1. Introduction

Modern telecommunications fibers have virtually eliminated excess attenuation at 1380 nm due to OH in the waveguide core [1, 2]. As a result, these low water peak fibers have <0.3 dB/km attenuation from 1400 nm to 1600 nm. However, modern telecom systems employ only C and L band wavelengths from 1530 nm to 1620 nm. This is in part because a key requirement for a modern fiber optic system is an efficient, low noise amplifier that can be installed at regular intervals to restore the power of the signal light as it propagates along the fiber. Currently only erbium fiber amplifiers, which amplify in the C and L bands meet the requirements of telecom system providers. A viable optical fiber amplifier in the E-band would enable a significant increase in the transmission capacity of an optical fiber.

There are several technologies that can provide amplification in the E-band wavelength region. Raman fiber amplifiers are the most well-developed technology and are currently used in telecom systems [3, 4]. However, a Raman amplifier has no energy storage, conversion of pump photons to signal photons occurs on sub-picosecond timescales. This very fast response time of the Raman effect leads to a number of noise sources unique to Raman amplifiers [4]. Bismuth fiber amplifiers have shown significant gain in the E-band wavelength region [5]. However, bismuth concentrations are limited to low doping levels leading to amplifier lengths on the order of 100 m with measured noise figures of 6-8 dB. A common challenge with long amplifier lengths (Raman and bismuth) is the impact of multipath interference from double Rayleigh scattering on the noise Figure [6].

Recently, significant amplification at 1427 nm (19.3 dB gain and 1.2 W of optical power) was attained using an Nd³⁺ doped silica optical fiber amplifier with a gain selection waveguide albeit with low (5%) optical efficiency [7, 8]. Nonetheless, this was a surprising result as past attempts to attain laser amplification on the 1300 nm laser transition of Nd³⁺ in silica glass optical fibers showed significantly less gain and power. In particular, Nd³⁺ in fused silica attained only 2 mW with 1% slope efficiency and negligible gain at 1365 nm with a phosphate co-doped silica core [9]. The best results employed non-fused silica glasses. 10 dB of gain was attained in a Nd³⁺ doped fluorozirconate fiber with 250 mW of pump power at 800 nm [10] and 14 mW of laser power was attained in a fluoride fiber laser pumped at 800 nm with 100 mW of pump power [11]. In addition to the expected gain competition from the 920 nm and 1064 nm laser transitions, the 1300 nm laser transition in Nd³⁺ has significant excited state absorption [12]. Excited state absorption (ESA) is still present but at a lower level in non-silica fibers [13]. In [12], Morkel, et al. notes that Nd³⁺ optical fibers that are co-doped with aluminum showed better performance than fibers co-doped with germanium. For the fiber reported upon here, aluminum co-doped silica was chosen for the amplifier material due to its high compatibility with standard telecom optical fibers. The basic waveguide structure should be applicable to other material systems such as fluorozirconate.

The fiber employed in the 1427 nm result [7] suffered from a number of drawbacks that prevented achievement of better performance. These drawbacks included: only the 1064 nm line was suppressed and amplified spontaneous emission (ASE) at 920 nm was significant; the background loss of the fiber was >0.2 dB/m in the 1400 nm wavelength region; the fiber was cladding pumped at 880 nm leading to a 60 m long optimal length that combined with high loss per meter resulted in a 10.5 dB insertion loss at 1427 nm and the experiment was limited to probing amplification only at 1427 nm whilst the gain peak appeared to be closer to 1400 nm. In this work a significantly improved fiber has been constructed and tested. This new fiber suppresses ASE from 850 nm to 1150 nm effectively eliminating gain competition at these wavelengths, the fiber background loss is improved and the fiber is core pumped resulting in significantly less total amplifier length and overall loss. Below the fiber’s design and performance is discussed in detail including measurements of the emission cross section of Nd³⁺ (from 800 nm to 1500 nm). The excited state absorption cross section from 1300 nm to 1500 nm was deduced from the combination of measured emission cross sections and measured gain spectrum. The measured cross-sections along with measured gain, fiber losses and fiber design are employed both to analyze the performance of the fiber reported upon in this work and to project potential performance attainable with additional improvements. These projections suggest a useful E-band amplifier with only 7 m of active fiber length and noise figure < 5 dB could be constructed with a further improved fiber.

2. Fiber design, fabrication and characterization

Figure 1 plots the fiber loss spectrum calculated via the method described in Pax, et al. [14] as well as a photograph (inset) of the as drawn fiber. The fiber has a calculated mode field diameter of 8.1 µm at 808 nm and 10.5 µm at 1400 nm. Physically, the fluorinated depressions (darkest regions in the photograph) can be thought of as forming a low index cladding region creating a waveguide around the center Nd³⁺ doped rod. Light at some wavelengths propagating in the core is phase matched to the LP11 mode of the GRIN inclusions (brightest spots in the photograph) and subsequently coupled out of the fiber core into the space filling mode via the “bridge” formed by the GRIN inclusions. The space filling mode is unguided, creating high loss (calculated > 30 dB/m) in the wavelength region from 850 nm to 1150 nm. This 300 nm wide high loss region is significantly wider than that obtained previously [7, 8, 14] and was a result of employing GRIN inclusions of two different diameters. The expected loss at both the pump wavelength at 808 nm and the signal wavelength at 1400 nm is less than 0.05 dB/m due to the micro-structured waveguide. A key feature of this fiber design is that it blocks only a well-defined band of light while enabling low loss guiding at both longer and shorter wavelengths. Though the amplifier fiber is constructed via a micro-structured based stack and draw approach, the solid, all-silica fiber cleaves and splices with standard telecom tools.

 

Fig. 1 Theoretical waveguide loss vs. wavelength in the absence of Nd³⁺ absorption and end face of the as-drawn, 126 µm diameter, Nd³⁺ optical fiber (inset), note the dark regions are fluorinated index depressions, the fiber has no holes or voids.

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The fabricated fiber is an all-solid microstructure with a glass diameter of 126 µm and a micro-structure pitch of 6.6 µm. The center rod of the preform from which the fiber was drawn was fabricated by repeatedly drawing a mix of Nd³⁺ doped glass rods with fluorine doped glass rods and fused silica rods and tubes in order to create a final rod closely matched to the index of fused silica. The Nd³⁺ doped glass rod was produced by Optacore SA and was co-doped with 0.75 mol % Al₂O₃. The Nd³⁺ ion concentration creates a small signal absorption of 57 dB/m at 808 nm as measured by Optacore SA from a slice of the glass rod. The refractive index of the Nd³⁺ rod was measured by Optacore SA to be an average of 1.9 x 10⁻³ higher than that of fused silica. The rod had a fused silica outer layer such that the Nd³⁺ region was 90% of the total diameter of the rod. The fluorine doped glass rod was produced by Prysmian and had a refractive index relative to fused silica of −6.7 x 10⁻³ as measured by Prysmian. These starting rods were drawn to daughter canes and a new preform was stacked from the daughter canes that contained 44 Nd³⁺ doped canes, 11 fluorine doped canes and 1 thin outer tube of fused silica. The starting canes were drawn to nominally 1.3 mm in diameter with the cane diameters adjusted such that the area weighted refractive index of the preform was as closely matched to fused silica as possible. This preform was subsequently drawn down to grand-daughter canes while applying a vacuum to the outer tube to remove air-pockets. These canes were then re-stacked and again over-sleeved with a thin silica tube and drawn to 1.3 mm great-granddaughter canes. One of these great-granddaughter canes became the center rod of the preform from which the fiber of Fig. 1 was drawn. This final great-granddaughter rod is calculated to have a refractive index matched to within 10⁻⁵ of fused silica, the Nd³⁺ concentration is estimated to be diluted to 40% of its original value and the feature sizes of the original starting rods were reduced to <81 nm in the final fiber. All fused silica rods and tubes used in this effort were Hereaus produced low OH, F300 glass.

The Nd³⁺ doped center rod was surrounded by six rods drawn from a preform also produced by Prysmian the center of which was fluorine doped glass with a refractive index relative to fused silica of −6.7 x 10⁻³ and the outside of which was fused silica. The diameter ratio of the fluorine doped region to the fused silica region in the original rod was 75%. The six fluorine doped rods appear in Fig. 1 as dark, slightly hexagonal shaped regions around the center Nd³⁺ doped region. The remaining four rings of the micro-structure contain additional rods drawn from the same original preform and also appear as dark, slightly hexagonal shaped regions. It is emphasized that these dark regions are fluorine doped fused silica, not air holes. The twenty-four bright spots seen radiating in six spokes from the center of the fiber in Fig. 1 are GRIN elements. These GRIN elements were drawn from a Prysmian produced GRIN preform with a peak refractive index relative to fused silica of 2.4 x 10⁻². The ratio of GRIN diameter to outer glass diameter ratio of the preform was 0.5. This GRIN preform was cut in half and one half was subsequently ground down to 93% of the original diameter. Three of the six spokes were fabricated from daughter canes drawn from the original unground portion of the GRIN preform with a GRIN/silica diameter ratio of 0.5 and the remaining three spokes were fabricated from daughter canes drawn from the ground portion of the GRIN preform with a GRIN/silica diameter ratio of 0.535. The 0.5 ratio elements and 0.535 ratio elements were alternated such that similar spokes had an angular separation of 120°. An additional two layers of fused silica rods completed the stack which was over-sleeved with a fused silica tube. A vacuum was applied to the resultant preform to remove all air holes and fiber of 126 µm outer diameter was drawn.

Figure 2 is the measured attenuation spectrum of the core of the fiber in the pump wavelength range from (700 nm to 850nm, Fig. 2(a)) and signal wavelength range (1300 nm to 1500 nm, Fig. 2(b)). Attenuation measurements were made using the standard cut-back method. The pump wavelength range contains strong pump absorption lines from 720 nm to 760 nm and the standard pump line from 780 nm to 830 nm with its peak at 808 nm. At the edge of this wavelength window the waveguide loss is seen to be increasing where the waveguide induced loss region begins. Attenuation at wavelengths a little beyond 850 nm out to 1150 nm were not accurately measurable as there was too little signal even for very short fiber lengths. Indeed, measurement of the strong pump absorption required performing the cutback measurement on a short (<2 m) length of fiber. Signal wavelength attenuation was measured using 25 m fiber lengths. A strong (225 dB/km) OH induced peak is observed at 1380 nm. This peak is significantly reduced (<¼) from the prior fiber [7, 8, 14], but still much higher than attainable in state of the art fibers. The original starting materials from all suppliers were confirmed to have OH induced attenuation peaks much less than that shown in Fig. 2(b) and the large peak is attributed to contamination in the stack and draw process. Background loss in the region of interest outside the OH peak region is between 0.1 and 0.15 dB/m. This is also believed to be driven by either contamination in the stack and draw process or Mie scattering from the residual ~100 nm size features in the Nd³⁺ doped core. A logical next step in improving this fiber type is development of a waveguide design where the Nd³⁺ core is not index matched to fused silica, so as to avoid the numerous processing steps that dilute the concentration and introduce contaminants. Such a design should reduce the material component of the attenuation at the signal wavelength to < 10 dB/km (i.e. 0.01 dB/m). Such a design would also have a higher numerical aperture. The rising loss at 1500 nm is bend induced and increases with tightening bend radius. This measurement was taken with the fiber coiled to 12 inches in diameter.

 

Fig. 2 (a) Measured attenuation spectrum in the pump (700 nm to 850 nm) and (b) signal (1300 nm to 1500 nm) wavelength regions.

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Higher numerical apertures fibers should bend to tighter coil diameters without impacting the loss. Bending does not appear to have a significant effect on the wavelength region where high loss is deliberately induced by the waveguide structure. Calculations show a smearing out of the sharp peaks observed in Fig. 1, but no reduction in the minimum loss nor significant shifting of the loss band edges. Experimentally, bending of the fiber was not observed to alter the fluorescence spectrum in the 850 nm to 1150 nm wavelength region.

In order to assess the ability of the fiber to suppress ASE from 850 nm to 1150 nm, a 250 mW, 808 nm diode laser (Lumics model LU808M250) was coupled to the Nd³⁺ fiber through an 808 nm/1400 nm WDM (Gooch & Housego model SFO4521-FFW-808X0230-001, fabricated from SMF-28 fiber). The experimental assembly was fusion spliced together and an SMF-28 pigtail was fusion spliced to the end of a 4 m piece of the fiber in order to couple transmitted light to an optical spectrum analyzer (OSA, Ando model AQ-6315E). Standard telecom cleaving tools and an Ericsson FSU 995PM fusion splicer were employed. The manufacturer recommended fusion splice program for 80µm telecom fiber was found to consistently provide splice losses between SMF-28 and the Nd³⁺ fiber of < 0.25 dB at 1400 nm. The manufacturer recommended fusion splice program for SMF-28 to SMF-28 was found to provide slightly higher losses of < 0.4 dB. An optimized fusion splice program may improve on these results, but such optimization has not been performed. Figure 3(a) shows the spectral transmission through the fiber pumped with the full diode power. Residual pump light is observable at 808 nm. Fluorescence power is equal to or less than the OSA noise floor in the wavelength region from 850 nm to 1120 nm. Some fluorescence is observable in the 1120-1160 nm corresponding to the long wavelength edge of the 1064 nm fluorescence peak. There is strong fluorescence in the designed signal wavelength band from 1300 nm to 1500 nm. This plot illustrates the wavelength selection fiber is working as designed in that it is transmitting the pump and signal, while suppressing the expected ASE bands with peaks at 920 nm and 1064 nm.

 

Fig. 3 (a) Optical spectra from 4 m of the fiber excited by 200 mW 808 nm co-propagating pump light. (b) Pump transmission vs. pump power for 0.5 and 1.0 m fiber lengths with fits to assess the percentage of Nd³⁺ ions that are quenched (<1%).

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The fiber was cut back to 1.0 m and 0.5 m lengths and a pump transmission vs. pump power measurement was performed at each length to assess the fiber for concentration quenching following the method of Bartolacci, et al. [15]. The measured data for the two lengths is plotted as black diamonds (0.5 m case) and red triangles (1.0 m case) in Fig. 3(b). Equation (1) of Bartolacci, et al. [15] was employed to generate a fit to the measured data and these curves are plotted as black and red dashed lines using the fraction of clustered ions as the fit parameter. For the 1.0 m case the fraction of cluster ions from the fit was 0.9% and for the 0.5 m case, 0.6%. These values are sufficiently low to rule out concentration quenching as a concern. Additional parameters employed in generating the fit curves were: pump absorption cross section (taken to be 1.16 x 10⁻²⁰ cm² as in Bartolacci, et al. [15]), upper state lifetime (assumed to be 450 µs consistent with Bartolacci, et al. [15]), pump area (the fiber was core pumped thus the 8.1 µm calculated mode field diameter was used to calculate pump area) and pump overlap integral (0.786, calculated). The ion concentration was calculated by dividing the measured small signal absorption at 808 nm (14.3 dB) by the product of the pump absorption cross section and pump area overlap integral per Eq. (1) of Giles, et al. [16] and found to be 3.6 x 10¹⁸ ions/cm³.

To complete the characterization of the fiber, the emission cross sections from 800 nm to 1500 nm were measured. A short piece (1.5 cm) of the core rod was end pumped with 25 W of power from an 808 nm fiber coupled diode laser (LIMO model LIMO25-F100-DL808), the emission spectra was measured by butt coupling one end of a multimode fiber pigtail (62.5 µm GRIN fiber) to the side of the core rod to collect side-emitted fluorescence. The other end of the multimode fiber was connected to the OSA. The measured fluorescence spectrum was processed using the method of Caird, et al. [17] employing the previously assumed upper state life time of 450 µs as the only non-measured parameter. The results are plotted in Fig. 4. Measured cross sections and shapes at 905 nm and 1064 nm are consistent with prior reports [16, 18] of Nd³⁺ aluminum co-doped fused silica fiber. The measured 1330 nm emission cross section for Nd³⁺ in aluminum co-doped fused silica reported here was not found in the previously published literature on optical fiber amplifiers.

 

Fig. 4 Measured emission cross sections of Nd³⁺ core glass.

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3. Performance of the fiber as an E-band amplifier

The experimental set-up used to test the Nd³⁺ fiber as an E-band amplifier is shown in Fig. 5. One amplifier consisting of two gain assemblies was constructed. Each assembly was bi-directionally pumped with 808 nm laser diodes (Lumics model LU808M250) that were coupled to the Nd³⁺ fiber via an 808 nm/1400 nm WDM (Gooch & Housego model SFO4521-FFW-808X0230-001, fabricated from SMF-28 fiber). The entire experimental set-up was a fusion spliced monolithic all-fiber assembly. The Nd³⁺ fiber in each assembly was 7 m long. A 3.5 m length of Nd³⁺ fiber was found to be sufficient to absorb >90% of one of the 808 nm pump lasers with no applied signal light. Thus a 7 m long fiber ensures no pump light from one diode is incident on another avoiding possible diode damage concerns. A calculation using the equation employed to estimate concentration quenching concurs that 250 mW of 808 nm pump diode light should be attenuated by greater than 90% in 3.5 m of the Nd³⁺ fiber. Physically, this is the amount of 808 nm power required to maintain the Nd³⁺ ion population at high inversion given the total number of ions and upper state lifetime. The number of assemblies was limited by available components (pump diodes, drivers and WDMs). A polarization independent fiber coupled optical isolator (Thorlabs model CDI8886, 1400 nm center wavelength, 0.42 dB insertion loss, 47 dB isolation, SMF-28 fiber pigtails all measured by the manufacturer) was fusion spliced to the input of the first assembly. A number of sources could then be fusion spliced to the input of the isolator for the purpose of testing the amplifier performance.

 

Fig. 5 Block-diagram of the experimental set-up used to test E-band amplifier performance.

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Prior to the construction of the second assembly pictured in Fig. 5, an ASE seed source was constructed from ½ of the second assembly and connected to the input of first assembly through the optical isolator, permitting a direct measurement of the gain and loss of one of the two assemblies [19]. The measured and processed data from this measurement is shown in Fig. 6 below. The Fig. 6(a) shows the measured data as taken with the OSA. The output of the ASE seed source was fusion spliced to the optical isolator and an SMF-28 pigtail was fusion spliced to the output of the optical isolator. The connector side of this pigtail was plugged into the OSA and the first black curve was measured establishing the input power spectra from the ASE seed source and is labeled “Seed Amp In” in Fig. 6(a). The connector was left plugged into the OSA and the first assembly was fusion spliced into the optical path between the optical isolator output and input pigtail. Other than the losses associated with the two fusion splices (typically <0.1 dB as these were SMF-28 to SMF-28 type splices) all other losses were constant. The black dotted line is the measured spectra of the ASE source as propagated through assembly 1 with no pump power applied and is labeled “Seed Amp Out” in Fig. 6(a). Dividing the measured ASE spectra at the output of the amplifier by the measured ASE spectra at the input of the amplifier with the pump lasers off permits calculation of the loss spectrum of the as built amplifier assembly. The amplifier assembly loss spectrum is plotted in Fig. 6(b) as the solid black line labeled “Amplifier Loss.” Based upon the known Nd³⁺ fiber loss spectrum and the separately measured, but not shown loss spectrum of the WDMs, the splice losses between the Nd³⁺ fiber and the WDM pigtails is 0.18 dB each. The overall curvature of the Amplifier Loss curve is primarily attributable to the WDM loss with the exception of the OH peak at 1380 nm, which is attributable to the 7 m of Nd³⁺ fiber.

 

Fig. 6 (a) Measured OSA data obtained by probing assembly 1 with an ASE seed source (solid black curve was taken at the input of assembly 1, output of isolator, remaining curves were taken at the output of assembly 1). (b) Processed gain and loss data calculated from measured OSA data.

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With the ASE seed on, the two diode pump lasers were turned on at full power (450 mW total power coupled to the Nd³⁺ fiber) and the resulting measured spectrum is the red curve labeled “Amplified Seed,” Fig. 6(a). The ASE seed was then turned off with the pump diode lasers left on at the same power and the measured spectrum is the green curve labeled “ASE,” Fig. 6(a). From these curves the spectral gain of the amplifier assembly was calculated assuming the seed source was sufficiently weak that it did not saturate the amplifier nor reduce the ASE. That is, the measured ASE spectral power was subtracted from the Amplified Seed power and the difference was divided by the measured Seed Amp In power in order to establish the amplifier gain [19]. The resulting spectrally resolved amplifier gain is plotted in Fig. 6(b) as the red curve labeled “Amplifier Gain”. The green curve labeled “Intrinsic Gain” in Fig. 6(b) is the Amplifier Gain with the Amplifier Loss subtracted from it and is representative of the intrinsic gain of the Nd³⁺ fiber in the absence of any losses from either the passive components in the assembly or the fiber itself. It is representative of the attainable gain spectrum of an ideal, lossless E-band Nd³⁺ amplifier.

From the Amplifier Gain curve in Fig. 6(b), it is observed that there is positive gain from 1337 nm to 1344 nm and 1376 nm to 1468 nm and the assembly has a peak gain of 6.2 dB at 1402 nm. The Intrinsic Gain curve suggests positive gain may be attainable from 1334 nm to 1351 nm and from 1372 nm to 1500 nm and the intrinsic gain peak is closer to 1397 nm with a peak gain of 7.8 dB. Comparing the Figs. 6(a) and 6(b) with the measured emission cross section from Fig. 4, the impact of excited state absorption on the gain spectrum is clear. The expected gain peak at 1340 nm is greatly suppressed and indeed at wavelengths shorter than 1337 nm and between 1344 nm and 1375 pumping the amplifier assembly generates a very strong induced absorption or optical loss.

The data from Figs. 4 and 6 permit calculation of the excited state absorption cross section of the Nd³⁺ core material. Following Eq. (27) of Giles, et al. [16], the expected spectrally resolved gain coefficient may be calculated as σ_e Γ n_T (n₂/n_T) L where σ_e is the emission cross section from Fig. 4, Γ is the overlap integral (0.583 at the signal wavelength), n_T is the Nd³⁺ ion density (3.6 x 10¹⁸ cm³), n₂/n_T is the fraction of the total ion population in the upper level laser state and L is the fiber length (7 m). There is no ground state absorption in the signal wavelength band. This calculation is an interim step in calculating the excited state absorption cross section. The fraction of the total ion population in the upper level laser state is employed as a fit parameter to match the expected spectrally resolved gain coefficient to the measured Intrinsic Gain from Fig. 6 in the long wavelength region of the gain spectrum where ESA is expected to be minimal. In Fig. 7(a), the Intrinsic Gain of the Nd³⁺ fiber from Fig. 6 is replotted again as a green line labeled “Intrinsic Gain.” The expected gain coefficient calculated by the method described above is plotted in Fig. 7(a) as a black line labeled “Emission Cross Section Gain.” The fraction of the total ion population employed as the fit parameter was 86.6%. Figure 7(a) has been scaled to show the full intrinsic gain spectrum including the strong pump induced absorption below 1325 nm that was not shown in Fig. 6 in order to provide a better resolved representation of the positive gain spectrum.

 

Fig. 7 (a) Intrinsic gain of single assembly from Fig. 5 and fit of expected gain based on emission cross section measurement of Fig. 4. (b) Derived excited state absorption cross section (red) plotted along with emission cross section from Fig. 4.

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Subtracting the Emission Cross Section Gain from the measured Intrinsic Gain plotted in Fig. 7(a) generates a curve that is the spectrally resolved absorption due to the presence of ESA in the fiber (this curve is not plotted). The excited state absorption cross section as a function of wavelength can then be determined by dividing the spectrally resolved absorption by Γ n_T (n₂/n_T) L where the values are the same as those used to calculate the Emission Cross Section Gain. The resultant ESA cross sections are plotted in Fig. 7(b) as the red line label “Excited State Absorption.” The black line in Fig. 7(b) labeled “Emission” is the emission cross section from Fig. 4 above replotted here for easy reference. Both cross sections are needed to accurately model the potential performance and are used below to calculate the best case amplifier noise figure and efficiency for this material system.

At this point assembly 2 was completed and the experimental system set up was as shown in Fig. 5 above. The combination of assembly 1 and 2 will be referred to as the integrated amplifier. Three fiber coupled diode seed lasers (procured from Qphotonics) were employed to as the input source in order to test the integrated amplifier performance. These three lasers were a 10 mW, 1390 nm DFB (QDFBLD-1390-10), a 150 mW, 1420 nm fiber Bragg grating stabilized laser diode (QFBGLD-1420-150) and a 200 mW, 1440 nm Fabry-Perot laser (QFLD-1440-200S). The 1390 nm DFB was employed first and initially run below threshold in order to create a broadband light source that enabled measurement of the small signal gain of the combined amplifier system. The process for making this measurement was the same as the process employed to measure the single amplifier assembly detailed in Fig. 6 above, however the diode based seed spectra was weaker, resulting in a slightly noisier processed data set. The processed data from this measurement is shown in Fig. 8 below at the maximum total applied pump power of 888 mW. The black line, labeled “Amplifier Loss” is the passive loss of the integrated amplifier with all pump lasers off. As expected the passive loss is approximately twice the loss of a single assembly. The red line, labeled “Amplifier Gain” is the measured small signal gain of the integrated amplifier.

 

Fig. 8 Measured gain, loss and noise figure of the integrated amplifier. Also plotted is the best case theoretical noise figure derived from the emission and ESA cross sections.

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Having measured the unseeded amplifier ASE power spectrum as part of the process of determining the small signal amplifier gain and knowing the amplifier gain it is possible to directly calculate the integrated amplifier noise Fig [19]. This was done by dividing the measured ASE power spectrum by (G-1) hν Δν, where G is the linear amplifier gain (as measured), h is Plank’s constant, ν is the photon frequency at that specified wavelength and Δν is the resolution bandwidth of the OSA employed to measure the ASE power spectrum (1 nm). The noise figure for the integrated amplifier as calculated by this method is shown in Fig. 8 as the green line labeled “Noise Figure.” The amplifier noise figure is a measure of twice the effective spontaneous photon number of the amplifier, n_sp. The desired value for n_sp is 1, leading to the desired noise figure of 3 dB. As the gain approaches unity or less while there is still measurable fluorescence power the noise figure rises rapidly (thus the noise figure is plotted only in the wavelength region from 1376 nm to 1464 nm where the gain is positive). Due to the presence of ESA, the best case noise figure for this amplifier is not 3 dB across the full spectrum. In the case of ESA, n_sp = σ_e/(σ_e-σ_ESA), where σ_e is the emission cross section and σ_ESA is the excited state absorption cross section. Using the measured emission and excited state absorption cross sections from Fig. 7(b), the best case noise figure attainable by this material system in the high gain, low loss fiber case is calculated and plotted in Fig. 8 as the blue line labeled “Theoretical Noise Figure.” The measured noise figure and theoretical noise figure show good qualitative agreement. Near 1372 nm, the emission and ESA cross sections are equal and the noise figure diverges as expected. The measured noise figure is higher than the theoretical noise figure due to the relatively high passive fiber loss. This is particularly clear at the long wavelength edge where the measured noise figure diverges as the per unit length gain approaches the per unit length loss. Future fiber iterations with lower per unit length losses and higher per unit length gains will enable an E-band amplifier with <5 dB noise figure at wavelengths longer than 1393 nm.

To complete characterization of the integrated amplifier the three seed sources were employed to measure the gain saturation curves at the three laser wavelengths as well as the fully saturated power conversion efficiency. The gain saturation curves are plotted in Fig. 9(a). These were taken with the full pump power (888 mW) applied to the integrated amplifier. In order to accurately measure the lower power regions in the 1427 nm and 1440 nm case, these sources were launched into free space and coupled to the integrated amplifier after passing through a variable attenuator. The known passive loss of the amplifier was used to calculate the coupled input power. Total ASE power (71.4 µW) was subtracted from the amplified power when calculating the gain. For the higher power regions, where the diode laser output power could be reliably adjusted by adjusting the diode current, the seed sources were directly fusion spliced to the integrated amplifier input. In this configuration, with each diode at maximum output power, an output power vs. pump power curve was measured to assess the attainable power conversion efficiency. These curves are plotted in Fig. 9(b).

 

Fig. 9 (a) Gain saturation curves of amplifier. (b) Power conversion efficiency curves.

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The gain saturation curves for the 1390 nm and 1427 nm case at the lowest input powers are in good agreement with the small signal gain curve from Fig. 8. However, the 1440 nm curve shows a slightly higher than expected gain at the lowest powers. The 1440 nm diode had no wavelength stabilization and as a result had a relatively broad emission spectrum with a center wavelength significantly shorter than 1440 nm. The shorter wavelength combined with the slope of the gain spectrum in this region accounts for the apparent discrepancy.

The power conversion efficiency curves in Fig. 9(b) show a peak slope efficiency of 18.5% at 1427 nm. This slope efficiency is significantly degraded by the high background loss of the integrated amplifier (−2.4 dB) compared to the net gain of the amplifier at full pump power (1.6 dB). The maximum attainable slope efficiency given the quantum defect at 1427 nm is 56.6%. The high background loss and low gain reduces the attainable slope efficiency to 25.7%. Thus the 18.5% value is 72% of the ideal value in the presence of the high background loss. An identical measurement taken on a single assembly attained slope efficiencies of 4.8% at 1390 nm, 20.8% at 1427 nm and 19.9% at 1440 nm, further indicating the background loss is degrading amplifier efficiency. Finally, we note the slight curvature of the power conversion efficiency curves. This suggests that the signal power is comparable to but not much, much greater than the saturation power of the amplifier. Reduction of the mode field diameter of the fiber by 2x (as discussed below), leading to a 4x increase in signal intensity will further improve power conversion efficiency.

4. Projected E-band amplifier performance for an optimized fiber

The current fiber described a significant improvement over the original [7]. However, the background loss (0.1 – 0.2 dB/m, refer to Fig. 2 and associated discussion) is still significantly higher than attainable by state of the art techniques (<0.01 dB/m) and the mode field diameter (10 µm) is larger than desired for maximum gain and power conversion efficiency. Further, the process of matching the core index to that of fused silica has reduced the attainable Nd³⁺ ion density by at least 2.5x. Given that no concentration quenching was observed in the current sample, attainable Nd³⁺ ion density is likely >3x higher than the current fiber. This increase in ion density may be achievable via altering the current waveguide design such that the core is not index matched to fused silica, removing the fabrication process step that dilutes the core glass. This will require some additional design development beyond what has been discussed in this effort. The measurements detailed above, particularly the detailed emission and excited state absorption cross sections can be employed to make an assessment of the attainable performance of an E-band amplifier based upon a Nd³⁺ doped wavelength selection all-solid micro-structured optical fiber. The current fiber mode field diameter is 8.1 µm at the pump wavelength and 10.5 µm at the signal wavelength with a 6.6µm doped region. It is not implausible that these dimensions could be reduced by a factor of two by not matching the index of the doped core to that of fused silica (enabling a higher NA structure to be constructed) and instead attaining the wavelength selection via coupling to a multi-mode secondary waveguide surrounding the overall structure similar to the initial fiber [7, 14] in this case likely formed by a large ring of GeO₂ co-doped glass surrounding the microstructure. The Nd³⁺ concentration of this core would not be diluted by the index matching process. Thus a Nd³⁺ fiber with the desired filtering effect to suppress ASE between 850 nm and 1150 nm should be attainable with the following nominal parameters; a doped core region of 3.3 µm with a Nd³⁺ ion concentration of 1.13 x 10¹⁹ ions/cm³, a pump mode field diameter at 808 nm of 4 µm and a signal mode field diameter at 1400 nm of 5.25 µm. Such a fiber would absorb 600 mW of 808 nm pump light in 7 m (calculated using Eq. (1) of Bartolacci, et al. [15]). Given current commercial off the shelf 976 nm diode lasers have output powers of 750 mW, 600 mW is not an unreasonable value and could also be attained via bidirectional pumping with two 300 mW diodes. The small signal gain is then (σ_e-σ_ESA) Γ n_T (n₂/n_T) L, where σ_e is the emission cross section, σ_ESA is the excited state absorption cross section, Γ is the overlap integral at the pump wavelength (0.583), n_T is the Nd³⁺ ion concentration, n₂/n_T is the population inversion (86.6%, consistent with that attained in the current experiment) and L is the fiber length (7 m). The projected gain is plotted in Fig. 10(a) as the black line labeled “Projected Gain.” The theoretical noise figure from Fig. 8 above is replotted on the same plot as the red line labeled “Projected Noise Figure.” The peak gain is 23.1 dB at 1398 nm with a 30 nm projected bandwidth (1386 nm to 1416 nm). Given the 5 dB noise figure at the gain peak, total integrated ASE power is estimated at 1.6 mW a small fraction (<0.25%) of the applied pump power and thus unlikely to impact the expected inversion. At 1386 nm the expected noise figure is 6.3 dB falling to less than 5 dB at 1394 nm and continuing to trend downwards thereafter. Gain flattening filters and other advanced amplifier techniques may permit broadening the amplifier bandwidth further and re-centering the gain towards the lower noise end of the spectrum.

 

Fig. 10 (a) Projected gain and noise figure of an optimized amplifier. (b) Quantum defect and excited state absorption limited power conversion efficiency.

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Finally, the attainable power conversion efficiency is assessed. The 808 nm to 1400 nm wavelength difference between the pump and signal wavelengths is a large quantum defect, but not more so than the 976 nm to 1550 nm quantum defect of an Er³⁺ doped fiber amplifier. The quantum defect vs. wavelength (assuming an 808 nm pump) is plotted in Fig. 10(b) as the red line labeled “Quantum Defect.” However, the presence of ESA negatively impacts the power conversion efficiency. Thus the maximum attainable power conversion efficiency is η σ_e/(σ_e + σ_ESA) where η is the quantum defect and σ_e and σ_ESA are the emission and ESA cross sections. This quantity is the real upper bound on power conversion efficiency and is plotted as the black line label “Excited State Absorption Limit” in Fig. 10(b). Noise in the emission and ESA cross section measurements leads to a slightly higher ESA limited power than the quantum defect in the wavelength range >1440 nm, clearly this range is quantum defect limited.

A comparison of the potential performance of this amplifier to that of current erbium doped fiber amplifiers in the 1550 nm wavelength range suggests a number of comparative weaknesses and strengths. The Nd³⁺ upper state lifetime is 450 µs vs. >10 ms for Er³⁺. This difference in upper state lifetime leads to an intrinsic need for higher pump power to maintain the small signal gain as ions must be restored to their upper level laser state 20 times more often. While the power conversion efficiency for Nd³⁺ is comparable to that of Er³⁺ when Er³⁺ is pumped at 976 nm, the lower quantum defect of Er³⁺ when pumped at 1480 nm allows for higher power conversion efficiency in this case. An advantage of the Nd³⁺ amplifier is that Nd³⁺ is a four level laser transition, thus the gain shape and noise figure are not sensitive to variation in amplifier length and pump power. The primary advantage of Nd³⁺ is that it acts as an amplifier in the E-band wavelength range and has favorable properties over Raman and Bismuth amplifiers in that overall amplifier length can be kept to under 10 m, minimizing multi-path Rayleigh scattering effects on the noise figure. Further, the Nd³⁺ amplifier employs a common, well-understood rare earth laser ion as the active medium. This latter advantage includes a well-developed semiconductor materials system for the pump laser at 808 nm. It is shown here that the disadvantages of competing laser transitions can be overcome with an all-solid micro-structure fiber design and that excited state absorption is not a significant issue for wavelengths greater than 1390 nm contrary to current common understanding.

5. Conclusions

The design and performance of a Nd³⁺ doped optical fiber with wavelength selective, all-solid micro-structure that completely suppresses ASE in the 850 nm to 1150 nm wavelength range has been fabricated and demonstrated as an amplifier. Detailed measurements of the amplifier properties of an example amplifier have been described as well as measurements of the Nd³⁺ emission and excited state absorption cross sections. Reducing the fiber background loss and mode field diameter combined with the measured data suggest the potential for an improved version of this fiber type to perform as a useful E-band telecom fiber amplifier with >30 nm of bandwidth a noise figure of <5 dB and a fiber length <10 m. Further improvements might be attained by varying the fiber glass composition, which could impact the values of the emission and excited state absorption cross sections in a favorable way. Nd³⁺ optical fibers may have potential for use in an E-band amplifiers for telecom applications when combined with a wavelength selective waveguide to suppress gain on alternate laser transitions.