Channel waveguides based on a polymer, 6-fluorinated-dianhydride/epoxy, which is actively doped with a Nd complex, $Nd(thenoyltrifluoroacetone)_{3}$ 1,10-phenanthroline, are fabricated by a simple and reproducible procedure, spin coating a photodefinable cladding polymer onto a thermally oxidized silicon wafer, photopatterning, backfilling with the active core polymer, and spin coating with an upper cladding layer. Photoluminescence at 1060 nm from the $Nd^{3+}$ ions with a lifetime of 130 μs is observed. Optical gain at 1060 nm is demonstrated in channel waveguides with different $Nd^{3+}$ concentrations. By accounting for the waveguide loss of 0.1 dB/cm, an internal net gain of 8 dB is demonstrated for a 5.6-cm-long channel waveguide amplifier. Owing to the nature of the $Nd^{3+}$ complex, energy-transfer upconversion affects the gain only at $Nd^{3+}$ concentrations above $1 x 10^{20} cm^{-3}$

Diemeer, Mart B.J.

Driessen, Alfred

Geskus, Dimitri

Pollnau, Markus

Sengo, Gabriël

Yang, Jing

Polymer-based, 6-FDA/epoxy channel waveguides doped with a Nd complex, $Nd(TTA)_3phen$, are fabricated by a simple and reproducible procedure mainly based on spin coating and photo-definition. Photoluminescence at 1060 nm from the $Nd^{3+}$ ions with a lifetime of 130 μs is observed. Optical gain at 1060 nm is demonstrated in channel waveguides with different $Nd^{3+}$ concentrations. By accounting for the waveguide loss, an internal net gain of 8 dB is demonstrated for a 5.6-cm-long channel waveguide amplifier. Due to the nature of the $Nd^{3+}$ complex, energy-transfer upconversion affects the gain only at $Nd^{3+}$ concentrations above 1×$10^{20}cm^{-3}$

Yang, J.

Diemeer, Mart

Geskus, D.

Sengo, G.

Driessen, A.

University of Twente Research Information

Neodymium-complex-doped, photo-defined polymer channel waveguide amplifiers J. Yang, M. B. J. Diemeer, D. Geskus, G. Sengo, M. Pollnau, and A. Driessen Integrated Optical Micro Systems, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands  Polymer-based, 6-FDA/epoxy channel waveguides doped with a Nd complex, Nd(TTA)3phen, are fabricated by a simple and reproducible procedure mainly based on spin coating and photo-definition. Photoluminescence at 1060 nm from the Nd3+ ions with a lifetime of 130 μs is observed. Optical gain at 1060 nm is demonstrated in channel waveguides with different Nd3+ concentrations. By accounting for the waveguide loss, an internal net gain of 8 dB is demonstrated for a 5.6-cm-long channel waveguide amplifier. Due to the nature of the Nd3+ complex, energy-transfer upconversion affects the gain only at Nd3+ concentrations above 1×1020 cm-3. Introduction Rare-earth-ion-doped planar waveguide amplifiers are attractive, e.g., for high-speed data communication. Polymers are promising host candidates for these applications due to their low cost and simple processing technologies. In our work, an optical gain of 8.0 dB at a wavelength of 1060 nm was measured in a 5.6-cm-long Nd(TTA)3phen-doped 6-FDA/epoxy photo-definable channel waveguide. Fabrication and characterization Polymers are usually poor host materials for luminescence emission from rare-earth ions due to the presence of high-energy vibrations from C-H and O-H chemical bonds. To suppress the luminescence quenching of rare-earth ions in polymer hosts they were encapsulated in fluorinated chelates in addition to doping them into a fluorinated polymer. The fluorinated neodymium complex, Nd(TTA)3phen, was synthesized according to the procedure described in [1] and doped into the fluorinated host 6-FDA/epoxy. By spin-coating and subsequently photodefining of a cycloaliphatic epoxy prepolymer (code name CHEP) [2, 3], inverted channels in the low-refractive-index CHEP polymer were obtained on a thermally oxidized silicon wafer. The core material, a Nd(TTA)3phen doped 6-FDA/epoxy solution, was then backfilled via spin-coating twice and the 5×5 µm2 Nd-complex-doped channel waveguides were realized after thermal curing. An additional 5-µm-thick CHEP layer was spin-coated on top of the channels as the upper cladding layer. The optical loss of these channel waveguides was determined with the cut-back method. With a broadband white-light source (FemtoPower1060, SC450, Fianium) at the input of the samples of different lengths, the optical output was collected by a spectrum analyzer (Spectro320, Instrument System). Figure 1 shows the loss spectrum of a Nd3+-complex-doped 6-FDA/epoxy channel waveguide from 750 nm to 1350 nm. The peaks around 800 nm and 860 nm are caused by the absorption transitions 4I9/2 → 4F5/2 and 4I9/2 → 4F3/2, respectively, of the Nd3+ ions, while the peak around 1200 nm is due to the Proceedings Symposium IEEE/LEOS Benelux Chapter, 2008, Twente123absorption of the polymer host. The measured waveguide loss at 1060 nm is ~0.1 dB/cm. Figure 2 shows a partial photoluminescence spectrum of the Nd3+-doped polymer. The Nd3+ concentration is 1.03×1020 cm-3. A Ti:Sapphire laser operating at a wavelength of 800 nm was used as the excitation source, and the fluorescence peak near 1060 nm due to the 4F3/2 → 4I11/2 transition of Nd3+ was detected by a spectrum analyzer. It indicates that Nd3+ in this polymer host is optically active at 1060 nm. The luminescence lifetime of Nd3+ in the 6-FDA/epoxy host was measured to be about 130 µs.  800 900 1000 1100 1200 130002468Propagation and absorption loss (dB/cm)Wavelength (nm)1000 1050 11000.00.20.40.60.81.0Normalized intensity (arb. units)Wavelength (nm)  Fig. 1.  Loss spectrum of Nd3+-doped 6-FDA/epoxy Fig. 2.  Luminescence spectrum at the 4F3/2 → 4I11/2 transition of Nd3+-doped 6-FDA/epoxy  Demonstration of optical net gain A pump-probe method was used for the small-signal-gain measurement. A schematic of the experimental setup is shown in Fig. 3. A Ti:Sapphire laser operating at 800 nm was used as the pump source. A Nd:YAG laser (FemtoPower1060, SC450, Fianium), which emits a narrow band (about 3 nm) around 1064 nm when operating at the lowest output power, was applied as the signal source. A mechanical chopper was inserted into the beam path to modulate the signal light and connected to a lock-in amplifier. Pump light at 800 nm and modulated signal light at 1064 nm were combined by a dichroic mirror and coupled into and out of the waveguide via microscope objectives. The unabsorbed pump light coupled out of the waveguide was blocked by a high-pass filter (RG850), and the signal light was measured by a germanium photodiode and amplified with the lock-in technique. The optical gain was determined by measuring the ratio of the transmitted signal intensities Ip and Iu with pump on and off, respectively. By subtracting the waveguide propagation and absorption loss α (dB/cm) at the signal wavelength around 1064 nm, the internal net gain was obtained. The small-signal-gain coefficient in dB/cm was calculated from the equation  10log ( )10puIIlγ α= ⋅ − ,  Neodymium-complex-doped, photo-dened polymer channel waveguide ampliers124where l is the length of the waveguide channel.              Fig. 3.  Schematic of the experimental setup  Experimental data from the gain measurements are shown in Fig. 4, which displays the internal net gain as a function of pump power launched into the channel. The gain increases with increasing pump power and saturates at high power. The saturation is due to ground-state bleaching [4] and energy-transfer upconversion among neighboring Nd3+ ions in the 4F3/2 level [4, 5]. The highest internal net gain of 8 dB, equal to 1.4 dB/cm, was measured for a Nd3+ concentration of 1.03×1020 cm-3. When further increasing the Nd3+ concentration, the gain decreases, indicating the detrimental influence of energy-transfer upconversion at these elevated concentrations.  0 5 10 15 20 25 30 35-0.20.00.20.40.60.81.01.21.41.6  0.30x1020 cm-3 0.61x1020 cm-3 1.03x1020 cm-3 2.03x1020 cm-3 3.08x1020 cm-3Internal net gain (dB/cm)Launched pump power (mW) Fig. 4.  Net gain at 1060 nm as a function of pump power at 800 nm  Conclusion In conclusion, Nd-complex-doped, photo-defined polymer channel waveguides were realized on thermally oxidized silicon wafers with a simple fabrication procedure. An internal net gain of 8 dB was obtained in a 5.6-cm-long channel waveguide with a Nd3+ concentration of 1.03×1020 cm-3, which indicates that a Nd-complex-doped polymer waveguide is well suited for optical amplification and potentially lasing. Microscope Objective Microscope ObjectiveTi:Sapphire Laser 800 nmMirror Mirror Photodiode Nd-doped waveguide Filter Lock-in amplifier White-light Source 1060 nm Chopper Proceedings Symposium IEEE/LEOS Benelux Chapter, 2008, Twente125 References [1] L.R. Melby, N.J. Rose, E. Abramson, and J.C. Caris, “Synthesis and fluorescence of some trivalent lanthanide complex”, J. Am. Chem. Soc. 86, 5117 (1964). [2] M.B.J. Diemeer, L.T.H. Hilderink, R. Dekker, and A. Driessen, “Low-cost and low-loss multimode waveguide of photodefinable epoxy”, IEEE Photon. Technol. Lett. 18, 1624 (2006). [3] M.B.J. Diemeer, L.T.H. Hilderink, H. Kelderman, and A. Driessen, “Multimode waveguides of photodefinable epoxy for optical backplane applications,” in Proc. Annual Symposium IEEE/LEOS Benelux Chapter 2006, 53 (2006). [4] M. Pollnau, P.J. Hardman, W.A. Clarkson, and D.C. Hanna, “Upconversion, lifetime quenching, and ground-state bleaching in Nd3+:LiYF4”, Opt. Commun. 147, 203-211 (1998). [5] M. Pollnau, P.J. Hardman, M.A. Kern, W.A. Clarkson, and D.C. Hanna, “Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG”, Phys. Rev. B 58, 16076-16092 (1998). Neodymium-complex-doped, photo-dened polymer channel waveguide ampliers126

English

Neodymium-complex-doped, photo-defined polymer channel waveguide amplifiers

Sengo, Gabrie͏̈l

NARCIS 

Neodymium-complex-doped, photo-defined polymer channel waveguide ampliers

February 15, 2009 / Vol. 34, No. 4 / OPTICS LETTERS 473Neodymium-complex-doped photodefined polymerchannel waveguide amplifiersJing Yang,* Mart B. J. Diemeer, Dimitri Geskus, Gabriël Sengo, Markus Pollnau, and Alfred DriessenIntegrated Optical Micro Systems, MESA Institute for Nanotechnology, University of Twente, P.O. Box 217,7500 AE Enschede, Netherlands*Corresponding author: j.yang@ewi.utwente.nlReceived September 30, 2008; revised December 16, 2008; accepted December 23, 2008;posted January 13, 2009 (Doc. ID 102249); published February 10, 2009Channel waveguides based on a polymer, 6-fluorinated-dianhydride/epoxy, which is actively doped with a Ndcomplex, Ndthenoyltrifluoroacetone3 1,10-phenanthroline, are fabricated by a simple and reproducibleprocedure, spin coating a photodefinable cladding polymer onto a thermally oxidized silicon wafer, photo-patterning, backfilling with the active core polymer, and spin coating with an upper cladding layer. Photo-luminescence at 1060 nm from the Nd3+ ions with a lifetime of 130 s is observed. Optical gain at 1060 nmis demonstrated in channel waveguides with different Nd3+ concentrations. By accounting for the waveguideloss of 0.1 dB/cm, an internal net gain of 8 dB is demonstrated for a 5.6-cm-long channel waveguide am-plifier. Owing to the nature of the Nd3+ complex, energy-transfer upconversion affects the gain only at Nd3+concentrations above 11020 cm−3. © 2009 Optical Society of AmericaOCIS codes: 130.3120, 130.5460, 160.5690, 220.4000, 230.4480, 230.7380.Rare-earth ions are suitable as active dopants forwaveguide lasing [1–3] and amplification [4,5] in ac-tive integrated optical devices. Rare-earth-ion-dopedplanar waveguide amplifiers have been widely stud-ied owing to their potential use in many integratedoptical applications, e.g., in high-speed data commu-nications to compensate losses and provide efficientlight transmission. Polymers are promising host can-didates for integrated optical devices and, in particu-lar, for high-density optical interconnects owing totheir high packaging density, low cost, ease of fabri-cation, and potential combination with many sub-strate materials. Recent work [6,7] on polymer-basedrare-earth-ion-doped planar optical waveguides hasresulted in the demonstration of optical gain, e.g., inerbium-doped [8,9] and neodymium-doped [10–13]polymer waveguide amplifiers. In [10], a net opticalgain in Nd3+ of 0.35 dB at 863 nm was reported. In[11,12] Nd3+-doped photolime gel polymer planarwaveguides were demonstrated with a maximum sig-nal enhancement of 8.5 dB. However, the photolimegel polymer contains a significant amount of O–Hgroups, which leads to a decrease in the signal out-put, and the device does not possess long-term stabil-ity. In [13], after a highly complex fabrication proce-dure involving a multilayer architecture, a signalenhancement of 8 dB at 1060 nm was obtained in aNdCl3-doped polymer channel waveguide. Polymer-based Nd3+-doped channel waveguide amplifiers thatexploit the potential simplicity of polymer depositionand microstructuring have not yet been demon-strated.In this Letter, Nd3+-complex-doped channel wave-guide amplifiers are obtained with a simple fabrica-tion procedure by dividing the functionalities of pho-todefinition and active doping over two differentpolymers. An internal optical gain of 8 dB at 1060 nmis experimentally demonstrated.The Nd3+ 1060 nm gain transition possesses a four-level-energy structure, and many polymers exhibitvery low loss around this wavelength. However, poly-0146-9592/09/040473-3/$15.00 ©mers are usually poor host materials for lumines-cence emission from rare-earth ions owing to thepresence of high-energy vibrations from C–H andO–H chemical bonds. To suppress the luminescencequenching of rare-earth dopants and also overcomethe insolubility problem of inorganic rare-earth saltsin polymer hosts, the Nd3+ ions were encapsulated influorinated chelates in addition to doping them into apolymer host with fluorination. Compared tonanoparticle-doped polymers [10], polymers dopedwith an organic complex offer the advantages of a ho-mogeneous distribution of active ions, allowing forhigher doping concentrations before luminescencequenching occurs and lower sidewall roughness ofwaveguide channels. The fluorinated Nd3+ complex,NdTTA3phen (TTA=thenoyltrifluoroacetone, phen=1,10-phenanthroline), was synthesized according tothe procedure described in [14] and dissolved into asolution of 6-FDA/epoxy (6FDA=6-fluorinated-dianhydride), which is a fluorinated polymer mate-rial with low loss at 1060 nm. This Nd3+-complex-doped polymer material is stable and—in contrast toorganic dyes—has not shown any sign of luminescentbleaching even after hours of intense laser irradia-tion in excess of 1 GW/m2. The luminescent proper-ties of a Nd3+ complex have been studied [7], and op-tical gain has been reported in an Er3+-complex-doped waveguide [9], whereas Nd3+-complex-dopedpolymer channel waveguides have not yet been dem-onstrated.NdTTA3phen-doped channel waveguides were re-alized by patterning of inverted channels into a suit-able cladding layer. Figure 1 indicates the fabricationprocess. Thermally oxidized silicon wafers were usedas substrates, with the 8 m thick oxide layer act-ing as the lower cladding layer. For side and top clad-ding a photodefinable epoxy material, cycloaliphaticepoxy prepolymer (CHEP), was chosen because it canbe patterned with simple processes, e.g., spin coating,photolithography, and thermal curing [15]. It acts asa negative photoresist and combines the aforemen-2009 Optical Society of America474 OPTICS LETTERS / Vol. 34, No. 4 / February 15, 2009tioned attractive processing properties with a low re-fractive index, low optical loss, and low yellowingproperties. A 5-m-thick CHEP layer with a low re-fractive index of 1.51 at 633 nm was spin coated ontothe oxidized silicon wafer [Fig. 1(a)]. After UV expo-sure (350 W, I-line) through a mask with 5-m-widedark lines [Fig. 1(b)], and subsequent curing and de-velopment, inverted channels were obtained [Fig.1(c)]. The Nd3+-complex-doped core material wasthen backfilled via spin coating twice to achieve asmooth topwall after thermal curing [Fig. 1(d)]. As aresult, 5 m5 m Nd3+-complex-doped polymerchannels with a refractive index of 1.53 at 633 nmwere obtained. An additional 3-m-thick CHEP layerwas deposited on top of the channels as the uppercladding layer by spin coating and thermal curing[Fig. 1(e)]. The Nd3+-complex-doped layer depositedon the surface of the CHEP side cladding is suffi-ciently thin 0.5–1 m that it can be ignored [Fig.1(f)].The optical loss of these channel waveguides wasdetermined with the cut-back method. With a broad-band white-light source (FemtoPower1060, SC450,Fianium) at the input of the samples of differentlengths, the optical output was collected by a spec-trum analyzer (Spectro320, Instrument System).Figure 2(a) shows the loss spectrum of aNd3+-complex-doped 6-FDA/epoxy channel wave-guide from 750 to 1350 nm. The peaks around 800and 860 nm are caused by the absorption transitions4I9/2→ 4F5/2 and 4I9/2→ 4F3/2, respectively, of the Nd3+ions, while the peak around 1200 nm is due to the ab-sorption of the polymer host. The measured wave-guide loss at 1060 nm is 0.1 dB/cm.Figure 2(b) shows a partial photoluminescencespectrum of the Nd3+-doped polymer. The Nd3+ con-centration is 1.031020 cm−3. A Ti:sapphire laser op-erating at a wavelength of 800 nm was used as theFig. 1. (Color online) Fabrication process of Nd-complex-doped polymer channel waveguides. (a) Spin coating CHEPlayer onto a thermally oxidized Si wafer; (b) UV exposure;(c) developing in a standard developer (Fujifilm RER 600);(d) backfilling core solution; (e) spin coating CHEP uppercladding layer. (f) Microscope image of the cross section of achannel waveguide.excitation source, and the fluorescence peak near1060 nm due to the 4F3/2→ 4I11/2 transition of Nd3+was detected by a spectrum analyzer. It indicatesthat Nd3+ in this polymer host is optically active at1060 nm. The FWHM of this transition is about23 nm. It is broader and less structured than that ofNd3+ luminescence in crystals [16], thus providing alarge gain bandwidth in an optical amplifier. The lu-minescence lifetime of Nd3+ in the 6-FDA/epoxy hostwas measured to be about 130 s.A pump-probe method was used for the small-signal-gain measurement. A Ti:sapphire laser operat-ing at 800 nm was used as the pump source. ANd:YAG laser (FemtoPower1060, SC450, Fianium),which emits a narrow band (about 3 nm) around1064 nm when operating at the lowest output power,was applied as the signal source. A mechanical chop-per was inserted into the beam path to modulate thesignal light and connected to a lock-in amplifier. Inthis way, we also eliminated the influence of ampli-fied spontaneous emission on the measured gain. Thepump light at 800 nm and modulated signal light at1064 nm were combined by a dichroic mirror andcoupled into and out of the waveguide via microscopeobjectives. The channels supported transverse multi-mode light propagation at both the pump and the sig-nal wavelengths. The unabsorbed pump light coupledout of the waveguide was blocked by a high-pass fil-ter (RG850), and the signal light was measured by agermanium photodiode and amplified by lock-in tech-niques. The optical gain was determined by measur-ing the ratio of the transmitted signal intensities Ipand Iu with the pump on and off, respectively. By sub-tracting the waveguide propagation and absorptionloss  (dB/cm) at the signal wavelength around1064 nm, the internal net gain was obtained. Theinternal-net-gain coefficient in dB/cm was calculatedfrom the equation = 10 log10Ip/Iu/l − ,where l is the length of the waveguide channel.Experimental data from the gain measurementsare shown in Fig. 3. Figure 3(a) displays the internalnet gain as a function of the pump power launchedinto the channel. The gain increases with the increas-ing pump power and saturates at high power. TheFig. 2. (a) Broadband loss spectrum and (b) luminescencespectrum at the 4F3/2→4I11/2 transition of Nd3+-doped6-FDA/epoxy.saturation may be due to ground-state bleaching [17]February 15, 2009 / Vol. 34, No. 4 / OPTICS LETTERS 475and energy-transfer upconversion among neighbor-ing Nd3+ ions in the 4F3/2 level [17,18]. At an elevatedpump power, thermal effects also occur in the poly-mer material, owing to partial conversion of the ab-sorbed pump power into heat [18].Polymer channel waveguides with various Nd3+concentrations were investigated experimentally tounderstand the effect of energy-transfer upconver-sion among neighboring Nd3+ ions and optimize thenet optical gain. The sample lengths used in thesmall-signal-gain measurement were 5.5–5.6 cm.The highest internal net gain of 8 dB, equal to1.4 dB/cm, was measured for a Nd3+ concentration of1.031020 cm−3. Figure 3(b) shows the internal netgain versus Nd3+ concentration for a launched pumppower of 28.6 mW. The gain increases when increas-ing the Nd3+ concentration from 0.301020 to 1.031020 cm−3. When further increasing the Nd3+ con-centration, the gain decreases, indicating the poten-tial detrimental influence of energy-transfer upcon-version at these elevated concentrations. In [12],serious gain quenching was observed in a Nd3+-dopedphotolime gel polymer waveguide already at Nd3+concentrations higher than 7.81019 cm−3. A com-parison of these results indicates that polymerwaveguides doped with a Nd3+ complex can diminishgain quenching by energy-transfer upconversion,hence allowing for higher dopant concentrations.In conclusion, by dividing the functionalities ofphotodefinition and active doping over two differentpolymers, Nd-complex-doped photodefined polymerchannel waveguides were realized on thermally oxi-Fig. 3. (Color online) Internal net gain at 1060 nm (a) as afunction of launched pump power at 800 nm for differentNd3+ concentrations and (b) versus Nd3+ concentration fora launched pump power of 28.6 mW.dized silicon wafers with a simple fabrication proce-dure. Luminescent quenching was reduced by dopinga fluorinated Nd3+ complex into a fluorinated poly-mer host. An internal net gain of 8 dB was obtainedin a 5.6-cm-long channel waveguide with a Nd3+ con-centration of 1.031020 cm−3 during several hours ofoperation and repeated over a period of severalmonths, thus demonstrating that this approach iswell suited for optical amplification and potential las-ing. With this result a route toward low-cost inte-grated devices with optical gain has been opened.Higher gain can be achieved by extending the wave-guide length, and doping with other rare-earth ionsfor amplification in different wavelength regions ispossible.This work was supported by the Dutch TechnologyFoundation (STW) within the framework of projectTOE 6986.References1. D. S. Gill, A. A. Anderson, R. W. Eason, T. J.Warburton, and D. P. Shepherd, Appl. Phys. Lett. 69,10 (1996).2. J. R. Lee, H. J. Baker, G. J. Friel, G. J. Hilton, and D.R. Hall, Opt. Lett. 27, 524 (2002).3. Y. E. Romanyuk, C. N. Borca, M. Pollnau, S. Rivier, V.Petrov, and U. Griebner, Opt. Lett. 31, 53 (2006).4. E. Lallier, J. P. Pocholle, M. Papuchon, M. De Micheli,M. J. Li, Q. He, D. B. Ostrowsky, C. Grezes-Besset, andE. Pelletier, Opt. Lett. 15, 682 (1990).5. K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P.Blauwendraat, and M. Pollnau, submitted to IEEE J.Quantum Electron.6. L. H. Slooff, A. van Blaaderen, A. Polman, G. A.Hebbink, S. I. Klink, F. C. J. M. Van Veggel, D. N.Reinhoudt, and J. W. Hofstraat, J. Appl. Phys. 91, 3955(2002).7. S. Lin, R. J. Feuerstein, and A. R. Mickelson, J. Appl.Phys. 79, 2868 (1996).8. W. H. Wong, E. Y. B. Pun, and K. S. Chan, Appl. Phys.Lett. 84, 176 (2004).9. A. Quoc, L. Quang, R. Hierle, J. Zyss, I. Ledoux, G.Cusmai, R. Costa, A. Barberis, and S. M. Pietralunga,Appl. Phys. Lett. 89, 141124 (2006).10. R. Dekker, D. J. W. Klunder, A. Borreman, M. B. J.Diemeer, K. Wörhoff, A. Driessen, J. W. Stouwdam,and F. C. J. M. Veggel, Appl. Phys. Lett. 85, 6104(2004).11. R. T. Chen, M. Lee, S. Natarajan, C. Lin, Z. Z. Ho, andD. Robinson, IEEE Photon. Technol. 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Neodymium-complex-doped, photo-defined polymer channel waveguide ampliers

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