Open Access
Add to BibSonomy
Abstract
Although χ(2) nonlinear optical processes, such as difference frequency generation (DFG), are often used in conjunction with fiber lasers for wavelength conversion and photon-pair generation, the monolithic fiber architecture is broken by the use of bulk crystals to access χ(2). We propose a novel solution by employing quasi-phase matching (QPM) in molecular-engineered hydrogen-free, polar-liquid core fiber (LCF). Hydrogen-free molecules offer attractive transmission in certain NIR-MIR regions and polar molecules tend to align with an externally applied electrostatic field creating a macroscopic $\chi ^{(2)}_{ {eff}}$. To further increase $\chi ^{(2)}_{ {eff}}$ we investigate charge transfer (CT) molecules in solution. Using numerical modeling we investigate two bromotrichloromethane based mixtures and show that the LCF has reasonably high NIR-MIR transmission and large QPM DFG electrode period. The inclusion of CT molecules has the potential to yield $\chi ^{(2)}_{ {eff}}$ at least as large as has been measured in silica fiber core. Numerical modeling for the degenerate DFG case indicates that signal amplification and generation through QPM DFG can achieve nearly 90% efficiency.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
23 January 2024: A correction was made to the author affiliations.
1. Introduction
Difference frequency generation (DFG) is a critically important nonlinear process with application for generation of near to mid-IR (MIR) sources through optical parametric oscillators and generators, entangled and unentangled photon pairs through spontaneous parametric down conversion, and quantum frequency conversion for quantum technology. Nonlinear crystals employing quasi-phase matching (QPM) are commonly used for these applications. [1–8] QPM introduces a periodic modulation in a material property such that the spatial modulation frequency corrects for the residual phase mismatch; in periodically poled lithium niobate (PPLN) the LN electric dipole orientation is modulated along the interaction length. [9] In spite of the broad use of nonlinear crystals for DFG, fiber-based techniques would be very attractive as they would enable integration of the DFG device into a monolithic fiber laser for wavelength conversion or into a quantum network for photon pair generation.
Third-order nonlinear optical processes, based on $\chi ^{(3)}$, can provide an alternative to second-order frequency conversion in a bulk noncentrosymmetric crystal with nonlinear susceptibility, $\chi ^{(2)}$. Amorphous materials such as glass, liquid, and gas are macroscopically centrosymmetric and have negligible $\chi ^{(2)}$. However, an electric field, $\ E_{ {dc}}$, applied across the centrosymmetric medium can induce an effective second-order nonlinearity, $\chi ^{(2)}_{ {eff}}\propto \chi ^{(3)}E_{ {dc}}$. Extensive investigation of QPM second harmonic generation (SHG) in silica fibers has been pursued since 1990. [10,11] Thermal poling is the process of applying an external electrostatic field to the sample while it is maintained at an elevated temperature to liberate and redistribute free charge. Thermal poling of a 1.6mm thick silica sample sandwhiched between electrodes has yielded $\chi ^{(2)}_{ {eff}}\sim 1$ pm/V over a $\sim 4$ µm region near the anode. [12] However, in thermal poling of silica fiber the authors estimated $\chi ^{(2)}\sim 0.2$ pm/V; thermal poling process for fibers requires considerable effort due the distance of the core from the electrodes and difficulty in changing the free charge distribution. [13] The fiber had twin capillary holes on either side of the the core with anode electrodes inserted into these holes; the assembly is secured on top of a heated ground plate. Application of a strong electric field and elevated temperatures accomplishes poling. To achieve QPM, a UV laser then periodically erases the poling to leave periodic poling along the fiber length; the poling was observed to be long lived. QPM SHG was demonstrated in Xe-filled hollow-core fiber (HCF) but efficiency was $< 0.1$% due to the short 16 cm electrode and small $\chi ^{(3)}$. [14,15] The poling configuration involved a $\sim$ 1mm period electrode that secured the fiber against a ground plane.
To enable wavelength-agile laser sources and pair production, it is relevant to consider optical parametric amplification (OPA) and generation (OPG) based on the DFG interaction. The OPA involves a strong pump field and a weak seed field to be amplified, whereas the OPG only involves the strong pump field and leverages quantum noise as the weak signal field to initiate the mixing process. We investigated a QPM OPA in Xe-filled HCF due the attractiveness of a Raman-free medium, long electrode poling period, broad spectral transmission, and the ability to operate near the Xe supercritical state to obtain high nonlinearity. The Raman-free characteristic was a particularly strong motivator to avoid parasitic competition between stimulated Raman scattering (SRS) and the wave mixing process; however, we concluded this approach was unlikely to be practical due to the requirement of very high Xe pressure. [16–18] As part of this investigation we identified methods by which molecular engineering of liquids could provide LCF with $\chi ^{(2)}_{ {eff}}$ at least as high as that in thermally poled silica fibers, but with improved MIR transmission. Recently LCF have gained attention in investigation of new fiber designs and for $\chi ^{(3)}$ nonlinear fiber optics. Kuhlmey investigated liquid filled photonic bandgap fiber designs, Xiao investigated selective liquid injection in microstructure fiber, and Dobrakowski investigated the transmission spectrum of liquid filled anti-resonant hollow-core fibers. [19–21] LCF have been numerically and experimentally studied for Raman lasers and supercontinuum sources. [22–25] Kieu developed a method to fusion splice solid-core fiber to LCF to enable monolithic fiber systems. [26] Lastly, Junaid recently measured NIR-MIR attenuation coefficients of organic and inorganic solvents over long interaction length for LCF. [27]
In this paper we outline a path to QPM OPG and OPA in LCF and provide numerical estimates of performance in the quasi-CW regime where the fiber length is shorter than the dispersion length and the walk-off length. Critical to QPM OPA/G in LCF is simultaneous consideration of several interrelated elements which include identification of LCF with acceptable transmission, high $\chi ^{(2)}_{ {eff}}$, and QPM electrode designs that yield large $\ E_{ {dc}}$ in the fiber core. Promising paths to high visible-MIR LCF transmission are pursued through the use of hydrogen-free solvents. High $\chi ^{(2)}_{ {eff}}$ may be achieved through the use of polar solvents and molecular engineering of CT molecule hyperpolarizability. A primary molecular engineering consideration is to ensure that the QPM OPA/G gain exceeds the SRS gain to ensure that pump energy is not transferred to the parasitic Raman emission.
One of the challenges faced in this investigation is the sparsity of data on linear and nonlinear properties of hydrogen-free, polar solvents and charge transfer molecules. To the extent possible, we use the data measured for specific candidate molecules and solvents recorded in the literature but, for molecules that haven’t been fully characterized, we represent their properties by those of similar molecules that are characterized in the literature. When cases requiring approximation arise, we will explicitly state our approach. The paper outline is as follows. In section 2 we provide a brief introduction to QPM DFG and discuss the influence of electrode design. In section 3 we consider relevant hydrogen-free solvents and LCF based on total internal reflection (TIR) fiber guidance. In section 4 we consider nonlinearity of polar solvents and discuss how they can be used in conjunction with CT molecules to engineer large $\chi ^{(2)}_{ {eff}}$. Lastly, in section 5 we introduce a numerical model and proceed to estimate QPM OPA/G performance for several cases.
2. Fundamentals of QPM DFG
When one of the electric fields involved in a four-wave mixing process is an electrostatic field, the resulting equations look similar to DFG equations with $\chi ^{(2)}_{ {eff}}\propto \chi ^{(3)}E_{ {dc}}$. The basic LCF QPM OPA architecture under consideration is shown in Fig. 1. The LCF is placed between periodic electrodes providing a modulated electrostatic field, and therefore a $\chi ^{(2)}_{ {eff}}$ modulated along the fiber length. Figure 1(a) illustrates the degenerate optical parametric amplifier based on a 1.06 $\mathrm {\mu }$m pump laser coupled into the LCF along with a 2.12 $\mathrm {\mu }$m seed that undergoes amplification when the QPM conditions are met. The QPM condition is
The nonlinear constant is defined as $d_{ {eff}}=\mathcal {F}\chi ^{(2)}/2$. In Eq. (3) we show $d_{ {eff}}$ for noncentrosymmetric media and isotropic media (LCF) in the presence of $E_{ {dc}}$:
The prefactor $\mathcal {F}$ is a geometric factor associated with the QPM geometry and order. For $m^{ {th}}$ order QPM with step function modulation, as in PPLN, $\mathcal {F}=\frac {2}{\pi m}$; $m=1$ yields the largest $d_{ {eff}}$. For QPM in LCF, $\mathcal {F}$ differs from the conventional PPLN case since the $\chi ^{(2)}_{ {eff}}$ modulation goes from a square wave distribution to a sinusoidal-like distribution. In Eq. (3) for LCF, the factor $\frac {D_{E_{ {dc}} {,FWM}}}{D_{ {DFG}}}$ accounts for the different degeneracies in crystal QPM DFG and $E_{ {dc}}$-induced DFG. For four-wave mixing, if one of the fields is an electrostatic field, $E_{ {dc}}$, the degeneracy is increased by a factor of two. [29,30] For nondegenerate $E_{ {dc}}$-induced QPM DFG $\frac {D_{E_{ {dc}} {,FWM}}}{D_{ {DFG}}}=12/2=6$. We include $y$ subscripts on $\chi ^{(3)}$ and $E_{ {dc}}$ to indicate that the highest $\chi ^{(2)}_{ {eff}}$ occurs when all fields have parallel transverse polarization; this is because isotropic media have largest nonlinearity for $\chi ^{(3)}_{y,y,y,y}$. High gain QPM DFG operation requires the design to meet the QPM requirement, employ high $\chi ^{(2)}_{ {eff}}$ material, attain high $E_{ {dc},y}$ in the LCF core, and provide parallel polarization for all fields.
Fig. 1. (a) Optical parametric amplifier configuration employing periodic electrodes to achieve seed amplification. (b) Cross-section of LCF and LCF-electrode assembly along with model of electrode $E_{ {dc}}$ and potential distribution for a 90:10 mixture of bromotrichloromethane and perfluorohexane filled capillary fiber with $V=600$ V, fiber diameter $=105\;\mathrm {\mu }$m, poling period $\Lambda =322\;\mathrm {\mu }$m. Red and blue blocks on LCF-electrode assembly are the electrodes that sandwich the fiber from top and bottom. (c) $y$ component of $E_{ {dc}}$ vs. $z$ normalized to electrode period $\Lambda$.
Proper design of the LCF-electrode assembly is critical to efficient QPM DFG operation since $\chi ^{(2)}_{ {eff}}\propto E_{ {dc},y}$ and $E_{ {dc},y}$ is degraded by field fringing. Figure 1(b) illustrates the fiber electrode geometry; we choose a fiber that can be procured from Polymicro with outer diameter $D_{ {f}}=105\;\mathrm {\mu }$m and inner diameter $d = 40\;\mathrm {\mu }$m. The $E_{ {dc},y}$ distribution calculated with COMSOL is shown in Fig. 1(c), along with the potential distribution for a 90:10 bromotrichloromethane (CBrCl3) : perfluorohexane (C6F14) (BTM:PFH) mixture. The electrode period is $\Lambda =322\;\mathrm {\mu }$m. Figure 1(d) shows $E_{ {dc},y}$ versus $z$. For the sinusoidal distribution and $m=1$, numerical modeling indicates that $\mathcal {F} \approx 1/2$. [16,18]
As $\Lambda /2$ approaches $D_{ {f}}$, the distance between opposing transverse electrodes, $E_{ {dc}}$ begins to fringe so that there are field components in the $z$ direction. For $\Lambda /2=D_{ {f}}$ the $E_{ {dc}}$ tends to be evenly split between the transverse and longitudinal directions. Ideally, one would pursue designs that yield $\Lambda /D_{ {f}}>>2$ to achieve $E_{ {dc}}$ entirely in the transverse direction. For $V=600$ V, $E_{ {dc,max},y}\approx 10$ kV/mm in the liquid core. Due to the presence of contaminants, we anticipate electrical breakdown at $\approx 10$ kV/mm for V pules $>> 10\;\mathrm {\mu }$s and breakdown at $\approx 100$ kV/mm for V pulse $<10\;\mathrm {\mu }$s. [31]
3. LCF design considerations
LCF designs may be based on simple hollow capillaries filled with a high-index liquid to produce TIR guidance or low index liquids can be employed to design anti-resonant LCF and photonic crystal bandgap confinement LCF. Recently, the index of refraction was measured for several high and low index liquids. [32,33] Consider the high-index liquid BTM ($n\sim$ 1.49 at 1.5 $\mathrm {\mu }$m), and the low-index liquid PFH ($n\sim$ 1.24 at 1.5 $\mathrm {\mu }$m); varying the relative mixture concentrations can enable any $n$ in the range $1.24\leq n\leq 1.49$ and therefore enable increased control over the dispersion of the fiber. In generating the results of Fig. 1 we created a 90:10 mixture of BTM:PFH to attain $\Lambda /D_{ {f}}=3.04$. For a 83:17 BTM:PFH mixture, the liquid index $=$ the silica index.
Absorption from fundamental and overtone molecular vibrations is widely known to decrease IR transmission in organic compounds. The energy of a molecular vibration ($\nu$) is inversely proportional to the reduced mass ($M$) of the atoms involved in the vibration: $\nu =\frac {1}{2\pi c}\sqrt {\frac {k}{M}}$ where k is a constant and c is the speed of light. The high energy (due to low M) and anharmonicity of X-H vibrations are particularly problematic. The fundamental vibrations of X-H bonds can introduce MIR absorption features whereas the the overtones are the primary cause of NIR-SWIR (short-wave IR) absorption. However, increasing M shifts corresponding vibrations to longer wavelengths, motivating use of heavier atoms. We employ H-free solvents such as BTM and PFH. Replacing hydrogen-1 with deuterium isotopes (heavy hydrogen) is another avenue to shift vibrational overtones of hydrogen towards longer wavelengths. [34]
Junaid measured absorption for several H-free solvents ($\sim$ 99% pure). [27] Each is characterized by large spectral regions where NIR-MIR absorption is $\lesssim 1$ dB/cm. Beyond 3.7 $\mathrm {\mu }$m the BTM LCF has much better transmission than silica and at 5 $\mathrm {\mu }$m the LCF has attenuation coefficient $\sim 1$ dB/cm. It is possible that higher purity samples lacking C-H bond precursor molecules from manufacturing will achieve even lower absorption. To supplement Junaid measurements, we measured BTM loss at $\lambda =1.06\;\mathrm {\mu }$m and found $\alpha \approx 0.08$ m-1. The relative absorption spectrum of the low index liquid PFH was measured by Campo. [35] Our spot measurements for PFH yielded $\alpha$($\lambda =0.6328\;\mathrm {\mu }$m) $\approx \alpha$($\lambda =1.064\;\mathrm {\mu }$m) $\approx 0$ (we measured no loss over 16 cm), and $\alpha$($\lambda =2.12\;\mathrm {\mu }$m) $\approx 5.3$ m-1.
Using the Junaid data and our spot measurements, Fig. 2 illustrates the transmission calculated with COMSOL for a TIR LCF using mixtures of BTM:PFH to tune dispersion but maintain $n_{ {liquid}} > n_{ {silica}}$. The transmission is sensitive to the core diameter; the larger the liquid filled core the less overlap of the electromagnetic field with the silica cladding thereby reducing silica absorption above 2 $\mathrm {\mu }$m. Below $\sim 2\;\mathrm {\mu }$m the absorption is limited by the liquid absorption. In the event that $\chi ^{(2)}_{ {eff}}$ is large enough to enable device length less than a few cm, efficient operation at some MIR wavelengths may be possible.
Fig. 2. Absorption coefficient for 90:10 BTM:PFH mixture in TIR LCF along with silica fiber. The LCF coefficients are shown for fiber core sizes D=10 $\mathrm {\mu }$m and D=30 $\mathrm {\mu }$m along with silica fiber.
Figure 3 shows the impact of BTM:PFH concentration $C$ and core diameter $d$ on QPM DFG $\Lambda$. Unlike silica fiber with limited control over index of refraction, liquid mixtures enable unmatched control over dispersion and $\Lambda$. This plot illustrates that BTM:PFH LCF can have much larger QPM periods than silica fiber; this greatly eases periodic electrode manufacturing and, by reduced $E_{ {dc}}$ fringing, increases $\chi ^{(2)}_{ {eff}}$. For reference, a core size larger than $d\approx 3\;\mathrm {\mu }$m with BTM $C=1$ corresponds to multimode fiber.
Fig. 3. Poling period of various BTM:PFH mixtures and silica fiber versus core size for the degenerate OPA/G case (1.06 $\mathrm {\mu }$m $\rightarrow$ 2.12 $\mathrm {\mu }$m). LCF enables much larger poling period than silica.
The design flexibility provided by liquid dispersion control and tailored nonlinear optical properties offers a dramatic increase in the range of custom fiber properties, and could be useful for mode size control for power scaling and single mode operation, zero-dispersion point control for short pulse propagation, and phase mismatch control in four-wave mixing and QPM DFG.
4. Nonlinearity in polar liquids
Polar molecules in the presence of an electrostatic field can provide an additional contribution to $\chi ^{(2)}_{ {eff}}$ through the molecular first hyperpolarizatibility ($\beta$) and dipole moment ($\mu$). The electrostatic field tends to align the molecular dipoles producing a macroscopic $\chi ^{(2)}_{ {eff}}$ given by
Given that SRS has large gain and no phase matching requirement, it is imperative to ensure that QPM DFG gain > SRS gain so that laser energy is not channeled into the SRS emission. Measurements of polar solvents, such as CH3I and CH2I2 yield $\chi ^{(2)}_{ {eff}} \approx 0.05$ pm/V at $E_{ {dc}}=10$ kV/mm. [36] Although this value is quite small compared to PPLN ($\chi ^{(2)} \approx 25$ pm/V) the high guided optical intensity, large degeneracy, and long interaction length can can help improve conversion efficiency. The SRS electric field gain is $\propto P_{ {pump}}$ whereas the QPM OPG gain is $\propto \sqrt {P_{ {pump}}}$. Figure 4 illustrates the $\frac {g_{ {OPG}}}{g_{ {SRS}}}$ ratio vs. pump peak power on a log scale plot. The BTM SRS gain coefficient is $g_{ {SRS}}$($\lambda _{p} = 1.06\;\mathrm {\mu }$m) $\approx 2.2$ cm/GW. [25] The red and green lines are for BTM with $E_{ {dc,max},y}=10$ kV/mm and $E_{ {dc,max},y}=50$ kV/mm, respectively. It is evident that large $E_{ {dc,max},y}$ and/or lower pump peak power is necessary for QPM OPG gain to exceed the SRS gain.
Fig. 4. $\frac {g_{ {OPG}}}{g_{ {SRS}}}$ ratio for several LCF cases with fiber core diameter $= 40\;\mathrm {\mu }$m, fiber diameter $= 105\;\mathrm {\mu }$m, and $\Lambda =322\;\mathrm {\mu }$m. Red and green lines are for BTM with $E_{ {dc,max},y}=10$ kV/mm and $E_{ {dc,max},y}=50$ kV/mm, respectively. Blue line is for 50:50 mixture of BTM:TCA and $E_{ {dc,max},y}=30$ kV/mm. Purple is for $E_{ {dc,max},y}=18$ kV/mm and a 3:2 mixture of BTM:TCA with 10 mM CT molecule solute yielding maximum $\beta$. Black dashed line corresponds to $\frac {g_{ {OPG}}}{g_{ {SRS}}}=1$.
We outline two interrelated approaches for improving the $\frac {g_{ {OPA/G}}}{g_{ {SRS}}}$ ratio. First, mixtures of solvents can be used to reduce the SRS gain. Since the SRS gain is proportional to molecular density, $N$, mixing solvents reduces the number of molecules contributing to a SRS emission line. As long as the solvents do not have overlapping SRS spectra the mixture will reduce the SRS emission in accordance with the reduced $N$. However, the mixture does not reduce the QPM OPA/G gain in proportion to $N$ since both molecular species contribute coherently to the QPM OPA/G gain through the wave mixing process. We illustrate the improvement to $\frac {g_{ {OPG}}}{g_{ {SRS}}}$ by consideration a 50:50 mixture of BTM and trichloracetonitrile (TCA, C2Cl3N, n20/D = 1.44) as shown by the blue line in Fig. 4. We use TCA here for consistency with the next section where we discuss the benefits of BTM:TCA for tuning charge transfer nonlinearity. TCA has similar transmission to BTM. [35] We assume its SRS gain is $\sim$ BTM gain which tends to be larger than most other liquids in literature. In the event that TCA SRS gain is smaller than assumed, then the impact on performance simulations is negligible as BTM will be the dominant SRS mode that QPM OPA/G will compete with. If TCA SRS gain is larger, then other variables such as lower pump peak power, longer fiber length, and/or larger electrostatic field will be necessary to accommodate the higher SRS gain. A more dramatic improvement to the ratio can be attained by directly engineering $\chi ^{(2)}_{ {eff}}$; the second approach is based on employing CT molecules dissolved in polar liquid mixtures.
4.1 Charge transfer molecules for efficient nonlinearity
Intramolecular CT can take place in organic push-pull compounds wherein an electron donor functional group is connected by a conjugated bridge to an electron acceptor. Such a push-pull compound can be represented by two resonance structures of the neutral, $\lvert \psi _{N} \rangle$, and zwitterionic, $\lvert \psi _{Z} \rangle$, forms. Figure 5(a) shows the two resonance structures of an example push-pull azobenzene derivative. Within the simple two state model, the electronic ground $\Psi _g$ and excited $\Psi _e$ states are superpositions of the resonance structures. [37–39]
Fig. 5. Neutral and zwitterionic resonance structures (a) as well as $\pi$ (bottom) and $\pi ^*$ (top) molecular orbitals (b) of a push-pull azobenzene derivative. Molecular orbitals are adapted with permission from [40]. Copyright American Chemical Society.
For certain values of $\theta$, the ground and excited electronic states are dominated by the neutral and zwitterionic resonance structures, respectively. In this way, it is possible for a push-pull molecule to undergo intramolecular CT upon excitation resulting in a change in dipole moment whose magnitude and sign can vary depending on $\theta$. For example, Fig. 5(b) shows that $\pi$ electron density of an example push-pull compound shifts away from the donor (amine functional group) towards the acceptor (nitro functional group) when populating the electronic excited state. The change in dipole moment ($\Delta \mu$) afforded by intramolecular CT endows certain push-pull molecules with extremely large non-resonant hyperpolarizabilities. [38,41–43]
Here $E_{ge}$ and $\mu _{ge}$ are respectively the energy and transition dipole moment between the ground and excited state.
Reports have given the hyperpolarizabilities in terms of the two-state model showing that they evolve with - $\cos (\theta )$ (or another related parameter). [38,44,45] Fig. 6(a) illustrates, under the assumption that vibrations are harmonic, that the vibrational part of $\beta$ ($\beta _{ {vib}}$) can be maximized and the vibrational part of $\gamma$ ($\gamma _{ {vib}}$) from the effective conjugation coordinate vanishes. It has been shown that $\gamma _{ {vib}}$ vanishes because the product of the negative hyper Raman and IR cross sections cancels the positive square of the spontaneous Raman cross section. [45,46] This simple model powerfully predicts the qualitative behavior featured in experimental results for the hyperpolarizabilities. [41,47] Specifically, researchers have shown that the donor/acceptor strength and aromatic stability strongly influence hyperpolarizability. [42,48] Also, the dielectric constant of the solvent also significantly changes a parameter directly related to $\cos (\theta )$ to modulate the vibrational hyperpolarizabilities and in some cases actually change the sign of hyperpolarizabilities. [41,46]
Fig. 6. Vibrational parts of hyperpolarizabilities in arbitrary units as a function of - $\cos (\theta )$ in the two state model (a) and the molecular structure of DHHNDN (b)
4.2 Molecular design for QPM DFG in LCF
In this subsection we show the design rational for a CT compound likely to be a good candidate for QPM DFG in LCF. We consider nonlinearity, solubility, and chemical stability. The $\beta _{ {vib}}$ of 1,1 dicyano,6-(di-methyl amine) hexatriene has been experimentally shown to be maximum (indicating $\gamma _{ {vib}}$ is 0) when the compound is dissolved in a solvent where the dielectric constant $\epsilon \approx 5$. [47] It has been shown that the nonlinearity increases to $365\cdot 10^{-30}$ esu by the addition of a double bond to make 1,1 dicyano,8-(di-methyl amine) octatetraene without changing the optimal solvent dielectric constant. [47] Unfortunately, push-pull molecules with more than 2 double bonds tend to be chemically unstable due to isomerization followed by intramolecular reactivity. However, the polyene bridge of 1,1 dicyano,6-(di-methyl amine) can be conformationally locked in place to prevent isomerization by introducing ring structures to make DHADC-MPN. [49] Additionally, the di-hexyl amine functional group was used instead of di-methyl amine to increase solubility. In the same way, we add alkyl rings to 1,1 dicyano,8-(di-methyl amine) octatetrene and extend the methyl groups to hexyl groups to make 2-2-[7-(dihexylamino)-2,3,4,4a,5,6-hexahydronaphthalen-2-ylidene]ethylidenepropanedinitrile (DHHNDN) shown in Fig. 6(b). Since the donor, acceptor, and conjugated bridge are the same as 1,1 dicyano,8-(di-methyl amine) octatetrene, it is likely that the hyperpolarizability of DHHNDN will be optimal in a solvent wherein $\epsilon \approx 5$ which can be achieved using a $\sim$ 3:2 ratio of BTM ($\epsilon = 2.47$) and TCA ($\epsilon = 7.74$).
Since the SWIR transmission of organic compounds containing H is low, it is critical that the concentration of DHHNDN be kept low enough to allow the DFG signal to propagate through the fiber with minimal loss but also large enough to achieve large $\chi ^{(2)}_{ {eff}}$. The absorption coefficient of toluene at 2.1 $\mathrm {\mu }$m is 500 dB/m. [50] We assume this value is representative of DHHNDN. A DHHNDN concentration of 1/1000 in a 3:2 ratio of BTM and TCA would produce a loss of 0.5 dB/m from DHHNDN. This value would result in a concentration of 10 mM, a solubility scale achievable by push-pull azobenzene compounds and 1,1 dicyano,6-(di-methyl amine) hexatriene. [51,52]
Employing Eq. (4) with $\mathrm{N} \approx 6 \cdot 10^{24} ~m^{-3}, \beta \approx 365 \cdot 10^{-30}$ esu, $\mu \approx 10\; \mathrm{D}$, and $E_{ {dc}} = 10$ kV/mm we estimate $\chi_{e f f, C T M}^{(2)} \approx 0.1$ pm/V so that the total, the sum of the solvent and CT molecule contributions, is $\chi_{e f f}^{(2)} \approx 0.15$ pm/V. While SRS is directly related to $\gamma _{ {vib}}$, it is uncertain if a vanishing $\gamma _{ {vib}}$ would actually result in vanishing SRS due to destructive interference between the previously mentioned terms. The spontaneous Raman scattering activity of conjugated organic molecules is potentially significant. We calculate the resulting Raman gain based on the spontaneous Raman activity rather than $\gamma _{ {vib}}$. Based on literature values for C=C Raman shifts, line width for 1,1 dicyano,6-(di-methyl amine) and scattering activity for 1,1 dicyano,8-(di-methylamine) octatetrene, the SRS gain is much less than that of BTM. [47,53,54] Fig. 4 illustrates how the 3:2 BTM:TCA solvent mixture with 10mM DHHNDN strongly improves the $\frac {g_{ {OPG}}}{g_{ {SRS}}}$ ratio. The purple line illustrates the ratio for this molecular design at $E_{ {DC}} = 18$ kV/mm; this configuration is observed to provide over an order of magnitude improvement in the ratio compared to the pure BTM case. Although we believe DHHNDN will have nonlinearity similar to 1,1 dicyano,8-(di-methyl amine) octatetrene but have better long term stability and solubility, we will employ 1,1 dicyano,8-(di-methyl amine) octatetrene properties in performance simulations since its properties are well characterized.
5. LCF QPM DFG performance modeling
In this section we numerically analyze the performance of QPM DFG in LCF for two fundamental cases based on the 40 $\mathrm {\mu }$m core TIR LCF design in section 3 and degenerate operation (1.06 $\mathrm {\mu }$m $\rightarrow$ 2.12 $\mathrm {\mu }$m). For Case 1 we consider a 50:50 mixture of BTM and TCA with no CT molecule. Given the lack of characterization data on H-free, polar molecules in literature we assume nonlinear values of CH3I; $\chi ^{(2)}_{ {eff}} \approx 0.05$ pm/V at $E_{ {DC}} = 10$ kV/mm. [36] For Case 2 we consider the theoretically optimized BTM:TCA + 1,1 dicyano,8-(di-methyl amine) octatetrene mixture from section 4.2 that maximizes nonlinearity $\chi ^{(2)}_{ {eff}} \approx 0.15$ pm/V at $E_{DC} = 10$ kV/mm. For each case we consider OPA and OPG operation as seems feasible. The general set of coupled differential equations describing the competition between wave mixing and SRS are solved in Mathematica.
These equations describe a quasi-continuous wave operation where the fiber length is shorter than the dispersion length and the walk-off length. The amplitude, $A_{\xi }(z)$, of each field is related to peak power, $P_{\xi }(z)$ by $A_{\xi }(z)=\sqrt {\frac {P_{\xi }(z)}{\pi r^{2}}\cdot \frac {1}{2n_{\xi }\epsilon _{0}c}}$ and $\xi =p$, $s$, or $i$ corresponds to the pump, signal, and idler fields, respectively. $\alpha _{\xi }$ is the intensity attenuation coefficient in the LCF.
To quantify temperature control tolerances we calculated $\Delta k_{ {QPM}}(T)$ as a function of temperature ($T$). We were not able to find thermo-optic data for our solvents so we used data for CCl4. [55] Assuming the usual $sinc^{2}$ phase matching functional dependence and the CT molecule case with length $= 7$ cm, we estimate the full width at half maximum temperature tolerance for the degenerate case considered to be $\Delta T \sim$ 0.1 C°. As the device cools, the signal wavelength tuning rate is $\sim$ 300 nm/C°. The temperature bandwidth narrows as the interaction length increases making the non CT molecule more challenging from the context of temperature control. Higher $E_{ {dc,max},y}$, $P_{ {pump}}$, or $P_{ {seed}}$ could enable shorter LCF length and reduced temperature sensitivity. Thermal engineering will likely be necessary to enable stable spectral control of this OPA/G.
Dispersion data for TCA has not yet been measured therefore we assume that the BTM:PFH $\Lambda = 322\;\mathrm {\mu }$m is representative. This seems reasonable as other liquid candidates we have considered had $\Lambda \sim$ 200 to 400 $\mathrm {\mu }$m and the effect of smaller $\Lambda$ can be accommodated by larger electrostatic field, longer fiber length, or smaller diameter fiber (to reduce field fringing). The SRS gain coefficient is $g_{ {SRS}}$($\lambda _{p} = 1.06\;\mathrm {\mu }$m) $\approx 2.2$ cm/GW for pure BTM and we assume TCA has similar value. [25] By mixing liquids, we can reduce the SRS gain of individual Raman lines as long as the two liquids do not have the same Raman shift. The spatial variation of $\chi ^{(2)}_{ {eff}}(z)$ from the $E_{ {dc}}(z)$ is calculated using COMSOL and shown in Fig. 1(c). [16,18]
As indicated in Fig. 4, the BTM:TCA mixture with $E_{ {dc,max},y} = 10$ kV/mm has low QPM OPG gain compared to the SRS gain. For the Case 1 QPM OPA to be effective, larger electrostatic fields are necessary to enable the QPM OPA to dominate over SRS. Figure 7 shows performance for $E_{ {dc,max},y} = 30$ kV/mm and 50 kV/mm, pump peak power $= 6.3$ kW, and $P_{ {seed}} = 2$ mW. For $E_{ {dc,max},y} = 30$ kV/mm full conversion to the signal wavelength occurs at $L \sim 0.35$ m; at longer interaction length, following back conversion, the SRS is able to dominate over OPA action. For the $E_{ {dc,max},y} = 50$ kV/mm case, full signal generation occurs at $L \sim 0.2$ m; the vertical grey line indicates where we stopped the high field plot case to avoid overlap with the low field case. For both cases the model predicts that the conversion efficiency from pump to signal is greater than $\sim$ 70%. For the nondegenerate case, where signal and idler wavelengths are different, one would expect lower conversion efficiency to signal or idler individually. Although not shown in Fig. 7, SRS may limit conversion efficiency at higher pump peak power since the QPM OPA gain scales as $g_{ {DFG}} \propto E_{ {dc},y} \sqrt {P_{ {pump}}}$ whereas SRS gain scales as $g_{ {SRS}} \propto P_{pump}$. In Case 1, the seed and high electrostatic field (short V pulse regime) are necessary for efficient signal amplification.
Fig. 7. Model of OPA operation in 40 $\mathrm {\mu }$m core TIR LCF design with $\Lambda \approx 322\;\mathrm {\mu }$m for a 50:50 mixture of BTM:TCA, $P_{ {pump}} = 6.3$ kW, and $P_{ {seed}} = 2$ mW. Solid lines are for $E_{ {dc,max},y} = 50$ kV/mm and dashed lines are for $E_{ {dc,max},y} = 30$ kV/mm. (green – pump peak power, purple – signal peak power, orange – SRS peak power). Parasitic SRS is generated for $E_{ {dc,max},y} = 30$ kV/mm case. The vertical grey line indicates where we stopped the high field plot case to avoid overlap with the low field case.
As indicated in Fig. 4, Case 2 with the CT molecule 1,1 dicyano,8-(di-methyl amine) octatetrene attains QPM OPG gain significantly larger than Case 1. This allows operation at lower pump peak power and lower $E_{ {dc,max},y}$. Figure 8 simulates the OPG with $P_{pump}= 5$ kW, no laser seed, and $E_{ {dc,max},y} = 18$ kV/mm and 50 kV/mm. The signal is seeded from quantum noise; the quantum noise power at the signal wavelength is given by $h\nu _{s}B$ where $B$ is $\approx$ bandwidth of the pump laser. $\chi ^{(2)}_{ {eff}} \approx 0.15$ pm/V for $E_{ {dc,max},y} = 10$ kV/mm. Lower voltage operation is very attractive as it does not require an expensive short pulse voltage supply to avoid electrical breakdown at the higher electrostatic field. Full conversion occurs for $L \sim 0.14$ m and $L \sim 0.45$ m for $E_{ {dc,max},y} = 50$ kV/mm and 18 kV/mm, respectively. The grey line indicates where we cut off the high field plot to avoid overlap with the low field plot. Modeling shows that conversion efficiency greater than $\sim$ 88% may be possible. The CT molecule enables an efficient QPM OPG source with low pump peak power and no seed. Also, there is no significant competition with SRS. Higher concentration CT molecule could also be explored but it will come with the cost of increased absorption. The modeling results illustrate the exciting potential for polar, H-free solvents and CT molecules to enable a new class of QPM OPA/G devices in LCF.
Fig. 8. Model of OPG operation in 40 $\mathrm {\mu }$m core TIR LCF design, with $\Lambda \approx 322\;\mathrm {\mu }$m for a 57:43 BTM:TCA mix with 10 mM 1,1 dicyano,8-(di-methyl amine) octatetrene CT molecule concentration and $P_{ {pump}} = 5$ kW. Solid lines are for $E_{ {dc,max},y} = 50$ kV/mm and dashed lines are for $E_{ {dc,max},y} = 18$ kV/mm. (red – pump peak power, blue – signal peak power, orange-SRS peak power) The vertical grey line indicates where we stopped the high field plot case to avoid overlap with the low field case.
6. Conclusion
Molecular engineering of the fill media in LCF offers new degrees of freedom in fiber design and QPM wave mixing interactions. In contrast to QPM interactions in silica fiber, the poling periods in LCF tend to be larger than common fiber diameters ($\Lambda /D_{f}>1$), which reduces field fringing and enables larger $\chi ^{(2)}_{ {eff}}$. Hydrogen-free liquids provide attenuation $< 1$ dB/cm for large spectral regions from the visible to 5 μm and appropriate selection of liquid can provide attenuation ~1dB/m. Through a survey of literature on nonlinear properties of solvents and CT molecules we identified conditions to achieve $\frac {g_{ {OPA/G}}}{g_{ {SRS}}} > 1$. In particular, for OPA operation without CT molecules, high electrostatic fields ($E_{ {dc,max},y} \sim 30$ kV/mm) are necessary for efficient operation. We identified the CT molecule 1,1 dicyano,8-(di-methyl amine) octatetrene as a promising candidate to achieve large $\frac {g_{ {OPGA/G}}}{g_{ {SRS}}}$. We proposed a modified molecular structure, DHHNDN, that should maintain the large $\frac {g_{ {OPGA/G}}}{g_{ {SRS}}}$ but increase long term stability and solubility. Numerical modeling of the OPG employing the CT molecule shows that lower electrostatic fields ($E_{ {dc,max},y} \sim 10$ kV/mm) and lower pump peak power can be used to achieve efficient operation. For the degenerate case, modeling indicates that conversion efficiency $\approx$ 90% in fiber length of $\sim 10$ cm may be realizable. Lastly, it is interesting to note that even with a moderate electrostatic field, the CT molecule case is predicted to achieve similar $\chi ^{(2)}_{ {eff}}$ as has been measured in the core of silica fiber; $\chi ^{(2)}_{ {eff}} \sim 0.2$ pm/V at $E_{ {dc}} = 15$ kV/mm.
Acknowledgments
We thank Dr. Robert Norwood and Dr. Khanh Kieu from University of of Arizona for helpful conversations regarding LCF. We thank Dr. Seth Marder from University of Colorado, Boulder, and Dr. David Hagan and Dr. Eric Van Stryland from University of Central Florida for helpful conversations regarding properties of solvents and CT molecules. We thank Dr. Lasse Jensen for discussions of nonlinear properties of polar molecules.
Disclosures
The authors declare no conflicts of interest.
Data availability
Linear and nonlinear materials properties used in the models are cited in the relevant sections of this paper.
References
1. L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33(10), 1663–1672 (1997). [CrossRef]
2. M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286(5444), 1513–1517 (1999). [CrossRef]
3. Y. Wu, Q. Fu, S. Liang, L. Xu, and D. J. Richardson, “Compact picosecond mid-ir ppln opo with controllable peak powers,” OSA Continuum 3(10), 2741–2748 (2020). [CrossRef]
4. H. G. de Chatellus, A. V. Sergienko, B. E. Saleh, M. C. Teich, and G. Di Giuseppe, “Non-collinear and non-degenerate polarization-entangled photon generation via concurrent type-i parametric downconversion in ppln,” Opt. Express 14(21), 10060–10072 (2006). [CrossRef]
5. B. Wei, W.-H. Cai, C. Ding, G.-W. Deng, R. Shimizu, Q. Zhou, and R. Jin, “Mid-infrared spectrally-uncorrelated biphotons generation from doped ppln: a theoretical investigation,” OSA Continuum 29(1), 256–271 (2021). [CrossRef]
6. J. Hannegan, U. Saha, J. D. Siverns, J. Cassell, E. Waks, and Q. Quraishi, “C-band single photons from a trapped ion via two-stage frequency conversion,” Appl. Phys. Lett. 119(8), 084001 (2021). [CrossRef]
7. J. S. Pelc, L. Ma, C. Phillips, Q. Zhang, C. Langrock, O. Slattery, X. Tang, and M. M. Fejer, “Long-wavelength-pumped upconversion single-photon detector at 1550 nm: performance and noise analysis,” Opt. Express 19(22), 21445–21456 (2011). [CrossRef]
8. J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, “Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters,” Opt. Lett. 35(16), 2804–2806 (2010). [CrossRef]
9. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962). [CrossRef]
10. R. Kashyap, “Poling of glasses and optical fibers,” in Fiber Bragg Gratings, (Academic Press, 2009).
11. F. De Lucia and P. J. Sazio, “Thermal poling of optical fibers: A numerical history,” Micromachines 11(2), 139 (2020). [CrossRef]
12. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16(22), 1732–1734 (1991). [CrossRef]
13. F. DeLucia, R. Bannerman, N. Englebert, M. N. Velazquez, F. Leo, J. Gates, S. Gorza, J. Sahu, and P. Sazio, “Single is better than double: theoretical and experimental comparison between two thermal poling configurations of optical fibers,” Opt. Express 27(20), 27761–27776 (2019). [CrossRef]
14. J. Ménard and P. S. J. Russell, “Phase-matched electric-field-induced second-harmonic generation in xe-filled hollow-core photonic crystal fiber,” Opt. Lett. 40(15), 3679–3682 (2015). [CrossRef]
15. J. Ménard, F. Köttig, and P. S. J. Russell, “Broadband electric-field-induced lp01 and lp02 second harmonic generation in xe-filled hollow-core pcf,” Opt. Lett. 41(16), 3795–3798 (2016). [CrossRef]
16. T. L. Courtney, C. Lopez-Zelaya, R. Amezcua-Correa, and C. K. Keyser, “Modeling quasi-phase-matched electric-field-induced optical parametric amplification in hollow-core photonic crystal fibers,” Opt. Express 29(8), 11962–11975 (2021). [CrossRef]
17. W. Larson, T. L. Courtney, and C. Keyser, “Spectrally pure photons generated in a quasi-phase matched xenon-filled hollow-core photonic crystal fiber,” Opt. Express 30(4), 5739–5757 (2022). [CrossRef]
18. C. Lopez-Zelaya, T. L. Courtney, P. Hemmer, and C. K. Keyser, “Analysis of quasi-phase-matched optical parametric amplification in hollow-core fibers using analytical static electric field solutions,” Opt. Express 29(26), 43544–43555 (2021). [CrossRef]
19. B. T. Kuhlmey, B. J. Eggleton, and D. K. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27(11), 1617–1630 (2009). [CrossRef]
20. L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, “Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer,” Opt. Express 13(22), 9014–9022 (2005). [CrossRef]
21. D. Dobrakowski, G. Stepniewski, R. Kasztelanic, D. Pysz, K. X. Dinh, M. Klimczak, M. Smietana, and R. Buczynski, “Antiresonant fibers with single-and double-ring capillaries for optofluidic applications,” Opt. Express 28(22), 32483–32498 (2020). [CrossRef]
22. D. Churin, T. Nguyen, K. Kieu, R. Norwood, and N. Peyghambarian, “Mid-ir supercontinuum generation in an integrated liquid-core optical fiber filled with cs 2,” Opt. Mater. Express 3(9), 1358–1364 (2013). [CrossRef]
23. R. Zhang, J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express 14(15), 6800 (2006). [CrossRef]
24. M. Vieweg, T. Gissibl, S. Pricking, B. Kuhlmey, D. Wu, B. Eggleton, and H. Giessen, “Ultrafast nonlinear optofluidics in selectively liquid-filled photonic crystal fibers,” Opt. Express 18(24), 25232–25240 (2010). [CrossRef]
25. A. R. Chraplyvy and T. J. Bridges, “Infrared generation by means of multiple-order stimulated raman scattering in ccl4-and cbrcl3-filled hollow silica fibers,” Opt. Lett. 6(12), 632–633 (1981). [CrossRef]
26. K. Kieu, L. Schneebeli, R. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20(7), 8148–8154 (2012). [CrossRef]
27. S. Junaid, W. Huang, R. Scheibinger, K. Schaarschmidt, H. Schneidewind, P. Paradis, and M. A. Schmidt, “Attenuation coefficients of selected organic and inorganic solvents in the mid-infrared spectral domain,” Opt. Mater. Express 12(4), 1754–1763 (2022). [CrossRef]
28. R. Boyd, “Nonlinear optics fourth edition,” in Nonlinear Optics, (Academic Press, 2020).
29. P. Maker and R. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965). [CrossRef]
30. C. A. Sapiano, J. S. Aitchison, and L. Qian, “Quasi-phase-matched dc-induced three wave mixing versus four wave mixing: a simulated comparison,” Opt. Lett. 37(7), 1262–1264 (2012). [CrossRef]
31. K. D. Singer, “Experimental studies of second order nonlinear optical susceptibilities in organic systems,” Ph.D. thesis, University Pennsylvania (1981).
32. H.-J. Chang, N. Munera, C. Keyser, S. Webster, E. W. Van Stryland, and D. H. Hagan, “Refractive index measured by common path interferometry for solvents from visible to infrared,” in Frontiers in Optics, (Optical Society of America, 2021), pp. FM6C–3.
33. H.-J. Chang, N. Munera, C. Lopez-Zelaya, D. Banerjee, E. W. Van Stryland, and D. J. Hagan, “Refractive index measurements of liquids from visible to near ir using a common path interferometry,” to be published (2023).
34. L. Ma, Y. Peng, Y. Pei, J. Zeng, H. Shen, J. Cao, Y. Qiao, and Z. Wu, “Systematic discovery about nir spectral assignment from chemical structural property to natural chemical compounds,” Sci. Rep. 9(1), 1–17 (2019). [CrossRef]
35. J. Campo, F. Desmet, W. Wenseleers, and E. Goovaerts, “Highly sensitive setup for tunable wavelength hyper-rayleigh scattering with parallel detection and calibration data for various solvents,” Opt. Express 17(6), 4587–4604 (2009). [CrossRef]
36. B. Levine and C. G. Bethea, “Second and third order hyperpolarizabilities of organic molecules,” J. Chem. Phys. 63(6), 2666–2682 (1975). [CrossRef]
37. M. Barzoukas, C. Runser, A. Fort, and M. Blanchard-Desce, “A two-state description of (hyper) polarizabilities of push-pull molecules based on a two-form model,” Chem. Phys. Lett. 257(5-6), 531–537 (1996). [CrossRef]
38. M. Barzoukas, A. Fort, and M. Blanchard-Desce, “Quadratic hyperpolarizability of push—pull polyenes: a two-form analysis of the length effect,” Synth. Met. 83(3), 277–280 (1996). [CrossRef]
39. G. Chen, D. Lu, and W. A. Goddard III, “Valence-bond charge-transfer solvation model for nonlinear optical properties of organic molecules in polar solvents,” J. Chem. Phys. 101(7), 5860–5864 (1994). [CrossRef]
40. M. Poprawa-Smoluch, J. Baggerman, H. Zhang, H. P. Maas, L. De Cola, and A. M. Brouwer, “Photoisomerization of disperse red 1 studied with transient absorption spectroscopy and quantum chemical calculations,” J. Phys. Chem. A 110(43), 11926–11937 (2006). [CrossRef]
41. G. Bourhill, J.-L. Bredas, L.-T. Cheng, S. R. Marder, F. Meyers, J. W. Perry, and B. G. Tiemann, “Experimental demonstration of the dependence of the first hyperpolarizability of donor-acceptor-substituted polyenes on the ground-state polarization and bond length alternation,” J. Am. Chem. Soc. 116(6), 2619–2620 (1994). [CrossRef]
42. M. Blanchard-Desce, V. Alain, P. Bedworth, S. Marder, A. Fort, C. Runser, M. Barzoukas, S. Lebus, and R. Wortmann, “Large quadratic hyperpolarizabilities with donor–acceptor polyenes exhibiting optimum bond length alternation: correlation between structure and hyperpolarizability,” Chem. - Eur. J. 3(7), 1091–1104 (1997). [CrossRef]
43. S. R. Marder, B. Kippelen, A. K.-Y. Jen, and N. Peyghambarian, “Design and synthesis of chromophores and polymers for electro-optic and photorefractive applications,” Nature 388(6645), 845–851 (1997). [CrossRef]
44. D. M. Bishop, B. Champagne, and B. Kirtman, “Relationship between static vibrational and electronic hyperpolarizabilities of π-conjugated push–pull molecules within the two-state valence-bond charge-transfer model,” J. Chem. Phys. 109(22), 9987–9994 (1998). [CrossRef]
45. H.-S. Kim, M. Cho, and S.-J. Jeon, “Vibrational contributions to the molecular first and second hyperpolarizabilities of a push–pull polyene,” J. Chem. Phys. 107(6), 1936–1940 (1997). [CrossRef]
46. M. Cho, “Vibrational characteristics and vibrational contributions to the nonlinear optical properties of a push- pull polyene in solution,” J. Phys. Chem. A 102(4), 703–707 (1998). [CrossRef]
47. P. Zuliani, M. Del Zoppo, C. Castiglioni, G. Zerbi, S. Marder, and J. Perry, “Solvent effects on first-order molecular hyperpolarizability: A study based on vibrational observables,” J. Chem. Phys. 103(23), 9935–9940 (1995). [CrossRef]
48. S. R. Marder, L.-T. Cheng, B. G. Tiemann, A. C. Friedli, M. Blanchard-Desce, J. W. Perry, and J. Skindhøj, “Large first hyperpolarizabilities in push-pull polyenes by tuning of the bond length alternation and aromaticity,” Science 263(5146), 511–514 (1994). [CrossRef]
49. B. Kippelen, S. Marder, E. Hendrickx, J. Maldonado, G. Guillemet, B. Volodin, D. Steele, Y. Enami, Sandalphon, Y. J. Yao, and J. F. Wang, “Infrared photorefractive polymers and their applications for imaging,” Science 279(5347), 54–57 (1998). [CrossRef]
50. M. Plidschun, M. Chemnitz, and M. A. Schmidt, “Low-loss deuterated organic solvents for visible and near-infrared photonics,” Opt. Mater. Express 7(4), 1122–1130 (2017). [CrossRef]
51. M. E. Raab, “Multiphoton processes involving extrinsically coupled transitions for surface spectroscopy, theranostics and nanothermometry,” Ph.D. thesis, State University of New York at Buffalo (2021).
52. G. Bourhill, K. Mansour, B. G. Tiemann, C. B. Gorman, S. Biddle, S. R. Marder, and J. W. Perry, “Third-order polarizabilities of symmetric and nonsymmetric polyene and cyanine-like organic molecules,” in Organic and Biological Optoelectronics, vol. 1853 (SPIE, 1993), pp. 208–220.
53. C. Castiglioni, M. Tommasini, and M. Del Zoppo, “Experimental vibrational contributions to molecular hyperpolarisabilities: methods and measurements,” J. Mol. Struct. 521(1-3), 137–155 (2000). [CrossRef]
54. T. Bridges, J. Bergman, and A. Chraplyvy, “Broadband infrared generation by stimulated raman scattering in liquid filled fibers,” in Advances in infrared fibers II, vol. 320 (SPIE, 1982), pp. 60–61.
55. K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116(3), 617–622 (2014). [CrossRef]
