1. Introduction

Low cost and high performance optical amplifier and laser integration is a challenge for future optical communication networks and for optical interconnection [1,2]. Several technologies are under investigation in order to realize integrated amplifiers and lasers compatible with current electronic technology; among the possible technologies under investigation silicon photonics is one of the most attractive for dense component integration using standard high-volume and low-cost manufacturing techniques [1]. However, the difficulties in realizing silicon based active optical devices have recently led to alternative approaches, such as hybrid integration, in which electrically pumped AlGaInAs quantum-well materials are bonded on silicon waveguide structures [3]. Nevertheless this attractive technique is still very expensive and in addition III-V semiconductor based amplifiers would likely suffer from cross gain modulation effects [4], due to the short carrier lifetime of the active material. On the other hand, current Er³⁺ doped glass waveguide amplifiers (EDWAs) present lower performance compared to available EDFAs (Erbium doped fiber amplifiers) as well as higher cost. The main reason that has inhibited their practical application up to now is the requirement of expensive single mode pump lasers at 980nm, in resonance with the sharp Erbium absorption peak. However EDWAs present a higher gain per unit length [5] compared to standard EDFAs, offering an attractive solution in terms of potential integration of compact active devices.

In order to overcome the pumping scheme limits, different cladding pumping techniques have been proposed to enhance the optical conversion efficiency in planar or tapered waveguide lasers [6,7] and short-length microstructured fiber lasers [8]. In those papers confinement structures for laser and pump radiations are separate, even if the pump radiation can propagate in the core of the laser cavity. A possible approach for improving current EDWA performance relies on the use of efficient sensitizers for Er³⁺ ions in glass hosts [9], among which Ytterbium (Yb³⁺) ions are considered the most attractive [10]. High quality Er³⁺/Yb³⁺ co-doped phosphate glasses are available on the market and ready for deployment [11]; moreover the co-doping with Yb³⁺ provides several benefits such as inhibiting Er³⁺ cluster formation and relaxing part of the constraints on the pump laser thanks to their broader and higher absorption peak in the 980nm band.

In our preliminary study [12,13], we proposed a 2D design of an efficient EYDWA using a novel multimode pumping scheme based on low-cost laser source combined with Yb³⁺ as efficient sensitizer of Er³⁺ ions.

In this novel pumping approach, light from a high-power and low-cost broad area laser at around 975 nm is not coupled into the cladding of the structure as in case of cladding pumped waveguide lasers [6–8], but into a multimode silica passive waveguide and progressively absorbed by the sensitizers (Yb³⁺) in a single mode active waveguide, which can be realized on the top of the passive one.

In this paper we have further investigated this pumping scheme using a more realistic 3D model developed and used to design an optical waveguide amplifier structure which has also been realized by ion exchange technology.

Even if the presented pumping scheme for single active waveguide has low pump efficiency [14], an array of active waveguides could be easily pumped by a single low cost broad area source. Note that the exploitation of the efficient energy transfer from Yb³⁺ to Er³⁺ ions and the strong pump absorption from Yb³⁺ ions [15] are key issues to achieve good performance.

The model we have developed is based on the Finite Element Method (FEM) for modal analysis and propagation, and allows to take into account the refractive index profile of the ion exchange waveguides. Numerical simulations, based on realistic glass and waveguide parameters and the rate equations of the coupled Er³⁺/Yb³⁺ system, demonstrate the great potential of this multimode pumping scheme for low-cost amplifiers.

Afterwards, we have realized a first simple device where the pump light is exclusively injected in a passive multimode waveguide and Amplified Spontaneous Emission (ASE) light is collected at the active waveguide output, confirming the possibility to effectively excite the active core using such a pumping scheme. The ion exchange process, which provides a mature technology for the integration of both passive and active components on a same chip [11], offers extremely low propagation and fiber coupling losses; moreover Er³⁺/Yb³⁺ co-doped glass waveguide structures developed by ion-exchange and bonding techniques are already commercially available [16], and guarantee reliable fabrication and processing [17,18].

A single broad area laser can be effectively used to pump an array of active cores in parallel configuration, achieving interesting structures for spatial and wavelength division multiplexing, as shown in Fig. 1 . Nevertheless, for simplicity, we focused the presented analysis on a single active core waveguide. The argumentations and results shown in this paper can be well applied to an array of active waveguides as long as the y transversal dimension of the multimode waveguide is overlapping with all parallel cores; note that spatial separation among the active cores must be large enough to prevent their interaction. The device top view, in Fig. 1(a), highlights the pump laser and signals coupling. In particular, the proposed solution allows to easy butt-couple a broad area laser into the multimode buried waveguide, while the signals are coupled exploiting the lateral side of the device. The buried multimode waveguide, which can be easily fabricated using IE technology [19], is clearly shown in Fig. 1(b) which is a longitudinal view of the amplifier along the segment 1 [shown in Fig. 1(a)]; in Fig. 1(c) the transverse cross-section of the structure along segment 2 is depicted. The figure is not at scale and aims at pointing out how the proposed pumping mechanism can be potentially used to pump many active cores in parallel configuration.

 

Fig. 1 Schematic representation of an integrated array of EYDWAs exploiting the proposed technology and pumping mechanism. Passive waveguide is represented in blue while active waveguides are in red.

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2. Theoretical model

2.1 Propagation equations and Er³⁺/Yb³⁺ system rate equations

As the proposed pumping scheme is based on pump light coupling from a multimode low loss waveguide to a single mode active core along the amplifier length, the used 3D model requires a propagation analysis, directly derived from Maxwell’s equations. The propagation equations under the slowly varying amplitude approximation for the transverse electric polarized signal and pump fields are not reported here for compactness and can be found in reference [20]. Pump and signal propagation equations are coupled by means of the complex permittivities at the signal and pump wavelengths, ε_s,p, which can be written as follows:

In Eq. (1), (2) ε_Rs,p are the real parts of the complex permittivity at the signal and pump wavelengths (λ_P and λ_S, respectively), and α_P, α_S the background losses at λ_P and λ_S, σ_Er12 and σ_Er21 are the Er³⁺ absorption and emission cross-sections at the signal wavelength, σ_Er13, σ_Er31, σ_Yb45 and σ_Yb54 are respectively the Er³⁺ and Yb³⁺ absorption and emission cross-sections at the pump wavelength [21]. Table 1 reports the main parameter values used in our simulations. The imaginary parts of the complex permittivities ε_s,p in Eqs. (1), (2) take into account pump and signal light interaction with Er³⁺ and Yb³⁺ ions within the active material; in fact n₁, n₂, n₄ are computed by solving the following steady-state population rate-equations and conservation laws of the coupled Er³⁺/Yb³⁺ system [22].

Table 1. Simulation parameters

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In Eqs. (3)–(7) n₁, n₂, and n₃ are respectively the population densities corresponding to levels ⁴I_15/2, ⁴I_13/2 and ⁴I_11/2 of Er³⁺ ions, which are described by a three energy level system, n₄ and n₅ are the population densities of levels ²F_7/2 and ²F_5/2 of Yb³⁺ ions, described by a two energy level system. N_Er and N_Yb are respectively the concentration of Er³⁺ and Yb³⁺ ions in the active glass. W₁₂ and W₂₁ are the stimulated absorption and emission rates between levels ⁴I_15/2 and ⁴I_13/2 induced by signal photons, while A₂₁ = τ₂₁⁻¹, A₆₅ = τ₆₅⁻¹ are the spontaneous transition rates defined as the inverse of the spontaneous decay lifetime reported in Table 1; finally A₃₂ is the non-radiative relaxation rate.

The rate equations also include the concentration dependent up-conversion (C_up) from the Er³⁺ metastable level as well as the energy transfer from Yb³⁺ to Er³⁺ ions described by the coefficient C_cr. This cross-relaxation coefficient has been estimated using the Forster-Dexter energy transfer model [23], assuming that each Er³⁺ ions is clustered to Yb³⁺ ions, and neglecting clusters among Er³⁺ ions. Care is required in choosing the total concentrations N_Er and N_Yb. Indeed, if the ratio N_Yb/N_Er is too small, Er³⁺ clusters may form and the energy transfer would not be very effective; on the other hand, if N_Yb/N_Er is too high, the model should account for Yb³⁺ clusters which waste pump energy and reduce amplifier efficiency. For this reason we have always assumed 2N_Er < N_Yb < 20N_Er. The uniform up-conversion mechanisms from the erbium metastable and pump levels are modeled through quadratic terms in n₂ and n₃. At high Er concentration levels it can strongly degrade the amplifier performance. In our simulations C_up is an increasing function of the total Er³⁺ concentration, given by C_up = 3,5×10⁻²⁴ + (7×10⁻²⁴)×((N_Er – 4,4×10²⁵)/3,2×10²⁵) as reported in [24]. Note that amplified spontaneous emission is not included in the model for the sake of numerical simplicity.

2.2 Propagation equations and Er³⁺/Yb³⁺ system rate equations

Modal analysis is numerically performed through a scalar finite-element method [25], reducing the differential Maxwell’s equations to an eigenvalue problem in which the mode propagation constant is the eigenvalue while the electric field distribution is the eigenvector. This analysis allows us to compute realistic input excitations and effective propagation constants for the propagation algorithm at both pump and signal wavelengths. The modal analysis is first performed to compute the signal mode at λ_S = 1536nm. The propagation analysis is performed by exciting the active waveguide structure by its fundamental mode at λ_S; a bi-dimensional Gaussian field (with different spot sizes ω_x and ω_y) at λ_P = 975 nm is considered to excite the passive waveguide, well representing the output of broad area lasers.

The waveguide cross-section discretization in the x-y plane plays a key role for the numerical accuracy and computational efficiency in both modal analysis and propagation. In particular non uniform meshes are required in order to accurately discretize the regions where large refractive index changes are present and where we expect the electromagnetic fields to be more tightly confined.

Taking this into account, a suitable finite-element discretization is applied to the transverse waveguide cross-section in the x-y plane; the set of basis functions is chosen according to the Galerkin method, and the approximated solutions of Maxwell’s equations at z = z + Δz (z is the propagation direction) are obtained by solving two linear systems (Crank-Nicolson scheme) in conjunction with the splitting operator technique [26]. At each step of the propagation algorithm (the longitudinal step, Δz, is kept constant), the rate equations [Eqs. (3)–(7)] are locally computed in steady state condition, and the resulting population values in each finite element are used to evaluate the complex permittivities [Eqs. (1), (2)] in each nodal point of the transverse waveguide cross-section.

2.3 IE refractive index profile numerical evaluation

The refractive index profile n = n(x,y), representing the active and passive ion exchange waveguides, is computed analytically. Its value is assigned to each corresponding triangular finite element of the mesh used to discretize the waveguide transverse cross-section. It is well known that n(x,y) follows the concentration profile of ions given by their diffusion in the glass, which can be calculated by solving the diffusion equations with appropriate boundary conditions [19]. In the binary case, cations A diffuse from a molten salt towards the glass where they substitute other alkali cations B, present in the host glass with mole fraction N_B, and which exit the glass by diffusion. Assuming unidirectional diffusion and a mole fraction of incoming ions N_A<<N_B, N_A can be calculated through the simplified diffusion equation [27]:

 

Fig. 2 Contour plot over the amplifier transverse cross-section of refractive index profiles in the IE waveguides.

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We have used the complete refractive index profile of the 3D amplifier structure in order to perform modal analysis and then pump and signal propagation along the amplifier structure. The complex permittivities, ε_s,p, as well as the steady-state population rate-equations and conservation laws [Eq. (1)–(7)] of the coupled Er³⁺/Yb³⁺ system are solved in each transverse section mesh element and for each propagation step along z.

3. Pumping scheme description and amplifier performance

Waveguide geometries and ion-exchange parameters have to be carefully designed in order to ensure signal monomodal behaviour, with good field confinement in the active waveguide, easy coupling of the broad area laser into the passive multimode waveguide and a uniform pump energy transfer. This pump transfer into the active region is fundamental to achieve population inversion of the active ions all along the amplifier length. The broad area laser can be simply butt-coupled to the large passive waveguide, overcoming the alignment and cost issues of current available EDWAs.

The proposed waveguide structure includes a multimode core (m_p = 43 μm, W_0p = 4.9 μm), and a single mode active core at around 1.55 μm (m_s = 2 μm, W_0s = 2.8 μm), both shown with their refractive index profiles in Fig. 2. The multimode core is realized onto a silicate glass which can be grown onto a silicon substrate exploiting conventional electronic fabrication techniques, while the active core is realized by IE on a phosphate glass co-doped with Er³⁺ and Yb³⁺. The two glasses are then bonded together with the waveguides in contact side by side. The proposed structure along with the refractive index profile has been optimized in order to achieve the best amplifier performance. The adopted pumping scheme allows, during pump and signal propagation within the amplifier structure, to couple the pump light from the large passive core to the small active one, avoiding signal coupling back from the active core to the passive waveguide, as can be seen in Fig. 3(a) . This intensity plot represents the signal field distribution over the amplifier transverse cross section after 1mm of propagation. The signal mode is shown to maintain its single mode operation along the propagation direction, with most of its power well confined in the active core. On the other hand the pump field modifies its shape while propagating, as shown in Figs. 3(b) and 3(c), which are respectively the input excitation of the passive waveguide at λ_P, and the output pump field distribution after 1mm propagation. The pump field becomes multimode and develops numerous lobes; in particular three strong lobes propagate in the active core, allowing active material excitation and eventually signal gain.

 

Fig. 3 Contour plots over the amplifier transverse cross-section of output signal field distribution after 1mm of propagation (active core) (a), pump field distribution at the amplifier input (b) and after 1 mm propagation (multimode core) (c).

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After having performed the modal analysis, we have studied the amplifier performance as a function of input pump power, waveguide length, for typical values of Er³⁺ and Yb³⁺ concentrations (respectively N_Er = 2×10²⁶ ions/m³ and N_Yb = 5×10²⁶ ions/m³). Those values can however be optimized according to the specific amplifier requirements, such as device length, total gain or available pump power.

Considering those concentrations of rare-earth ions, we have first studied the gain per unit length versus pump power for 1 cm long amplifier. Figure 4 shows that gain values over 3 dB/cm can be achieved with realistic input pump power levels (commercially available broad area lasers can supply several Watt at 975nm) and input signal power of −30 dBm (so that the amplifier is not saturated). It is worth noting that, increasing the input pump power, the gain per unit length is saturated, and too high pump power is useless since it does not significantly improve the amplifier performance.

 

Fig. 4 Amplifier Gain versus Input pump power

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We have then investigated the small signal gain versus waveguide length at different pump power values (see Fig. 5 ); gain values around 9 dB can be obtained with realistic and affordable pump values. As in typical commercial EDWAs, there is an optimum amplifier length (which is a function also of the pump power launched into the amplifier), which allows a maximum gain; above this device length the small signal gain starts to slowly decrease. Note that pump absorption is very high in the proposed structure, due to pump light absorption in areas of the active glass where signal is not present (outside the IE region); we are currently studying how to limit this unwanted absorption by slightly burying the multimode passive core realized by IE as in [25], so that pump light would not be overlapping with active areas in which no signal is present. Furthermore higher signal gain can be achieved using a complex serpentine structure, simultaneously obtaining smaller form factor and higher available gain length [28].

 

Fig. 5 Amplifier Gain versus Device length for different input P_P.

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4. Waveguides fabrication and preliminary experimental characterization

The device is based on an array of active waveguides which are in contact side by side with a multimode passive waveguide as can be seen in Fig. 6 ; the array of active cores and the passive waveguide have been separately realized by ion-exchange. Two wafers have been prepared: a passive silicate glass wafer with large multimode waveguides optimized to allow efficient light coupling from broad area lasers at 980nm, and an active Er³⁺/Yb³⁺ co-doped phosphate glass wafer (ensuring good solubility of the dopants) with smaller waveguides.

 

Fig. 6 Microscope picture of the large passive waveguide (100μm) aligned with a small active waveguide (2.6μm) – top view.

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The passive waveguide width was 100 μm; the selected sample of active waveguides has been characterized in terms of losses at 1.3μm. We chose the waveguide with lowest loss (insertion losses = 2.25dB, waveguide length: 42 mm, waveguide width: 2.6 μm). The device was then assembled by bringing the two separately prepared glasses together through a bonding technique [11]. Figure 6 shows the two fabricated glasses, in which only one active and passive waveguides are respectively formed and bonded together.

Figure 7 schematically shows the assembly of the two waveguides, which we have experimentally realized in order to demonstrate the working principle of this new pumping scheme.

 

Fig. 7 Schematic longitudinal view of the tested structure and working principle of pumping scheme

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The chosen active waveguide was pigtailed to ensure optimized output light collection (as shown in Fig. 7 and Fig. 8 ) and glued together with the passive waveguide in order to ensure the stability of the sample in terms of relative position of the waveguides. After the assembly of the sample schematically shown in Fig. 7, we have tested the configuration shown in Fig. 8 in which we can clearly see the broad area laser coupled to the passive waveguide on the right side. The sample was set in place in front of the laser diode as can be seen in Fig. 8, with the diode placed on a micro-positioner to enable a precise alignment. The active waveguide output was collected through the pigtailed fiber and sent to an optical spectrum analyzer (OSA).

 

Fig. 8 Pumping of the device by Broad area laser. Guided green light is uniformly observed along the active waveguide

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Although the particular mount used for the laser diode did not allow us to place the laser emitting area close enough to the passive waveguide, in Fig. 8 we can clearly see the active waveguide core becoming green when switching the pump light on. Due to the residual distance between the laser and passive waveguide facet, much of the diode laser power was not coupled into the waveguide.

Nevertheless, the green luminescence along the active waveguide clearly implies that the passive waveguide was effectively pumped, and it was able to transfer such light into the whole active waveguide as predicted by numerical modelling. We can clearly conclude that the pumping mechanism is effective in exciting the Er³⁺ ions trough Yb³⁺ absorption and subsequent energy transfer.

We also measured residual pump power at the active waveguide output as reported in Fig. 9 , the residual pump power values are higher than the typical ones and although much of the laser power is lost and the pumping scheme efficiency is low, high pump power is uniformly coupled all along the active waveguide.

 

Fig. 9 Residual pump power measured at the output pigtailed active waveguide.

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The ASE spectra measured at the pigtailed output of the Er/Yb co-doped phosphate glass waveguide using a pump power value of 2.5 W is shown in Fig. 10 . Although these preliminary results do not report gain and noise figure measurements, they well confirm the effectiveness of the proposed pumping scheme.

 

Fig. 10 ASE spectra (on 0.2 Resolution Bandwidth and arbitrary units) at the pigtailed output of the active waveguide using a pump power value of 2.5 W.

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It is worth noting that the high residual pump power at the device output suggests that this pumping scheme allows to effectively pump the whole waveguide length, permitting the realization of long, high gain waveguide amplifiers, also in serpentine configurations [28]; in addition these devices would not likely suffer from noise figure degradation due to the uniform pumping characteristic all along the waveguide length.

Current activities are focused on experimental techniques to couple the pump and signal lights respectively into the passive and active waveguides simultaneously and extracting the output signal light after amplification along the active cores. This requires a specific design of the input/output coupling and pigtailing, as well as optimization of the waveguide geometry.

The working principle of the coupling scheme has been shown in Fig. 1; in particular the light from the broad area laser is coupled to the multimode waveguide, which is broader and buried at its input. The laser can be simply butt-coupled to such a multimode waveguide, without the need for any further expensive component. In the final device, in which several active cores will be present, the signal lights will be coupled exploiting the device’s lateral facets; they will propagate on passive glasses until they come in contact with the array of parallel pumped waveguides [Fig. 1(b)], then avoiding unwanted signal absorption in the coupling regions.

5. Conclusions

We have presented a model which allows an accurate design of Er³⁺/Yb³⁺ co-doped waveguide amplifiers realized by ion exchange technique on silica/phosphate glasses and longitudinally pumped by broad area lasers at around 980 nm. The proposed amplifier structure offers an attractive solution for optical amplifier and laser integration, with interesting applications in wavelength and space division multiplexing for high capacity optical communication systems, networks and optical interconnection. The model we have developed accounts for the real IE refractive index profiles, thus allowing for an accurate modal analysis and propagation along realistic guiding structures. The proposed model, which is based on 3D FEM modal analysis and a 3D Split-Step FEM propagation algorithm, can be effectively used to design integrated waveguide amplifiers. Numerical results, based on actual material parameters, point out that gain values of over 3 dB/cm can be achieved in short waveguide devices; pumping by low cost, high power broad area lasers at around 980 nm is proved to be an effective way to overcome the main limitation of commercially available EDWAs. Preliminary experimental results concerning IE waveguide fabrication, active and passive waveguide assembly, well confirm the effectiveness of this new pumping scheme. The proposed amplifier structure can also be integrated with further passive and active devices based on IE technology, allowing the realization of integrated optical chip with dedicated functionalities such as the attractive possibility to amplify spatially multiplexed WDM signal using a single broad area laser to simultaneously pump an array of active waveguides.