Enhancement of nonlinear functionality of step-index silica fibers combining thermal poling and 2D materials deposition

: This work proposes a new route to overcome the limits of the thermal poling technique for the creation of second order nonlinearity in conventional silica optical ﬁbers. We prove that it is possible to enhance the nonlinear behavior of periodically poled ﬁbers merging the eﬀects of poling with the nonlinear intrinsic properties of some materials, such as MoS 2 , which are deposited inside the cladding holes of a twin-hole silica ﬁber. The optical waves involved in a second harmonic generation process partially overlap inside the thin ﬁlm of the nonlinear material and exploit its higher third order susceptibility to produce an enhanced SHG.


Introduction
The thermal poling technique is a method to create permanently a second order nonlinear susceptibility in centrosymmetric materials such as glasses. Since its first demonstration [1] and its application to waveguides such as optical fibers [2], a continuous effort has been produced to increase the efficiency of nonlinear phenomena related to the induced second order susceptibility, such as for example second harmonic generation (SHG), spontaneous parametric down conversion (SPDC), or linear electro-optic effect (Pockel's effect).
As the poling-induced second order nonlinear susceptibility is related to the third order nonlinear susceptibility through the formula χ (2) eff = 3 χ (3) E dc [3], it is clear that it is limited by the maximum electric field that can be frozen inside the glass E dc (linked to the dielectric strength of the glass) and by the intrinsic χ (3) of the material the fiber is made of. So far a huge effort has been dedicated to the maximization of E dc via the study and optimization of the poling conditions, in terms of electric configuration of the embedded electrodes [4,5,6,7], type of electrodes adopted for the poling process [8], temperature of the fiber to be poled, or voltage applied through the fiber's core and duration of the poling process [9].
Nevertheless, the maximum electric field E dc that can be frozen inside the glass is ultimately limited by the breakdown field, the maximum static electric field that can be applied through a glass before the latter breaks, and has a value of approximately 1 × 10 7 V/cm [10].
In this paper we demonstrate, both theoretically and experimentally the possibility to enhance the efficiency of the SHG observed in a periodically poled twin-hole silica fiber (PPSF) functionalized with layers of a 2D material deposited inside both the cladding holes (see Fig. 1). As in a twin-hole silica fiber such as the one commonly used for thermal poling experiments [4], the pump and the second harmonic fundamental modes involved in the SHG process can partially overlap even at the interface hole/cladding, if the geometry of the fiber is appropriately chosen (see Fig. 2). If at those interfaces there is a thin layer of a 2D material, characterized by an intrinsic third order susceptibility χ (3) higher than the fused silica one [11], the two waves involved in the second-order nonlinear process partially see this higher χ (3) , with a consequent enhancement of the effective second order nonlinear susceptibility of the periodically poled silica fiber (PPSF).

Fig. 1.
Cross section of the twin-hole fused silica fiber (etched in HF for 60 seconds) used for experimental tests of the enhancement of the second order nonlinearity of a PPSF. The fiber is characterized by a core of 4 µm, a cladding of 125 µm, a "close" air channel of 27 µm of diameter (whose closest edge is located at a distance of 7.2 µm from the fiber's center) and a "far" air channel of 27 µm of diameter (whose closest edge is located at a distance of 13.6 µm from the fiber's center). The same geometry was adopted for the numerical simulations. The shadowed region (highlighted by the dashed red line) surrounding the closest of the two cladding holes indicates the depletion region of the fiber when it is poled in single anode configuration. The rings concentric to the fiber's core instead are due to the fiber fabrication process and do not depend at all on the poling process.

SHG in a periodically poled fiber
Once the χ (2) eff is created inside the optical fiber, in order to observe an efficient second order nonlinear effect, such as for example SHG, it will be necessary to fulfil a quasi-phase matching condition between pump and second harmonic waves [12] by erasing the nonlinearity in a periodic fashion via the method described in [7].
In a PPSF, the second order susceptibility is the result of a third order nonlinear optical rectification process, as suggested by the expression of χ (2) eff reported in section 1. If we consider the SHG, the expression of the nonlinear coefficient related to it will be given by [7]: where the coordinates x and y identify the transverse plane to the direction of propagation (z) of the fundamental mode of the optical fiber, E dc (x, y) is the spatial distribution on the same plane of the frozen-in electric field created via thermal poling, F i (i = 1, 2) is the spatial profile of the modes at the fundamental (i = 1) and at the second harmonic (i = 2) normalized such that: and γ is given by: where ω 1 and β 1 are respectively the pump angular frequency and propagation constant, χ (3) is the third order nonlinear susceptibility of the glass the fiber is made of, c the speed of light, ε 0 the vacuum permittivity and n 2ω 1 eff the effective refractive index of the second harmonic frequency 2ω 1 in the optical field considered.
If the fiber considered is a step-index silica fiber, χ (3) can be assumed constant over the whole cross section of the fiber and has the value of 2 × 10 −22 m 2 V −2 [13].

Layered TMDC materials
Transition metal dichalcogenides (TMDCs) are layered materials with strong (covalent) in-plane bonding and weak (van der Waals) out-of-plane interactions. The combination of these two features enables their exfoliation in two-dimensional layers of single unit cell thickness [14]. Studied for long time, they have become very popular in the last decade, in consequence of the most recent advances in both methods of characterization and device fabrication. Materials such as MoS 2 , MoSe 2 , WS 2 and WSe 2 belong to this category.
What makes TMDCs very attractive for information technology applications is the fact that they are characterized by a wide range of electronic, mechanical, thermal and optical properties which depend on the number of layers the material consists of. Tailoring the number of layers will consequently correspond to changing these properties. A typical example of this versatility is the transition from indirect bandgap to direct bandgap of the MoS 2 , obtained passing from its bulk form (few layers) to its monolayer form. An image of the structure of a generic TMDC layered material, such as MoS 2 , is reported in Fig. 3.

Nonlinear optical properties of TMDCs
TMDCs possess many diverse and interesting optical, electronic and thermal properties that make them very appealing for electronic and nanophotonic applications. Their simplicity of integration with planar devices is a further relevant technological advantage they possess. More Fig. 3. Image representing the schematic of two monolayers of a generic TMDC (M is the transition metal element and X is a chalcogen (S, Se or Te)) extracted from [14]. The monolayer is formed by an atomic trilayer (TL) structure [15].
recently, an attempt has been realized to embed these TMDC layered materials inside the hollow core of anti-resonant silica fibers to modulate their guidance properties by exploiting the change of the electro-absorption of the 2D layer under the action of an external electric field [16].
In the present work we focused on TMDCs nonlinear optical properties, which have been studied in recent years but whose potentialities have been only partially unveiled and exploited so far.
TMDCs have shown nonlinear optical effects of the second order, such as for example SHG [17]. The typical values of χ (2) obtained are ∼10 5 pm/V for mechanical exfoliated monolayer MoS 2 and 5×10 3 pm/V for the CVD-grown films [18]. Those values are both much higher than the best value of χ (2) obtained in a PPSF (0.13 pm/V [8]). Nevertheless, for the type of method of fabrication adopted, which does not allow to get a deposition of the 2D material in a periodic fashion, an eventual contribution to the enhancement of the effective second order susceptibility of the fiber would be negligible due to non-phase matching conditions. Nevertheless, the enhancement of the effective second order nonlinearity of a PPSF could be still pursued via the exploitation of the third order nonlinear susceptibility χ (3) of these materials, which has been estimated to be of the order of 10 −19 m 2 V −2 , approximately three orders of magnitude higher than silica [11,19,20] in the telecom range of wavelengths. As already explained in section 1 we plan to exploit the higher χ (3) for an "enhanced" third order nonlinear optical rectification process.

Methods of fabrication of TMDCs
There are mainly two categories of TMDCs fabrication methods, namely top-down exfoliation and bottom-up synthesis [14]. In the first case flakes atomically thin of the TMDC are peeled from their parent bulk crystal adopting a micromechanical cleavage by means of adhesive tape. Exfoliation in liquids (often organic solvents), associated to a process of ultrasonication, is also a valid alternative to obtain large quantities of TMDC nanosheets.
The bottom-up approaches include chemical vapor deposition (CVD)-type methods, where usually different solid precursors are heated to high temperatures: Sulphur powder and MoO 3 powder are vaporized and co-deposited onto a nearby substrate. Chemical preparation of MoS 2 and MoSe 2 have also been demonstrated using hydrothermal synthesis, which consists in the growth of single crystals from an aqueous solution in an autoclave at high temperature and pressure.
In our work, a bottom-up approach has been adopted to synthesize the MoS 2 inside the cladding holes of a twin-hole fiber (see Fig. 1), consisting on thermal decomposition of liquid precursors at high temperature and low pressure. The fabrication process will be described in more details in section 5.

Enhancement of the nonlinear properties of PPSFs (theory)
In section 2 we have reported the expression of the nonlinear coefficient of the SHG process κ for a step-index fused silica fiber with a germanium doped core. In that case the value of χ (3) can be assumed constant on the whole cross section of the fiber.
If, instead, the fiber is a twin-hole silica fiber with a film of 2D material deposited inside both the cladding holes and running all along the fiber's length, in the calculation of κ we should consider that the χ (3) will assume two different values according to the region of the fiber's cross section considered, and in particular it will assume the value of silica inside the core and the cladding region, while it will assume the value of the 2D material in the tiny ring of the film deposited inside the two cladding holes. It is also important to highlight that the presence inside the cladding holes of this film affects the spatial distribution of the light modes guided inside the optical fiber.

Numerical simulations
In order to take into account the variations in the spatial distribution of the guided modes at the pump and second harmonic we computed their profile with Lumerical. The fiber simulated is a twin-hole fused silica fiber (NA = 0.17) with a geometry identical to the one reported in Fig. 1. The latter is characterized by a core of 4 µm, a cladding of 125 µm, a "close" air channel of 27 µm of diameter (whose closest edge is located at a distance of 7.2 µm from the fiber's center) and a "far" air channel of 27 µm of diameter (whose closest edge is located at a distance of 13.6 µm from the fiber's center). Then a layer of a material characterized by a refractive index of 4 at 1550 nm (simulating a 2D material such as the MoS 2 ) has been added to the geometry of the fiber inside each channel. The thickness of this layer has been varied from 1 nm to 5 nm in step of 1 nm and the spatial distributions of the fundamental modes for pump (1550 nm) and second harmonic (775 nm) have been calculated. The refractive indices used in the simulations are the ones of fused silica for the cladding region and doped silica for the core (supplied by the library of Lumerical).
The distribution of the frozen-in electric field due to the thermal poling process has been obtained via COMSOL Multiphysics for a fiber of identical geometry. The simulated poling conditions are a temperature of the sample of 265°C, a single-anode poling configuration (V app = 8 kV), and a duration of the poling process of 120 minutes. The initial concentration of the Na + charges (characterized by a mobility of 2 × 10 −15 m 2 V −1 s −1 at 265°C and uniformly distributed inside the cross section of the fiber) is 1 ppm, while the concentration of the H 3 O + (characterized by a mobility of 2 × 10 −18 m 2 V −1 s −1 ) is initially null and then varies in time proportionally to the electric field at the interface hole/cladding, as suggested by Eq. (5) of [3]. The proportionality coefficient σ 2 , appearing in the same equation, is assumed identical to the one adopted in [3].
The value of κ has been calculated using the formula given by the Eq. (1) over a rectangular area limited by the points of coordinates x and y (-7, 7), (13, 7), (-7, -7) and (13, -7)µm plus some points located along the two semicircles representing the interfaces between the cladding holes and the 2D material layers deposited. Figure 4 reports the schematics of all the points of the fiber's cross section where κ has been computed.
The value of κ calculated for a deposited fiber has been compared to the value obtained for the same fiber empty (with no 2D films deposited). The ratio between the two values of κ represents the net enhancement of the quadratic nonlinearity of the PPSF due to the interaction between the light waves involved in the SHG process. The ratio has been calculated for the five possible thicknesses of the deposited 2D films and is reported in Table 1.  Fig. 1, where it is shown a matrix of vertical and horizontal lines whose intersections represent the discrete points where the value of κ has been calculated using the formula of the Eq. (1). Only the intersections located between the two semicircles are actually considered for the calculation of κ. In bold squares are instead highlighted the points along the two semicircles corresponding to the interfaces between the cladding holes and the 2D layered material deposited. In the case of the empty fiber these two semicircles correspond to the interfaces between the cladding holes and the fiber's cladding. The center of the fiber is located at (0,0) coordinates and the central dashed red circle indicates the region occupied by the core of the fiber. The results reported in Tab.1 indicate that for a fiber with a geometry such as the one of Fig. 1 the enhancement effect (due to the presence of the 2D film deposited inside the two channels of the PPSF) on the SHG nonlinear coefficient κ is ∼1.7%. The effect of the enhancement is due to the interaction of the two light waves involved in the nonlinear process with the 2D material, characterized by a value of χ (3) of 10 3 times bigger than the value of χ (3) of fused silica [11].
Although the result of 1.7% for the enhancement factor could appear not extraordinary, it represents first of all a theoretical proof of principle of a more general approach which sees in the fusion of the two aspects (nonlinearity due to thermal poling and to 2D material) a potential way forward towards a better exploitation of the effects of thermal poling in conventional and non-conventional optical fibers. Furthermore, we performed few more simulations with the aim of demonstrating that the enhancement of the nonlinear coefficient κ depends also on the geometry of the fiber chosen. We assumed two alternative situations, namely the same type of twin-hole fiber shown in Fig. 1 and adopted for the simulations reported so far, but with the cladding channel where the electric potential is applied (the closest hole to the fiber's core) located alternatively at 6.2 µm and 5.2 µm of distance from the fiber's center (instead of the original distance of 7.2 µm). The position of the second hole (the farthest one) is assumed the same as before (13.6 µm) from the fiber's center, for the sake of simplicity. The fiber was assumed to be poled in the same conditions as before, apart of course for the distance of the single electrode from the fiber's core, and the κ factor was calculated for two conditions, namely fiber empty (not functionalized) and fiber functionalized with 5 nm of 2D film in both the cladding holes. Enhancement factors of 5.9% and 18.1% were respectively obtained for the two cases considered (1 µm and 2 µm closer). This means that by slightly changing the position of the 2D film with respect to the center of the fiber it is possible to significantly change the overlap between the modes involved in the nonlinear process considered and the intrinsically nonlinear layer, enhancing more significantly the nonlinear response of the functionalized PPSF.

Enhancement of the nonlinear properties of PPSFs (experiments)
In section 4 we have theoretically detailed the possibility of enhancing the nonlinear properties of a periodically poled fiber merging the effect of the thermal poling with the presence of a film of a material characterized by a third order susceptibility significantly higher than the one of the glass the fiber is made of. This section is dedicated to reporting the experimental evidence of this theoretical prediction.

Fabrication of functionalized PPSF: deposition of TMDC film
The fabrication of the fiber functionalized with MoS 2 inside the cladding channels was realized adopting a solution-based thermal decomposition processing method presented by Liu et al. [21] who used a mixture of dimethylformamide (DMF) with an ammonium tetrathiomolybdate, (NH 4 ) 2 MoS 4 single source precursor. Yang et al. [22] further improved the wettability of the solvent through the introduction of aminoethanol and butylamine to the solvent solution.
Taking inspiration from [22], a solution of 0.1 g of single source precursor dissolved in a mixture of 4.5 ml butylamine, 4.5 ml dimethylformamide and 1 ml of aminoethanol was prepared. The solution prepared was then infiltrated into the two channels of the twin-hole fused silica Ge-doped step index fiber (see Fig. 1) until approximately 0.3 m of the 0.8 m long fiber had been filled. The fiber partially filled with the solution was placed in a Petri dish and kept at a temperature of 90°C for 15 minutes to promote an initial thermal annealing process. The fiber has been then placed into a furnace and heated at 26 mbar pressure with 100 sccm of 6% H 2 /Ar flow, annealing for 2 hours at 500°C.
The synthesized MoS 2 film was then characterized using a Renishaw InVia micro-Raman system. All measurements were performed using 532 nm excitation wavelength, with 20 mW incident power and 50x (0.63 NA) objective. This allows for a non-destructive probe to determine both the film quality and thickness. A typical Raman response obtained from our twin-hole fiber is reported in Fig. 5, where the in-plane E 1 2G and the out-of-plane A 1G Raman modes, located at 382.9 cm −1 and 403.8 cm −1 respectively, are reported. For 2D-TMDC films, it is well known [23] that the wavenumber separation of the Raman peaks is strongly indicative of the number of layers composing the film. Figure 5 shows the Raman spectra collected at three different positions along the length of the deposited sample, namely 0, 12 and 23 cm. An average separation (∆k) between the two peaks of 23.2 cm −1 has been found, corresponding to a trilayer film thickness [23]. Furthermore, the 8.1 cm −1 FWHM of the peaks suggests a polycrystalline deposition [24].
The fiber was analyzed with the 532 nm excitation laser focused through the silica cladding. A baseline measurement of the data was therefore also performed to remove the silica Raman background and any additional noise arising from scattering. The Raman spectra have been collected all along the 25 cm of the fiber, and Fig. 5 reports three of those peaks collected respectively at the beginning, half and end of the fiber. The similarity between all the peaks recorded along the whole sample demonstrates the good homogeneity of the deposition process.

Fabrication of functionalized PPSF: poling and UV erasure of χ (2)
After the Raman-based analysis of the sample deposited, the piece of the fiber identified as correctly functionalized with the MoS 2 film has been selected and equipped with a metallic liquid electrode (Mercury) in the cladding channel closer to the fiber's core. The fiber was then thermally poled in single anode configuration at 265°C with an electric potential of +8 kV applied to the embedded electrode, for 2 hours (experimental conditions identical to the ones of the numerical simulations reported in section 4). The liquid electrode was afterword removed and the fiber was tested again with Raman analysis, to confirm that the layer of TMDC materials has not been damaged or removed by the thermal poling process. We did not find any significant difference to the film quality post-poling. A piece of the fiber deposited and poled was selected to be UV erased (using the same setup already described in [7]) to observe SHG at a wavelength around 1550 nm.
The UV light source is CW argon ion laser frequency doubled to 244 nm, with an acousto-optic modulator (AOM, Gooch and Housego: M110-10UV-SU8) used to modulate the laser output. The laser is focused to a circular spot, 20 µm in diameter, above an Aerotech A3200 four axis linear stage. The poled fiber to be UV erased is clamped onto the linear stage by two fiber rotator clamps, with one clamp mounted on a vertical axis manual translation stage and the other mounted on a force gauge. The laser is modulated using the AOM while translating the fiber core through the spot to achieve a grating of the desired duty cycle and period. For the grating a fluence of 14 J/cm 2 and a duty cycle of 5% was used to periodically erase the nonlinearity. The period of the grating was chosen to be 55 µm in order to have quasi-phase matching at a wavelength of ≈ 1550 nm. The sketch of the setup used to realize the UV erasure process is reported in Fig. 12 of [7]. A grating of the same period was written on an untreated sample of fiber poled in the same experimental conditions as the one functionalized.
Before erasing the nonlinearity, both the untreated and the functionalized fiber were spliced on both sides to two pieces of step index fiber (Thorlabs, SM980).

Experimental results
After the erasure process, the fibers have been characterized in terms of nonlinear coefficient of the quasi-phase matched SHG process. The setup used to realize the characterization is the same reported in Fig. 13 of [7]. The polarization of the pump light has to be aligned to the axis of orientation of the frozen-in electric field E dc such that in the SHG process only the type-I process X + X → X is considered [25]. Figure 6 shows the tuning curves obtained for the two different fibers. The ratio between the nonlinear coefficient κ of the two PPSFs (respectively one functionalized with MoS 2 and one untreated) experimentally obtained produced an enhancement factor of 10% (best value obtained over few samples).
The discrepancy between the values of the enhancement factors of κ numerically calculated and experimentally obtained (1.7% and 10% respectively) for the fiber of Fig. 1 is mainly due to the possible differences between the parameters of the fiber used in the numerical simulations (core's diameter, effective refractive indices of core and cladding) and the actual parameters of the fiber experimentally used. In section 4.1 we have indeed demonstrated numerically for example that by slightly changing the relative position of the cladding holes and the fiber's core the value of κ changes significantly. Another source of discrepancy can be represented by the possible experimental errors done in the two distinct grating fabrication processes of the two different fibers (functionalized and pristine).
The linear losses measured at 1550 nm for the PPSF are 2.5 dB for 30 cm (including the splice losses due to the two interfaces between the PPSF and the buffer fibers (SM980), while the linear losses measured at 1550 nm for the PPSF functionalized with MoS 2 are of 5 dB. The increase of the linear losses is likely due to increased scattering from the interaction between the pump at 1550 nm and the polycrystalline 2D film, as well as with an increased contribution to the splice losses due to the presence of this 2D layer during splicing. This last contribution could be easily reduced by choosing more appropriately the position of the splices to avoid the MoS 2 . It is worth also considering that the SH light generated at 775 nm is close to the electronic bandgap of the MoS 2 layer which could result in increased optical loss due to 2D material self-absorption. This contribution would cause an underestimation of the final SHG efficiency.

Conclusions
The comparison between the enhancement factor experimentally obtained and the values theoretically calculated and reported in Table 1 demonstrates both experimentally and theoretically that the introduction of a film of 2D material such as the TMDC MoS 2 inside the cladding holes of a PPSF produces an effective increase of the nonlinear susceptibility created inside it via thermal poling. The phenomenon is due to the increase of the third order nonlinear susceptibility χ (3) of the fiber due to the presence of the 2D film.
The discrepancy between the values of κ numerically calculated and experimentally obtained can be mainly explained as due to the difference between the fiber's geometry used in the numerical simulations and the actual geometry of the fiber used experimentally. Apart from this discrepancy in the absolute value of κ, the proof of principle method correlates well to both the numerical simulations and experiments. Nevertheless, we are necessarily limited by the step index poling configuration, while well-engineered overlap integrals such as those we can tailor via microstructured fibre design could result in orders of magnitude SHG efficiency increase.
Furthermore, this result can open up the way towards a revolution in the nonlinear functionalization of optical fibers through not only the merge of thermal poling and deposition of intrinsically nonlinear materials, but also the exploitation of the higher second order nonlinearity of these materials provided that they are synthesized in a periodic fashion to guarantee the Quasi Phase Matching between the wavelengths involved in the nonlinear process considered. Apart from TMDCs, other potential candidates for the scope are for example Tellurium and Tellurium-based materials [26,27].