Degenerate intermodal four-wave mixing with Q-switched nanosecond pulses in SMF-28 for the generation of discrete ultraviolet-visible wavelengths

Sudip K. Chatterjee; R. Vijaya

doi:10.1364/OSAC.1.001360

1. Introduction

Nonlinear optical processes in multimode fibers (MMFs) have led to the development of new spatiotemporal phenomena such as multimode solitons, geometric parametric instability, and supercontinuum generation [1–6]. Among all nonlinear optical processes, the study of intermodal four-wave mixing (IMFWM) in MMFs has emerged as an active field of research in recent times [7–16] due to its novelty and promise of applications. Conventional FWM in single mode fiber refers to the selective energy conversion from the source laser to the frequency-shifted Stokes and anti-Stokes wavelengths which are phase-matched [17]. In such intra-modal FWM, the pump has to lie in the vicinity of zero dispersion wavelength (ZDW) of the fiber to achieve high wavelength-conversion efficiency [18]. However, in this case, the presence of other nonlinear effects at ZDW such as modulation instability, soliton-fission, and intra-pulse Raman scattering would severely contaminate the output spectra [19]. IMFWM can resolve this limitation as the pump is launched in the deeply normal dispersion regime and the Stokes and anti-Stokes are generated based on the large difference in the propagation constants of the participating higher order modes [7]. Following this approach, one can generate IMFWM-assisted spectral components which are largely detuned (~200 THz) from the pump. In fact, J. Yuan experimentally demonstrated the generation of discrete ultraviolet (UV) peaks down to 375.8 nm by cascaded IMFWM process [15]. In that work, pump pulses at 800 nm of femtosecond duration were launched into the fundamental guided mode of a multimode photonic crystal fiber (PCF) and were found to transfer significant power to the first anti-Stokes line, which then acted as the secondary pump to generate UV sideband. Such large spectral shifts of the generated Stokes/anti-Stokes lines from the pump also make IMFWM an ideal platform for the generation of photon pair from highly entangled to factorable photon pairs free from the contamination of both the residual pump and spontaneous Raman scattered (SpRS) photons (bandwidth~50 THz) [20]. Such photon pairs would find applications in quantum information processing, quantum cryptography and would serve as an essential source for the implementation of linear optics quantum computation (LOQC) [21,22]. Among the MMFs, mainly parabolic graded-index multimode fiber (GRIN-MMF) [13,14,16], custom-fabricated photonic crystal fiber (PCF) [12] or higher order mode (HOM) fiber [10] pumped either by a Q-switched picosecond laser or a Ti-Sapphire femtosecond laser have been utilized to observe such phenomena. Recently, Mafi et al. have demonstrated the spontaneous generation of red Stokes and blue anti-Stokes from a commercial grade SMF-28 fiber when pumped with a 680 ps high peak power green laser [23].

In this work, we have experimentally investigated IMFWM process in SMF-28e + fiber pumped by a Q-switched nanosecond laser at 532 nm in the normal dispersion range. Apart from reproducing the results reported in Ref [23]. i.e. the generation of first Stokes and anti-Stokes at 655.3 nm and 447.5 nm in LP₀₂ and LP₀₁ mode respectively, we have observed various other kinds of IMFWM phenomena. In one process, two green pump photons in LP₀₁ mode get annihilated to give rise to one Stokes photon at 715.2 nm and one anti-Stokes photon at 423.2 nm, both propagating in LP₀₂ mode. We have also generated discrete UV wavelengths at 390.7 nm and 396.7 nm in SMF-28 fiber for the first time, to the best of our knowledge, by a complex cascaded IMFWM (C-IMFWM) process. Here, the strong anti-Stokes at 447.5 nm in LP₀₁ mode of the first IMFWM serves as the secondary pump. The spectral position of each sideband in the output spectrum has been mapped theoretically by considering the phase matching conditions of multiple IMFWM processes.

2. Experimental results

Figure 1

Fig. 1 Illustration of experimental setup for degenerate IMFWM. M′: High reflecting mirror at 1064 nm; D: Beam Dump; λ/2: Half-wave plate; MO: Microscope objective with magnification of 20X; 3D Translational stage; SMF-28e + : Fiber under test; BPF: Band pass filter; M: High reflecting mirror at 532 nm; USB4000: Ocean Optics Spectrometer; L₁: Lens; CCD: camera.

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shows the experimental setup for investigating the single-pump IMFWM in SMF-28 fiber. We use a Q-switched frequency-doubled Nd:YAG laser with 7 ns pulse duration and 10 Hz repetition rate as the pump source. The fundamental wavelength at 1064 nm is first filtered out by using a highly reflecting mirror (M’) at 1064 nm and a beam dump (D). The filtered input beam at 532 nm is then passed through a variable attenuator (comprising of two polarizers P₁ & P₂) and a half-wave plate (HWP). Finally, the pump pulses are coupled by a 20 × microscope objective (MO) into a Corning SMF-28e + fiber. Two different fiber lengths of 28 cm and 51 cm have been studied in this work. The output of the fiber is monitored by a spectrometer (USB-4000, Ocean Optics) in the range of 200-900 nm after it passes through a highly reflecting mirror (M) at 532 nm to reduce the transmitted pump intensity. The modal content of the output beam profile is characterized by using a set of 10 nm band-pass filters (BPF) and a CCD camera. The fiber supports four modes (V~5.7) at the pump wavelength. However, the pump is carefully aligned through proper injection conditions (offset/tilt with respect to fiber longitudinal axis) to predominantly excite the LP₀₁ mode. A free-space-to-fiber coupling efficiency up to 50% has been achieved using our setup.

Figure 2

Fig. 2 Observed output spectra for a 28 cm long SMF-28 fiber at a peak input power of (a) 4.61 kW, (b) 5.65 kW, and (c) 6.71 kW. Here, A₁−A₃ and S₁−S₃ denote the observed anti-Stokes and Stokes waves respectively. Inset of Fig. 2c shows the spectrum of the residual pump at 6.71 kW.

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shows the evolution of the spectra at the output of a 28 cm long SMF-28e + fiber as the input peak power (P_P) is increased from 4.61 kW to 6.71 kW. For a P_P of 4.61 kW, we observed the generation of a pair of sidebands at 447.5 nm and 655.3 nm (A₁ and S₁ in Fig. 2a respectively), highly detuned from the pump ( ± 106 THz). Such spectral separations are the characteristic features of intermodal phase matching under single/degenerate pump configuration. With increase in P_P to 5.65 kW (Fig. 2b), the power content in these two sidebands increases due to increase in conversion efficiency. At a higher P_P of 6.71 kW, we observed four additional spectral peaks (Fig. 2c) i.e. anti-Stokes at 454.4 nm (A₂), 423.2 nm(A₃) and Stokes at 642.6 nm (S₂), 715.2 nm (S₃). We then performed a series of experiments by increasing the fiber length. The spectrum around the pump has not been shown in Fig. 2 in order to depict the power relation among the various sidebands. However, in the inset of Fig. 2c, the spectrum of the residual pump as it passes through M (Fig. 1) is shown.

Figure 3

Fig. 3 Observed output spectra for a 51 cm long SMF-28 fiber at a peak input power of (a) 2.17 kW, (b) 2.67 kW, and (c) 4.61 kW. Here, A₁−A₆ and S₁−S₄ denote the observed anti-Stokes and Stokes waves respectively.

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depicts three spectra measured from a 51 cm long fiber sample at P_P of 2.17 kW, 2.67 kW and 4.61 kW. Interestingly, here we have witnessed the appearance of new sidebands along with all the six spectral peaks (A₁−A₃, S₁−S₃) which have already been observed in the 28 cm long fiber. At P_P of 2.17 kW (Fig. 3a), two anti-Stokes (A₁, A₂) and one Stokes (S₁) sideband are obtained. At P_P of 2.67 kW (Fig. 3b), new discrete peaks at 419.7 nm (A₄) and 704.7 nm (S₄) have been observed. Narrow sidebands in the ultra-violet range at 390.7 nm (A₅) and 396.7 nm (A₆), far-detuned from the pump (~204 THz), have also been observed for the first time in SMF-28e + fiber (Fig. 3c) at a P_P of 4.61 kW.

3. Intermodal phase matching in SMF-28 fiber: theoretical formulation

To explain the origin of the experimentally obtained spectral peaks, we consider IMFWM with degenerate (single) pump configuration. In this process, two fundamental (LP₀₁) pumpphotons at λ_P simultaneously generate one Stokes and one anti-Stokes photon in the fundamental (LP₀₁) or, higher order modes (LP_lm). The wavelength of the Stokes (λ_S) and anti-Stokes (λ_A) waves can be calculated from the energy conservation and phase matching conditions, given by [17]:

\frac{2}{λ_{P}} = \frac{1}{λ_{S}} + \frac{1}{λ_{A}}

Δ β = 2 β_{01}^{P} (λ_{P}) - β_{l m}^{S} (λ_{S}) - β_{l^{'} m^{'}}^{A} (λ_{A}) = 0

where β₀₁^P(λ_P), β_lm^S(λ_S) and β_l’m’^A(λ_A) are the propagation constants of the pump, Stokes and anti-Stokes waves which belong to LP₀₁, LP_lm and LP_l’m’ mode respectively. The nonlinear contribution to the intermodal phase matching has been neglected because of its insignificant effect. The conversion efficiency of a phase-matched IMFWM can be defined by the coefficient (σ) associated with the overlap integral among the spatial modes involved in the process [20]:

σ = | \iint d x d y {| F_{P} (λ_{P}) |}^{2} F_{S} (λ_{S}) F_{A} (λ_{A}) |

Here, F_P(λ_P), F_S(λ_S) and F_A(λ_A) are the normalized spatial mode profiles at the pump, Stokes and anti-Stokes wavelength respectively.

The linear phase matching (PM) term (Δβ) in Eq. (2) can be approximated, by considering the Taylor series expansion of the Stokes and anti-Stokes wave around the pump wavelength, as follows [23]:

Δ β (Ω) = - δ β^{(0)} - δ β^{(1)} Ω + \sum β^{(2)} Ω^{2}

where, Ω is defined as the spectral shift in cm−1 of the Stokes and anti-Stokes wave with reference to the pump: Ω = 1/λ_P − 1/λ_S = 1/λ_A − 1/λ_P and δβ⁽⁰⁾, δβ⁽¹⁾, Σβ⁽²⁾ are defined as [23],

δ β^{(0)} = 2 β_{01}^{P} (λ_{P}) - β_{l m}^{S} (λ_{P}) - β_{l^{'} m^{'}}^{A} (λ_{P})

δ β^{(1)} = 2 π c [β_{l m}^{S}^{(1)} (λ_{P}) - β_{l^{'} m^{'}}^{A}^{(1)} (λ_{P})]

Σ β^{(2)} = 4 π^{2} c^{2} \frac{1}{2} [β_{l m}^{S}^{(2)} (λ_{P}) + β_{l^{'} m^{'}}^{A}^{(2)} (λ_{P})]

Here,

β_{l m}^{i}^{(n)} (λ_{P}) = \partial^{n} β_{l m}^{i} (λ_{P}) / \partial ω^{n}

.The SMF-28e + fiber used in our experiment has a core diameter of 8.4 μm, while the core (n₁) and cladding (n₂) refractive indices are related as, n₁² ≈n₂² [1 + 2Δ] with Δ≈0.3% and n₂ = 1.4607 at 532 nm.

4. Analysis of generated sidebands

4.1 Output spectrum

We consider the degenerate IMFWM process named IMFWM#1, wherein two pump photons in LP₀₁ mode annihilate to produce one Stokes photon in LP₀₂ mode (i.e. lm → 02 in Eq. (2) and one anti-Stokes in LP₀₁ mode (i.e. l’m’ → 01 in Eq. (2). The values of the parameters in Eq. (5), (6), and (7) for IMFWM#1 are δβ⁽⁰⁾ = 271.8 cm⁻¹, δβ⁽¹⁾ = 7.40 × 10⁻³, Σβ⁽²⁾ = 2.34 × 10⁻⁵ cm. In Fig. 4

Fig. 4 Phase matching curve for the IMFWM#1, IMFWM#2 and U-IMFWM process for initial pump pulses at 532 nm. The points with Δβ = 0 depict the perfect phase matching condition.

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, the PM curve has been plotted (blue curve) as a function of Ω and the intersection point (ISP), Δβ = 0 corresponds to the perfect phase matching condition. The first ISP at 3572 cm⁻¹ (P₁ in Fig. 4) gives rise to the Stokes wave at 656.9 nm in LP₀₂ mode and anti-Stokes wave at 447 nm in LP₀₁ mode which matches quite well with the experimental spectra (Table 1

Table 1. Experimental (Ex.) vs Theoretically (Th.) calculated parametric wavelengths, i.e. Stokes (S), Anti-Stokes (A) of different intermodal phase matching configurations

View Table

) at a P_P of 4.61 kW. The second ISP at −3256 cm⁻¹ (P₂ in Fig. 4) indicates another IMFWM process (named IMFWM#2) where the Stokes at 643.4 nm and anti-Stokes wave at 453.5 nm have been generated in LP₀₁ and LP₀₂ mode respectively. This set of sidebands resembles the experimental peaks A₂ (454.4 nm), S₂ (642.6 nm) in Fig. 2 and Fig. 3 (Table 1).

To understand the reason behind the generation of third set of discrete peaks i.e. peaks A₃ and S₃ in Fig. 2c and Fig. 3b, we consider another degenerate IMFWM process, which we refer to as Unconventional-IMFWM (U-IMFWM) as this process, although theoretically postulated by Mafi et al. [20], has not been experimentally demonstrated in an all-fiber platform. Unlike IMFWM#1, here both the Stokes and anti-Stokes photons, propagate in LP₀₂ mode. To determine the positions of phase-matched Stokes and anti-Stokes waves for thisprocess, Δβ(Ω) in Eq. (4) has been re-evaluated using the modified parameters given as: δβ⁽⁰⁾ = 2[β₀₁^P(λ_P) − β₀₂^S(λ_P)], δβ⁽¹⁾ = 0, Σβ⁽²⁾ = 4π²c²β₀₂^S(2). The red curve in Fig. 4 represents the PM curve for this U-IMFWM process. The two ISPs (Q₁ and Q₂ in Fig. 4) at ± 4811.7 cm⁻¹ on either side of the pump indicate a single set of Stokes and anti-Stokes spectral lines at 715 nm and 423.5 nm respectively. This is in good agreement with our experiment which showed peaks S₃ (715.2 nm) and A₃ (423.2 nm) in Fig. 2 and Fig. 3 at P_P of 6.71 kW and 2.67 kW respectively. The associated value of σ for all these processes have also been evaluated. Noteworthy is the fact that although the σ values for IMFWM#1 and U-IMFWM are close to each other (0.0135 μm⁻² and 0.0157 μm⁻²), an increase in P_P of 45% was required to distinctly observe the second one. This is so because the overall efficiency of FWM in few-mode fiber is proportional to σ, third-order nonlinear susceptibility (χ⁽³⁾), and most importantly, it is inversely proportional to the normalized average of the group-velocity dispersion evaluated in the Stokes/anti-Stokes modes at the pump wavelength i.e. Σβ⁽²⁾ and to spectral separation between sidebands from pump i.e. Ω [20]. Therefore, (Σβ⁽²⁾.Ω)⁻¹ equals 12.0 and 8.8 for IMFWM#1 and U-IMFWM respectively which ensures the higher conversion efficiency of the first process over the second one.

The generation of peaks at 704.7 nm and 419.7 nm (S₄ and A₄ in Fig. 3b, 3c) can be explained as an outcome of another U-IMFWM process (U-IMFWM #2). Here, a source at 525.1 nm in LP₀₁ mode is considered as the pump (the peak ‘X’ in the inset in Fig. 2c). Such a strong pump is actually initiated from the modulation instability induced by cross-phase modulation [24]. Lastly, to clarify the origin of the generation of discrete ultraviolet peaks at 390.7 and 396.7 nm (A₅ and A₆ in Fig. 3c), we consider cascaded IMFWM process where the anti-Stokes of IMFWM#1 at 447.5 nm plays the role of a secondary pump and generates new spectral sidebands. The positions of the Stokes in LP₀₂ (LP₀₁) and anti-Stokes in LP₀₁ (LP₀₂) can be predicted theoretically by evaluating δβ⁽⁰⁾, δβ⁽¹⁾ and Σβ⁽²⁾ around the secondary pump as follows: δβ⁽⁰⁾ = 245.5 cm⁻¹, δβ⁽¹⁾ = 7.18 × 10⁻², Σβ⁽²⁾ = 2.94 × 10⁻⁵ cm. The two ISPs at 90.4 THz and −83.1 THz anticipates the generation of anti-Stokes wave at 394.3 nm in LP₀₁ mode and 398.1 nm in LP₀₂ mode respectively and resembles the experimental peaks. The corresponding Stokes wave at the expected wavelength of 517.3 nm in LP₀₂ mode and 510.9 nm in LP₀₁ mode is not visible in the spectrum due to its low intensity and to its superposition with the broad spectral components around the residual pump. Note that the C-IMFWM process considering the Stokes of IMFWM#1 at 655.3 nm as the secondary pump is forbidden since δβ⁽⁰⁾ = −292.6 m⁻¹, δβ⁽¹⁾ = −2.34 × 10⁻³ make Δβ(Ω) positive for the whole spectral range (Eq. (4)). The power level of individual spectral lines including pump is dominated by the self-phase modulation based spectral broadening. This is so because the pump pulse is located deeply in the normal dispersion regime (ZDW for SMF-28e+ ~1.3 μm) and yields a large dispersion length (L_D >> 1 km).

4.2 Output intensity profile

Next, we tried to record the transverse intensity profile of each sideband in order to match them with the theoretically prescribed mode pattern. In order to do so, the spectrometer at the fiber output has been replaced with a CCD camera (Fig. 1). Figures 5(a)-(c)

Fig. 5 Output beam profiles imaged at (a) 447.5 nm, (b) 532 nm, and (c) 655.3 nm using a 10 nm band pass filter along with the respective intensity of spatial profile in (d), (e) and (f). Inset in Fig. 5b depicts transverse field profile consisting of a mixture of LP₀₂ (80%) and LP₂₁ (20%) mode at 655.3 nm.

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display the imaged beam profiles of the pump, Stokes and anti-Stokes waves of IMFWM#1 process at 532 nm, 655.3 nm and 447.5 nm respectively. The spatial intensity profile of individual sideband as extracted from the beam profile is also shown in Fig. 5 (d)-(f). The pump is seen to be guided in LP₀₁ and LP₀₂ mode whereas the predominant excitation of only LP₀₁ mode as the pump is required to trigger IMFWM#1 (Fig. 5a, 5d). Here, the intensity profile (Fig. 5d) which essentially saturates the CCD is depicted to clearly show the presence of LP₀₂ mode in pump. The complete extinction of pump power in LP₀₂ mode is not possible as the circularly symmetric Gaussian beam would always excite azimuthally symmetric fiber modes which, in the present case, are LP₀₁ and LP₀₂ modes. However, special care can be taken to reduce the power content in the undesired LP₀₂ mode by optimizing the position of 3-D translational stage at the input end of the fiber. The spatial profile of the Stokes (red-shifted) also deviates from the expected LP₀₂ mode as there exists an azimuthal asymmetry in the outermost ring (Fig. 5b, 5e). Such a variation occurs due to the simultaneous excitation of the azimuthally asymmetric LP₂₁ mode which exhibits near-degeneracy with LP₀₂ mode [16]. The inset in Fig. 5b depicts the transverse field profile that comprises a mixture of 80% LP₀₂ and 20% LP₂₁ mode at the Stokes wavelength. The resemblance of the above pattern with the experimentally obtained Stokes wave justifies our understanding.

Quite surprisingly, the anti-Stokes has field components in LP₀₁ and LP₀₂ modes (Fig. 5c, 5f) although theoretically the anti-Stokes must solely belong to the LP₀₁ mode. The occurrence of LP₀₂ mode in anti-Stokes wave can be explained as follows: the simultaneous presence of LP₀₁ and LP₀₂ pump mode and their intermodal beatings results in a Kerr-induced grating [25]. As a result, there will exist nonlinear coupling of power from the anti-Stokes in LP₀₁ mode to anti-Stokes in LP₀₂ mode which is initiated by the phase-matching condition ofthe form: $β_{01}^{P} (λ_{P}) - β_{02}^{P} (λ_{P}) = β_{01}^{A} (λ_{A}) - β_{02}^{A} (λ_{A})$ as proposed by Pourbeyram et al. [26]. However, it is the presence of LP₀₁ anti-Stokes wave in IMFWM#1, which is responsible for obtaining UV spectral peaks (A₅, A₆ in Fig. 3) as a result of cascaded IMFWM process. The intensity profile of sidebands which belongs to the other IMFWM processes (U-IMFWM, C-IMFWM) has not been captured as their power was below the detectable range of the CCD being used. It is important to note that the mode profile of the Stokes and anti-Stokes wave for the U-IMFWM would not be influenced by the above mentioned NLC process because the required phase-matching condition would not be satisfied as $β_{02}^{A} (λ'_{A}) < β_{01}^{A} (λ'_{A})$ .

5. Discussion

In the following, we will discuss the influence of the effects of input power, fiber length, pulse walk-off, bending and other related issues with the present experimental configuration. The increase in pump power enhances the intensity in the generated Stokes/anti-Stokes bands. However, the peak power beyond a particular value causes the burning of fiber tip due to high pump intensity (~30 GW/cm²). The issue can be resolved by shifting to picosecond or even shorter pulses. The power in the sidebands can also be increased with the increase in fiber length. However, inevitable variation in long fiber causes linear intermodal coupling and degrades the FWM efficiency. Furthermore, the power content in spontaneously Raman scattered photons increases exponentially with the fiber length [17]. As a result, available power for the IMFWM processes would be reduced for the long fiber. The intermodal walk-off between pump and Stokes/anti-Stokes pulses, defined as [17] $d_{12} = 1 / v_{g}^{(1)} (λ_{P}) - 1 / v_{g}^{(2)} (λ_{P})$ where v_g⁽¹⁾(λ_P) and v_g⁽²⁾(λ_P) are the group velocities of the LP₀₁, LP₀₂ modes, can significantly affect the IMFWM process. However, one can ignore this effect in the present setup as the calculated d₁₂ of 40 fs/cm at 532 nm is found to be negligible considering the input pulse-width and fiber length. Any bending close to the input end of the fiber can also reduce the IMFWM efficiency. However, such effect can be suppressed by keeping the fiber extremely straight which, in our case, has been done by keeping the whole fiber on a flat fiber holder.

6. Conclusions

In summary, we have experimentally demonstrated intermodal four-wave mixing in a standard SMF-28e + fiber through pumping in the deeply normal dispersion regime by a commercial Q-switched nanosecond laser at a low input peak power (< 7 kW). We identified a new U-IMFWM where two pump photons in LP₀₁ mode are completely annihilated to give rise to Stokes and anti-Stokes photons both in LP₀₂ mode. A cascaded IMFWM leading to a discrete peak in the UV at 390.7 nm and 396.7 nm in the communication-grade fiber, considering the first anti-Stokes as secondary pump, is also reported for the first time to the best of our knowledge. The spectral position of each peak has been found to be in good agreement with theoretical predictions. No significant SpRS peak is observed as the intensity lies below the detectable range. The negligible role of intermodal walk-off effect of pulses on the process has also been confirmed. We expect our results on the generation of a pair of Stokes/anti-Stokes line, far-detuned from the pump, would be useful for the generation of high-purity quantum entangled photon which has practical implementation in quantum information processing technologies. Our finding on the generation of discrete UV wavelengths by a simple setup would be of interest in biomedical science and fluorescence spectroscopy.

Acknowledgments

We thank Dr. Arash Mafi, Interim Director, Centre for High Technology Materials, University of New Mexico, for the valuable feedback/suggestions regarding the experimental procedure. We would also like to acknowledge Dr. Pramod Kumar Pandey and Ms. Suchita at IIT Kanpur for the technical help.

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Degenerate intermodal four-wave mixing with Q-switched nanosecond pulses in SMF-28 for the generation of discrete ultraviolet-visible wavelengths

Abstract

1. Introduction

2. Experimental results

3. Intermodal phase matching in SMF-28 fiber: theoretical formulation

4. Analysis of generated sidebands

4.1 Output spectrum

4.2 Output intensity profile

5. Discussion

6. Conclusions

Acknowledgments

References

Cited By

Figures (5)

Tables (1)

Equations (7)

OSA Continuum

Process	Anti-Stokes			Stokes
	Wavelength (nm)		Mode	Wavelength (nm)		Mode
	Ex.	Th.	Mode	Ex.	Th.	Mode
IMFWM #1	447.5	447.0	LP₀₁	655.3	656.9	LP₀₂
IMFWM #2	454.4	453.5	LP₀₂	642.6	643.4	LP₀₁
U-IMFWM	423.2	423.5	LP₀₂	715.2	715.0	LP₀₂
C-IMFWM	390.7	394.3	LP₀₁	–	517.3	LP₀₂
C-IMFWM	396.7	398.1	LP₀₂	–	510.9	LP₀₁