1.2 mT. When the sign of l is reversed, the optomagnetic field is both flipped and confined at the beam center (Fig. 3(i)) and it peaks at 1.8 mT. The topological charge (i.e., OAM) of the collimated light entering the microscope objective thus provides a new degree of freedom in the control of the optomagnetism.

VII. CONCLUSION

On the basis of a hydrodynamic model of the conduction electron gas, we give a spin and orbital angular momentum representation of the IFE in a metal. Both SAM and OAM contributions to the IFE in the metal bulk rely on an optical drag effect [57,74]: the underlying optoinduced current densities are proportional to the Poynting energy flow (optical momentum) inside the metal. In the case of an axisymmetrical optical system, we show a direct proportionality between the opto-induced drift current at metal surfaces and the radial component of the SAM of light. In the paraxial approximation, the contribution of the SAM vanishes and the IFE is solely driven by the OAM of light, which is consistent with the interpretation of the spin and orbital angular momenta of purely transverse light fields [49,51]. We also evidence that the SOI of light plays a significant role in the IFE. Finally, we numerically quantify the relative contributions of the SAM and OAM to the IFE in a thin gold film illuminated with four different focused beams carrying SAM and/or OAM. We find that the SAM of light is the main source of drift current density regardless of the helicity of the incident light. However, compensation effects between SAM-driven surface and bulk currents of opposite handedness reduces the contribution of the SAM to the observable opto-induced magnetization. Except for circular polarization, the OAM of light is found to be the main contributor to the IFE. We also numerically confirm the importance of the SOI of light in the IFE, which manifests both via SAM-to-OAM and OAMto-SAM conversions at focus. The OAM of light thus opens new degrees of freedom in the control of the IFE in metals, thus potentially impacting various research fields including all-optical magnetization switching and spinwave excitation.

FIG. 1 .

 1 FIG. 1. Schematic diagram of the focusing system which involves a microscope objective of circular pupil.

FIG. 2 .

 2 FIG. 2. Opto-induced current loops (a-d) at the bottom surface and (e-p) in the bulk of a thin gold film illuminated with (a,e,i,m) a circularly polarized light beam (s=1, l=0), (b,f,j,n) a radially polarized vortex beam (s=0, l=1), (c,g,k,o) a circularly polarized vortex beam (s=1, l=1), and (d,h,l,p) the same circularly polarized vortex with an opposite topological charge (s=1, l=-1). The helicity of each beam is shown with the l and s numbers on top of each column of the figure. The bottom surface ((xOy)-plane, see (d)) of the thin gold film matches the focal plane of the incoming light. The orientation of the surface currents in (a-d) is represented with white arrows. Eq. (37) is used to calculate the surface currents as it is assumed to be solely driven by the SAM of light (cf. TableI). Currents in the metal bulk are represented along the longitudinal (x0z)-plane (see (e)) and are decomposed in their (e-h) spin and (i-l) orbital parts (cf. Eqs.(35) and(33), respectively). The overall bulk current combining spin and orbital contributions is shown as well in (m-p) (cf. Eq. (32)). The color code used to represent these out-of-plane currents is defined in (e). All currents are given in nA.

FIG. 3 .

 3 FIG. 3. Optically induced static magnetic field in a (x0z)-plane perpendicular to the metal surfaces. The black arrows show the local orientation of the magnetic field. (a-d) Optomagnetic field (in linear scale) from the contribution of the OAM of light to the IFE. (e-h) Optomagnetic field (in logarithmic scale) from the contribution of the SAM of light to the IFE. (i-l) Overall optomagnetic field (in logarithmic scale). In all figures, the horizontal yellow lines are used to localize the 20nm thick gold layer. The gold film is illuminated from the substrate (see indications in (a)).

TABLE I .

 I βspn and β orb coefficient for four different combinations of the l and s parameters defining the incoming beam entering the microscope objective. βspn and β orb are defined from Eqs. (50) and(51), where µ orb and µ spn are given in (52) (total amount of e-OAM).

			l=0,s=1 l=1,s=0 l=1,s=1 l=-1,s=1
	Bulk	βspn	73%	55%	45%	55%
		β orb	27%	45%	55%	45%
	Surface βspn	99.8%	99.5%	99.3%	99.2%
		β orb	0.2%	0.5%	0.7%	0.8%
	Overall βspn	88%	76%	69%	71%
		β orb	12%	24%	31%	29%

TABLE II .

 II βspn and β orb coefficient for four different combinations of the l and s parameters defining the incoming beam entering the microscope objective. βspn and β orb are defined in Eqs. (50) and(51), where µ orb and µ spn are given in (53) (observable magnetization).

		l=0,s=1	l=1,s=0	l=1,s=1	l=-1,s=1
	βspn	78%	0.2%	36%	49%
	β orb	22%	99.8%	64%	51%

ACKNOWLEDGMENTS

The authors are indebted to Benoît Morel and Ulrich Fischer for helpful discussions. This work is funded by the EIPHI Graduate School (contract ANR-17-EURE-0002), the Region Bourgogne Franche-Comte, the French Agency of Research (contract ANR-18-CE42-0016), the I-SITE BFC (contract ANR-5-IDEX-0003).


Vage Karakhanyan

Clément Eustache

Yannick Lefier

Thierry Grosjean

Optoinduced magnetization from the spin and orbital angular momenta of light

FEMTO-ST Institute, CNRS, University of Bourgogne -Franche-Comté, Besanc ¸on, France *corresponding author, E-mail: thierry.grosjean@femto-st.fr

Abstract: We provide a spin and orbital angular momentum representation of the inverse Faraday effect in a metal. We analytically show the role of the spin and orbital angular momenta of light (SAM and OAM, respectively), as well as the spin-orbit interaction (SOI), in the generation of an optoinduced magnetization. We also show that resonances in plasmonic nanoantennas enhance and confine the IFE on the nanoscale, thereby leading to static magnetic fields directly applicable in a vast application domain including all-optical magnetization switching and spin-wave excitation.

Light is known to possess polarization and spatial degrees of freedom, manifested by its linear momentum as well as spin and orbital angular momenta [START_REF] Allen | Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes[END_REF]. Remarkably, the SAM of light can be transferred to electrons in matter, a phenomenon which refers to as the IFE [START_REF] Ps Pershan | Theoretical discussion of the inverse faraday effect, raman scattering, and related phenomena[END_REF][START_REF] Hertel | Theory of the inverse faraday effect in metals[END_REF]. The IFE has attracted much attention for its ability to generate lightinduced magnetization, thereby opening the prospect of an ultrafast magnetic data storage and a non-contact excitation of spin-waves. On the basis of a hydrodynamic model of the conduction electron gas [START_REF] Hurst | Magnetic moment generation in small gold nanoparticles via the plasmonic inverse faraday effect[END_REF][START_REF] Lefier | Etudes du couplage spin-orbite en nano-photonique. applications à l'excitation unidirectionnelle de modes plasmoniques guidés et à la génération d'opto-aimants nanométriques contrôlables par l'état de polarisation de la lumière[END_REF], we provide a spin and orbital angular momentum representation of the IFE in a metal [START_REF] Vage Karakhanyan | Inverse faraday effect from the orbital angular momentum of light[END_REF]. The OAM and SOI of light provide additional degrees of freedom in the control of the IFE usually solely attributed to the SAM. We also investigate a resonant IFE within individual nanoantennas [START_REF] Vage Karakhanyan | Optomagnets in nonmagnetic plasmonic nanostructures[END_REF][START_REF] Vage Karakhanyan | Plasmon-induced 0.13 t optomagnetic field in a gold coaxial nanoaperture[END_REF]. Upon illumination, individual subwavelength gold coaxes and cylinders are shown to develop a strong optomagnetic field on the nanoscale that is controllable by the helicity of the light. In pulse optical regime, this magnetic field is found to reach 0.3 T upon excitation at a light intensity below damage threshold.

Our model shows that both the SAM and OAM contributions to the IFE in the metal bulk rely on an optical drag effect [START_REF] Noginova | Light-to-current and current-to-light coupling in plasmonic systems[END_REF]: the underlying optoinduced current densities are proportional to the Poynting energy flow (optical momentum) inside the metal. In the case of an axisymmetric optical system, we find a direct proportionality between the optoinduced drift current at metal surfaces and the radial component of the SAM of light. In the paraxial approximation, the contribution of the SAM vanishes, and the IFE is driven solely by the OAM of light, which is consistent with the interpretation of the spin and orbital angular momenta of purely transverse light fields [START_REF] Michael | Optical currents[END_REF][START_REF] Bliokh | Extraordinary momentum and spin in evanescent waves[END_REF]. We also show that the SOI of light [START_REF] Ky Bliokh | Spin-orbit interactions of light[END_REF] plays a significant role in the IFE. Finally, we numerically quantify the relative contributions of the SAM and OAM to the IFE in a thin gold film illuminated with four different focused beams carrying SAM and/or OAM (see table 1). We find that the SAM of light is the main source of drift current density regardless of the helicity of the incident light. However, the compensation effects between SAM-driven surface and bulk currents of opposite handedness reduce the contribution of the SAM to the observable optoinduced magnetization. Except for circular polarization, the OAM of light is found to be the main contributor to the IFE. We also numerically confirm the importance of the SOI of light in the IFE, which manifests both via SAM-to-OAM and OAM-to-SAM conversions at the focus. The OAM of light thus opens new degrees of freedom in the control of the IFE in metals, thus potentially impacting various research fields, including alloptical magnetization switching and spin-wave excitation. l=0,s=1 l=1,s=0 l=1,s=1 l=-1,s=1 SAM 78% 0.2% 36% 49% OAM 22% 99.8% 64% 51%

Table 1: The table shows relative contribution of OAM and SAM of light into the IFE for four different combinations of the l and s parameters defining the incoming beam entering the microscope objective.

We also investigate the generation of an optomagnetic field in plasmonic nanoantennas upon illumination with a circularly polarized light (Fig. 1). We predict an optomagnetic field reaching 0.3 T at laser fluence below nanostructure damage threshold. We also show that the substrate introduces an important asymmetry of the optomagnetic response of plasmonic nanoantennas fabricated via a topdown technological approach. For a 50-nm thick gold coaxial nanoantenna (Fig. 1b), the optomagnetism is mainly localized within the substrate, which appears to be advantageous for many applications involving magnetic material within the substrate. Optomagnetism in resonant plasmonic nanoantennas may impact a broad field of applications and techniques including spintronics, magnonics and data storage via the development of on-chip nanoscale plasmonicmagnetic architectures. Optomagnetism may also provide new degrees of freedom in nano-object tweezing based on the combination of optomagnetic and pure optical forces.

Figure 1 :

 1 Figure 1: Optically-induced static magnetic field generated by (a) a gold nanocylinder (diameter: 50 nm, thickness: 12 nm) in oil (n=1.45), and (b), a coaxial nanoaperture in a 50-nm thick gold film on a glass substrate (n=1.5). The inner and outer diameters of the coax are of 50 nm and 70 nm, respectively. The wavelength is equal to 800 nm for each configuration.

The authors are indebted to Ulrich Fischer for helpful discussions. This work is funded by Conseil régional de "Bourgogne Franche-Comté"; EIPHI Graduate School (ANR-17-EURE-0002); Agence National de le Recherche (ANR-18-CE42-0016).


Vage Karakhanyan

Clément Eustache

Yannick Lefier

Thierry Grosjean
email: thierry.grosjean@femto-st.fr

Optoinduced magnetization in a metal from the spin and orbital angular momenta of light

We provide a spin and orbital angular momentum representation of the inverse Faraday effect in a metal. We analytically show the role of the spin and orbital angular momenta of light (SAM and OAM, respectively), as well as the spin-orbit interaction (SOI), in the generation of an optoinduced magnetization. We also show that resonances in plasmonic nanoantennas enhance and confine the IFE on the nanoscale, thereby leading to static magnetic fields directly applicable in a vast application domain including all-optical magnetization switching and spin-wave excitation.

Light is known to possess polarization and spatial degrees of freedom, manifested by its linear momentum as well as spin and orbital angular momenta [START_REF] Allen | Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes[END_REF]. Remarkably, the SAM of light can be transferred to electrons in matter, a phenomenon which refers to as the IFE [START_REF] Ps Pershan | Theoretical discussion of the inverse faraday effect, raman scattering, and related phenomena[END_REF][START_REF] Hertel | Theory of the inverse faraday effect in metals[END_REF]. The IFE has attracted much attention for its ability to generate light-induced magnetization, thereby opening the prospect of an ultrafast magnetic data storage and a non-contact excitation of spin-waves. On the basis of a hydrodynamic model of the conduction electron gas [START_REF] Hurst | Magnetic moment generation in small gold nanoparticles via the plasmonic inverse faraday effect[END_REF][START_REF] Lefier | Etudes du couplage spin-orbite en nano-photonique. applications à l'excitation unidirectionnelle de modes plasmoniques guidés et à la génération d'opto-aimants nanométriques contrôlables par l'état de polarisation de la lumière[END_REF], we provide a spin and orbital angular momentum representation of the IFE in a metal [START_REF] Vage Karakhanyan | Inverse faraday effect from the orbital angular momentum of light[END_REF]. The OAM and SOI of light provide additional degrees of freedom in the control of the IFE usually solely attributed to the SAM. We also investigate a resonant IFE within individual nanoantennas [START_REF] Vage Karakhanyan | Optomagnets in nonmagnetic plasmonic nanostructures[END_REF][START_REF] Vage Karakhanyan | Plasmon-induced 0.13 t optomagnetic field in a gold coaxial nanoaperture[END_REF]. Upon illumination, individual subwavelength gold coaxes and cylinders are shown to develop a strong optomagnetic field on the nanoscale that is controllable by the helicity of the light. In pulse optical regime, this magnetic field is found to reach 0.3 T upon excitation at a light intensity below damage threshold.

Our model shows that both the SAM and OAM contributions to the IFE in the metal bulk rely on an optical drag effect [START_REF] Noginova | Light-to-current and current-to-light coupling in plasmonic systems[END_REF]: the underlying optoinduced current densities are proportional to the Poynting energy flow (optical momentum) inside the metal. In the case of an axisymmetric optical system, we find a direct proportionality between the optoinduced drift current at metal surfaces and the radial component of the SAM of light. In the paraxial approximation, the contribution of the SAM vanishes, and the IFE is driven solely by the OAM of light, which is consistent with the interpretation of the spin and orbital angular momenta of purely transverse light fields [START_REF] Michael | Optical currents[END_REF][START_REF] Bliokh | Extraordinary momentum and spin in evanescent waves[END_REF]. We also show that the SOI of light [START_REF] Ky Bliokh | Spin-orbit interactions of light[END_REF] plays a significant role in the IFE. Finally, we numerically quantify the relative contributions of the SAM and OAM to the IFE in a thin gold film illuminated with four different focused beams carrying SAM and/or OAM (see table 1). We find that the SAM of light is the main source of drift current density regardless of the helicity of the incident light. However, the compensation effects between SAM-driven surface and bulk currents of opposite handedness reduce the contribution of the SAM to the observable optoinduced magnetization. Except for circular polarization, the OAM of light is found to be the main contributor to the IFE. We also numerically confirm the importance of the SOI of light in the IFE, which manifests both via SAM-to-OAM and OAMto-SAM conversions at the focus. The OAM of light thus opens new degrees of freedom in the control of the IFE in metals, thus potentially impacting various research fields, including all-optical magnetization switching and spin-wave excitation. l=0,s=1 l=1,s=0 l=1,s=1 l=- We also investigate the generation of an optomagnetic field in plasmonic nanoantennas upon illumination with a circularly polarized light (Fig. 1). We predict an optomagnetic field reaching 0.3 T at laser fluence below nanostructure damage threshold. We also show that the substrate introduces an important asymmetry of the optomagnetic response of plasmonic nanoantennas fabricated via a top-down technological approach. For a 50-nm thick gold coaxial nanoantenna (Fig. 1b), the optomagnetism is mainly localized within the substrate, which appears to be advantageous for many applications involving magnetic material within the substrate. Optomagnetism in resonant plasmonic nanoantennas may impact a broad field of applications and techniques including spintronics, magnonics and data storage via the development of on-chip nanoscale plasmonic-magnetic architectures. Optomagnetism may also provide new degrees of freedom in nano-object tweezing based on the combination of optomagnetic and pure optical forces.

Figure 1 :

 1 Figure 1: Optically-induced static magnetic field generated by (a) a gold nanocylinder (diameter: 50 nm, thickness: 12 nm) in oil (n=1.45), and (b), a coaxial nanoaperture in a 50-nm thick gold film on a glass substrate (n=1.5). The inner and outer diameters of the coax are of 50 nm and 70 nm, respectively. The wavelength is equal to 800 nm for each configuration.

Table 1 :

 1 The table shows relative contribution of OAM and SAM of light into the IFE for four different combinations of the l and s parameters defining the incoming beam entering the microscope objective.

	1,s=1

The authors are indebted to Ulrich Fischer for helpful discussions. This work is funded by Conseil régional de "Bourgogne Franche-Comté"; EIPHI Graduate School (ANR-17-EURE-0002); Agence National de le Recherche (ANR-18-CE42-0016).


Cindy Neuzillet

David Malka

Inderpreet Astrid Lièvre

Singh Khurana

Dewi Vernerey

Inderpreet Singh Khurana

Correlation between efficacy endpoints in patients with advanced biliary tract cancer treated by systemic second-line therapies: Analysis of aggregated data from a systematic literature review

Keywords: Chemotherapy, cholangiocarcinoma, endpoint, correlation, targeted therapy Lay

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

'Biliary tract cancer' (BTC) is a collective term encompassing a heterogeneous group of epithelial neoplasms [START_REF] Rizvi | Cholangiocarcinoma -evolving concepts and therapeutic strategies[END_REF]. Although they are the second leading cause of primary liver cancer after hepatocellular carcinoma, BTCs are rare tumours in most countries (apart from endemic areas in Asia) with less than six new cases per 100,000 people each year (10,000 and 12,000 new cases/year in Europe and the United States, respectively) [START_REF] Lepage | Survival in patients with primary liver cancer, gallbladder and extrahepatic biliary tract cancer and pancreatic cancer in Europe 1999-2007: Results of EUROCARE-5[END_REF][START_REF] Siegel | Cancer statistics[END_REF]. They are classified into three main subtypes based on their anatomical origin, each harboring specific epidemiological, clinical, molecular, and therapeutic features: intrahepatic cholangiocarcinoma (iCCA); extrahepatic cholangiocarcinoma (eCCA), which includes perihilar cholangiocarcinoma and distal cholangiocarcinoma; and gallbladder carcinoma [START_REF] Rizvi | Cholangiocarcinoma -evolving concepts and therapeutic strategies[END_REF]. Overall, BTCs display a poor prognosis, with a five-year overall survival (OS) rate (all stages) below 20% [START_REF] Lepage | Survival in patients with primary liver cancer, gallbladder and extrahepatic biliary tract cancer and pancreatic cancer in Europe 1999-2007: Results of EUROCARE-5[END_REF][START_REF] Siegel | Cancer statistics[END_REF].

Approximately 70% of BTCs cases are diagnosed at an advanced, non-resectable stage [START_REF] Valle | Biliary cancer: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up[END_REF]. In the first-line setting, the standard chemotherapy regimen is the cisplatin plus gemcitabine doublet (CISGEM regimen) [START_REF] Valle | Biliary cancer: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up[END_REF].

Studies of this regimen have demonstrated superiority over single-agent gemcitabine (ABC-02 and BT-22 randomized studies), with overall response rates (ORR) of 19.5% (95% confidence interval [CI]: 8.8-34.9) to 26.1%, median progression-free survival (PFS) of 5.8 months (95% CI: 4.1-8.2) to 8.0 months (95% CI: 6.6-8.6), and median OS of 11.2 months (95% CI: 9.1-12.5) to 11.7 months (95% CI: 9.5-14.3) [START_REF] Valle | Cisplatin and gemcitabine for advanced biliary tract cancer: a meta-analysis of two randomised trials[END_REF][START_REF] Okusaka | Gemcitabine alone or in combination with cisplatin in patients with biliary tract cancer: a comparative multicentre study in Japan[END_REF][START_REF] Valle | Cisplatin plus gemcitabine versus gemcitabine for biliary tract cancer[END_REF]. After failure of firstline treatment, chemotherapy may be offered in the second-line setting but is associated with low ORR (8% to 12%) and short median OS (7.2 months) [START_REF] Lamarca | Second-line chemotherapy in advanced biliary cancer: a systematic review[END_REF][START_REF] Brieau | Second-line chemotherapy for advanced biliary tract cancer after failure of the gemcitabine-platinum combination: A large multicenter study by the Association des Gastro-Entérologues Oncologues[END_REF]. The FOLFOX doublet regimen (fluorouracil/folinic acid plus oxaliplatin) recently demonstrated superiority over best supportive care alone in the ABC-06 phase III study but with limited OS (median OS gain <1 month) benefit and ORR (5%) [START_REF] Lamarca | Second-line FOLFOX chemotherapy versus active symptom control for advanced biliary tract cancer (ABC-06): a phase 3, open-label, randomised, controlled trial[END_REF], and the question of the best regimen in second-line is still open [START_REF] Neuzillet | Fluropyrimidine single agent or doublet chemotherapy as second line treatment in advanced biliary tract cancer[END_REF]. Hence, there is an urgent need to develop alternate therapies with higher activity in BTC.

Recently, a better understanding of the molecular biology of BTCs and their genomic and transcriptomic segmentation has led to the emergence of new therapeutic approaches such as inhibitors targeting fibroblast growth factor receptor gene (FGFR) fusions (including pemigatinib [START_REF] Abou-Alfa | Pemigatinib for previously treated, locally advanced or metastatic cholangiocarcinoma: a multicentre, open-label, phase 2 study[END_REF]) and isocitrate dehydrogenase (IDH) gene mutations (ivosidenib [START_REF] Abou-Alfa | Ivosidenib in IDH1-mutant, chemotherapy-refractory cholangiocarcinoma (ClarIDHy): a multicentre, randomised, double-blind, placebo-controlled, phase 3 study[END_REF]). Developing treatments that target rare molecular alterations in a rare condition comes with high challenges for the clinical research and practice due to the very low number of patients and the difficulty to identify them for enrollment. Hence, improving the predictability of phase II studies, i.e. identifying robust intermediate endpoints in phase II to predict clinical benefit and success in phase III, is an important issue in rare diseases such as BTCs.

ORR and PFS are commonly used as an endpoint for phase II trials. While ORR and PFS are relevant endpoints to use in trials assessing the level of activity of new drugs in malignant diseases, the ultimate goal is to bring benefit for the patients. OS and health-related quality of life (HRQoL), as they are patient-related, are considered as the best endpoints to capture such a benefit. Therefore, it is of interest to estimate the extent to which a gain in terms of ORR or PFS translates in a gain in OS or HRQoL.

In this work, we aimed to assess the correlation between ORR, median PFS and OS using aggregated data from published clinical trials selected by a systematic review for systemic therapies in advanced BTC patients in the second-line setting.

MATERIAL AND METHODS

Identification and selection of publications

We re-used a recent systemic literature review (21th of April 2020, Medline, EMBASE, Cochrane, Medline-inprocess/Pubmed) done by BresMed Health Solutions (not published) aiming at identifying studies that enrolled patients with advanced, metastatic, or surgically unresectable CCA/BTCs (iCCA, eCCA, and/or gallbladder carcinoma) for whom previous therapy had failed (see Appendix for search strategies). Studies only enrolling patients with gallbladder cancer were not included in the systematic literature review. A systematic selection of the relevant studies based on the inclusion and exclusion criteria is presented in Appendix.

Only prospective clinical trials were selected for the endpoint correlation. Assessments of ORR and PFS from retrospective studies and case reports were considered insufficiently reliable, based on a previously published research [START_REF] Lamarca | Second-line chemotherapy in advanced biliary cancer: a systematic review[END_REF]. Only studies evaluating systemic treatments (i.e. exclusion of locoregional therapies) were included. Phase I trials were excluded due to the specificities of patients enrolled in such trials and because their primary objective is usually the safety and not the efficacy. Studies without reported median OS value were also excluded because they were not usable for the endpoint correlation.

Quality control of the study selection and data

Several controls were carried out. First, a review of the publication was done when the study design was unclear in order to validate its inclusion or exclusion. Similarly, a review of the publication was performed when more details were requested for analyses by the statistician. Finally, all data kept for the endpoint correlation were checked in the original full-text publications to ensure their accuracy.

Endpoints

Data extraction was performed for all the clinical endpoints (ORR, PFS, OS). OS was defined as the time from treatment initiation (or randomization) to death. PFS was defined as the time from treatment initiation (or randomization) to disease progression or death. ORR was defined as the proportion of patients who achieved a complete response (CR; disappearance of all lesions) or partial response (PR; decrease of at least 30% in the sum of the longest diameter of the target lesions) according to the Response Evaluation Criteria in Solid Tumors (RECIST).

Statistical analysis

Weighted means and 95% confidence intervals (CIs) were calculated for median OS, PFS and ORR according to the number of patients evaluable in the studies. If several dates of data cut-off were available, the most recent was chosen. The evaluable population for efficacy criteria was privileged. When the number of evaluable patients differed between survival and ORR analysis, a conservative approach was adopted and the lowest number was chosen. Pearson weighted correlation was estimated between median OS and ORR and between OS and median PFS.

All analyses were performed using SAS version 9.4 (SAS Institute, Cary NC) and R software version 3.6.3 (R Development Core Team, Vienna, Austria; http://www.r-project. org).

Sensitivity analyses

A sensitivity analysis was conducted according to the treatment administered in the trials. Correlations between median OS and ORR and OS and median PFS were estimated in the following subgroups: trials of chemotherapy alone, trials of targeted therapy alone, trials of both chemotherapy and targeted therapy.

RESULTS

Studies included in the analysis and data

Figure 1 summarizes the flowchart for selection of eligible studies. From 108 studies including patients with advanced (metastatic or unresectable) BTC who had failed previous systemic treatment, 5 were randomized trials and 103 were non-randomized trials. Among the 5 randomized trials, one was excluded because no systemic treatment was involved. Among the 103 non-randomized studies, 90 were excluded because their design did not meet eligibility criteria for our study (77 studies), median OS was not reported (10 studies), median PFS and ORR were not reported (2 studies), or because no systemic treatment was involved (1 study).

Overall, 17 studies were selected for the endpoint correlation analysis: 10 assessing targeted therapy, 5 assessing chemotherapy, and 2 assessing a combination of chemotherapy and targeted therapy [Table 1].

Correlation between median OS and ORR

Correlation between median OS and ORR was assessed; results are summarized in Table 2. When all the studies were included for the weighted correlation index determination, the correlation between median OS and ORR was statistically significant (r=0.85; P<0.0001) [Figure 2A]. This significance was maintained in the sensitivity analyses for the chemotherapy subgroup (r=0.90; P=0.0152) [Figure 2B] and the targeted therapy subgroup (r=0.84; P=0.0006) [Figure 2C].

Correlation between median OS and PFS

In the overall analysis, the correlation between median OS and PFS was also statistically significant (r=0.80; P<0.0001) [Figure 3A]. However, in the sensitivity analyses, the correlation was significant for targeted therapy (r=0.83; P=0.0009) [Table 2 and Figure 3C] but not for chemotherapy [Table 2 and Figure 3B].

DISCUSSION

We found a strong correlation (Pearson correlation coefficient: 0.85) between median OS and ORR in clinical trials assessing second-line systemic treatment in patients with BTC, either with chemotherapy or targeted therapy. In contrast, the correlation between median OS and PFS, albeit significant in the overall analysis, remained significant only for targeted therapies in the sensitivity analysis. Based on these findings, ORR seems to be a more interesting intermediate endpoint in BTC in second line for both chemotherapy and targeted therapies, while PFS may be relevant only for targeted therapy trials. Further well-designed studies for surrogacy evaluation should be performed to confirm this observation.

In clinical trials in oncology, OS is the most robust and relevant primary endpoint so that it is frequently used in the evaluation of new therapies, particularly in phase III trials. Other endpoints such as ORR or PFS are preferred in phase II trials. However, these endpoints focus on the tumor rather than the patient and are thus considered less robust to evaluate the patient's benefit. Consequently, there is an obvious interest in assessing the association of tumor response with patient survival. The characterization of a surrogacy of alternate endpoint for OS is the highest level of demonstration for that purpose. A so-called "surrogate endpoint" predicts the primary endpoint (e.g. OS) under the conditions that it is reproducibly and reliably measurable, that the treatment has a significant effect on both the primary and surrogate endpoints, and that the effect on the surrogate endpoint captures the entire treatment effect on the primary endpoint. An example of surrogacy is 3-year disease-free survival predicting for 5-year OS in resected colorectal cancer as demonstrated by Sargent et al. [START_REF] Sargent | Two or three year disease-free survival (DFS) as a primary end-point in stage III adjuvant colon cancer trials with fluoropyrimidines with or without oxaliplatin or irinotecan: data from 12,676 patients from MOSAIC, X-ACT, PETACC-3, C-06, C-07 and C89803[END_REF]. In practice, the demonstration of surrogacy should be studied within and between trials and requires to run the analysis from patient-level data. Moreover, the lack of randomized studies in this context does not allow to used Hazard Ratios. Despite the fact that a correlation is necessary but not sufficient to establish the surrogacy, when individual data and randomized trial are not available, a "correlation" approach between two judgement criteria based on aggregated data is the unique information that can be provided; despite its limitations, this approach could be informative.

In a systematic review published in 2014, Lamarca et al. [START_REF] Lamarca | Second-line chemotherapy in advanced biliary cancer: a systematic review[END_REF] analyzed ORR and PFS as intermediate endpoints in trials published through 2013 that evaluated systemic second-line therapies in patients with advanced BTC. Twenty-five studies (phase II and retrospective studies) were available for OS and PFS/ORR correlation. When all the studies included in the statistical analysis were included for the weighted correlation index determination, the strongest correlation was shown between median OS and PFS (r=0.54; P=0.01). This significance was maintained in the phase II trial subgroup (r=0.61; P=0.04). Correlation between median OS and ORR was significant only in the phase II trial subgroup (r=0.62; P=0.03), showing weaker correlation when all the studies were included (r=0.34; P=0.16).

Here, we used a similar approach including more recent, randomized or non-randomized studies with median OS, ORR and median PFS data, evaluating second-line or later treatment line in advanced BTC. Overall, our results, obtained from an updated analysis and focusing on data from phase II trials (we excluded retrospective studies, phase I trials or unpublished studies where the measures of response and survival are likely to be less accurate), are consistent with and confirm the findings reported by Lamarca et al. [START_REF] Lamarca | Second-line chemotherapy in advanced biliary cancer: a systematic review[END_REF] in the phase II subgroup. We found a higher correlation coefficient and a statistically significant p-value, between ORR and median OS (r=0.85; p<0.0001) as well as between median PFS and OS (r=0.80; p<0.0001). These results are highlighted through scatter plot representations between ORR and median OS and between median PFS and ORR, showing a positive linear alignment of the points towards a positive relationship between the two variables.

Interestingly, our analysis included targeted therapies that recently emerged like FGFR inhibitors and IDH inhibitors. A scatter plot with stronger dispersion both on the abscissa (median OS) and ordinate (ORR, median PFS) axes may explain why the level of correlation is better here than in previous work.

The ORR is an intermediate criterion of the efficacy of cancer therapies that allows a direct measure of their activity. It has the advantage of estimating the therapeutic contribution of a treatment for one individual patient soon after the first dose given. Above all, ORR is not influenced by subsequent treatments received or by the life expectancy of patients (i.e. by potential co-existing prognostic factors). Thus, the lack of control arm is less an issue when using ORR (particularly, when the comparator would be a placebo, as no response would be expected in this arm) than when using PFS or OS. The clinical relevance of ORR is assessed through its magnitude, but also through the duration of that response and the percentage of CR. The relevance of this endpoint also depends on the clinical context [START_REF]Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics[END_REF]. In the context of BTC, a tumor response can bring a direct clinical benefit for a patient if the tumor reduction can avoid or delay complications due to biliary or vascular obstruction in relation with an increase in the size of the tumor (especially with regards to the Poiseuille's law, where parietal tension is proportional to the diameter at the power 4), and thereby may account for the existing correlation between ORR and OS. The outcomes from patients receiving placebo and included in one of our sensitivity analyses are actually very low both in terms of ORR and OS. This is also observed with treatments providing limited response rates.

Our study has several limitations. First, the analyses were based on published aggregated data and not on individual data, therefore only correlations between trials were analyzed and not inter-individual correlations, so we could not establish surrogacy between the endpoints. Moreover, no randomized trials with a common anchor are available and the number of studies and the number of patients enrolled into each were low. However, we demonstrated significant correlations between median OS and ORR/PFS, which can be of interest for designing future clinical trials and building statistical hypothesis. Hence, based on our Figures, one can infer the expected OS benefit resulting from a given ORR or PFS gain for systemic drugs used in second or later lines (for instance, a 10%-ORR gain translated into a 4.7-month benefit in OS and a 2-month PFS gain translated into a 7.4-month benefit in OS). Overall, these findings suggest the interest of tumor-related endpoints, i.e. ORR (for chemotherapy and targeted therapies) and PFS (for targeted therapies only), as intermediate endpoints to predict an OS benefit in the second-line setting for advanced BTCs. Of note, these findings may not apply to immune therapies, which were not included in our analyses and would warrant specific studies. Moreover, we previously showed that BTC patients display high heterogeneity in terms of survival, particularly depending on their performance status (PS), and that selection criteria in clinical trials (e.g. restriction to PS 0-1) may induce a selection bias toward more favorable survival [START_REF] Neuzillet | Prediction of survival with second-line therapy in biliary tract cancer: Actualisation of the AGEO CT2BIL cohort and European multicentre validations[END_REF]. These results strongly support the use of at least non-comparative randomized phase II design including a control arm to verify the calibration of the assumptions made in the experimental arm and to provide common anchor for indirect comparisons or surrogacy studies.

Overall, our works tries to offer a unifying approach for designing futures second-line trials in BTCs.

The considerable heterogeneity of treatments and the small numbers of patients in most trials available for this analysis may impact the robustness of our results.Chemotherapy strongly differs from most targeted therapies, and among the latter, substantial differences are also observed between tyrosine kinase inhibitors such as regorafenib with usual poor ORR in unselected patients, or new targeted therapies such as FGR or IDH1 inhibitors that are indicated in molecularly selected cholangiocarcinoma subgroups. Moreover, we do not have data concerning immunotherapy which is emerging. Our work constitutes a first step but should be confirmed by further prospective studies to better explore whether PFS or ORR is the most tightly correlated with OS, particularly for targeted therapies.

Taken together, these data suggest that the "optimal" design for a trial of second-line chemotherapy or targeted therapy in BTC is a randomized study with, if OS is deemed not appropriate, ORR as primary endpoint for chemotherapy and ORR or PFS for targeted therapies.

Funding sources

Sponsor of the systematic literature review: Incyte Biosciences UK. Sponsor of the correlation analyses (honorarium for conceptualization of the project and realization of statistical analyzes): Incyte Biosciences France. No payment has been done for authoring. "stage 3":ab,ti or "stage iii":ab,ti or "stage 3a":ab,ti or "stage iiia":ab,ti or "stage 3b":ab,ti or "stage iiib":ab,ti or "stage3":ab,ti or "stageiii":ab,ti or "stage 4":ab,ti or "stage iv":ab,ti or "stage4":ab,ti or "stageiv":ab,ti or metastatic or metasta*:ab,ti or advanced or advanc*:ab,ti or unresect*:ab,ti or relap*:ab,ti or resist*:ab,ti or refract*:ab,ti or ((late* NEAR/2 stag*):ab,ti) or nonresect*:ab,ti or ((non NEXT resect*):ab,ti) or inoperable:ab,ti or "locally advanced":ab,ti or "locally-advanced":ab,ti or local*:ab,ti or ((ineligible or "in eligible" or unfit or "un fit" or "un-fit" or unsuitable or "not amenable" or unamenable or inamenable or unhealthy or "not healthy") NEAR/2 surgery) 252,813

Declaration of

B. Primary systematic literature review of clinical studies

Potentially relevant publications were reviewed to collate a final set of studies which formed the main body of the clinical evidence. To determine which studies were eligible for review, explicit inclusion and exclusion criteria were applied to the literature search results (see Table 3).

Note:

a , the SLR was not limited by sample size. A study was also included if it reported data for one patient and met review criteria. b , if disease stage, FGFR2 status or treatment line were not clear at the primary screening stage, the study was included, and a decision was taken at the secondary screening stage after reviewing the full text. Studies with multiple lines of therapy were also included. c ,systematic reviews of randomized controlled trials, non-randomized controlled trials, single-arm, and observational studies were utilized only for bibliography searches. **, citations assessing patients receiving multiple lines of therapy were included at primary screening.

Study selection

All retrieved studies were assessed against the eligibility criteria. Primary (Level 1) screening was performed by two independent BresMed reviewers who reviewed each reference (title and abstract) identified in the literature search, applied basic study selection criteria (population, intervention, study design) and made decisions on whether to include or exclude the study reference at that stage. Any uncertainty regarding the inclusion of studies was checked by a senior BresMed reviewer, independent of the initial reviewers. For secondary (Level 2) screening of potentially relevant articles, the full articles were obtained. These were independently reviewed by two BresMed reviewers against each eligibility criterion. Any uncertainty regarding the inclusion of studies was again checked and judged by a senior BresMed reviewer independent of the initial reviewers. Electronic searches were conducted using English language keywords. All potential studies either had abstracts available in English, or the abstract was unavailable and thus a positive exclusion was not possible. For the full publication, if the language was not English the publication was excluded based on language. The SLR identified few published SLRs that were conducted in CCA or BTC patients receiving multiple lines of therapy. The published SLRs were used for bibliographic purposes; all studies relevant to the review objective have been included in the current SLR.

Figure 1 :Figure 2 :

 12 Figure 1: Flowchart of studies included in the analyses

Figure 3 :

 3 Figure 3: Correlation between OS and PFS; 3A: overall analysis; 3B: sensitivity analysis in the chemotherapy group; 3C: sensitivity analysis in the targeted therapy group

Interest statement

  CN: honoraria/consultancy: AAA/Novartis, Amgen, AstraZeneca, Baxter, Bristol-Myers Squibb, Fresenius Kabi, Incyte Biosciences, Merck, MSD, Mylan/Viatris, Nutricia, Pierre Fabre, Roche, Sanofi, Servier. Research funding: Roche. Clinical trials: OSE Immunotherapeutics, AstraZeneca, Bristol-Myers Squibb, Fresenius Kabi, Nutricia. Support for attending congress: Merck, MSD, Mylan/Viatris, OSE Immunotherapeutics. AL: honoraria/consultancy: AAA, Amgen, Bayer, BMS, HalioDx, Incyte, Ipsen, Merck, Novartis, Pierre Fabre, Roche, Sandoz, Sanofi and Servier; travel/congress support: AAA, Bayer, Ipsen, Merck, Mylan, Novartis, Pfizer, Roche and Servier; Research Funding: Bayer, Lilly, Novartis, Integragen DM: honoraria/consultancy: AbbVie, Amgen, AstraZeneca, Bayer, BMS, Incyte, Leo Pharma, Merck Serono, MSD, Pierre Fabre Oncologie, Roche, Sanofi, Servier, Taiho, Viatris.Travel expenses: Amgen, Bayer, BMS, Merck Serono, MSD, Pierre Fabre Oncologie, Roche, Sanofi, Servier, Viatris. ISK: BresMed Health Solutions Pvt. Ltd. (full employment); BresMed received a grant from Incyte Biosciences to conduct a systematic literature review DV: honoraria/consultancy: CellProthera, HalioDX, FSK, Gercor, Incyte Biosciences

Clinical Systematic Literature Review in CCA -09 November 2018Table 1 . Databases searched

 1

	S.	Database/website	Provider/Interface	Filter used for study	Coverage	Hits
	No.			design
	1.	Medline &	EMBASE.com	RCT, nRCT and	No limit	6,482
		EMBASE		observational
				studies
	2.	Cochrane	onlinelibrary.wiley.com	-	No limit	813
	3.	Medline-in-process Pubmed.com	-	No limit	156
	4.	Total				7,451
	1

. Medline and Embase: Embase.com Medline and Embase search strategy. 09 th November 2018

  ':ab,ti OR 'stage iii':ab,ti OR 'stage 3a':ab,ti OR 'stage iiia':ab,ti OR 'stage 3b':ab,ti OR 'stage iiib':ab,ti OR 'stage3':ab,ti OR 'stageiii':ab,ti OR 'stage 4':ab,ti OR 'stage iv':ab,ti OR 'stage4':ab,ti OR 'stageiv':ab,ti OR metastatic OR metasta*:ab,ti OR advanced OR advanc*:ab,ti OR unresect*:ab,ti OR relap*:ab,ti OR resist*:ab,ti OR

	2.	5.	#1 OR #2 OR #3 OR #4	49,375
		6.	'stage 3refract*:ab,ti OR ((late* NEAR/2 stag*):ab,ti) OR nonresect*:ab,ti OR	4,470,185
			((non NEXT/1 resect*):ab,ti) OR inoperable:ab,ti OR 'locally
			advanced':ab,ti OR 'locally-advanced':ab,ti OR local*:ab,ti OR
			((ineligible OR 'in eligible' OR unfit OR 'un fit' OR 'un-fit' OR unsuitable
			OR 'not amenable' OR unamenable OR inamenable OR unhealthy OR
			'not healthy') NEAR/2 surgery)
		7.	#5 AND #6	19,955
		8.	('clinical trial'/exp OR 'randomized controlled trial'/exp OR	2,041,012
		9.		4,657,738
			study OR
	Sr. No. 1. 10. 11. 2. 3. 4. 12. 13.	Query studies)):ab,ti) OR ((epidemiologic* NEAR/1 (study OR studies)):ab,ti) 'bile duct carcinoma'/exp OR 'bile duct carcinoma'/syn OR 'bile duct OR (('cross sectional' NEAR/1 (study OR studies)):ab,ti) #8 OR #9 carcinoma' OR 'bile duct cancer' OR cholangiocarcinoma OR 'biliary (review:it OR 'review literature as topic'/exp OR 'literature review':ti) tract cancer'/syn OR 'biliary tract cancer'/exp OR 'biliary tract cancer' NOT ('meta-analysis':it OR 'meta-analysis as topic'/mj OR 'systematic OR 'biliary tract carcinoma' cholangiocarcinom* review':ti OR 'systematic literature review':ti OR 'meta-analysis':ab,ti ('bile duct':ab,ti OR 'bile tract':ab,ti OR 'biliary tract':ab,ti) AND OR 'meta analysis':ab,ti) OR 'case report*':ab,ti OR 'case series':ab,ti OR ('animal'/exp NOT ('animal'/exp AND 'human'/exp)) OR letter:it OR (cancer*:ab,ti OR carcinom*:ab,ti OR malignan*:ab,ti OR editorial:it neoplasm*:ab,ti OR tumor*:ab,ti OR tumour*:ab,ti) #10 NOT #11 #7 AND #12	Hits 39,381 5,187,553 9,542,276 17,772 20,132 4,577,721 7,040 6,482

(('bile duct' OR 'bile tract' OR 'biliary tract') NEAR/2 (cancer* OR carcinom* OR malignan* OR neoplasm* OR tumor* OR tumour*)):ab,ti 'randomization'/de OR 'single blind procedure'/de OR 'double blind procedure'/de OR 'crossover procedure'/de OR 'placebo'/de OR ((randomi?ed NEAR/2 'controlled trial*'):ab,ti) OR rct:ab,ti OR 'random allocation':ab,ti OR 'randomly allocated':ab,ti OR 'allocated randomly':ab,ti OR ((allocated NEAR/2 random):ab,ti) OR ((single NEXT/1 blind*):ab,ti) OR ((double NEXT/1 blind*):ab,ti) OR (((treble OR triple) NEAR/3 blind*):ab,ti) OR placebo*:ab,ti OR 'prospective study'/de) NOT ('case study'/de OR 'case report':ab,ti OR 'abstract report'/de OR 'letter'/de) 'clinical study'/de OR 'case control study'/de OR 'clinical article'/de OR 'clinical trial'/de OR 'community trial'/de OR 'family study'/de OR 'intervention study'/de OR 'longitudinal study'/de OR 'major clinical study'/mj OR 'open study'/de OR 'postmarketing surveillance'/de OR 'prospective study'/de OR 'retrospective study'/de OR ('prospective study'/de NOT 'randomized controlled trial'/exp) OR 'cohort analysis'/de OR ((cohort NEAR/1 (study OR studies)):ab,ti) OR (('case control' NEAR/1 (study OR studies)):ab,ti) OR (('follow up' NEAR/1 (study OR studies)):ab,ti) OR ((observational NEAR/1 (

Cochrane Library: Wiley Interscience. Cochrane search strategy. 09 th November 2018

	Sr. No.	Query	Hits
	1.	MeSH descriptor: [Bile Duct Neoplasms] explode all trees	203
	2.	MeSH descriptor: [Biliary Tract Neoplasms] explode all trees	356
	3.	"bile duct carcinoma" or "bile duct cancer" or cholangiocarcinoma or	778
		"biliary tract carcinoma" or "biliary tract cancer"
	4.	cholangiocarcinom*	458
	5.	("bile duct" or "bile tract" or "biliary tract") and (cancer* or carcinom*	1,268
		or malignan* or neoplasm* or tumor* or tumour*)
	6.	("bile duct" or "bile tract" or "biliary tract") near/2 (cancer* or	900
		carcinom* or malignan* or neoplasm* or tumor* or tumour*)
	7.	#1 or #2 or #3 or #4 or #5 or #6	1,399
	8.		207,943
		not
		healthy") NEAR/2 surgery)
	9.	#7 AND #8	813
	10.	#9 In Trials	704
	11.	#9 In Cochrane Reviews	87
	12.	#9 in Cochrane Protocols, Clinical Answers, Editorials and Special	22
		collections
	3.

"stage 3":ab,ti or "stage iii":ab,ti or "stage 3a":ab,ti or "stage iiia":ab,ti or "stage 3b":ab,ti or "stage iiib":ab,ti or "stage3":ab,ti or "stageiii":ab,ti or "stage 4":ab,ti or "stage iv":ab,ti or "stage4":ab,ti or "stageiv":ab,ti or metastatic or metasta*:ab,ti or advanced or advanc*:ab,ti or unresect*:ab,ti or relap*:ab,ti or resist*:ab,ti or refract*:ab,ti or ((late* NEAR/2 stag*):ab,ti) or nonresect*:ab,ti or ((non NEXT resect*):ab,ti) or inoperable:ab,ti or "locally advanced":ab,ti or "locally-advanced":ab,ti or local*:ab,ti or ((ineligible or "in eligible" or unfit or "un fit" or "un-fit" or unsuitable or "not amenable" or unamenable or inamenable or unhealthy or "

Medline In-process: PubMed.com. Medline In-process search strategy. 09 th November 2018

	6.	#1 OR #2 OR #3 OR #4 OR #5	41,446
	7.	"stage 3"[tiab] OR "stage iii"[tiab] OR "stage 3a"[tiab] OR "stage	4,018,592
		iiia"[tiab] OR "stage 3b"[tiab] OR "stage iiib"[tiab] OR "stage3"[tiab] OR
		"stageiii"[tiab] OR "stage 4"[tiab] OR "stage iv"[tiab] OR "stage4"[tiab]
		OR "stageiv"[tiab] OR metastatic OR metasta*[tiab] OR advanced OR
		advanc*[tiab] OR unresect*[tiab] OR relap*[tiab] OR resist*[tiab] OR
		refract*[tiab] OR ((late* AND stag*)[tiab]) OR nonresect*[tiab] OR ((non
		AND resect*)[tiab]) OR inoperable[tiab] OR "locally advanced"[tiab] OR
		"locally-advanced"[tiab] OR local*[tiab] OR ((ineligible OR "in eligible"
		OR unfit OR "un fit" OR "un-fit" OR unsuitable OR "not amenable" OR
		unamenable OR inamenable OR unhealthy OR "not healthy") AND
		surgery)
	8.	#6 AND #7	14,717
	9.	(publisher[sb] NOT pubstatusnihms NOT pubstatuspmcsd NOT	449,212
		pmcbook) OR (pubstatusaheadofprint)
	10.	#8 AND #9	156
	Sr. No.	Query	Hits
	1.	Bile Duct Neoplasms[MeSH Terms]	16,747
	2.	Biliary Tract Neoplasms[MeSH Terms]	26,505
	3.	"bile duct carcinoma" OR "bile duct cancer" OR cholangiocarcinoma OR	15,023
		"biliary tract carcinoma" OR "biliary tract cancer"
	4.	cholangiocarcinom*	12,782
	5.		31,055

("bile duct" OR "bile tract" OR "biliary tract") AND (cancer* OR carcinom* OR malignan* OR neoplasm* OR tumor* OR tumour*)

Clinical Systematic Literature Review in rrCCA -21 april 2020Table 2 : Databases searched

 2

	S.	Database/website	Provider/Interface	Filter used for study	Coverage	Hits
	No.			design
	5.	Medline &	EMBASE.com	RCT, nRCT and	No limit	1,940
		EMBASE		observational
				studies
	6.	Cochrane	onlinelibrary.wiley.com	-	No limit	278
	7.	Medline-in-process Pubmed.com	-	No limit	164
	8.	Total				2,382
	1

. Medline and Embase: Embase.com Medline and Embase search strategy. 21 April 2020

	17. 25.	(('bile duct' OR 'bile tract' OR 'biliary tract') NEAR/2 (cancer* OR #10 NOT #11	7,968 5,306,466
	26.	carcinom* OR malignan* OR neoplasm* OR tumor* OR #7 AND #12	8,106
	27.	tumour*)):ab,ti #13 AND [1-10-2018]/sd	1,940
	18.	#1 OR #2 OR #3 OR #4	55,822
	19. 2. Cochrane Library: Wiley Interscience. 'stage 3':ab,ti OR 'stage iii':ab,ti OR 'stage 3a':ab,ti OR 'stage iiia':ab,ti	5,015,317
		OR 'stage 3b':ab,ti OR 'stage iiib':ab,ti OR 'stage3':ab,ti OR
	'stageiii':ab,ti OR 'stage 4':ab,ti OR 'stage iv':ab,ti OR 'stage4':ab,ti OR 'stageiv':ab,ti OR metastatic OR metasta*:ab,ti OR advanced OR Cochrane search strategy. 21 April 2020
	Sr. No.	advanc*:ab,ti OR unresect*:ab,ti OR relap*:ab,ti OR resist*:ab,ti OR Query	Hits
	13.	refract*:ab,ti OR ((late* NEAR/2 stag*):ab,ti) OR nonresect*:ab,ti OR MeSH descriptor: [Bile Duct Neoplasms] explode all trees	218
	14.	((non NEXT/1 resect*):ab,ti) OR inoperable:ab,ti OR 'locally MeSH descriptor: [Biliary Tract Neoplasms] explode all trees	415
	15.	advanced':ab,ti OR 'locally-advanced':ab,ti OR local*:ab,ti OR "bile duct carcinoma" or "bile duct cancer" or cholangiocarcinoma or	1,176
		((ineligible OR 'in eligible' OR unfit OR 'un fit' OR 'un-fit' OR unsuitable "biliary tract carcinoma" or "biliary tract cancer"
	16.	OR 'not amenable' OR unamenable OR inamenable OR unhealthy OR cholangiocarcinom*	662
	17.	'not healthy') NEAR/2 surgery) ("bile duct" or "bile tract" or "biliary tract") and (cancer* or carcinom*	1,760
	20.	#5 AND #6 or malignan* or neoplasm* or tumor* or tumour*)	22,986
	21. 18.	("bile duct" or "bile tract" or "biliary tract") near/2 (cancer* or	2,297,734 1,246
		carcinom* or malignan* or neoplasm* or tumor* or tumour*)
	19.	#1 or #2 or #3 or #4 or #5 or #6	1,992
	20.
		abstract
		report'/de OR 'letter'/de)
	22.	'clinical study'/de OR 'case control study'/de OR 'clinical article'/de OR	5,397,357
		'clinical trial'/de OR 'community trial'/de OR 'family study'/de OR
		'intervention study'/de OR 'longitudinal study'/de OR 'major clinical
		study'/mj OR 'open study'/de OR 'postmarketing surveillance'/de OR
		'prospective study'/de OR 'retrospective study'/de OR ('prospective
		study'/de NOT 'randomized controlled trial'/exp) OR 'cohort
		analysis'/de OR ((cohort NEAR/1 (study OR studies)):ab,ti) OR (('case
		control' NEAR/1 (study OR studies)):ab,ti) OR (('follow up' NEAR/1
		(study OR studies)):ab,ti) OR ((observational NEAR/1 (study OR
	Sr. No. 14. 23. 15. 24.	Query studies)):ab,ti) OR ((epidemiologic* NEAR/1 (study OR studies)):ab,ti) 'bile duct carcinoma'/exp OR 'bile duct carcinoma'/syn OR 'bile duct OR (('cross sectional' NEAR/1 (study OR studies)):ab,ti) #8 OR #9 carcinoma' OR 'bile duct cancer' OR cholangiocarcinoma OR 'biliary cholangiocarcinom* review':ti OR 'systematic literature review':ti OR 'meta-analysis':ab,ti OR 'biliary tract carcinoma' NOT ('meta-analysis':it OR 'meta-analysis as topic'/mj OR 'systematic tract cancer'/syn OR 'biliary tract cancer'/exp OR 'biliary tract cancer' (review:it OR 'review literature as topic'/exp OR 'literature review':ti)	Hits 45,053 6,011,022 20,930 10,162,518
	16.	it OR	22,282
		editorial:it

('bile duct':ab,ti OR 'bile tract':ab,ti OR 'biliary tract':ab,ti) AND (cancer*:ab,ti OR carcinom*:ab,ti OR malignan*:ab,ti OR neoplasm*:ab,ti OR tumor*:ab,ti OR tumour*:ab,ti) ('clinical trial'/exp OR 'randomized controlled trial'/exp OR 'randomization'/de OR 'single blind procedure'/de OR 'double blind procedure'/de OR 'crossover procedure'/de OR 'placebo'/de OR ((randomi?ed NEAR/2 'controlled trial*'):ab,ti) OR rct:ab,ti OR 'random allocation':ab,ti OR 'randomly allocated':ab,ti OR 'allocated randomly':ab,ti OR ((allocated NEAR/2 random):ab,ti) OR ((single NEXT/1 blind*):ab,ti) OR ((double NEXT/1 blind*):ab,ti) OR (((treble OR triple) NEAR/3 blind*):ab,ti) OR placebo*:ab,ti OR 'prospective study'/de) NOT ('case study'/de OR 'case report':ab,ti OR 'OR 'meta analysis':ab,ti) OR 'case report*':ab,ti OR 'case series':ab,ti OR ('animal'/exp NOT ('animal'/exp AND 'human'/exp)) OR letter:

Table 3 :

 3 Inclusion and exclusion criteria for the systematic literature review

	Category	Inclusion criteria a	Exclusion criteria
	Population	 Adults (≥18 years) with advanced,	 Publications reporting on
		metastatic, or surgically	patient populations in the
		unresectableFGFR2+ CCA for whom at	following categories:
		least one treatment has failed	 Children
		 Adults (≥18 years) with advanced, metastatic, or surgically unresectable CCA for whom at least one treatment has failed	 Patients without metastatic and advanced stage  Treatment-naïve patients
			 Resectable CCA
	Line of therapy Second or later lines of therapy**	First-line therapy

Key: CCA, cholangiocarcinoma; FGFR2+, fibroblast growth factor receptor-2.

Table 1 :

 1 Studies included in the endpoint correlation analysis. CR, complete response. DCR, disease control rate (CR+PR+SD). NR, not reported. ORR, overall response rate (CR+PR). OS, overall survival. PD, progressive disease. PFS, progression-free survival. PR, partial response. SD, stable disease. iFAM, 5-fluorouracil, doxorubicin, and mitomycin-C. mFOLFOX, modified FOLFOX, 5-fluorouracil, folinic acid, and oxaliplatin.

	Stu	M	Trial	Ph	Drugs	ORR	O	O	C	P	SD	P	DC	OS -	Med	Med
	dy	es		as		-	R	R	R	R	(%	D	R	Eval	ian	ian
	nu	h		e		Eval	R	R	(	(	)	(	(%	uabl	OS	PFS
	mb	id				uabl	(n	(	%	%		%	)	e	(mo
	er					e	)	%	)	)		)		patie	nths	(mo
						patie		)						nts	)	nths
						nts								(n)		)
						(n)
	Targeted therapies
	2	83	Demols	2R	Regorafenib	33	0	0	0	0	70	3	70	33	5.3	3
		25	2019 (17)									0
	14	84	Sun 2019	2	Regorafenib	34	5	1	0	1	55	2	70	34	7.3	3.6
		18	(18)					4.		4.	.9	3.	.6
								7		7		2
	15	84	Kim 2018	2	Regorafenib	32	2	6.	0	6.	NR N	62	32	9.9	3.7
		58	(19)					3		3		R	.5
	6	54	Goyal	2	Cabozantinib	19	0	0	0	0	26	6	26	19	5.2	1.8
		0	2017 (20)								.3	3.	.3
												2
	7	65	Neuzillet	2	Sunitinib	51	7	1	0	1	70	N	84	53	9.6	3.7
		7	2015 (21)					3.		3.	.6	R	.3
								7		7
	9	12	Buzzoni	2	Everolimus	38	2	5.	2.	2.	42	5	47	39	7.7	3.2
		39	2014 (22)					3	6	6	.1	5.	.2
												3

Table 2 .

 2 OS, Overall survival; PFS, Progression Free Survival; ORR, overall response rate; CI, confidence interval

	Weighted mean	Coefficient of weighted
		correlation
		p-value

Acknowledgements

Shevani Naidoo, Incyte Biosciences UK (project management for the systematic literature review) Jonathan Finzi, Incyte Biosciences FR (project management for the endpoints correlation analysis)

Appendix A

Study selection criteria in the Primary Systematic Literature Review

A. Search Strategies