1. Introduction

Ultra-fast all-optical switching (AOS) at a few Tbit/s rate is a key technology for the next data transmission rates exceeding 40 Gbit/s which are currently very difficult to achieve even with high-speed electronics. Ultra-fast optical switches require a highly nonlinear material with an extremely fast time response. Typically the Kerr nonlinearity is employed in ultra-fast AOS, since its non-resonant characteristics results in the required fast time response and low absorption. On the other hand, however, the small value of the Kerr nonlinear refractive index n₂ often requires excessive switching power and long fiber length [1, 2]. The goal is to maximize the nonlinearity and thereby to bring switching energy to the pJ regime while keeping the device dimension small.

To meet this need in real AOS application, non-resonant and resonant types of nonlinear fibers turned up within the past ten years. Non-resonant type of nonlinear fibers use the intrinsic polarization or hyper-polarization properties of glass materials and the novel design of small-size fiber core to get high non-resonant nonlinearity (1∼3 levels in magnitude larger than the non-resonant nonlinearity n_2,NR of the common single mode fiber (SMF) [3]) plus with ultra-fast response (fs-level), such as lead silicate glass holey fiber [4], bismuth oxide-based glass fiber [5, 6], bismuth oxide-based glass holey crystal fibers [7], which have the common disadvantages of high transmission loss or large splicing loss preventing these fibers from generating high efficient nonlinear signal in real application. On the other hand, resonant type of nonlinear fibers use the extrinsic transition properties of the impurities doped into the glass structure, represented by rare earth ions (typically Yb³⁺, Er³⁺ and Tm³⁺ ions) doped silica-based fibers [8-10] with extremely high nonlinearity (4∼6 levels larger in magnitude than n_2,NR of SMF) but rather slow response time (ms-level) related to the typically long lifetime of metastable state.

To find an appropriate nonlinear material which has low transmission and splicing losses, compatible with the current silica fiber system in use, competent and high nonlinearity (2∼4 levels in magnitude larger than n_2,NR of SMF) and ultra-fast response time (μs∼ps level), transition metal ions doped fibers go into the sight of the researchers. Among all the transition metal ions, Cu²⁺ ion has typically unfilled 3d⁹ electron shell, which means that Cu²⁺ ions have fairly simple absorption spectrum like Yb³⁺ with 4f¹³ electron shell. The refractive index change of a Cu²⁺-doped fiber is mainly due to the localized changes in absorption of the optically pumped 3d-shell electronic transitions themselves. What’s more, Cu²⁺ ions have ultra-fast time at the range from μs to ps [11], making the Cu²⁺-doped fiber a competent nonlinear component for the current optical communication system.

In this paper, we are, for the first time, to report on the formation of a Cu²⁺-doped germano-silicate glass fiber having broadband absorption around 700nm and high resonant optical nonlinearity around 1540nm. The resonant nonlinear refractive index n_2,R was measured by using a long period fiber grating (LPG) pair pumping with 980nm laser diode (LD). And the non-resonant optical nonlinearities n_2,NR were measured by the continuous wave self-phase modulation (cw-SPM) method . The reasons for the enhancement of n_2,R and the decrease of n_2,NR are analyzed in terms of the roles of Cu²⁺ ions in the host glass structure.

2. Experiments

2.1 Fabrication of a germano-silicate fiber doped with Cu²⁺ ions

The Cu²⁺-doped germano-silicate glass fiber was fabricated by using the modified chemical vapor deposition (MCVD) technique with the solution doping process. A doping solution containing 0.8mol/L CuCl₂∙2H₂O (99.99%, chemical purity) in the deionized (DI) water was prepared and incorporated into the core of the fiber using the solution doping method. The core diameter and the cut-off wavelength of the fiber were 7.35μm and around 881nm, respectively. The absorption spectrum of the fiber was measured by the optical spectrum analyzer (OSA, Ando AQ6315B). To compare and confirm the optical properties from Cu²⁺ ions themselves, a reference fiber without any dopant but with the same structure and MCVD recipe was also made.

2.2 Resonant optical nonlinearity measurement by the LPG pair method

To estimate the resonant optical nonlinearity of the fiber, the long period grating (LPG) pair method upon pumping was adopted [12]. A LPG pair was formed onto the Cu²⁺-doped fiber hydrogen-loaded at 100◻ for 5 days by irradiating with a KrF Excimer laser using an amplitude mask. The periodicity and the length of each grating were fixed at 500μm and 20mm, respectively. The LPG was adjusted to have ∼50% minimum transmissivity (3dB) at the third stop band near 1.55μm. The center-to-center separation between the gratings was 150mm with an accuracy of ±0.1 mm. The transmission spectrum of the LPG pairs was measured after annealing the fiber in an oven for 24h at 150◻. The OSA (Ando AQ6317B) used for the measurement had a 0.01nm spectral resolution, a broadband amplified spontaneous emission light source (ASE, Thorlabs, SOA240) had peak intensity at 1.5μm and the 980nm laser diode (M-Tech., MSMF-10) had a maximum power of 400mW. The shift of the LPG fringes upon pumping with the LD was measured to estimate the resonant optical nonlinearity of the Cu²⁺-doped fiber.

 

Fig. 1. Schematic diagram of the resonant nonlinearity measurement setup by using a LPG pair and two WDM couplers (980/1550nm)

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The schematic diagram of the measurement setup for resonant optical nonlinearity of the doped fibers using an LPG pair is shown in Fig. 1. The principle of the resonant nonlinearity measurement by using LPG method was described in Ref. [12]. The resonant optical nonlinearity n_2,R, the effective length Leff, and the effective area Aeff of the Cu²⁺-doped fiber, were estimated by Eq. (1), Eq. (2) and Eq. (3), respectively.

where λp is the peak wavelength of the LPG fringe, Δλ is the wavelength shift of the LPG fringe, S is the fringe spacing, b is the polarization-dependent parameter (2/3), P_pump is the launched pumping power, α is the absorption coefficient of the tested fiber at 980nm, L is the center-to-center grating separation between the gratings (L=150mm in this experiment), and E(x, y) is the optical mode field distribution.

2.3 Non-resonant optical nonlinearity measurement by the cw-SPM method

 

Fig. 2. Block diagram of n_2,NR measurement setup using cw-SPM method PC = polarization controller BPF = band pass filter ATT = optical attenuator OSA = optical spectrum analyzer FUT = fiber under test

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The non-resonant nonlinearities, n_2,NR, of the fibers were measured using the cw-SPM method [13, 14]. Figure 2 shows the block diagram of the experimental setup. The polarization state of the two input lights, λ ₁ and λ ₂, was made parallel by passing them through two polarization controllers (PCs). After a band pass filter with a 3dB bandwidth of 3nm to reduce the ASE, the coupled signals were amplified by using an Er-doped fiber amplifier (EDFA) and launched into the fibers under test. The power ratio of the output signal I₀ and I₁ was measured at an OSA by changing the electric current of EDFA. In order to protect the OSA from damage, an optical variable attenuator was used in this experiment.

To determine the non-resonant nonlinear coefficient of the optical fiber, the nonlinear phase shift φ _SPM and the corresponding power P_AVG were measured experimentally. φ _SPM was measured in spectral domain and determined from the shape of the spectrum just by measuring the relative heights of the spectral components. The ratio of the spectral intensities of the fundamental wavelengths to the first-order sidebands is given by Eq. (4):

Here I₀ is the intensity of the fundamental wavelength and I₁ the intensity of the first-order side-band. J_n is the n-th order Bessel function.

The non-resonant optical nonlinearity, n_2,NR, and the effective nonlinear parameters, γ, were estimated by using the cw-SPM method shown in Eq. (5) and Eq. (6) [13, 14]:

where P_AVG is the average power of the dual wave signal, L_eff is the effective length, A_eff is the effective area, λ = (λ ₁ + λ ₂)/2 is the center wavelength of the two signals (λ ₁ = 1549.84nm and λ ₂ = 1550.24nm in this experiment), and κ _ac is the slope coefficient determined from the linear region of the function φ _SPM/P_AVG.

3. Results and discussion

3.1 Linear absorptive optical properties

Figure 3 compares the absorption spectrum of the Cu²⁺-doped fiber with that of the reference germano-silicate glass fiber without Cu²⁺-incorporation. As shown in Fig. 3, the Cu²⁺-doped fiber has broadband absorption in the vicinity of 700nm and the difference compared with the no-dopant reference fiber is obvious. The absorption spectrum of the samples shown in Fig. 3 can be analyzed by invoking the familiar single energy level diagram of Cu²⁺ ion shown in Fig. 4 [15].

 

Fig. 3. Comparison of the absorption spectra of the Cu²⁺-doped germano-silicate glass fiber and the reference germano-silicate glass fiber without Cu²⁺-incorporation.

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Fig. 4. Energy level diagram for d⁹ Cu²⁺ as a free ion in octahedral, tetragonal, and square planar coordination

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It is known that the diluted Cu²⁺ ions inside glass matrix exhibit a broad optical absorption around 700nm, assigned to the ²E_g-²B_1g transition due to the Jahn-Teller splitting of 3d levels of Cu²⁺ ions in a ligand field [16]. The broad absorption band was observed in the NIR region which corresponds to three possible d-d electronic absorption transitions as per the diagram in Fig. 4, in which tetrahedral coordination and square planar coordination are thought more probable to exist inside the Cu²⁺-doped fiber than octahedral coordination as to the amorphous host of germano-silicate glass. The broadening of absorption band observed at around 700nm is attributed to the three electronic transitions in d orbital corresponding to ²E_g-²B_1g, ²A_1g-²B_1g, and ²B^2g-²B_1g. Pérez-Robles et al. suggested that the broad absorption around 750nm observed in the Cu²⁺ xerogel was due to the presence of Cu²⁺ ions in the interstitial positions in silica matrices [17]. The shift of the broad absorption toward shorter wavelength (blue shift) also shows that the water molecules as impurity in the core of the fiber were removed during the high temperature MCVD process up to 2300◻ and the following minor shrinkage of the core may increase the ligand field of the glass structure.

3.2 Resonant optical nonlinearity

As shown in Fig. 5, the total fringe shift of the Cu²⁺-doped fiber LPG pair was 0.083nm around 1540nm at the launched power of 97.87mW from a 980nm LD. The resonant nonlinear refractive index n_2,R was estimated to be 5.5×10^-17m²/W, which is three levels in magnitude larger than n_2,NR of SMF [3].

 

Fig. 5. Transmission spectrum of the Cu²⁺-doped fiber LPG pairs and the fringe phase shifts upon pumping with 980nm LD at 0 ∼ 100mW: (a) LPG fringes near 1550nm; (b) the enlarged fringe centered at 1539.9 nm

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In any absorptive medium the refractive index varies considerably in the vicinity of an absorption band with wavelength, and this variation in index can be described by the Kramers-Krönig relation [18]. Furthermore, any change in the absorption will result in an associated change in refractive index [10]. The origin of the high resonant nonlinear property of the Cu²⁺-doped fiber is mainly attributable to all the 3d-shell electronic transition-induced absorptions shown in Fig. 4, leading to the direct change in the refractive index at the communication window around 1550nm.

3.3 Non-resonant optical nonlinearity

 

Fig. 6. (a). cw-SPM spectrum of 151.6m Cu²⁺-fiber and (b) slopes of the phase shifts over different input power from EDFA.

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Table 1. Non-resonant nonlinear optical parameters of the Cu²⁺-doped fiber

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Figure 6(a) shows the cw-SPM spectrum of the Cu²⁺-fiber with 151.6m length as an example and Fig. 6(b) indicates the slope coefficients κ_ac of the fibers tested. κ_ac of the Cu²⁺-fiber was found to be much smaller than that of the SMF and the reference fiber without Cu²⁺ incorporation. According to the parameters listed in Table 1, we can see that the Cu²⁺ ions incorporation into the germano-silicate fiber heavily decreased the non-resonant nonlinearity of the germano-silicate glass fiber. The non-resonant nonlinear refractive index n_2,NR and the effective nonlinear parameter γ of the Cu²⁺-fiber were only about 20% of those of the SMF and the reference fiber.

In inorganic oxide glasses, positive and negative types of non-resonant nonlinearities coexist at the same time [19]. The positive non-resonant type optical nonlinearity is derived from the hyper-polarizabilities of the present glass constituents, such as bridging oxygens (BOs) and nonbridging oxygens (NBOs). The BOs are strongly and covalently bound to the Si/Ge atoms, whose valence electrons are mainly distributed directionally in highly covalent bonding, and difficult to be distorted when subjected to the applied optical electric field. Therefore, only a very weak anharmonic effect arises from the BOs. The higher ionicity in the NBO ions can result in higher positive nonlinear refractive index. The incorporation of Cu²⁺ ions cuts off the Si-O and Ge-O bonds, induces more NBOs and therefore slightly increases the positive nonlinear refractive index of the germano-silicate glass. On the other hand, however, the doped transition metal ions such as Cu²⁺ having 3d⁹ shell bring about negative nonlinear refractive index, resulting from the contribution of the resonant electronic transition processes, which can cancel the positive non-resonant nonlinear refractive index resulting from the hyper-polarizabilities of BOs and NBOs. When the concentration of Cu²⁺ ions is in extremely low level as ppm, that is, the negative nonlinear contribution from the electronic transition processes of the Cu²⁺ ions is comparable to the positive nonlinear contribution from BOs and NBOs. Consequently, the total non-resonant nonlinear refractive index of Cu²⁺-doped germano-silicate fiber is much smaller than those of the SMF and the reference fiber as shown in Table 1.

4. Summary

For the first time, we successfully made a Cu²⁺-doped germano-silicate glass fiber and measured the absorption spectrum comprising a broadband absorption in the vicinity of 700nm. The measured resonant nonlinear refractive index n_2,R of the Cu²⁺-doped fiber around 1540nm was estimated as 5.5×10^-17m²/W by using the LPG pair method. This high resonant nonlinearity was found to be mainly due to the electronic transitions among different splitting energy levels of 3d shell, and therefore its theoretical response speed is expected much faster than that of the rare-earth doped fibers [11]. In addition, the non-resonant nonlinearity n_2,NR and the effective nonlinear parameter γ were also measured by the cw-SPM method. On the contrary to the enhancement on the resonant nonlinearity, the incorporation of Cu²⁺ ions into the germano-silicate tetrahedron structure did not contribute to the increase of non-resonant nonlinearity at all. Although there was the increase in the positive nonlinear refractive index by increasing the number of NBOs, the negative nonlinear refractive index originating from Cu²⁺ ions themselves cancels the positive nonlinear refractive index from BOs and NBOs, leading to much smaller non-resonant nonlinearity than that of the SMF and the reference fiber.