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Abstract
Aiming at maintaining the chromatic dispersion properties and fiber optical parametric amplification (FOPA) performance when fiber core fluctuation occurs, we propose a buffer step-index optical fiber. The AsSe2 chalcogenide glass is employed as the core material due to its high nonlinearity and broad transmission spectrum. The calculated results in this study show that the chromatic dispersion variation due to the change of core diameter can be greatly suppressed and a continuous and very broad FOPA signal gain spectrum can be obtained and maintained by carefully controlling the core, buffer and cladding properties such as refractive index and diameters. The calculated results in this study showed that by using the proposed 3-cm-long fiber pumped at 5.02 µm, a broad signal gain bandwidth from 3 to 14 µm at about 15 dB is attainable although the fiber core diameter Dc drastically fluctuated from 2 to 5 µm and the buffer diameter Db varies from 8.9 to 9.3 µm. Moreover, when Dc varies in smaller range from 3 to 4 µm, the FOPA signal gain spectra calculated at different fixed values of Db in the range from 8.9 to 9.3 µm are highly maintained. When Db is kept at 9.0 µm and Dc varies from 3 to 4 µm, the calculated FOPA signal gain spectra at different pump wavelengths from 4.98 to 5.02 µm are also nearly identical in the wavelength range from 3 up to 13 µm.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber-based optical parametric amplification (FOPA) is one of typical applications of four-wave-mixing (FWM) process in highly nonlinear optical fibers which can transfer energy from one or two strong pump waves to amplify a weak signal wave and simultaneously generate a new idler wave. Compared to Erbium-doped fiber amplifiers (EDFA) in which signal gain bandwidths are as narrow as 30 nm from 1530 to 1560 nm [1], FOPA is very promising because they can provide broad gain bandwidths and high signal gain in many spectral bands where conventional EDFAs cannot reach. Therefore, FOPA has been exploited for various applications such as signal amplification [2], wavelength conversion [3], phase-conjugation [4], slow and fast lights [5], optical signal processing [6] and biomedical applications [7]. By extending FOPA signal gain bandwidth towards the mid-infrared (MIR) region which exceeds the transmission ranges of silica fibers, many novel applications in spectroscopy, sensing, biology and metrology are expected to be realized and developed. However, this is still a challenging task. In addition, highly efficient and stable FOPA performance is not easy to be obtained. It requires optical fibers with high nonlinearity, suitable control of chromatic dispersion and pump sources to satisfy the phase-matching condition which is the key for FWM process.
Recently, chalcogenide glasses have attracted great attention due to their very broad transmission window in the wavelength range more than 10 µm and very high nonlinearities [8–11] in comparison with other silica and non-silica glasses. These properties can make chalcogenide optical fibers advantageous to obtain FOPA with high signal gain and broad bandwidth in the MIR region. But, in the visible and near-infrared windows where many high power and tunable pump sources are commercially available, chalcogenide optical fibers have large normal dispersion which makes the phase-matching condition very difficult to be satisfied. Moreover, one of important technical issues for FOPA performance is that the phase-matching condition is very sensitive to the fluctuation of chromatic dispersion which is caused by the fiber transverse geometry variation [12–14]. In 2012, the calculation of B. P. P. Kuo [12] showed that dispersive characteristic of highly nonlinear silica fibers could be invariant to the fluctuation of the core diameter along the fiber. But, the study to suppress chromatic dispersion fluctuation in chalcogenide optical fibers has not been reported.
For these reasons, it is highly motivated to control the chromatic dispersion of chalcogenide optical fibers and to maintain it so as to maximize and maintain the FOPA performance when the fiber transverse geometry variation happens. In this work, we managed to obtain and maintain high and broad FOPA signal gain bandwidths in the MIR region by using a AsSe2 step-index optical fiber and a pump wavelength near 5.0 µm which is close to the zero-dispersion wavelength of the fiber. Based on our study of the fiber materials, the chromatic dispersion and FOPA performance when fiber core diameter fluctuated, it is realized that by adding a chalcogenide buffer layer with appropriate refractive index and diameter to the conventional chalcogeninde step-index structure, the performances of chromatic dispersion and FOPA signal gain can be improved and their fluctuation due to the change of fiber core can be greatly suppressed. As a result, a broad signal gain bandwidth from 3 to 14 µm at about 15 dB is attainable and can be maintained although the fiber core diameter drastically fluctuated from 2 to 5 µm.
2. Results and discussion
2.1 Glass material properties
2.1.1 Transmission
Figure 1 shows images of sulfide chalcogenide (As2S5) and selenide chalcogenide (AsSe2, As2Se3) glass samples which were synthesized by Furukawa Denshi Co., Ltd. The glass samples were cut by a low speed saw and finely polished to meet the requirements of transmission measurements. Their thickness is about 1 mm.
A UV-Vis-NIR spectrometer (PerkinElmer, Lambda900) and FT-IR spectrometer (PerkinElmer, Spectrum 100) were employed to measure the transmittance of our chalcogenide glasses in the wavelength ranges of 0.4–2.0 µm and 2.0–25 µm, respectively. The results are plotted in Fig. 2. In order to highlight the superior MIR transmission ranges of chalcogenide glasses, the measured transmission spectra of silica and tellurite glasses are included in Fig. 2 for comparison. As can be seen, silica and tellurite glasses are not transparent after 5 and 7 µm, respectively. But the chalcogenide transmission spectra are much wider. It can be as long as 13 µm for the sulfide chalcogenide As2S5 and even beyond 19 µm for the selenide chalcogenide (AsSe2, As2Se3). An absorption band above 9 µm of As2S5 glass originates in As–S bonds [15]. Absorption bands from 14 to 16 µm and above 17 µm of AsSe2 and As2Se3 glasses originate in As–Se bonds [15]. An absorption peak at 12.7 µm caused by Se–OH bonds [16] is found only for AsSe2. More absorption wavelengths due to typical impurities in As–S and As–Se glass systems were mentioned by R. Fairman et al. [17].
2.1.2 Linear Refractive index
To obtain the wavelength dependence of linear refractive index, glass prisms made of our chalcogenide glasses were measured at 20 different wavelengths from 0.4 to 4.0 µm by using the minimum deviation method [18]. The uncertainness of the measurement is as low as ±10−4. The measured linear refractive indices were fitted to the Sellmeier equation [19] as given in Eq. (1) and the index value at arbitrary wavelengths between 0.4 and 4.0 µm can be interpolated with high accuracy.
In Eq. (1), n is the refractive index of the material, λ is the wavelength and Ai, Bi are Sellmeier coefficients. The major drawback of this method is that the linear the refractive indices at wavelengths beyond 4.0 µm are unattainable or inaccurately extrapolated, especially at the wavelengths in the MIR up to 10 or 20 µm.
However, it is important to determine the wavelength-dependent linear refractive indices in these long wavelength ranges because they are involved in calculations of chromatic dispersion and FOPA in the MIR which are the major study in this work. For this reason, the interferometric method [20] was employed. Chalcogenide glass films which are about 0.15-mm-thin were prepared for the FTIR measurements. From the FTIR spectra and their fringe patterns, the linear refractive index can be calculated at more than 330 different wavelengths from 2.0 to 22 µm.
The combination of the two methods discussed above resulted in more than 350 values of linear refractive index at different wavelengths from 0.4 to 22 µm for each chalcogenide glass. They were fitted to the Sellmeier equation as Eq. (1) where i is equal to 5. In Fig. 3, wavelength-dependent linear refractive indices of As2Se3, AsSe2 and As2S5 glasses are plotted and Table 1 shows their Sellmeier coefficients.
Fig. 3. Measured and fitted wavelength-dependent linear refractive index of As2Se3, AsSe2 and As2S5 glass samples.
Table 1. Sellmeier coefficients of As2Se3, AsSe2 and As2S5 chalcogenide glasses.
2.1.3 Nonlinearity
In recent reports, nonlinearity of optical fibers can be manipulated and improved by adding complex microstructure in the cladding of the fibers [21–24]. But, for step-index optical fibers, the nonlinearity basically comes from those of the fiber materials. The nonlinearity of a glass material can be expressed by the nonlinear refractive index n2. Glasses with high nonlinearity are advantageous to the performance of nonlinear effects in optical fibers. Figure 4 which was reproduced from the Refs. [25–27] shows the linear and nonlinear refractive indices of several common glass systems such as silica, fluoride, silicate, tellurite and chalcogenide. Among them, chalcogenide glasses show very high nonlinear refractive index up to hundred or thousand times larger than the others. In Table 2, the n2 values of typical chalcogenide glasses are provided in comparison with those of silica and tellurite glasses.
Fig. 4. Linear refractive index and nonlinear refractive index n2 of silica, fluoride, silicate, tellurite and chalcogenide glass systems.
Table 2. Nonlinear refractive indices of As2Se3, AsSe2 and As2S5 chalcogenide glasses.
2.2 Numerical calculation
2.2.1 Chromatic dispersion
When an optical pulse propagates in a dielectric medium, it will interact with the bound electrons whose response depends on the optical frequency ω of the pulse. This property, referred to as chromatic dispersion, manifests through the frequency dependence of the refractive index n(ω). When a light wave propagates in an optical fiber, its transverse intensity can distribute in different profiles known as fiber modes. For each mode, the optical field distribution is a solution of the wave equation and satisfies the corresponding boundary conditions. The fiber mode whose optical field distribution can be approximately described by Gaussian profile is known as the fundamental mode. It provides the highest confinement of light power in the core [32].
The chromatic dispersion D of the fundamental mode is determined by Eq. (2)
where λ is the wavelength, c is the light speed in vacuum and the parameter neff is known as the effective refractive index. It depends on the following factors:- • The refractive index of the core
- • The refractive index difference between the core and the cladding
- • The fiber geometry
In this work, a full-vector mode solver (Mode Solution software) based on the finite difference method [33] and the perfectly matched layer boundary condition was used for chromatic dispersion calculations. The number of grid along the axis is 900 for the computation window size of 10 µm by 10 µm. This number of grid setting is expected to ensure the calculation accuracy because it is much higher than proposed in Ref. [33] (number of grid is 120 for the computation window size of 6 µm by 6 µm). The refractive index data mentioned in section 2.1.2 and the designed fiber geometry were used as input parameters.
2.2.2 FOPA calculation
Four-wave-mixing (FWM) in optical fibers is a third-order nonlinear parametric process. In this work, we considered the degenerate FWM which occurs when photons from the pump frequency (ωp) are annihilated and simultaneously new photons at the idler (ωi) and signal (ωs) frequencies are created such that the energy are conserved during the parametric interaction. The pump, the idler and the signal frequency must satisfy Eq. (3)
And the phase matching condition for this process is given by Eq. (4)
where P is the pump power, ωp, ωi and ωs are the angular frequencies of the pump, the idler and the signal waves, respectively. The nonlinear coefficient is calculated by γ =n2ω/cAeff where n2 is the nonlinear refractive index and Aeff is the effective mode area. The linear phase-mismatch Δβ is given byThe theory of degenerate FWM has been well described and can be expressed by the following equations if the loss confinement is low enough to be negligible [34]. By considering a strong pump and a weak signal incident at the fiber input such that the pump remains undepleted during the parametric gain process, the optical signal gain (Gs) is given by Eq. (6)
where L is the fiber length, Ps(L) and Ps(0) are the signal power at different ends of the fiber and the parametric gain coefficient g is in the form ofIt can be noted from Eq. (7) that chalcogenide fibers with large value of γ are advantageous to the signal gain as compared to silica and tellurite fibers. Due to the large value of γ, small values of pump power P and fiber length L are enough to have high signal gain. The benefit of using short fiber is to decrease the dispersion fluctuation along the fiber and small pump power prevents the fiber from damaging.
2.3 Effect of buffer layer
Our study started by investigating the performance of chromatic dispersion and FOPA’s signal gain when the core fluctuation occurs in a chalcogenide step-index fiber. According to the data in Table 2, AsSe2 was used as the core material because its nonlinearity is higher than the others. For the cladding material, we assumed a chalcogenide material which has the refractive index difference between the core and cladding, noted by ΔnClad=nClad - nCore, equal to −0.2 at 5.0 µm as shown in Fig. 5. The negative value of ΔnClad means that the refractive index of the cladding is lower than that of the core (nClad < nCore) and its absolute value means the size of the refractive index’s gap. In practice, by modifying the As and Se ratio, this material and refractive index can be achieved.
Fig. 5. Wavelength-dependent refractive indices which were assumed to differ from that of AsSe2 by Δn=−0.01, −0.02, −0.03, −0.04 and −0.2.
The AsSe2 step-index fiber was designed in Mode Solution software for chromatic dispersion calculation. The cladding diameter is 125 µm and the core diameter (Dc) was assumed to vary from 2 to 6 µm. Chromatic dispersion profiles which were calculated for different Dc are plotted in Fig. 6(a). In addition, the image of the calculated fundamental mode when Dc = 3 µm is also plotted in Fig. 6(b). The first thing to be noted for this chalcogenide step-index structure is that the variation in core diameter resulted in a tremendous fluctuation in chromatic dispersion. The change of Dc from 2 to 6 µm makes chromatic dispersion profiles very different in shape and value and all of them are in the normal dispersion regime (dispersion is less than 0). Considering that each chromatic dispersion profile has short and long-wavelength parts, it can be seen in Fig. 6(a) that the short-wavelength part tends to increase when Dc increase and the dispersion value can reach 0 in the wavelength range near 5.5 µm when Dc = 6 µm. Contrarily, the long-wavelength part tends to extend to longer wavelengths in the way that it makes the chromatic dispersion profiles become flattened.
Fig. 6. (a) Plot of calculated chromatic dispersion profiles when Dc of the AsSe2 step-index fiber varied from 2 to 6 µm and (b) image of the calculated fundamental mode when Dc=3 µm.
Using the results from mode analysis and dispersion calculation in Fig. 6, FOPA signal gain was calculated at different pump wavelengths λp from 3 to 14 µm when the fiber length L is as short as 3 cm and pump power P is 5 W. In Figs. 7(a) and 7(b), the signal gain maps when Dc = 3 and 6 µm are plotted on a blue background. The color scale indicates the magnitude of the signal gain in dB scale. At each pump wavelength, the intersection of a horizontal line and the color area is used to determine the gain bandwidth generated at that pump wavelength. A broad intersection refers to a broad gain bandwidth.
Fig. 7. FOPA signal gain maps calculated by using the results in Fig. 6 when Dc is 3 and 6 µm in Figs. 7(a) and 7(b), respectively.
When Dc is 3 µm, signal gain does not occur at all, except very narrow bands near the pump wavelength when it is about 12 µm. When Dc is 6 µm, wider gain bandwidth near the pump wavelength is found when the pump wavelength is about 5 to 6.5 µm. Looking back at the dispersion plot in Fig. 6(a), when Dc = 3 µm, the dispersion value is small (less than −50 ps/km.nm) at the wavelength range shorter than 9 µm. The dispersion value increases toward zero in longer wavelength range and is close to zero at 12 µm. But, when Dc = 6 µm, the dispersion value is very close to zero in the wavelength range from 4.5 to 6.5 µm and decreases in the long wavelength range. The observation of chromatic dispersion and signal gain properties in Figs. 6 and 7 implies that the broad FOPA signal gain can occur only in the wavelength range where the chromatic dispersion is very close to zero.
As a next step, the fiber structure in Fig. 6 was modified by adding a new chalcogenide layer which encloses the fiber core as depicted in Fig. 8. This layer is named as the buffer layer. Its diameter was 9 µm and the refractive difference between the core and buffer layer (ΔnBuff=nBuff - nCore) was assumed to be −0.02. The negative value of ΔnBuff means that the refractive index of the buffer layer is lower than that of the core (nBuff < nCore) and its absolute value means the size of the refractive index’s gap. The absolute value of ΔnBuff is much smaller than that of ΔnClad so as to preserve the light confinement in the fiber core. Similar to Fig. 6(b), chromatic dispersion profiles of the fundamental mode were calculated and plotted in Fig. 8(a) when Dc varies from 2 to 6 µm. The image of the calculated fundamental mode when Dc = 3 µm is also plotted in Fig. 8(b).
Fig. 8. (a) Plot of calculated chromatic dispersion profiles when Dc of the AsSe2 buffer step-index fiber varied from 2 to 6 µm and (b) image of the calculated fundamental mode when Dc=3 µm.
Unlike the results in Fig. 6(a), it is interesting to note in Fig. 8(a) that the fluctuation of chromatic dispersion is drastically suppressed. Despite large variation in core diameter from 2 to 6 µm, chromatic dispersion profiles are very similar in both shape and value. They have zero-dipersion wavelengths (ZDWs), the wavelength at which the dispersion value is zero, near 5.2 and 10.2 µm. Between these two ZDWs, chromatic dispersion is larger than 0 but smaller than 10 ps/km.nm. In addition, chromatic dispersion profiles in Fig. 8(a) becomes much flattened from 4 to 13 µm as compared to those in Fig. 6(a).
Figures 9(a) and 9(b) shows FOPA signal gain maps calculated using the results of mode analysis and dispersion calculation in Fig. 8(a) when Dc = 3 and 6 µm. The pumping conditions are the same as described for Fig. 7. Obviously, the two signal gain maps in Fig. 9 are highly analogous because they have similar chromatic dispersion profiles as shown in Fig. 8(a). Both of them show high-intensity and broad gain bandwidth along the pump wavelength when it is about 5 to 10 µm. These features are totally different from those observed in Fig. 7. Thanks to the buffer layer, signal gain maps in Fig. 9 are much larger, broader and can be maintained despite the change of Dc from 2 to 6 µm because chromatic dispersion profiles are much flattened and near-zero and dispersion fluctuation due to the Dc variation are greatly reduced as discussed in Figs. 6(a) and 8(a).
Fig. 9. FOPA signal gain maps calculated by using the results in Fig. 8 when Dc is 3 and 6 µm in Figs. 9(a) and 9(b), respectively.
When the pump wavelength is about 8.5 to 10 µm, the gain bandwidth can be continuous and broad (from 6 to 14 µm). Most notably, when the pump wavelength is about 5 µm, a continuous and very broad signal gain bandwidth can be obtained from about 3 to 14 µm. Looking back at the chromatic dispersion plot in Fig. 8(a), it is found that these broad signal gain bandwidths are generated when the pump wavelength corresponds to the wavelength range where chromatic dispersion is close to zero. This feature is in agreement with the discussion in Fig. 7.
When the pump wavelength is about 5.5 to 8.0 µm, large gap appears in the signal gain maps (in left and right sides of the pump wavelength) and make the gain bandwidth discontinuous. In particular, it can be seen that signal gain map and the gap when Dc = 6 µm is somewhat larger as compared to those when Dc = 3 µm. This difference in signal gain maps when Dc = 3 and 6 µm is reasonable because their chromatic dispersion profiles cannot be perfectly identical although the fluctuation was greatly reduced.
2.4 Effect of buffer layer’s refractive index
Further investigation into the properties of buffer layer was carried out in this section in order to improve the chromatic dispersion properties and enhance the performance of FOPA signal gain. At first, the effect of the buffer layer’s refractive index on the chromatic dispersion properties is considered while the buffer diameter (Db) is kept at 9 µm. The refractive index difference between core and buffer layer (ΔnBuff) which was assumed to be −0.02 in section 2.3 was changed from −0.01 to −0.04. For each value of ΔnBuff, chromatic dispersion calculations were performed when Dc varied from 2 to 6 µm and were plotted in Figs. 10(a-d) for comparison.
Fig. 10. (a-d) Plots of calculated chromatic dispersion profiles when ΔnBuff of the AsSe2 buffer step-index fiber changed from −0.01, −0.02, −0.03 to −0.04, respectively. The buffer diameter Db is kept at 9 µm and the core diameter Dc varied from 2 to 6 µm.
The results in Fig. 10 show that chromatic dispersion fluctuation due to Dc variation is smallest when the absolute value of ΔnBuff is as small as 0.01. As can be seen in Fig. 10(a), the chromatic dispersion curves are nearly identical for different Dc values from 2 to 6 µm when Db is kept at 9 µm. In this case, it can be explained that the effective core diameter of the mode is very close to Db and is much larger than Dc. Therefore, the effect of Dc variation is not dominant. Contrarily, the increase in the absolute value of ΔnBuff can make the effective core diameter closer to Dc and the effect of Dc variation becomes stronger. As a result, the chromatic dispersion fluctuation becomes larger when Dc varies. The dispersion value tends to reduce and the ZDW variation is much larger as can be seen in Figs. 10(a-d). The larger the chromatic dispersion fluctuation is, the more difficult the FOPA signal gain can be maintained.
Using ΔnBuff = −0.01 to take advantage of the smallest chromatic dispersion fluctuation as shown in Fig. 10(a), FOPA signal gain maps when Dc varies from 2 to 6 were calculated. The pumping conditions are the same as described for Fig. 7. The signal gain maps in the pump wavelength range from 4.5 to 5.5 are shown in Fig. 11 for comparison. As can be seen, the signal gain maps for different Dc are very similar except a noticeable change when Dc = 6 µm in the signal wavelength range from 10 to 14 µm. The red dashed-line shows the position of the pump wavelength at about 5.02 µm. The intersection of the red dashed-line and the signal gain maps shows the gain bandwidths that can be obtained at that pump wavelength. As can be observed, very broad and continuous gain bandwidth from 3 to 14 µm can be obtained at about 5.02-µm pump wavelength when Dc is 2, 3, 4 and 5 µm. But it will be narrower (from 3 to 11 µm) at the same pump wavelength when Dc is 6 µm.
Fig. 11. FOPA signal gain maps calculated for AsSe2 buffer step-index fiber when ΔnBuff = −0.01, Db = 9 µm and the core diameter Dc varied from 2 to 6 µm.
2.5 Effect of buffer layer’s diameter
Following the result in Fig. 11, the effect of buffer diameter (Db) on FOPA signal gain bandwidth was looked into. The value of Db was changed from 8 to 12 µm when ΔnBuff was kept at −0.01 and Dc = 3 µm, respectively. Figure 12 shows the calculated chromatic dispersion profiles and Fig. 13 shows their corresponding FOPA signal gain maps in the pump wavelength range from 4.5 to 5.5 µm for comparison. The pumping conditions are the same as described for Fig. 7. As can be seen in Fig. 12, when Db increases, chromatic dispersion in the wavelength range longer than 6 µm increases strongly in the way that it makes the chromatic dispersion profiles become flattened in the anomalous dispersion regime. But in the wavelength range shorter that 6 µm, a slight change occurs and the ZDW near 5 µm tends to shift toward longer wavelengths.
Fig. 12. Plots of calculated chromatic dispersion profiles for AsSe2 buffer step-index fiber when ΔnBuff = −0.01, Dc = 3 µm and the buffer diameter Db varied from 8 to 12 µm.
Fig. 13. FOPA signal gain maps calculated for AsSe2 buffer step-index fiber when ΔnBuff = −0.01, Dc = 3 µm and the buffer diameter Db varied from 8 to 12 µm.
In accord with this change, the signal gain maps are deformed as plotted in Fig. 13. The signal gain map has a convex shape when Db is as small as 8 µm and transforms into a concave shape when Db keeps increasing from 9 to 12 µm. Due to the convex shape of the signal gain map when Db=8 µm, continuous and broad signal gain bandwidth (from about 3 up to 13 µm) can be obtained when the pump wavelength is about 5 to 5.2 µm. On the other hand, gain bandwidth becomes discontinuous and narrower when Db≥10 µm due to the concave shape of the signal gain maps.
In Fig. 13, the red dashed-line shows the position of the pump wavelength at about 5.02 µm. The intersection of the red dashed-line and the signal gain maps shows the gain bandwidths that can be obtained at that pump wavelength. And it is interesting to note that the intersection can be continuous and broadest when Db is about 9 µm. In other words, a continuous and broadest gain bandwidth (from about 3 to 14 µm) can be obtained at the pump wavelength which is about 5.02 µm. It is because when Db=9 µm, the shape of the signal gain map becomes intermediate between convex and concave shapes as can be seen in Fig. 13.
In addition, Fig. 14 shows the signal gain maps calculated when Dc is 3 µm and Db varies near 9.0 µm. The results show that the shape of the signal gain maps changes slightly but the red dashed-line is still fully contained in it. This implies that a continuous and broad signal gain bandwidth can be maintained even when the buffer diameter varies from 8.9 to 9.3 µm and Dc = 3 µm. As a summary of this section, by reducing the refractive index difference between core and buffer materials and tailoring the buffer diameter so that the shape of signal gain map is intermediate between convex and concave shape, a continuous and broadest signal gain bandwidth can be obtained and maintained.
Fig. 14. FOPA signal gain maps calculated for AsSe2 buffer step-index fiber when ΔnBuff = −0.01, Dc = 3 µm and the buffer diameter Db varied from 8.9 to 9.3 µm.
Going into details, Fig. 15 shows signal gain spectra calculated when Dc varies from 2 to 5 µm, Db is 9 µm and ΔnBuff is −0.01. The pump wavelength is at 5.02 µm, pump power is 5 W and the fiber length L is as short as 3 cm. For each value of Dc, a continuous gain bandwidth at 15 dB, expanding from 3 up to 14 µm, can be obtained. The highest signal gain can reach the value near 60 dB. When Dc is 2 and 5 µm, a decrease in signal gain occurs in the wavelength ranges from 3 to 3.5 µm and from about 9 to 13 µm. But it is interesting that the signal gain spectra are nearly identical when Dc varies from 3 to 4 µm.
Fig. 15. FOPA signal gain spectra calculated for the AsSe2 buffer step-index fiber when ΔnBuff = −0.01, Db = 9 µm and the core diameter Dc varied from 2 to 5 µm.
In addition, FOPA signal gain spectra were also calculated when Dc varies from 2 to 5 µm and Db is equal to 8.9 and 9.3 µm as shown in Figs. 16(a) and 16(b), respectively. The pump conditions are the same as discussed for Fig. 15. The results show that when Dc is 3 and 4 µm, the FOPA gain spectra calculated from 3 to 14 µm are almost identical as plotted in Fig. 16(a), Fig. 15 and Fig. 16(b) when Db is equal to 8.9, 9.0 and 9.3 µm, respectively. The difference of calculated FOPA gain spectra becomes stronger when Dc varies in a wider range from 2 to 5 µm and when Db increases from 8.9 to 9.3 µm. However, it is obvious that the broad gain bandwidth from 3.0 to 14 µm at about 15 dB, which is mentioned in Fig. 15, is also achieved as shown in Figs. 16(a) and 16(b) although Dc drastically varies from 2 to 5 µm and Db increases from 8.9 to 9.3 µm. Therefore, these ranges can be considered as effective diameter ranges of the core and buffer valid for a broad gain bandwidth which can be attained at about 15 dB.
Fig. 16. FOPA signal gain spectra calculated for the AsSe2 buffer step-index fiber when ΔnBuff = −0.01 and the core diameter Dc varied from 2 to 5 µm. In Fig. 16(a), Db is 8.9 µm and in Fig. 16(b), Db is 9.3 µm.
Moreover, further calculation of FOPA signal gain spectra when Dc = 3 and 4 µm were done at different pump wavelengths near 5.02 µm. The results are plotted in Fig. 17. As can be seen, the FOPA signal gain spectra when Dc = 3 and 4 µm are nearly identical in the wavelength range from 3 up to 13 µm. In other words, they can be highly maintained when Dc varies from 3 to 4 µm.
Fig. 17. FOPA signal gain spectra calculated for the AsSe2 buffer step-index fiber when ΔnBuff = −0.01, Db = 9 µm, Dc = 3 and 4 µm, and the pump wavelength varied near 5.02 µm.
3. Conclusions
Using the refractive index of AsSe2 chalcogenide glass measured over a wide wavelength range from 0.5 to 18 µm, an AsSe2 highly nonlinear buffer step-index fiber was proposed to preserve the performances of chromatic dispersion and FOPA signal gain under the effect of fiber core diameter’s fluctuation. It is reported that by adding a buffer layer with appropriate properties to the conventional step-index structure, the performances of chromatic dispersion and FOPA signal gain can be maintained when the fiber core diameter’s fluctuation occurs.
The calculated results in this study showed that by using a 3-cm-long fiber of our proposed fiber pumped at 5.02 µm, a broad signal gain bandwidth from 3 to 14 µm at about 15 dB is attainable although the fiber core diameter Dc drastically fluctuated from 2 to 5 µm and the buffer diameter Db varies from 8.9 to 9.3 µm. Moreover, when Dc varies in smaller range from 3 to 4 µm, the FOPA signal gain spectra, calculated at different fixed values of Db in the range from 8.9 to 9.3 µm, are highly maintained. When Db is kept at 9.0 µm and Dc varies from 3 to 4 µm, the calculated FOPA signal gain spectra at different pump wavelengths from 4.98 to 5.02 µm are also nearly identical in the wavelength range from 3 up to 13 µm.
By further developing the properties of the proposed buffer step-index fibers, it is expected to highly maintain the chromatic dispersion and highly nonlinear performances when Dc and Db vary in a wide fluctuation ranges.
Funding
Japan Society for the Promotion of Science (18H01504).
Acknowledgments
We thank Furukawa Denshi Co., Ltd for providing the chalcogenide glasses.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. T. Jose and V. Narayanan, “Design of a gain flattened doped fiber amplifier with stabilized power output for WDM transmissions,” in 2015 International Conference on Microwave, Optical and Communication Engineering (ICMOCE) (2015), pp. 193–196.
2. G. Kalogerakis, K. Shimizu, M. E. Marhic, K. K. Y. Wong, K. Uesaka, and L. G. Kazovsky, “High-repetition-rate pulsed-pump fiber OPA for amplification of communication signals,” J. Lightwave Technol. 24(8), 3021–3027 (2006). [CrossRef]
3. G. Kalogerakis, M. E. Marhic, and L. G. Kazovsky, “Multiple-wavelength conversion with gain by a high-repetition-rate pulsed-pump fiber OPA,” J. Lightwave Technol. 23(10), 2954–2960 (2005). [CrossRef]
4. J. M. C. Boggio, A. Guimaraes, F. A. Callegari, J. D. Marconi, M. L. Rocha, M. R. X. deBarros, and H. L. Fragnito, “Parametric amplifier for midspan phase conjugation with simultaneous compensation of fiber loss and chromatic dispersion at 10 Gb/s,” Microw. Opt. Technol. Lett. 42(6), 503–505 (2004). [CrossRef]
5. D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express 13(16), 6234–6249 (2005). [CrossRef]
6. M. Matsumoto, “Regeneration of RZ-DPSK signals by fiber-based all-optical regenerators,” IEEE Photonics Technol. Lett. 17(5), 1055–1057 (2005). [CrossRef]
7. X. M. Wei, A. K. S. Lau, Y. Q. Xu, C. Zhang, A. Mussot, A. Kudlinski, K. K. Tsia, and K. K. Y. Wong, “Broadband fiber-optical parametric amplification for ultrafast time-stretch imaging at 1.0 µm,” Opt. Lett. 39(20), 5989–5992 (2014). [CrossRef]
8. B. Bureau, X. H. Zhang, F. Smektala, J. L. Adam, J. Troles, H. L. Ma, C. Boussard-Pledel, J. Lucas, P. Lucas, D. Le Coq, M. R. Riley, and J. H. Simmons, “Recent advances in chalcogenide glasses,” J. Non-Cryst. Solids 345-346, 276–283 (2004). [CrossRef]
9. J. Troles, V. Shiryaev, M. Churbanov, P. Houizot, L. Brilland, F. Desevedavy, F. Charpentier, T. Pain, G. Snopatin, and J. L. Adam, “GeSe4 glass fibres with low optical losses in the mid-IR,” Opt. Mater. 32(1), 212–215 (2009). [CrossRef]
10. O. Mouawad, J. Picot-Clemente, F. Amrani, C. Strutynski, J. Fatome, B. Kibler, F. Desevedavy, G. Gadret, J. C. Jules, D. Deng, Y. Ohishi, and F. Smektala, “Multi-octave midinfrared supercontinuum generation in suspended-core chalcogenide fibers,” Opt. Lett. 39(9), 2684–2687 (2014). [CrossRef]
11. C. R. Petersen, U. Moller, I. Kubat, B. B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Q. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 mu m molecular fingerprint region using ultra-high NA chalcogenide step-index fibre,” Nat. Photonics 8(11), 830–834 (2014). [CrossRef]
12. B. P. P. Kuo and S. Radic, “Highly nonlinear fiber with dispersive characteristic invariant to fabrication fluctuations,” Opt. Express 20(7), 7716–7725 (2012). [CrossRef]
13. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE J. Select. Topics Quantum Electron. 15(1), 103–113 (2009). [CrossRef]
14. E. Yaman, Q. Lin, S. Radic, and G. P. Agrawal, “Impact of dispersion fluctuations on dual-pump fiber-optic parametric amplifiers,” IEEE Photonics Technol. Lett. 16(5), 1292–1294 (2004). [CrossRef]
15. M. F. Churbanov, V. S. Shiryaev, I. V. Scripachev, G. E. Snopatin, V. V. Gerasimenko, S. V. Smetanin, I. E. Fadin, and V. G. Plotnichenko, “Optical fibers based on As-S-Se glass system,” J. Non-Cryst. Solids 284(1-3), 146–152 (2001). [CrossRef]
16. T. Kohoutek, J. Orava, A. L. Greer, and H. Fudouzi, “Sub-micrometer soft lithography of a bulk chalcogenide glass,” Opt. Express 21(8), 9584–9591 (2013). [CrossRef]
17. R. Fairman and B. Ushkov, Semiconducting Chalcogenide Glass III, Volume 80 Applications of Chalcogenide Glasses (Elsevier Science, 2004), Chap. 5.
18. A. J. Werner, “Methods in High Precision Refractometry of Optical Glasses,” Appl. Opt. 7(5), 837–843 (1968). [CrossRef]
19. J. W. Gooch, “Sellmeier Equation,” in Encyclopedic Dictionary of Polymers, J. W. Gooch, ed. (Springer, 2011), 653–654.
20. C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy,” J. Non-Cryst. Solids 223(1-2), 158–163 (1998). [CrossRef]
21. M. Szpulak and S. Fevrier, “Chalcogenide As2S3 Suspended Core Fiber for Mid-IR Wavelength Conversion Based on Degenerate Four-Wave Mixing,” IEEE Photonics Technol. Lett. 21(13), 884–886 (2009). [CrossRef]
22. C. Chaudhari, T. Suzuki, and Y. Ohishi, “Design of Zero Chromatic Dispersion Chalcogenide As2S3 Glass Nanofibers,” J. Lightwave Technol. 27(12), 2095–2099 (2009). [CrossRef]
23. M. El-Amraoui, J. Fatome, J. C. Jules, B. Kibler, G. Gadret, C. Fortier, F. Smektala, I. Skripatchev, C. F. Polacchini, Y. Messaddeq, J. Troles, L. Brilland, M. Szpulak, and G. Renversez, “Strong infrared spectral broadening in low-loss As-S chalcogenide suspended core microstructured optical fibers,” Opt. Express 18(5), 4547–4556 (2010). [CrossRef]
24. T. L. Cheng, Y. Kanou, K. Asano, D. H. Deng, M. S. Liao, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, “Soliton self-frequency shift and dispersive wave in a hybrid four-hole AsSe2-As2S5 microstructured optical fiber,” Appl. Phys. Lett. 104(12), 121911 (2014). [CrossRef]
25. J. Wang, E. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3(3), 187–203 (1994). [CrossRef]
26. J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef]
27. M. Feng, A. K. Mairaj, D. W. Hewak, and T. M. Monro, “Nonsilica glasses for holey fibers,” J. Lightwave Technol. 23(6), 2046–2054 (2005). [CrossRef]
28. G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S. W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25(4), 254–256 (2000). [CrossRef]
29. T. Kato, Y. Suetsugu, and M. Nishimura, “Estimation of Nonlinear Refractive-Index in Various Silica-Based Glasses for Optical Fibers,” Opt. Lett. 20(22), 2279–2281 (1995). [CrossRef]
30. S. Manning, H. Ebendorff-Heidepriem, and T. M. Monro, “Ternary tellurite glasses for the fabrication of nonlinear optical fibres,” Opt. Mater. Express 2(2), 140–152 (2012). [CrossRef]
31. J. Tasseva, R. Todorov, and K. Petkov, “Linear and non-linear optical properties of thin films from the system As-S-Se,” J. Optoelectron. Adv. M. 11(9), 1257–1260 (2009).
32. B. E. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, 2007).
33. Z. M. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002). [CrossRef]
34. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Select. Topics Quantum Electron. 8(3), 506–520 (2002). [CrossRef]
