Spiral-waveguide amplifiers in erbium-doped aluminum oxide on a silicon wafer are fabricated and characterized. Spirals of several lengths and four different erbium concentrations are studied experimentally and theoretically. A maximum internal net gain of 20 dB in the small-signal-gain regime is measured at the peak emission wavelength of 1532 nm for two sample configurations with waveguide lengths of 12.9 cm and 24.4 cm and concentrations of 1.92 × 1020 cm−3 and 0.95 × 1020 cm−3, respectively. The noise figures of these samples are reported. Gain saturation as a result of increasing signal power and the temperature dependence of gain are studied.
© 2014 Optical Society of America
Rare-earth-ion-doped materials are of high interest as amplifiers and lasers in integrated optics. Their significantly longer excited-state lifetime and weaker refractive-index change (Δn ~10−6) induced by the excitation of rare-earth ions , both compared to electron-hole pairs in III-V semiconductors, provide spatially and temporally stable optical gain, allowing for high-speed amplification  and narrow-linewidth lasers [3,4]. Highly rare-earth-ion-doped crystalline materials can provide optical gain per unit length of ~1000 dB/cm , making them competitive with waveguide amplifiers in III-V semiconductors. However, neither of these two material classes can easily be integrated on a silicon chip. Rare-earth-ion-doped amorphous materials can be monolithically integrated [6–9] on a number of passive photonic platforms, including silicon-on-insulator (SOI) . Unfortunately, inhomogeneous linewidth broadening diminishes the transition cross-sections of rare-earth ions in this class of materials. Besides, parasitic spectroscopic processes such as migration-accelerated energy-transfer upconversion (ETU) among rare-earth ions can counteract the establishment of high inversion. Moreover, fast quenching processes originating in static ETU among active ion pairs or clusters, energy transfer to undesired impurities, or trapping of excitation energy by host material defects, such as voids, may further reduce the available gain [11–13]. Consequently, gain per unit length of only up to ~10 dB/cm has been reported so far [14–18]. Whereas the resulting amplifier lengths of several to many centimeters required to achieve sufficient pump absorption and overall signal gain, often necessitating spiral designs , may render such devices unsuitable for very-large-scale integration, other applications allowing for more space per device, such as amplification in optical printed circuit boards (OPCBs) [19–21], may well profit from this approach.
Among the many materials for Er3+-doped integrated waveguide amplifiers and lasers around 1.5 µm , amorphous Al2O3:Er3+ exhibits remarkable performance . The waveguide amplifiers are realized by RF reactive co-sputtering of the material onto thermally oxidized silicon wafers  followed by optical lithography and chlorine-based reactive ion etching for the definition of low-loss channel waveguides . A peak gain per unit length of 2 dB/cm at 1533 nm and a gain bandwidth of 80 nm have been demonstrated . The gain is limited by migration-accelerated ETU from the 4I13/2 gain level and a fast quenching process . A theoretical model has been proposed, in which these processes are taken into consideration, permitting the design of on-chip waveguide amplifiers .
In this work, we experimentally verify the previously proposed theoretical model , which is utilized to design spiral channel waveguide amplifiers in Al2O3:Er3+. Several devices varying the Er3+ dopant concentration and spiral length are fabricated and characterized. A comparison of the experimental results with the theoretical model is presented. A small-signal gain of 20 dB at 1532 nm is demonstrated for two sample configurations with waveguide lengths of 12.9 cm and 24.4 cm and concentrations of 1.92 × 1020 cm−3 and 0.95 × 1020 cm−3, respectively. This achievement improves previous results in this host material of 2.3 dB , 5.4 dB , and 9.3 dB  by a factor of 9, 3.7, and 2.2, respectively.
2. Amplifier design and fabrication
Important design parameters for the optimization of a waveguide amplifier are the pump wavelength, the launched pump power, the geometrical waveguide cross-section providing fundamental-mode operation at both the pump and signal wavelengths, a good overlap of pump and signal modes with each other and with the active area, the dopant concentration, the amplifier length, and the waveguide propagation loss at the pump and, more importantly, the signal wavelength.
Stimulated emission on the pump transition 4I15/2 ↔ 4I13/2 at 1480 nm plays a more significant role than on the pump transition 4I15/2 ↔ 4I11/2 at 980 nm because of the significantly longer lifetime and, consequently, larger population density of the 4I13/2 compared to the 4I11/2 level. This fact governed our choice of the 976 nm pump wavelength.
Mode-field simulations at the pump and signal wavelengths were carried out using the Finite Difference (FD) algorithm in the Phoenix Field Designer software . The waveguide cross-section consisted of a 1-μm-thick by 1.5-μm-wide Al2O3:Er3+ channel with ridge height of 0.35 μm [Fig. 1 (a)]. This geometry allows high confinement in straight and bent sections of the waveguide. Moreover, higher signal and pump intensities are achieved in comparison with the channel geometry presented by Bradley et al. . The simulated pump and signal mode fields had an overlap of ~95% and ~85% with the doped region, respectively. The refractive indices employed in the simulations were taken from previous measurements . The waveguide cross-section and the mode-field distribution at the signal wavelength of 1532 nm are displayed in Fig. 1(a).
Understanding the performance of an Er3+-doped amplifier is significantly complicated by the spectroscopic processes of the Er3+ ion. The migration-accelerated ETU process (4I13/2, 4I13/2) → (4I15/2, 4I9/2) induces a concentration- and excitation-dependent quenching of the 4I13/2 amplifier level. More importantly, a fast quenching process of this level occurs in SiO2 , Al2O3:Er3+ , and potentially other Er3+-doped materials, which limits the optimum Er3+ concentration in Al2O3 to 1−2 × 1020 cm−3. As a consequence, waveguide lengths on the order of 10 cm are desired for efficient amplifier performance.
Al2O3 layers with Er3+ concentrations of 0.45 × 1020 cm−3, 0.95 × 1020 cm−3, 1.92 × 1020 cm−3, and 3.0 × 1020 cm−3 were deposited onto thermally oxidized silicon substrates by RF reactive co-sputtering . For each of the four different doping concentrations, spiral-shaped channel waveguides with different lengths varying from 12.9 cm to 41.6 cm were patterned into the Al2O3:Er3+ layers using standard lithographic techniques and chlorine-based reactive ion etching . The spiral shape [Fig. 1(b)] minimizes the device foot print. A minimum bending radius of R = 2 mm was selected. For this radius, the simulated additional bending loss of <10−6 dB/cm is negligible compared to the straight-waveguide propagation loss of ~0.1 dB/cm and the mode-mismatch loss of ~0.02 dB at the junction in the center of the spiral. Transverse-electric (TE) polarization was chosen for signal and pump light in the simulations and measurements.
A 5-μm-thick SiO2 layer was deposited on top of each patterned Al2O3 layer by PECVD as a protective cladding. Finally, waveguide end faces were prepared by dicing.
3. Propagation losses
The non-destructive method proposed by Okamura et al.  was applied to investigate the propagation loss in our devices. The method consists of capturing a top-view image (InGaAs camera Sensors Inc. SU320M-1.7RT, 320 × 240 px.) of the infrared light (λ = 1320 nm, Amoco laser model D200) scattered from a quarter of the spiral waveguide, as shown in Fig. 2(a). The wavelength selected for this experiment lies outside the Er3+ absorption bands and, thus, the passive characteristics can be determined. Background propagation losses around 1530 nm are expected to be similar to those at 1320 nm and 0.18 dB/cm higher at 980 nm due to Rayleigh scattering . A spatial calibration of the image was readily performed, since the dimensions of the spirals are well known from the lithographic mask. It was assumed that in average the intensity of scattered light is proportional to the intensity of light propagating within the channel. This is the case if the scattering centers (such as channel interface roughness) are uniformly distributed along the waveguide channel. It is then possible to correlate the intensity distribution of scattered light along the channel to the propagation length by the Lambert-Beer law when the propagation direction and the spiral dimensions are known. Only one quarter of the spiral [the top right quarter displayed in Fig. 1(b)] was imaged during the measurements, because the other three quarters were affected by scattered stray light coupled into the slab waveguide, which made those measurements less accurate. Nevertheless, by analyzing only a single quarter, the remaining three quarters are intrinsically evaluated due to the spiral shape of the waveguide. Thus, any defect causing a probe-signal loss in the channel waveguide outside the captured area is observed as a drop in intensity in one of the channels of the inspected quarter.
A MATLAB code was written for analysis of the intensity profiles. In the code, the intensity profiles were selected along the circular paths of the channels. The intensity profile of each selected channel was integrated radially and plotted in a logarithmic scale along the light-propagation direction, see Fig. 2(b). A linear fit to the experimental data [Fig. 2(b)] is shown as a continuous line, and its slope provides the propagation-loss coefficient in dB/cm, which was averaged over three independent measurements of the same spiral quarter.
Background propagation losses (αloss) derived from the fits were found to be in average 0.19 dB/cm within the range of 0.08−0.41 dB/cm. These results are similar to those reported by Bradley et al. . Variations between individual spirals are attributed to limitations in the sputtering and lithographic processes. Defects caused by residual resist and layer defects over or close to the channels increased the scattering and appeared as bright spots along the waveguides, see Fig. 2(a).
For the gain measurements, a fiber-based wavelength division multiplexer (WDM) was employed to combine (split) and launch (collect) the pump and signal. One of the WDM ports was used to launch a probe signal for the insertion-loss measurements. This enabled us to maintain the same fiber-waveguide-fiber alignment in the gain and insertion-loss measurements. Total insertion losses were measured to estimate the coupling loss right after each gain measurement. A probe signal scanned in the wavelength range from 1630 nm to 1640 nm was launched into the input end-facet of the waveguide. Potential errors in insertion-loss measurements, caused by destructive interference due to reflections at the fiber end facet and the chip front facet when launching highly coherent light, can be reduced by launching probe signals at different wavelengths. A second fiber-based WDM with the same characteristics as the launching, aligned to the output end-facet of the spiral, collected the transmitted signal. The coupling loss was calculated by subtracting the previously determined propagation loss from the total insertion loss. The Al2O3:Er3+ absorption cross-section in the 1630−1640 nm range is very low , however the corresponding absorption was considered in the calculations. Since the launching and collecting fibers have exactly the same characteristics, and index-matching-fluid (Diphenyl ether) was used in between fiber and waveguide facets during all the experiments, it was assumed that similar coupling efficiencies were achieved in both the input and output ports.
4. Optical gain
The pump-and-probe method was applied to measure the internal net gain in the Er3+-doped channel waveguides. The setup consisted of a fiber-pigtailed diode laser operating at 976 nm as the pump source. All gain measurements were performed at a signal wavelength of 1532 nm. The pump and signal light were combined by a fiber-based WDM, which was butt-coupled to the waveguide. Using a second WDM, the transmitted pump power was separated from the amplified signal, which was either investigated by an optical spectrum analyzer (OSA) or detected by an InGaAs detector. The signal was modulated at 280 Hz for lock-in amplification to remove the residual pump power and the amplified spontaneous emission (ASE) from the measured signal. The signal intensities Ip(λ) and Iu(λ) in the pumped and unpumped case, respectively, were measured at the output fiber. The internal net gain G(λ) was then calculated using the equation
4.1 Small-signal gain
The incident signal power was set to approximately 1 μW to assure that the measurements were performed in the small-signal-gain regime. The results of small-signal-gain measurements in 23 spiral-shaped waveguide amplifiers of different lengths with doping concentrations of 0.45 × 1020 cm−3, 0.95 × 1020 cm−3, 1.92 × 1020 cm−3, and 3.0 × 1020 cm−3 are presented in Fig. 3 as Series A, B, C, and D, respectively. One defective device was identified in each sample series A and C. In both cases, inspection with a microscope verified a large defect in contact with the waveguide channel, see Fig. 4(a), which probably is residual photoresist. These defects cause a strong scattering of pump and signal light, as can be seen from the significant drop in green upconversion luminescence in all waveguide regions following the defect, see Fig. 4(b), thereby substantially reducing the gain. For reference, the gain results of these devices are presented as cross symbols in Fig. 3. Those devices whose combination of dopant concentration and waveguide length led to an almost complete absorption of pump power and accordingly strong reabsorption in the rear unpumped part of the waveguide, resulting in negative net gain of < −20 dB, were not included in the plots.
An internal net gain of ~20 dB was measured for the 24.5-cm-long sample with an Er3+ concentration of 0.95 × 1020 cm−3 and for the 12.9-cm-long sample with an Er3+ concentration of 1.92 × 1020 cm−3. Samples with a smaller concentration-length product exhibited a lower gain because of insufficient pump absorption. Samples with a higher product exhibited increasing reabsorption of the signal in the rear part of the waveguide due to insufficient population inversion, hence lower gain. Moreover, samples with a concentration higher than 3.0 × 1020 cm−3 generally showed inferior performance due to an increased fraction of quenched ions, as previously predicted .
Compared to the highest gain that has previously been reported, ~9.3 dB in the small-signal-gain regime , the pump wavelength, typical waveguide propagation losses, optimum range of dopant concentrations, and measured gain per unit length are similar. The improvement achieved in this work stems from the different waveguide cross-section, which is smaller by a factor of three (1.0 × 1.5 µm2 compared to 1.1 × 4.0 µm2), and the significantly larger etch depth (350 nm compared to 43−99 nm). These parameters result in similar waveguide propagation losses and simultaneously accept smaller bending radii, thereby allowing for exploitation of the spiral design that provides the longer waveguide lengths that are necessary to achieve 20 dB of optical gain.
4.2 Gain calculation
The amplifier model utilized here  accounts for the fractions fa and fq of active and quenched ions, respectively, and is based on the following steady-state rate equations:13]
Besides intrinsic decay and ETU, the concentration-dependent fraction fq of Er3+ ions undergoes a fast quenching process, which may be caused by, e.g., static ETU among active ion pairs or clusters, energy transfer to undesired impurities, or trapping of excitation energy by host material defects, such as voids, resulting in a lifetime τ1q on the order of, or even less than, 1 µs . The model does not take into account higher energy levels of Er3+, because the high phonon energies (~870 cm−1)  in Al2O3 induce a fast multiphonon decay to the lower-lying energy levels. Hence, the excitation density of the 4I9/2 level that is induced by ETU rapidly decays back to the 4I11/2 level via multiphonon relaxation. However, excited-state absorption (ESA) at the pump wavelength on the transition 4I11/2 → 4F7/2 is considered in the modeling of the pump intensity propagating along the waveguide. It is described by the equation26], αloss(λP) is the background propagation loss at the pump wavelength, σe,P/S and σa,P/S are the effective emission and absorption cross-sections for pump and signal, respectively, and σESA,P is the pump-ESA cross-section . Similarly, the signal power propagating in the waveguide is described by the equation
As previously described in section 3, an insertion-loss measurement was carried out immediately after the gain measurement to estimate the coupling efficiency. For the simulation it was assumed that signal and pump wavelengths have similar coupling efficiencies. This assumption is in agreement with the mode-overlap calculation between the simulated mode profiles of the waveguide and the launching and collecting fibers. Due to the small variation (<1%) in refractive index with increasing doping concentration  one would expect similar mode-field distributions in the waveguides and, therefore, similar coupling efficiencies for all the samples. Nevertheless, different imperfections at the end faces of each sample were observed and attributed to the dicing finish. These imperfections caused in average a 24% deviation of the coupling efficiency from the theoretical prediction. However, in the gain simulations presented in Fig. 3 a constant coupling efficiency was assumed for each sample series. All values applied in the simulations are presented in Table 1.
Two different simulations of gain versus waveguide length for the four different concentrations are presented in Fig. 3. In both simulations the ETU process is taken into account. In the first case (dashed line) we assume that all Er3+ ions are active, whereas in the second case (solid line) we consider that the 4I13/2 excitation density of the fraction fq of ions is quenched. As becomes clear from Fig. 3, only when including the fast quenching process, the measurements can be reproduced with good accuracy. This model also correctly reproduces the gain-saturation results presented in the following subsection and the gain measurements presented in , where ~9.3 dB of gain in the small-signal-gain regime was measured for a 5.4-cm-long straight ridge waveguide with a doping concentration similar to that in sample series B. The agreement of the simulations with all the experimental results is a direct consequence of applying the correct values of the transition cross-sections and the ETU parameter and by taking into account the concentration-dependent fraction of quenched ions in the amplifier model .
4.3 Gain saturation and power amplification
The small-signal-gain regime provides the maximum gain achievable by an optical amplifier. However, for telecommunication applications stronger signals of ~−10 dBm are required, and usually the optical amplifier works in a saturated-gain regime. Here we investigate the two best performing samples from section 4.2 by applying different incident signal powers. These samples will be referred to as Sample I from sample series B, and sample II from series C. Sample I and II have a waveguide length of 24.45 cm and 12.91 cm, respectively. Experimental and simulated gain results at different launched signal and pump powers are shown in Fig. 5(a) for sample II.
Good agreement between the measured and simulated gain as a function of launched pump power for different signal powers is obtained. As expected, gain saturation is observed as a result of increasing the input-pump power, because a larger fraction of the active ions becomes excited and the ground state is bleached by the increasing pump power, until the waveguide becomes almost transparent at the pump wavelength and an additional increase in pump power does not further improve the gain. Moreover, gain saturation is also observed when increasing the input-signal power, because stimulated emission triggered by the propagating signal photons introduces an additional decay rate of the excited level, thereby reducing the excitation density that is obtained for the same amount of launched pump power. In Fig. 5(b) the gain dependence on the signal power is shown for both samples I and II. The parameters specified in Table 1 were used for the simulation results presented in Fig. 5, except for the coupling efficiency and propagation losses, for which the actual determined values for these two spirals were employed. These were 8% and 16% for the coupling efficiency and 0.16 dB/cm and 0.17 dB/cm for the propagation losses for sample I and II, respectively.
As can be seen from Fig. 5(b), sample I with lower concentration exhibited a slightly inferior performance, caused by the lower coupling efficiency for the same incident signal and pump powers. Thus, the lower pump power available at the rear part of the waveguide caused a smaller population inversion and, therefore, lower gain, which was observed by the lower amount of pump power measured at the waveguide output. In spite of the lower performance observed in sample I, one can presume that lower launched pump powers are required in this configuration to obtain similar gain values. This is a direct consequence of the larger fraction of quenched ions that is present at higher doping concentrations. When neglecting the fraction of quenched ions, the gain performance is overestimated, as shown by the dotted lines in Fig. 5(b). Net gain was observed in the saturated-gain regime for both samples for launched signal powers in the range of 0.1−0.5 mW, which are typically applied in integrated optical circuits . The output saturation power  was −7.75 dBm and −4.27 dBm for sample I and II, respectively.
An OSA was used to measure the signal-to-noise ratio (SNR) of the signal before and after amplification in the small-signal-gain regime. Amplifier-noise figures  of 3.75 dB and 4.58 dB were determined for sample I and II, which are similar to the typical values of >3 dB .
By tapering the waveguide cross-section at the input and output ports, one can increase the overlap between the pump mode-field profiles of the Al2O3:Er3+ waveguide and the coupling fiber and, thereby, increase the coupled pump power and the overall fiber-chip-fiber efficiency. In a similar fashion, matching the pump and signal mode-field profiles of the Al2O3:Er3+ waveguide with those of a passive optical circuit based on, e.g., polymer, Si3N4, or SOI  will be fundamental for optimum amplifier operation in an integrated optical circuit. Since our aim is not the application of this amplifier as a stand-alone device within a fiber-based environment but its direct integration with a passive integrated optical circuit, where its potential advantages over other amplification technologies can be better exploited, we have not optimized the fiber-to-Al2O3 coupling efficiency in the present work. For the proof of principle demonstrated here, optimization of the coupling efficiency is not crucial, because high internal net gain is demonstrated and gain saturation is reached already with a launched pump power of ~30 mW.
4.4 Gain dependence on temperature
Small-signal-gain measurements at 1532 nm, as described in section 4.1, were conducted at temperatures from 20°C to 140°C in steps of 10°C. For this study, unlike the other gain measurements, index-matching-fluid was not used due to its low flash point and, therefore, the signal and, more importantly, the pump coupling efficiency were decreased. The shortest spiral waveguide (12.9 cm-long) from sample series B was used in this gain study to compensate for the lower launched pump power and still measure net signal gain.
The sample was placed on a bronze vacuum chuck and a thermal compound (DOW CORNING 340) was employed between the sample and the chuck to guarantee good heat conduction. The temperature of the chuck was controlled using a thermo-electric-controller and monitored additionally at the chuck top surface (where the sample was placed) using a thermo-couple. Results of the internal-net-gain measurements at different temperatures are presented in Fig. 6(a). A linear fit to the gain as a function of temperature resulted in a decrease rate of −4.05 × 10−3 ± 2.26 × 10−3 dB/°C. The ASE spectrum collected from the output end facet of the pumped spiral waveguide was recorded with an OSA at 17.5 and 142.4°C. The area-normalized ASE spectra in linear scale are shown in Fig. 6(b). A decrease rate of −7.28 × 10−3 dB/°C was determined by taking the values of the ASE spectra at the peak wavelength at both temperatures, which is on the same order of magnitude. A temperature dependence of gain on a ground-state transition is expected from studies in erbium-doped fiber amplifiers (EDFA) . The rather weak dependence of the gain performance on temperature increases the potential for integration of Al2O3:Er3+ waveguide amplifiers in OPCBs, since no active control of the temperature will be required.
We have presented an experimental study of the amplification characteristics of Er3+-doped aluminum oxide waveguides at 1532 nm and compared the results with a recently established comprehensive model . As predicted, a fast quenching process strongly deteriorates the amplifier performance of the Al2O3:Er3+ waveguide amplifiers. This effect is accentuated for concentrations higher than 2 × 1020 cm−3. Nevertheless, by carefully choosing the geometrical waveguide cross-section to obtain a large field confinement within the doped region and a good overlap of pump and signal modes, and using correct spectroscopic parameters in the model one can accurately predict and optimize an Al2O3:Er3+ waveguide amplifier. An internal net gain of 20 dB was measured for two different spiral configurations with waveguide lengths of 12.9 cm and 24.5 cm and Er3+ concentrations of 1.92 × 1020 cm−3 and 0.95 × 1020 cm−3, respectively. The experimental results confirm the validity of the model developed by Agazzi et al. , which successfully simulates the characteristics of Er3+-doped aluminum oxide waveguides. Positive net gain was measured in the saturated-gain regime in the range of launched signal powers of 10−3−10−1 mW, and the simulations predict that net gain can be achieved up to the mW regime. An amplifier noise figure of 3.75 dB was determined in the small-signal-gain regime. A weak temperature dependence of the gain was measured in the small-signal-gain regime at 1532 nm in the temperature range from 20°C to 140°C.
This work was supported by the Dutch Technology Foundation (STW) within the framework of project No. 11689. Sergio A. Vázquez-Córdova gratefully acknowledges CONACyT for its partial scholarship support of his postgraduate studies.
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