Monolithic optofluidic mode coupler for broadband thermo- and piezo-optical characterization of liquids

: We present a monolithic ﬁber device that enables investigation of the thermo- and piezo-optical properties of liquids using straightforward broadband transmission measurements. The device is a directional mode coupler consisting of a multi-mode liquid core and a single-mode glass core with pronounced coupling resonances whose wavelength strongly depend on the operation temperature. We demonstrated the functionality and ﬂexibility of our device for carbon disulﬁde, extending the current knowledge of the thermo-optic coe ﬃ cient by 200 nm at 20 °C and uniquely for high temperatures. Moreover, our device allows measuring the piezo-optic coe ﬃ cient of carbon disulﬁde, conﬁrming results ﬁrst obtained by Röntgen in 1891. Finally, we applied our approach to obtain the dispersion of the thermo-optic coe ﬃ cients of benzene and tetrachloroethylene between 450 and 800 nm, whereas no data was available for the latter so far.


Introduction
Integrated optofluidics combines photonics with microfluidics and represents an emerging research field which spawned several revolutionizing innovations such as liquid crystal displays, liquid lenses and microfluidic sensor chips. Liquids possess unique features such as tunability, exchangeability and the capability to transport high concentrations of particles, which make them highly attractive for photonics. First pioneering approaches combining these advantages with the properties of optical waveguides were demonstrated on optofluidic chips to study biological samples in-vivo [1], to analyze the refractive index (RI) of aqueous solutions [2], to achieve mechanically tunable optical switching and lasing in the visible [3], as well as to efficiently couple light into plasmonic architectures [4]. With respect to fiber optics, liquid-filled optical fibers were successfully employed for photonic bandgap guidance [5], all-fiber integrated dye lasers [6], chemical microreactors [7], nonlinear optical coupling [8], and nonlinear light generation [9][10][11].
Taking full advantage of the tuning capabilities of the optical properties of liquids for further improvements of optofluidic devices requires understanding the dependency of liquids on various external influences such as temperature or pressure, i.e., obtaining knowledge on thermo-and piezo-optic properties. Although the RI of most liquids is known, only little work was conducted to unlock their relation to temperature [12] or pressure [13]. The spectral distribution of the thermo-optic coefficient (TOC) is largely unknown for many liquids, even though this quantity offers great potential with regard to, e.g., dispersion tuning for nonlinear light generation or tunable integrated filters. Even less knowledge is present for the piezo-optic coefficient (POC), which is hardly measured for almost any liquid.
Determination of TOC and POC requires sensors of high sensitivity operating at multiple wavelengths. For instance, devices based on fiber Bragg gratings [14] and interference effects [15][16][17] enable RI sensing at sufficiently high sensitivity levels but suffer from rather limited spectral bandwidths. Other approaches rely on monitoring the transmission bands of complex liquid-filled photonic bandgap fibers [18,19] or other microstructured fibers [20]. Although the mentioned approaches work in principle, they require complex fiber designs, sometimes extensive post-processing and precise knowledge about the respective microstructure, which demand extensive numerical calculations using commercial finite element solvers to correlate the measured results with simulations. The use of simpler geometries can circumvent those issues and in particular allow for the fast and precise determination of TOC and POC over a sufficiently large spectral domain as we will show within this work.
Recently, a comparably simple fiber-based unidirectional mode coupler consisting of a liquid channel and an adjacent dielectric core was shown to enable high-precision temperature measurement [21]. This device relies on coupling of the modes of a liquid channel and a glass core, yielding precisely defined dips in the transmission spectrum, with the resonance wavelength strongly depending on the RI of the liquid. The spectral positions and thus the analysis of the resonances only requires determining the phase matching points of the isolated (uncoupled) modes involved, which is substantially faster than simulating supermodes of complex fiber architectures. Therefore, this device offers a straightforward analysis approach which does not demand intense numerical calculations.
Here, we extend the work by Lee et al [21] in order to determine the spectral distributions of the TOCs and POCs of carbon disulfide (CS 2 ), tetrachloroethylene (TCE, C 2 Cl 4 ) and benzene (C 6 H 6 ) over a large range of wavelengths, temperatures and pressures using a monolithic liquidencapsulating and fiber-based hybrid bidirectional coupler (HyBiC). The working principle and the optical properties of the device are described in Sec. 2 followed by sample fabrication, measurement setup and data processing (Sec. 3). The results referring to TOC measurements and a detailed description of the POC determination technique including results are presented in Sec. 4.

Background
The operational principle of our fiber device relies on coupling of the fundamental mode of a glass core to the guided higher-order modes propagating in a parallel liquid-filled channel (see Fig. 1(a)). At characteristic wavelengths both modes phasematch, leading to pronounced dips in the transmission spectrum of the glass core mode. The spectral positions of these dips strongly depend on the RI of the enclosed liquid, which allows analyzing its TOC and POC via examining the change of the individual resonance wavelength.
In our situation, the modal behavior in the coupling section can be described by coupled mode theory (CMT), which is an appropriate mathematical description in case the modes only weakly interact via their evanescent fields, i.e., the coupling does not significantly change the mode pattern of the isolated Eigenstates. The weak coupling assumption holds for large separations between the cores, allowing to define the normalized power p(z) in the glass core by [21,22] with the coupling constant C, the isolated mode dephasing, i.e., difference in propagation constant, ∆β = ∆β co − ∆β liq (corresponding to ∆n eff = ∆βλ/2π with the effective mode index n eff ) and the propagation coordinate z. In case of phase-matching the modal dispersions cross (∆n eff = 0) at the phase-matching wavelength λ PM and maximum power transfer is possible, with the energy oscillating between the two cores according to p(z) = cos 2 (Cz). This leads to a strongly modified transmission of the glass core mode at characteristic wavelengths, which we denote here as resonances (e.g., Fig. 2). A more rigorous, assumption free, description of the modal behavior in the dual-core waveguide section relies on modal interference of the supported supermodes and becomes relevant in case of small waveguide separations. This description requires calculating the modes of the entire dual-core waveguide geometry, the so-called supermodes. Here, we calculated the dispersions of supermodes using a commercially available finite-element solver (COMSOL Multiphysics) for a few resonances using the parameters of our experimentally fabricated device  (glass core and liquid channel diameters: D C = 1.7 µm, D L = 2.66 µm, center-to-center pitch: 4 µm, core RI distribution at 479 nm: n co = 1.4636 + 14.45 × 10 −3 (1 − (r/0.85 µm) 2 ) with r as radial coordinate in µm, n liq = 1.6558, n cl = 1.4636). The simulations reveal that the CMT sufficiently approximates the modal behavior for our fiber design since the phase-matching wavelengths (minimum of red line in the inset of Fig. 2) excellently agree with the minimum of the supermode dephasing (minimum of blue line in inset of Fig. 2).
Here, the supermode theory is only required for optimizing the coupler with respect to fringe contrast (i.e., depth of transmission dip) being directly related to the coupling length. Due to the beating, i.e., interference of the two supermodes within the coupling section, the output intensity of the glass-core mode is strongly wavelength dependent [23] and in the case of a lossless system is given by [24] I out (z) = I in cos 2 ∆β S M 2 z with ∆β S M = 2π/λ(n e eff − n o eff ) being the supermode dephasing between the even and odd supermodes. From Eq. (2) the coupling length is defined by L C = 1/∆β S M , which approaches experimentally feasible lengths of the order of a few millimeters at resonance, i.e., at the wavelengths of smallest ∆β S M . To achieve a strong fringe contrast, i.e., for the most efficient energy transfer into the liquid core, the periodic condition L f /L C = mπ (m: integer) has to be fulfilled, indicating multiple optimal propagation lengths L f per resonance. In case multiple resonances at different wavelengths are present, the periodicity of the optimal coupling condition allows to make use of the wavelength dependency of L C to find an optimized length of the liquid column (see Fig. 8 in Appendix) to achieve a sufficient fringe contrast for all transmission dips considered.
The measurement of the TOC relies on the fact that the individual phase-matching wavelength strongly depends on the dispersions of the modes involved. It is important to note that many liquids exhibit TOCs which can be up to two orders of magnitude larger than that of fused silica  (0.1 × 10 −4 K −1 ; visible to NIR [25]), and thus the dominant contribution of the measured resonance shift can be attributed to the thermal-optic response of the liquid as verified by simulations. The resonance shifts also allow measuring the POC as discussed later.

Sample geometry
The fiber geometry considered here is a partially liquid-filled modified graded-index fiber (MGIF) with a graded-index GeO 2 -doped core (doping level: 11 mol%, diameter: 1.7 µm, n co = n glass +14.45 × 10 −3 (1−(r/0.85 µm) 2 )) and a parallel running microchannel (diameter: 2.66 µm (slightly deviating for different samples)), both embedded in silica (core-channel center-to-center distance: 4 µm). Preliminary measurements confirmed that the glass core is single mode for the wavelength range relevant here and guidance can be achieved up to 0.9 µm. The final device can be divided into three sections (see Fig. 1(a), 1(c) top): (i) a delivery section with an empty channel, (ii) a coupling section where the glass core and the liquid channel form a hybrid directional coupler, and (iii) a second empty section for guiding the light to the diagnostics.

Sample fabrication
The fabrication of the empty fiber host relies on the stack-and-draw approach and is described elsewhere [26,27]. To provide reproducible measurement conditions and samples with long-term stability the liquid under investigation was enclosed in the middle of a 30 cm long MGIF (see Fig. 1(a)) using the following procedure: The empty MGIF was cleaved, inserted into a large liquid reservoir and partially filled via capillary action. After filling, the channel was collapsed at one side using a fusion ring-arc splicer directly next to the liquid's meniscus (see Fig. 1 The other side of the sample was shut at a desired liquid column length by a second fusion arc either directly within the liquid-filled section or after stepwise evaporation with low power arcs or via slow evaporation on a hot plate until the second collapse point. This procedure was successfully employed to encapsulate several hundreds of picoliters of carbon disulfide (CS 2 ), tetrachloroethylene (TCE, C 2 Cl 4 ), and benzene (C 6 H 6 ). Due to its low boiling point CS 2 allowed a controlled collapse at any desired position by just applying one single arc, whereas benzene (low power arcs) and tetrachloroethylene (hot plate) had to be evaporated until the desired filling length before collapsing.

Measurement setup
The optical characterization setup consists of a broadband light source, a temperature-controlled sample mount and spectral diagnostics (see Fig. 3). The probe light was delivered by a supercontinuum source (0.4 µm to 2.4 µm, NKT Photonics SuperK) and polarization-controlled via a thin-film polarizer. A water cuvette in the beam path avoided undesired heating of the sample by removing the near-IR contributions. The light was coupled into and out of the fiber with 20x microscope objectives (OBJs). The sample was mounted in fiber clamps and fixed either on a Peltier element or a hot plate, with the temperature being measured close to the liquid-filled section by a thermocouple. A multimode fiber (MMF) was used to direct the light into an optical spectrum analyzer (OSA, Instrument Systems Spectro 320), with an additional iris diaphragm blocking undesired cladding light. For each sample the transmitted spectrum was measured at different temperatures. No polarization dependence was found in case of CS 2 and therefore the input polarization was arbitrarily chosen to be parallel to the connection line between glass core and channel for all measurements.
Due to the multimodeness of the liquid core the measured spectra reveal multiple resonances (i.e., transmission dips), which allow determining the TOCs with high precision at different spectral locations. However, due to the encapsulation of the liquid, the device operates in two types of modes depending on temperature (see Fig. 1(c)): 1. In the isobar regime (regime 1 in Fig. 1(c)), the liquid can freely expand in the enclosed volume and the resonance shift is dominated by the temperature dependency of the RI, allowing to determine the TOC. Here, the internal pressure of the liquid is given by its vapor pressure, which is typically very low, allowing to neglect the contribution of the POC in this regime.
2. In the isochor situation (regime 2 in Fig. 1(c)), the liquid has achieved its maximum expansion, and the resonance shift is additionally influenced by the pressure dependency of the RI of the liquid which allows investigating the POC. The latter is typically not straightforwardly accessible and measurements (if existing) are limited to comparably low pressure domains.

Data processing and TOC extraction
The determination of the TOC requires the following data processing: Residual Fabry-Pérotlike oscillations from the laser source were removed from the measured spectra via Fourier filtering. By removing the resonance dips from the spectrum at 20°C (25°C for C 2 Cl 4 ) and fitting the resulting envelope spectrum by a polynomial of ninth degree a spectral reference was created. All other spectra were subtracted from this reference to isolate the transmission dips. To determine the resonance wavelengths a threshold transmission level (e.g. -5 to -10 dB transmission contrast) was defined to identify the left and right edge of the individual dips, with the resonance wavelength λ R ,m (m: resonance number) being the geometrical weight of the two edge wavelengths, which allows for fast data processing. Finally, the TOC is determined via simulations by adjusting the RI of the liquid core ∆n m such that the phase-matching wavelengths λ PM of the freshly calculated liquid-core modes with the glass-core mode match the measured resonance wavelengths λ R ,m (i.e., n eff ,glass = n eff ,liq (n liq +∆n m ) ⇒ λ PM = λ R ,m with the effective index in the respective medium n eff ,i ). This overall translates the wavelength shift into an RI change. Using the known fiber geometry and material parameters at 20°C (25°C for C 2 Cl 4 , see Appendix Table 3), the dispersions of liquid and glass cores have been calculated by using the fiber dispersion relation [22] and a Finite-Element solver (COMSOL Multiphysics), respectively. Small systematic derivations have been compensated by matching experiment and simulation at 20°C (25°C for C 2 Cl 4 ) (calibration step). For each resonance a linear fit of the temperature dependent RI change ∆n m (∆T ) vs. temperature yields a TOC value for the corresponding wavelength λ R ,m and temperature range.

Thermo-optic coefficient
The measured transmission spectra of the CS 2 -samples show strong transmission dips distributed over the entire transmission window of the HyBiC (see Fig. 4(a)). Reducing the temperature results in a red-shift of the dips indicating an increase of the RI of the CS 2 (see Fig. 4(b)). Conversely, the transmission dips shift to shorter wavelengths for higher temperatures due to a decreasing RI. Both facts suggest that CS 2 exhibits a negative TOC, which is in accordance with literature. Depending on temperature, several dips shift out of the transmission window of the fiber and new ones appear. It is important to note that the encapsulation of the liquid allows heating the liquid above its boiling point without enforcing a first-order phase transition, i.e., the liquid does not migrate into the gas phase at any of the temperatures considered.
For temperatures above a certain threshold the device enters the second operation (isochor) regime (see Fig. 1(c) right) in which the wavelengths of the resonances do not change when increasing temperature (see Fig. 5(a)). This regime allows determining the POC and is investigated in more detail in Sec. 4.2. A second sample confirms the emergence of the isochor regime (see Fig. 5(b)) at a different transition temperature.
The isobar regime (indicated by the light yellow background in Fig. 5) below the plateau allows the determination of the TOC of CS 2 . We measured the transmission spectrum for different temperatures between -10°C and 125°C in steps of 5 K. Using the procedure mentioned in Sec. 3, the spectral distribution of the TOC of CS 2 was determined and compared with published data (see Fig. 6(a)). The error bars result from the statistical error of the linear fit. The measured TOCs fit very well to the existing literature data and extend the known TOC distribution of CS 2 for about 200 nm towards the near-IR up to a wavelength of 900 nm.
The encapsulation prevents CS 2 from evaporation and, thus, allows for the investigation of the temperature dependency of the TOC within certain wavelength domains (see Fig. 6(b)). The absolute TOC value of CS 2 increases for increasing temperature as shown in Fig. 6(b). To our knowledge this behavior was not observed for a liquid before, but it matches the general behavior  of other materials such as glasses [28] or crystals [29] and highlights the unique measurement capabilities offered by the HyBiC design. We repeated the TOC determination procedure for fibers filled with benzene and TCE. We chose benzene due to the large amount of available reference data and its moderate RI (n D = 1.447 [35]) which suggest the appearance of a significant number of resonances. TCE instead is barely investigated in literature, but offers a comparably large RI (n D = 1.504 [36]) and a wide transmission window into the mid-IR [37]. Preliminary simulations and experiments have shown that in case of the low RI liquids the difference of the resonance wavelengths of the two different polarization Eigenstates is negligible and does not influence the values of TOC and   [30], 2 [31], 3 [32], 4 [33] and 5 [34]). The inset is a close-up of the measured wavelength region of this work. Each red dot relates to one resonance. The vertical error bars correspond to error margins of the fits and the dashed horizontal lines indicate the spectral interval of the resonance data used for the TOC fit. (b) Measured temperature dependence of the TOC for different wavelengths. The given wavelengths are mean values and the corresponding raw data can be found in the Appendix (see Fig. 9). POC presented in the following, as only the relative temperature-induced spectral shift is relevant for determining TOC and POC and the shift obtained from the initial calibration step (performed to match simulation and measurement at room temperature) is significantly larger than 1 nm. As a result, the influence of input polarization on TOC and POC values is negligible as long as the input polarization state is identical within one measurement set, which was ensured in our experiments.
Due to the simplicity of the fabrication process four to six samples were fabricated with different filling lengths and the samples with highest resonance contrasts were chosen for the further experiments. In case of benzene the transmission window on the long wavelength side was limited to about 700 nm (see Fig. 7) which we attribute to high absorption of carbon oxide residuals in the thermally processed areas next to the collapse points. Instead the TCE samples were partially placed on a hot plate and slowly tempered to adjust the length of the liquid column, reducing impurities inside the hollow channels and thus maintaining the transmission.
Using the same procedure as described for CS 2 , the TOCs of both liquids have been determined, with an excellent agreement with literature for benzene (see Fig. 7(a)). In case of TCE, no literature values were found and the data shown in Fig. 7(b) represent, to our knowledge, the first TOC values of this liquid made available for the international community.
The two TOC values in the near-IR come with rather large error margins due to strong spectral modulations of the two last resonances (insets in Fig. 7 above 700 nm), making the determination of the center wavelength of these resonances critical.
It is important to note that we did not observe a change in the slope of the resonance shift as in case of the plateau formation of CS 2 for high temperatures. This can be explained by smaller TOC values of benzene and TCE and larger empty gaps between the collapse points and the two menisci (Sec. 4.2), providing more free volume for the liquids to expand. Moreover, the lower RIs of the two liquids lead to a smaller number of modes being supported by the liquid-core, with the consequence that at comparably high temperatures, the RIs of the liquids approach such small values that all phase-matching wavelengths shift out of the transmission window of the fiber, leaving no resonance to monitoring the isochor regime. As we explain in Sec. 5, this problem can be circumvented by an improved MGIF design.

Piezo-optic coefficient
As next step we investigated the plateau behavior of CS 2 for high temperatures (see Fig. 5), which results in a novel method to determine the POC. As described above increasing temperature enforces CS 2 to expand until filling out the entire available channel volume between the two collapses. A further increase in temperature leads to a drastic increase of the internal pressure of the liquid, with the consequence that the piezo-optic effect cannot be neglected anymore and the device operates in a different regime, which, in the CS 2 situation, leads to the observed plateau effect (Fig. 5 for T > 100°C). The transition (or plateau onset) temperature can be calculated from the maximum length the liquid can expand, i.e., the distance between the two collapses minus the initial liquid-filled column length. The transition temperature T t in°C at which the initial volume of the liquid V 0 has reached its maximum extension V C is given by: with collapse distance l C , initial liquid column length l 0 and the volumetric coefficient of expansion α V (assumed to be temperature independent) In the case of CS 2 α V is 1.12 × 10 −3 K −1 at 20°C [39]. The calculated and measured values of the transition temperature are close to each other (see Table 1) and confirm the restricted volume available for expansion as the origin of the different resonance shifting behavior, i.e., the emergence of the plateau. The deviations in temperature (see Table 1) can be explained by (i) the shape of the tapered channel located in the vicinities of the collapses which were neglected in our estimation, by (ii) pressure variations in the residual gap volume, and by (iii) the assumption of a temperature independent volumetric coefficient of expansion. Above T t the internal pressure of the liquid dramatically increases to several hundreds of MPa (i.e., several thousands of bars) and therefore the POC neglected so far has to be taken into account. The internal pressure change of the liquid can be estimated via the isothermal compressibility κ Eq. (4) allows to calculate the theoretical volume change dV = V α V dT in absence of confinement which is treated here as compression, and is inserted with negative sign in Eq. (5). The resulting expression dp = α V /κdT connects a temperature change with a pressure change. The change of RI including the piezo-optic effect is then given by  with (dn/dp) T = 682 × 10 −12 Pa −1 (546 nm, at 23°C) [34], κ = 9.38 × 10 −10 Pa −1 (at 20°C) [39] and α V of CS 2 as given above. The second term in the bracket of Eq. (6) becomes 8.14 × The observed pressure dependency allows introducing a novel method for determining the POC. First, the TOC is determined with the above mentioned technique near T t and is treated as constant in the following. The term in the brackets of Eq. (6) is defined as the slope parameter a of a linear fit of the resonance shift above the transition temperature which is accessible by measurements. If literature data for κ and α V is available, the POC is given in the vicinity of the transition point by dn dp This POC value is an approximation since the isobaric (see Eq. (4)) and the isothermal (see Eq. (5)) conditions have been neglected. However, the following calculations and the agreement to the literature values confirm the validity of the approach under the present experimental conditions. Three modes of the sample shown in Fig. 5(a) have a near-zero slope (a ≈ 0) allowing to obtain POC values at different wavelengths (listed in Table 2) using the corresponding measured TOCs. The pressure of CS 2 in the vicinity of the transition point is in the range of several hundred bars. Röntgen and Zehnder [13] investigated the temperature dependence of the POC of CS 2 at 589.5 nm with an interferometric method and proposed a linear relation between temperature and POC. A linear extrapolation of their values gives a POC of 999 × 10 −12 Pa −1 at 113°C, which is very close to the last value in Table 2, and confirms that the POC determined with our method yields a physically reasonable value being consistent with a measurement from 1891.

Discussion of device properties
Here, we have demonstrated that a fiber-based HyBiC allows measuring TOCs and POCs at usually inaccessible high temperatures and pressures. In the following, we discuss the characteristics of this measurement approach and how the operation domain of the current device can be extended.
A major advantage of the HyBiC is that it is not restricted to the geometric parameters used in this work. The phase-matching wavelengths can be controlled mainly via the channel diameter. For instance, liquids with lower RI than CS 2 show a small number of resonances in our current HyBiC geometry, which can be substantially increased by using larger channel diameters. Furthermore, higher GeO 2 doping levels and larger glass cores can extend the spectral transmission window into the near-IR. The temperature regime for TOC (and POC) measurements can be adjusted via the filling ratio, i.e., the ratio between filled and unfilled volumes (l 0 /l C ) in the channel. Liquids with RIs below silica can be made accessible by mixing them with known high RI liquids such as CS 2 or C 2 Cl 4 (e.g. 50 mol% ethanol in CS 2 yield n mi x = 1.494 > n glass = 1.458 at 600 nm wavelength).
A further advantage of the HyBiC concept is that the temperature and wavelength at which the POC can be determined, i.e., the transition point, can also be adjusted via the filling ratio l 0 /l C and the channel diameter. Here we claim that the determination of POC values is also possible for other liquids and mixtures in case the volumetric coefficient of expansion α V and the isothermal compressibility κ are known.
Beyond that, our device allows the measurement of the TOC and POC under extreme pressure and temperature conditions. The calculated pressure of the liquid column at our maximum operation temperature of 383°C is beyond 1000 bar -an extreme pressure domain, which is hardly accessible by classical methods, which are based on macroscopically sized liquid reservoirs.

Conclusion
In this contribution we presented a monolithic and easy-to-use fiber device and an associated data analysis procedure which allows determining the TOCs and POCs of liquids on the basis of straightforward accessible spectral measurements. The device is formed by a directional mode coupler consisting of a doped glass core and an adjacent liquid channel, with the liquid being fully encapsulated inside the bore. Phase-matching of higher-order liquid modes to the fundamental glass-core mode imposes a significant number of high-contrast dips (up to 30 dB) in the transmission spectra, which strongly shift in case the temperature is varied, even in situations above the liquid's boiling point. Two operation regimes have been identified, which we demonstrated on the example of CS 2 : In the isobar regime, the internal pressure in the liquid is small and the liquid is free to expand, allowing the determination of the spectral distribution of the TOC. The results confirm published data and extend the current knowledge of CS 2 200 nm into the near-IR. We were also able to measure the TOCs of benzene and C 2 Cl 4 , whereas the TOC of the latter was previously unknown. In the isochor regime, the internal pressure of the liquid has to be taken into account, allowing to determine the POC. The measured values for CS 2 , which were conducted at pressures greater than 100 bars, confirm those of Röntgen et al [13] from 1891, showing that the hybrid fiber coupler represents a new tool to gain insights into the piezo-optic behavior of liquids at various wavelengths and temperatures. Further research will aim to extend the operation domain spectrally, and to unexplored extreme thermodynamic regimes (i.e. high pressures and temperatures), and the applicability to other liquids by optimizing the hybrid coupler design.

Material parameters
Sellmeier equation [40]: Extended Cauchy equation [35]:  [11] and Cauchy coefficients refereed to Eq. (9) for benzene (C 6 H 6 , 0.3-2.1 µm, 20°C) [35]. For the calculation of the modes of the C 2 Cl 4 -core we used an own Sellmeier fit which will be published elsewhere.  Fig. 8. Dependence of the output intensity of the glass core mode on the length of the CS 2 filled column for different anti-crossings between the CS 2 modes and the fundamental glass mode (see Fig. 4