Tapered photonic crystal fiber for supercontinuum generation in telecommunication windows

Abstract

We numerically studied supercontinuum generation in a tapered photonic crystal fiber with flattened dispersion properties. The fiber was weakly tapered to have normal dispersion at wavelengths around 1.55 μm after a certain distance. We pumped 4 ps pulses with low peak power and found that flatly broadened, wideband supercontinuum was generated in telecommunication windows. Furthermore, we also demonstrated the effects of tapered length and pulse width of the pump pulse on supercontinuum generation.

Keywords

fiber optics / photonic crystal fiber / dispersion / supercontinuum

1 1 Introduction

Recently, terahertz (THz) technology has gained a considerable attention as it can exploit the untapped slice of electromagnetic (EM) spectrum called “THz gap” which is flanked between microwave and optical regions [1,2]. While either side of this THz region has been commercialized to a larger extent by electronics and photonics, there have been many attempts to explore this virgin area too for commercialization. One of the properties of the THz region, namely, non-ionizing radiation finds potential applications in non-destructive testing, security screening and medical field [3,4]. At this juncture, we emphasize that most of the natural materials show the non-conductive and non-polar characteristics at THz frequencies and eventually result in less absorption.

It is to be noted that there are two types of classical absorbers, namely, Salisbury and Jaumann. The Salisbury absorber absorbs the incident radiation only at a particular desired frequency. On the other hand, in the Jaumann absorber, the absorption takes place at multiple resonance frequencies due to the multiple resonators and increment in the number of dielectric layers. Thus, the former one works only in the narrow band and the later one becomes bulky as it is designed with multiple resonators and several dielectric layers [5,6]. To address the above mentioned issues, metamaterial based perfect absorbers (MPAs) have been proposed. MPAs are artificial devices proposed for particular bands of the incident electromagnetic radiation and they consist of periodic structures with sub-wavelength unit cells. In general, MPAs comprise of three layers, where a dielectric layer is sandwiched between two distinct metallic layers. The absorption can be maximized by minimizing the reflection and the transmission characteristics of the proposed device. There are two key roles in designing these two distinct metallic layers. The patterned layer is used to match the surface impedance of the absorber with the surrounding air medium. This can be achieved by tailoring the constituent parameters, such as an electric permittivity and the magnetic permeability of the unit cell. As a result, reflection is minimized. The continuous metallic layer at the bottom completely blocks the transmittance of the incoming electromagnetic wave since the penetration depth of the incoming wave is greater than the thickness of the bottom layer. Hence, the absorption of the device is maximized with the minimization of both the reflectance and transmittance [7].

MPAs were introduced in 2008 by Landy et al., and almost unity absorption in the microwave frequency regime has been reported [8]. To date, various MPAs have been designed which work in the microwave [9,10], THz [11], infrared [12] and visible [13] frequencies. Of these frequency regions, designing a perfect absorber using metamaterials (MM) in the THz frequency becomes an attractive research area. Tao et al. designed the perfect absorption in the narrow frequency range [14]. Then, dual-band [15,16], triple band [17,18], and quad-band [19,20] absorbers had been designed. These absorbers exhibited only narrow absorption bandwidth because of the resonant response of the metamaterials. Further, it is challenging to find materials with a broad absorption bandwidth and high absorption coefficients. In general, the bandwidth of the absorber is fixed once the geometrical parameters are optimized. For most of the practical applications, tunable absorption is preferred. In the THz frequency range, the following active materials, such as graphene [21–23], thermal [24–27], phase change materials [28–30], and intensity tunable materials [31,32], are used for the controllable absorption.

An ultra-broadband absorber of compact size with tunable absorption and greater efficiency is highly suitable for various applications. In this work, we design an absorber with above mentioned traits for a wide range of frequency by using a resonator made of VO₂ metasurface. The paper is written as follows. In Section 2, we present a geometrical dimension of the unit cell with material parameters. Absorption of the designed device, the associated mechanism and the material parameters are explored in Section 3. In Section 4, we have explored the physical mechanism for the generation of multiple resonances in the absorber. Further, in Section 5, we analyze the variations of the absorption spectra against the geometrical parameters of the unit cell. Finally, in Section 6, the core of the research work findings is presented.

2 2 Geometrical design and analysis

In this section, we describe the geometrical structure of the proposed absorber in detail. Figures 1(a) and 1(b) depict the geometrical structure of the proposed THz absorber in 3D view and front view in 2D, respectively. Here, each unit cell consists of three layers. The top layer is made of thermally tunable metasurface designed with circle and cross geometries. The metasurface is made of vanadium dioxide (VO₂) material, which varies its state from an insulator to a metal as a function of temperature. The various physical parameters of the unit cell are as follows: periodicity of the unit cell is p = 24 μm and the various dimensions of the resonators are l = 24 μm, b = 2 μm, r = 5 μm, and w = 1.5 μm. The second layer is a dielectric material made of polyimide with the dielectric permittivity of ε = 3.5(1+ i0.002). The bottom layer, which is made of gold, has electrical conductivity (σ) of 5.8 × 10⁷ S/m.

The parameters, t₁ = 0.4 μm, t₂ = 10 μm, and t₃ = 0.2 μm, represent the thicknesses of the bottom, middle and top layers, respectively. Here, the periodic boundary conditions are applied to represent a plane wave. Further, the thickness of the bottom layer is greater than the skin depth or penetration depth of the EM waves for the operating frequency range. Thus, the bottom layer prohibits the transmission of the EM waves.

Fig.1 Geometry of the designed absorber. (a) 3D view. (b) 2D view. p = 24 μm, t1 = 0.4 μm, t2 = 10 μm, t3 = 0.2 μm, l = 24 μm, b = 2 μm, r = 5 μm, and w = 1.5 μm

Full size|PPT slide

At this juncture, it should be emphasized that the proposed geometrical structure can be fabricated with the existing technology. In general, the polyimide is used as a middle layer during the fabrication process. A continuous and uniform VO₂ layer can be grown by the molecular beam epitaxy method. Then the resulting layer can be patterned into a circle and cross resonator arrays using a photolithography technique. Finally, Au layer is deposited on the other side of the polyimide by electron beam lithography [33].

VO₂ acts as an insulator at room temperature and behaves as a metal beyond critical temperature (340 K). During the phase transition of VO₂, the lattice structure is changed from monoclinic to tetragonal state. Thus, the conductivity (σ) of VO₂ is increased from 200 to 200000 S/m. Hence, VO₂ can be used as an active material for realizing controllable optical properties. The dielectric constant of VO₂ in the THz frequency range can be represented by using the Drude model [34],

(1)$\epsilon (\omega )\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}{\epsilon }_{\infty }\mathrm{\hspace{0.17em}}-\mathrm{\hspace{0.17em}}{\displaystyle \frac{{\omega }_{\mathrm{p}}^{\mathrm{2}}\mathrm{\hspace{0.17em}}(\sigma )}{{\omega }^{\mathrm{2}}\mathrm{\hspace{0.17em}}+\mathrm{\hspace{0.17em}}\mathrm{i}\gamma \omega }},$

where the physical parameters ${\epsilon }_{\infty }$( = 12) and $\gamma$(5.75 × 10¹³ rad/s) represent permittivity of the material at high frequency and collision frequency, respectively. Here, the frequency independent plasma frequency of VO₂ at THz frequency can be expressed as

${\omega }_{\mathrm{p}}^{\mathrm{2}}\mathrm{\hspace{0.17em}}(\sigma )={\displaystyle \frac{\sigma }{{\sigma }_{\mathrm{0}}}}{\omega }_{\mathrm{p}}^{\mathrm{2}}\mathrm{\hspace{0.17em}}({\sigma }_{\mathrm{0}}),$

where σ₀ = 3 × 10⁵ S/m, and ${\omega }_{\mathrm{p}}\mathrm{\hspace{0.17em}}({\sigma }_{\mathrm{0}})$ = 1.4 × 10¹⁵ rad/s. The parameters ${\omega }_{\mathrm{p}}^{\mathrm{2}}\mathrm{\hspace{0.17em}}(\sigma )$ and σ depend on the free carrier density of the electrons.

It is well known that based on the circuit model, the resonance frequency (f) is related to the inductance (L), and capacitance (C) of the resonator. Further, it can also be related to the geometrical parameters of the resonator by [35,36]

(2)$f\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}{\displaystyle \frac{\mathrm{1}}{\mathrm{2}\mathrm{\pi }\sqrt{LC}}}\mathrm{\hspace{0.17em}}\propto \mathrm{\hspace{0.17em}}{\displaystyle \frac{\mathrm{1}}{l}}.$

Here, l represents the length of the resonator.

3 3 Absorption characteristics of designed unit cell

The schematic diagram shown in Fig. 2 represents the broadband absorption of designed unit cell. The maximum absorption exceeding 90% is observed from 2.54 to 5.54 THz, and the corresponding bandwidth of the absorber is 3 THz. At the resonance frequencies, the absorption reaches 100%. The relative bandwidth of the designed absorber is determined using

$R_{\mathrm{BW}}\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}\mathrm{2}\mathrm{}\mathrm{\hspace{0.17em}}\times \mathrm{\hspace{0.17em}}(f_{\mathrm{u}}-f_{\mathrm{l}})/(f_{\mathrm{u}}+f_{\mathrm{l}})\mathrm{\hspace{0.17em}}\times \mathrm{100}\%,$

where f_u and f_l represent the upper and lower range of frequencies with 90% of absorption efficiency [37]. The estimated relative bandwidth of the designed absorber is 74.16 %.

Fig.2 Absorption of the proposed metasurface absorber in different states of the resonator

Full size|PPT slide

As has been discussed in the previous chapter, to understand the maximum absorption of the absorber, next, we analyze the surface impedance of the absorber in the operating frequency from 2.54 to 5.54 THz. For the metamaterials, the frequency dispersion of the effective surface impedance $(Z\left(\nu \right))$ can be described as [38]

(3)$Z(\nu )\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}\sqrt{{\displaystyle \frac{\mu (\nu )}{\epsilon (\nu )}}}\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}{Z}^{\prime }\mathrm{\hspace{0.17em}}+\mathrm{\hspace{0.17em}}\mathrm{i}\mathrm{\hspace{0.17em}}{Z}^{″}.$

Here, $\mu \left(\nu \right)$ represents the magnetic permeability, and $ϵ\left(\nu \right)$ describes the electric permittivity of the designed absorber. $Z^{\prime }$ and $Z^{\prime }$ describes the real and the imaginary component of the surface impedance

Further, the normalized form of the surface impedance in terms of the reflection $\left(S_{\mathrm{11}}\right)$ and transmission $\left(S_{\mathrm{21}}\right)$ coefficients is as follows

(4)$Z(\nu )\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}\sqrt{{\displaystyle \frac{{(\mathrm{1}+S_{\mathrm{11}})}^{\mathrm{2}}-S_{\mathrm{21}}^{\mathrm{2}}}{{(\mathrm{1}-S_{\mathrm{11}})}^{\mathrm{2}}-S_{\mathrm{21}}^{\mathrm{2}}}}}\mathrm{\hspace{0.17em}}.$

It is to be noted that the transmission of the absorber turns zero as the proposed unit cell possesses continuous metal plate at the bottom. Hence, the surface impedance can now be related to the reflection coefficients of the absorber as follows

(5)$Z(\nu )\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}\sqrt{{\displaystyle \frac{(\mathrm{1}+S_{\mathrm{11}})}{(\mathrm{1}-S_{\mathrm{11}})}}}\mathrm{\hspace{0.17em}}.$

The surface impedance of the absorber can be calculated by using Eq. (5). Figure 3(a) represents the real and imaginary components of the effective surface impedance of the designed absorber. From this analysis, the real part of Z_eff is close to unity in the frequency range from 2.54 to 5.54 THz. This clearly shows the matching of surface impedance between the top layer of the absorber with that of the surrounding air medium. As a result, the reflection turns minimum.

To understand the maximum absorption of the proposed device, now, we calculate the effective material parameters such as the effective permittivity (ε_eff) and effective permeability (μ_eff). Figure 3(b) illustrates the real and imaginary parts of ε_eff and μ_eff. From Fig. 3(b), it is observed that the real part of effective permittivity is equal to real part of effective permeability (ε_eff = μ_eff) at resonance frequencies. As a result, the surface impedance of the proposed absorber is nearly equal to the free space. Further, the magnitude of the imaginary part of the effective material parameters turns maximum and is also equal. Thus, this ensures the maximum absorption characteristics of the absorber.

Fig.3 Extracted material parameters. (a) Z. (b) ε-μ

Full size|PPT slide

Now, we investigate the individual absorption characteristics of inner and outer resonators. In addition, we also investigate the absorption characteristics of the combined one. Figure 4(a) illustrates the absorption of the inner and the outer resonators of the unit cell. From Fig. 4(a), it is very clear that inner resonator exhibits higher absorption (50%) than the outer resonator (18%). However, we find that the absorption turns a maximum of 90% as shown in Fig. 4(b) when the outer and the inner resonators are combined.

Fig.4 Absorption. (a) Separate resonator. (b) Combination of the resonator

Full size|PPT slide

As has been discussed in Section 2, the top layer of the resonator is made of VO₂. In this section, to understand the thermal tunable behavior of the designed absorber, we vary the electrical conductivity of the VO₂. As illustrated in Fig. 5(a), the reflection decreases as and when the electrical conductivity is increased. In other words, the corresponding absorption is increased as depicted in Fig. 5(b). We observe that absorption increases from 10% to nearly 100% when the conductivity is increased from 200 to 200000 S/m. At this juncture, we emphasize that the absorption is different for different electrical conductivity within the operating frequency. Thus, such a flexible dual-functional resonator-based absorber can be used as a perfect reflector or broadband absorber.

Fig.5 Tunable reflection and absorption with electrical conductivity of VO2. (a) Reflection. (b) Absorption

Full size|PPT slide

4 4 Physical mechanism

Having discussed the broadband absorption of the proposed unit cell, next, we turn to delineate the physical mechanism. Here, we analyze both the electric and the magnetic fields of the device at resonance frequencies of 3.09 and 4.89 THz. Figures 6(a), 6(b), and 6(c) represent the variations of electric field along the z-direction (E_z), normalized electric field (|E|), and the magnetic field along the y-direction (H_y), respectively, at the above mentioned resonance frequencies.

Figures 6(a₁) and 6(a₂) represent the electric field distributions of E_z at 3.09 and 4.89 THz resonance frequencies, respectively. At the first resonance frequency 3.09 THz, the z-component of the electric field is distributed mainly in the cross region of the resonator and also part of the field is extended to inner resonator. This is mainly because of the resonance coupling between the inner and the outer resonators. For the second resonance frequency of 4.89 THz, the E_z field is distributed corner edges of the cross resonators.

Fig.6 Field distribution at resonance frequencies of 3.09 and 4.89 THz. (a) Electric field along the z-direction. (b) Normalized electric field. (c) Magnetic field along the y-direction

Full size|PPT slide

To identify the various parts of the resonator where the charge distribution is maximum, we study the normalized electric field distributions and they are plotted in Figs. 6(b₁) and 6(b₂). From these figures, the electric field distributions of the resonator are conspicuous at the two resonance frequencies. Figures 6 (c₁) and 6 (c₂) represent the variation of perpendicular component of the magnetic field (H_y) at two resonance frequencies of 3.09 and 4.89 THz, respectively. The perpendicular magnetic field is distributed between the inner resonator of the metasurface and the bottom metal plate at resonance frequency of 3.09 THz. This analysis is shown in Fig. 6(c₁).

In the second resonance frequency, 4.89 THz, the distribution of the H_y component takes place between the outer resonator of the metasurface and the bottom metal plate as shown in Fig. 6(c₂). Thus, this kind of field analysis demonstrates the generation of the electric and the magnetic field distributions at the resonance frequencies.

5 5 Variations of absorption spectrum dependents on geometrical parameters

It is known that the EM properties of the MM are dependent on the geometrical parameters. Hence, in this section, it is of paramount importance to analyze the response of the geometrical parameters on the absorption spectra. In the parametric analysis, when one parameter of the unit cell is varied, the other parameters remain constant. To study the parametric analysis, we consider the following geometrical parameters of the absorber such as the periodicity of the unit cell (p), length of the cross shape resonator (l), width of the arm (b), radius of the circle (r), width of the circle (w), dielectric thickness (t₂), and thickness of VO₂ (t₃).

Now, we analyze the influence of length of the cross shape resonator (l) in the absorption spectra. Figure 7(a) portrays the variation of absorption spectra when the length of the cross shape resonator is varied. As shown in Fig. 7(a), increase (decrease) in length of the cross shape resonator l causes the redshift (blueshift) in the resonance frequency of the absorption spectrum. Here, the redshift (blueshift) takes place since the resonance frequency of the resonator is directly proportional to the inverse length of the resonator based on Eq. (2). As a result, the bandwidth of the absorber is increased in the former case and it is decreased in the later case.

As shown in Fig. 7(b), width of the arm affects both the absorption bandwidth and the resonance frequency. We note that the lower resonance frequency does undergo blueshift (redshift) and the higher resonance frequency undergoes redshift (blueshift) when the width of the arm is decreased (increased) from the optimized value. Thus, the bandwidth of the absorber decreases (increases) when width of the arm is decreased (increased) from the optimized value.

From Fig. 7(c), it is very clear that the radius of the circle does not affect the absorption spectra as the variations are very tiny. However, there is appreciable change in absorption spectra when the width of the circle is varied. As depicted in Fig. 7(d), the bandwidth increases (decreases) when the width of the circle is decreased (increased).

As shown in Fig. 7(e), we find that the absorption bandwidth and the resonance frequency of the designed absorber are changed with the periodicity of the unit cell. As a result, the bandwidth increases (decreases) when the periodicity of the unit cell is decreased (increased) from the optimized value. This is because of the resonance coupling between the resonators of the unit cell.

Fig.7 Analysis of absorption over various geometrical parameters. (a) Length of the strip. (b) Width of the strip. (c) Outer radius of the circle. (d) Width of the circle. (e) Periodicity of the unit cell

Full size|PPT slide

So far, we have discussed the impact of length and width of the unit cell against absorption spectra. In the last part of the parametric analysis, we delineate the influence of the thickness of VO₂ as well as thickness of dielectric layer over the absorption spectra. Here, we vary the thickness of VO₂ by keeping the electrical conductivity as 200000 S/m. Figures 8(a) and 8(b) show the variations of the absorption against the thickness of the metasurface VO₂ resonator and the dielectric layer, respectively. From Fig. 8(a), the absorption decreases (increases) when the thickness of VO₂ is increased (decreased) from the optimized value. From Fig. 8(b), we observe that both the lower and higher resonance frequencies undergo blueshift when the dielectric thickness is decreased. As a result, there is an increment in the bandwidth and decrement in the efficiency. We find that both bandwidth and efficiency decrease when the dielectric thickness is increased from the optimized value. The reason for this shift is due to the changes in the effective cavity length of the absorber. Further, increase in dielectric thickness affects the interaction between the bottom metal plate and the top metal resonator. These parametric studies corroborate that the absorption spectra are robust against variations in most of the geometrical parameters.

Fig.8 Thickness response of (a) top resonator VO2 (t3) and (b) dielectric layer (t2)

Full size|PPT slide

To understand the performance of the absorber, we analyze the absorption responses for the various oblique incidences other than the normal incidence angle. Here, the incident EM waves make an angle θ with the unit cell of the absorber. Further, the absorption characteristics are examined for various incident angles of transverse electric (TE) and transverse magnetic (TM) polarizations. Figures 9(a) and 9(b) describe the absorption response of the absorber for various incident angles (θ) from 0° to 80°. From the analysis, the absorber exceeds the absorption efficiency of 90% up to 40° of the incident angles. Because of the symmetry of the geometry, the absorption response is the same for the TM polarization. Here, the maximum absorption is maintained up to 40°.

Fig.9 Incident angle sensitivity of the absorber. (a) TE mode of polarization. (b) TM mode of polarization

Full size|PPT slide

Fig.10 Absorption of proposed absorber for different polarization angle. (a) TE polarization. (b) TM polarization

Full size|PPT slide

Next, we analyze the absorption characteristics for the various polarization angles. Figures 10(a) and 10(b) illustrate the absorption of the unit cell for different polarization angles. From this analysis, we find that the absorption characteristics remain same for various polarization angles. Because of the geometrical symmetry of the absorber, the absorption exhibits the same responses for both the TE and TM polarizations. Thus, the proposed unit cell is polarization insensitive.

6 6 Conclusions

In conclusion, we have designed a three layer metamaterial absorber that absorbs the incoming radiation for a wide range of frequencies. The proposed absorber exhibits a maximum absorption exceeding 90% from 2.54 to 5.54 THz when the conductivity is 200000 S/m. Thus, the bandwidth of the absorber is 3 THz. Then, we have discussed the physical mechanism of the proposed absorber with the help of field analysis. Further, in order to study the robustness of the proposed absorber, we have carried out the influence of the various geometrical parameters over the absorption spectra. These numerical results encourage that the proposed absorber is a robust one against the variations in the various geometrical parameters of the unit cell. Finally, we have also studied the sensitivity for various incident and polarization angles. It has been found that the absorber maintains 90% efficiency up to 40° incident angles and it is also polarization insensitive. Based on the above results, we are of the opinion that the designed THz metasurface absorber would turn out to be a potential candidate in communication, radar and stealth technology.

References

[1] Ravi Kanth Kumar V V, George A K, Reeves W H, Knight J C,Russell P St J . Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation. Optics Express, 2002, 10(25): 1520-1525

[2] Yu Y Q, Ruan S C, Du C L, Yao J Q. Spectral broadening in the 1.3 μm region using a 1.8-m-long photonic crystal fiber by femtosecond pulses from an optical parametric amplifier. Acta Photonica Sinica, 2005, 34(4): 481-484 (in Chinese)

[3] Xu Y Z, Ren X M, Wang Z N, Zhang X, Huang Y Q. Flat supercontinuum generation at 1550 nm in a dispersion-flattened microstructure fibre using picosecond pulse. Chinese Physics Letters, 2007, 24(3): 734-737

[4] Hu M L, Wang Q Y, Li Y F, Wang Z, Zhang Z G, Chai L, Zhang R B. Experimental analysis of the dependence factor during supercontinuum generation in photonic crystal fiber. Acta Physica Sinica, 2004, 53(12): 4243-4247 (in Chinese)

[5] Yu Y Q, Ruan S C, Du C L, Yao J Q. Supercontinuum generation using a polarization-maintaining photonic crystal fibre by a regeneratively amplified Ti:sapphire laser. Chinese Physics Letters, 2005, 22(2): 384-387

[6] Kudlinski A, George A K. Knight J C. Travers J C, Rulkov A B, Popov S V, Taylor J R. Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation. Optics Express, 2006, 14(12): 5715-5722

[7] Ohara T, Takara H, Yamamoto T, Masuda H, Morioka T, Abe M, Takahashi H. Over-1000-channel ultradense WDM transmission with supercontinuum multicarrier source. Journal of Lightwave Technology, 2006, 24(6): 2311-2317

[8] Xu Y Z, Ren X M, Wang Z N, Zhang X, Huang Y Q. Flatly broadened supercontinuum generation at 10 Gbit/s using dispersion-flattened photonic crystal fibre with small normal dispersion. Electronics Letters, 2007, 43(2): 87-88

[9] Yusoff Z, Petropoulos P, Furusawa K, Monro T M, Richardson D J. A 36-channel × 10-GHz spectrally sliced pulse source based on supercontinuum generation in normally dispersive highly nonlinear holey fiber. IEEE Photonics Technology Letters, 2003, 15 (12): 1689-1691

[10] Nakasyotani T, Toda H, Kuri T, Kitayama K. Wavelength-division-multiplexed millimeter-waveband radio-on-fiber system using a supercontinuum light source. Journal of Lightwave Technology, 2006, 24(1): 404-410

[11] Lee J H, Kim C H, Han Y G, Lee S B. WDM-based passive optical network upstream transmission at 1.25 Gb/s using Fabry–Pérot laser diodes injected with spectrum-sliced, depolarized, continuous-wave supercontinuum source. IEEE Photonics Technology Letters, 2006, 18 (17–20): 2108-2110

[12] Wu W Q, Chen X W, Zhou H, Zhou K F, Lin X S, Lan S. Investigation of the ultraflattened dispersion in photonic crystal fibers with hybrid cores. Acta Photonica Sinica, 2006, 35(1): 109-113 (in Chinese)

[13] Saitoh K, Koshiba M. Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window. Optics Express, 2004, 12(10): 2027-2032

[14] Wu T L, Chao C H. A novel ultraflattened dispersion photonic crystal fiber. IEEE Photonics Technology Letters, 2005, 17 (1); 67-69

[15] Matsui T, Nakajima K, Sankawa I. Dispersion compensation over all the telecommunication bands with double-cladding photonic-crystal fiber. Journal of Lightwave Technology, 2007, 25(3): 757-762

[16] Liu J G, Xue L F, Wang Z, Kai G Y, Liu Y G, Zhang W G, Dong X Y. Large anomalous dispersion at short wavelength and modal properties of a photonic crystal fiber with large air holes. IEEE Journal of Quantum Electronics, 2006, 42 (9): 961-968

[17] Ju J, Jin W, Suleyman Demokan M. Design of single-polarization single-mode photonic crystal fiber at 1.30 and 1.55 μm. Journal of Lightwave Technology, 2006, 24(2): 825-830

[18] Yamamoto T, Kubota H, Kawanishi S, Tanaka M, Yamaguchi S. Supercontinuum generation at 1.55 μm in a dispersion-flattened polarization-maintaining photonic crystal fiber. Optics Express, 2003, 11(13): 1537-1540

[19] Saitoh K, Koshiba M. Full-vectorial imaginary-distance beam propagation method based on finite element scheme: application to photonic crystal fibers. IEEE Journal of Quantum Electronics, 2002, 38 (7): 927-933

[20] Agrawal G P. Nonlinear Fiber Optics. 2nd ed. New York: Academic Press, 1995

Acknowledgements

This work was supported by the Foundation for Key Program of Ministry of Education, China (Grant No. 104046).

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg