Thulium-doped fiber laser utilizing a photonic crystal fiber-based optical low-pass filter with application in 1.7 μm and 1.

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1 Thulium-doped fiber laser utilizing a photonic crystal fiber-based optical low-pass filter with application in 1.7 μm and 1.8 μm band Siamak Dawazdah Emami, 1,* Amin Khodaei, 2 Shumithira Gandan, 1,Richard Penny, 2 Kok Sing Lim, 2 Hairul Azhar Abdul-Rashid, 1 and Harith Ahmad 2 1 Faculty of Engineering, Multimedia University, Cyberjaya, Selangor, Malaysia 2 Photonic Research Center, University of Malaya, Kuala Lumpur, Malaysia * s.d.emami@gmail.com Abstract: This paper describes a low pass filter based on photonics crystal fiber (PCF) partial ASE suppression, and its application within a 1.7 µm to 1.8 µm band thulium-doped fiber amplifier (TDFA) and a thulium-doped fiber laser (TDFL). The enlargement of air holes around the doped core region of the PCF resulted in a low-pass filter device that was able to attenuate wavelengths above the conventional long cut-off wavelength. These ensuing long cut-off wavelengths were 1.85 μm and 1.75 μm, and enabled a transmission mechanism that possessed a number of desirable characteristics. The proposed optical low-pass filter was applied within a TDFA and TDFL system. Peak spectrum was observed at around 1.9 μm for conventional TDF lasers, while the proposed TDF laser with PCF setup had fiber laser peak wavelengths measured at downshifted values of 1.74 μm and 1.81 μm Optical Society of America OCIS codes: ( ) Optical amplifiers; ( ) Rare-earth-doped materials. References and links 1. D. J. Richardson, J. M. Fini, and L. E. Nelson, Space-division multiplexing in optical fibres, Nat. Photonics 7(5), (2013). 2. S. Berdagué and P. Facq, Mode division multiplexing in optical fibers, Appl. Opt. 21(11), (1982). 3. M. Koshiba, K. Saitoh, and Y. Kokubun, Heterogeneous multi-core fibers: proposal and design principle, IEICE Electron. Express 6(2), (2009). 4. Z. Li, A. M. Heidt, N. Simakov, Y. Jung, J. M. Daniel, S. U. Alam, and D. J. Richardson, Diode-pumped wideband thulium-doped fiber amplifiers for optical communications in the nm window, Opt. Express 21(22), (2013). 5. M. Yamada, H. Ono, and J. Ono, 1.7 um band optical fiber amplifier, in Optical Fiber Communication Conference(Optical Society of America, San Francisco, California, 2014), p. Tu2D M. Yamada, K. Senda, T. Tanaka, Y. Maeda, S. Aozasa, H. Ono, K. Ota, O. Koyama, and J. Ono, Tm3+-Tb3+doped tunable fibre ring laser for 1700 nm wavelength region, Electron. Lett. 49(20), (2013). 7. H. Fatehi, S. D. Emami, A. Zarifi, F. Z. Zahedi, S. E. Mirnia, A. Zarei, H. Ahmad, and S. W. Harun, Analytical Model for Broadband Thulium-Bismuth-Doped Fiber Amplifier, IEEE J. Quantum Electron. 48(8), (2012). 8. M. Yamada, S. Aozasa, and H. Ono, Broadband ASE light source for 1800 nm wavelength region, Electron. Lett. 48(23), (2012). 9. L. M. Yang, P. Wan, V. Protopopov, and J. Liu, 2 µm femtosecond fiber laser at low repetition rate and high pulse energy, Opt. Express 20(5), (2012). 10. P. Kadwani, R. A. Sims, J. Chia, F. Altal, L. Shah, and M. C. Richardson, Atmospheric gas detection using broadband mid-ir thulium fiber-based sources, Proc. SPIE 8039, 80390L (2011). 11. M. J. Bader, R. Sroka, C. Gratzke, M. Seitz, P. Weidlich, M. Staehler, A. Becker, C. G. Stief, and O. Reich, Laser Therapy for Upper Urinary Tract Transitional Cell Carcinoma: Indications and Management, Eur. Urol. 56(1), (2009). 12. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, Low-loss hollow-core silica/air photonic bandgap fibre, Nature 424(6949), (2003). 13. P. S. J. Russell, Photonic-Crystal Fibers, J. Lightwave Technol. 24(12), (2006) OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19681

2 14. M. W. Phillips, Thulium Doped Fiber Amplifier Development for Power Scaling the 2 Micron Coherent Laser Absorption Instrument for ASCENDS, (NASA, 2011). 15. Z. Li, A. M. Heidt, J. M. Daniel, Y. Jung, S. U. Alam, and D. J. Richardson, Thulium-doped fiber amplifier for optical communications at 2 µm, Opt. Express 21(8), (2013). 16. S. D. Emami, A. R. Muhammad, S. W. Harun, H. Ahmad, and H. A. Abdul Rashid, S-band Thulium-doped Fiber Amplifier Enhancement using ASE Suppression, Optical Fiber Communication Conference Tu2D.4 (2014). 17. C. B. Olausson, C. I. Falk, J. K. Lyngsø, B. B. Jensen, K. T. Therkildsen, J. W. Thomsen, K. P. Hansen, A. Bjarklev, and J. Broeng, Amplification and ASE suppression in a polarization-maintaining ytterbium-doped allsolid photonic bandgap fibre, Opt. Express 16(18), (2008). 18. P. Kadwani, C. Jollivet, R. A. Sims, A. Schülzgen, L. Shah, and M. Richardson, Comparison of higher-order mode suppression and Q-switched laser performance in thulium-doped large mode area and photonic crystal fibers, Opt. Express 20(22), (2012). 19. J. B. Rosolem and A. A. Juriollo, S Band EDFA Using Standard Erbium Doped Fiber, 1450 nm Pumping and Single Stage ASE Filtering, in Optical Fiber communication/national Fiber Optic Engineers Conference OFC/NFOEC, 1 3(2008). 20. L. Vincetti, M. Foroni, F. Poli, M. Maini, A. Cucinotta, S. Selleri, and M. Zoboli, Numerical modeling of S- Band EDFA based on distributed fiber loss, J. Lightwave Technol. 26(14), (2008). 21. S. K. Varshney, K. Saitoh, M. Koshiba, B. P. Pal, and R. K. Sinha, Design of S-Band Erbium-Doped Concentric Dual-Core Photonic Crystal Fiber Amplifiers With ASE Suppression, J. Lightwave Technol. 27(11), (2009). 22. S. D. Emami, H. A. A. Rashid, S. Z. M. Yasin, K. A. M. Shariff, M. I. Zulkifli, Z. Yusoff, H. Ahmad, and S. W. Harun, New Design of a Thulium-Aluminum-Doped Fiber Amplifier Based on Macro-Bending Approach, J. Lightwave Technol. 30(20), (2012). 23. S. D. Emami, A. R. Muhammad, S. Z. Muhamad-Yasin, K. A. Mat-Sharif, M. I. Zulkifli, F. R. M. Adikan, H. Ahmad, and H. A. Abdul-Rashid, S-Band Gain Improvement Using a Thulium-Aluminum Co-Doped Photonic Crystal Fiber Amplifier, IEEE Photonics J. 6(6), 1 10 (2014). 24. S. K. Varshney, K. Saitoh, N. Saitoh, Y. Tsuchida, M. Koshiba, and R. K. Sinha, Strategies for realizing photonic crystal fiber bandpass filters, Opt. Express 16(13), (2008). 25. F. Fogli, L. Saccomandi, P. Bassi, G. Bellanca, and S. Trillo, Full vectorial BPM modeling of Index-Guiding Photonic Crystal Fibers and Couplers, Opt. Express 10(1), (2002). 26. F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer, 2007). 27. S. K. Varshney, M. P. Singh, and R. K. Sinha, Propagation characteristics of photonic crystal fibers, J. Opt. Commun. 24(5), (2003). 28. B. M. Azizur Rahman and A. Agrawal, Finite Element Modeling Methods for Photonics (Artech House, 2013). 29. S. D. Emami, H. A. Abdul-Rashid, F. Z. Zahedi, M. C. Paul, S. Das, M. Pal, and S. W. Harun, Investigation of bending sensitivity in partially doped core fiber for sensing applications, IEEE Sens. J. 14(4), (2014). 30. D. J. Creeden and B. R. Johnson, Highly efficient thulium doped fiber laser, US Patent (December 5, 2013). 1. Introduction Fulfilling the demand for faster and more capable communication networks requires continual research and utilization of various methods for increasing network bandwidth and transmission capacity. Such approaches include spatial division multiplexing (SDM) [1], multimode [2] and multicore fibers [3], alongside exploration of the promising transmission capacity of additional bands outside the conventional 1.55 µm region [4]. One of the key challenges of the latter method involves achieving transmission at the 1.7 µm to 1.9 µm operating region in such a way so as to compensate for the higher losses acquired outside the low-loss transmission window [5 8]. Amplification at the 1.7 µm to 1.9 µm bandwidth is popular due to the subsequent output having high efficiency, high power, and retina-safe features. This amplification step allows for device applications in diverse fields such as medical surgery, industrial machining, light detection and ranging (LIDAR) systems [9], optical sensing [10], spectroscopy, and potentially in palliative care research [11]. Hollow-core photonic bandgap fibers (HC-PBGFs) are typically used in practice, since the background loss of silica fiber is significant at 1.7 µm to 1.9 µm [12]. These HC-PBGFs are able to overcome the capacity limit of traditional systems due to their ultra-low non-linearity and near-vacuum latency [13]. Additionally, the 1.7 μm band can be exploited for applications involving the high absorption characteristic of 2015 OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19682

3 methane [6], while 1.7 μm lasers find applications in astronomy whereby iodine atoms can be stimulated in order to evaluate correct atmospheric tilts [5, 14]. Thulium-doped fiber amplifiers (TDFA) operating around the 1.9 µm region provide the broadest gain spectrum of all rare-earth doped optical amplifiers [4, 15]. The amplified spontaneous emission (ASE) suppression method is one of the possible ways to shift functional amplification range and change operating laser wavelength [16, 17]. Partial ASE suppression methods involve suppressing a portion of the unwanted ASE spectrum in order to improve the gain of the requisite transmission window [18]. Techniques to achieve amplification at a wavelength of 1.7 μm using terbium-thulium doped fibers are presented in [6]. Terbium doping in the cladding of thulium-doped fiber (TDF) permits the occurrence of terbium ion absorptions from levels 7F6 to 7F0, with a consequent suppression of the 1.7 μm to 2.0 μm region. It has also been demonstrated that the suppression of ASE in the C-band erbium-doped fiber amplifier (EDFA) leads to S-band amplification [19]. Depressed cladding fiber based on refractive index variation (W fiber) [20] and photonic crystal fiber (PCF) [21] are two candidates thus far for S-band EDFAs. Macro-bending [22] and utilization of PCF [23] are two methods used on alumino-silicate TDFA to suppress 0.8 μm and 1.8 μm ASE and increase gain in the S-band region [16]. An optimized PCF geometrical structure based on appropriate profile parameters will facilitate the occurrence of short and long cut-off wavelengths that can be used to achieve desired filtering performance [23]. This paper contains a report on the experimental results of an optical low-pass filter that was proposed in [24]. The low-pass long cut-off wavelengths of the described PCF were achieved by enlarging the air holes surrounding the doped core region. It is shown here that the optimized PCF geometrical structures resulted in long cut-off wavelengths of 1.85 μm and 1.75 μm to achieve the intended transmission characteristics. The experimental loss spectrum has been verified through numerical transmission characteristics using fully-vectorial finite element method (V-FEM) [25]. Additionally, a description is included on the application of the proposed optical low-pass filter in a TDFA system so as to partially suppress the ASE in the 1.9 μm region. The paper furthermore describes how the ASE peak and operating laser wavelengths could be shifted towards shorter wavelengths by rescaling the opto-geometrical parameters of the PCF fibers. The nonlinear polarization rotation (NPR) technique was used to achieve the self-started mode-locking of the laser, whereby the nonlinear polarization evolutions induced wavelength dependent loss of the cavity to alleviate the mode competition caused by the homogeneous gain broadening. 2. PCF low pass filter The transmission window characteristics of PCFs are typically dissimilar due to inherent structural variations in PCFs [13, 26, 27]. There are four important geometrical properties for PCF characterization, namely the lattice constant Λ, core diameter D (whereby Λ = D), diameter d corresponding to the first air hole ring that surrounds the core, and the outer ring air hole diameter d. It is essential that the diameter sizes between d and d are dissimilar as this will affect the cut-off wavelengths of the low-pass filter. In the proposed low-pass filter, the long cut-off wavelength was obtained by controlling the size of air holes in the first ring that surrounded the central core [24]. A simulation was performed whereby diameters for the first ring air holes were varied (d /Λ from 0.30 to 0.55) and cladding air-holes diameters were additionally varied (d/λ from 0.25 to 0.40) in order to attain the intended cut-off wavelength [23]. Table 1 lists opto-geometrical parameters of two fabricated PCFs based on the desired filter criteria. Table 1. Characteristics of the fabricated PCF fibers Fiber Λ D d d PCF(1) 3.2 µm 3.2 µm 2.5 µm 1.1 µm PCF(2) 3.2 µm 3.2 µm 1.9 µm 0.70 µm 2015 OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19683

4 The fabrication process exploited the classical stack and draw method, whereby the various capillary sizes of the first layer and ensuing seven layers were stacked hexagonally around a central rod fabricated via MCVD. Subsequent application of an intra-air hole overpressure enabled control of the air hole dimensions in the final course of the drawing stage from the cane to the fiber. An electron microscope photograph of the cane end face is shown in Fig. 1(a). Figure 1(b) shows the fundamental mode refractive index and cladding refractive index as a function of wavelength for the two fabricated PCFs. The intersection point between the effective refractive index of the fundamental mode and the effective refractive index of the cladding mode determines the long cut-off wavelengths for the PCF in question. The relation between the diameter size of the air holes first ring and the core effective refractive index becomes apparent when the latter parameter becomes smaller than the effective cladding refractive index n eff at a particular wavelength. It can be seen from Fig. 1(b) that an intersection point for n eff and n cladding, termed as long cut-off wavelength, occurs beyond 1850 nm for PCF(1) and 1750 nm for PCF(2). Fig. 1. (a) electron microscope photograph of PCF (cross sectional view), and (b) fundamental mode and cladding effective refractive index variation for wavelength for PCF(1) and PCF(2). The modeled transmission spectra results and the spectral response of the fabricated PCF fibers and are shown in Fig. 2(a) and 2(b) respectively. Figure 2(a) shows the results of the transmission spectra taken from the V-FEM method [28]. Transmission characteristics of the proposed PCF design with five rings of air holes were subsequently evaluated based on confinement loss [27]. Simulation results indicated that more than 80% of the transmission could be obtained for cases involving five or more rings of air holes. For PCF (2) fiber, HE 11 x mode beam losses were calculated as db/m and db/m at 1.7 μm and 1.9 μm respectively. In order to get the spectral response, a white light source with an input power of 58 dbm was injected into the 1 m length PCF fibers. The fiber was spliced to SMF fiber using a 45PM Fujikura splicer, with a resulting 0.8 dbm total splice loss as measured using the splicer. As can be observed from the fundamental mode and cladding effective refractive index variation graph in Fig. 1(b), there was a high loss of 15 dbm at wavelengths longer than 1.85 µm for PCF(1) and 1.75 µm for PCF(2). Examination of the results shown in Fig. 2(a) revealed a total 1.68 db loss measured at 1560 nm. Consideration of total measured loss, modeled PCF loss and splicing loss revealed an unaccounted 0.65 db loss, which was most likely connected with PCF and SMF overlapping loss. A white light source with an input power of 58 dbm was injected into the PCF fibers in order to get the spectral response. It can be clearly seen that experimental and numerical results were both in agreement for cases with the same design parameters. As the wavelength approached values further than the long cut-off wavelength, the electric field increasingly radiated inside the cladding region OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19684

5 Fiber losses significantly increased as the operating wavelength exceeded the long cut-off wavelength. Fig. 2. (a) spectral response of the fabricated PCF fibers, and (b) modeled transmission spectra. 3. Configuration Figures 3(a) and 3(b) show the configuration and measurement setup of the 1.75 μm and 1.85 μm band fiber optic amplifier and fiber laser respectively. The architecture of the single pass TDFA, as seen in Fig. 3(a), consisted of a thulium-doped fiber (TDF), a wavelength division multiplexing (WDM) coupler, a PCF, a pump laser and an optical isolator. The TDF fiber concentration was 2150 ppm with db/m core absorption at μm wavelength, while numerical aperture (NA) and core diameter were 0.15 and 9.0 μm respectively. The TDF length was optimized at 2 m whereas the PCF was arranged at a length of 10 cm. A WDM coupler was used to combine the input signal with the pump light. The optical isolator was placed after the signal to ensure a unidirectional operation of the optical amplifier. A continuous wave (CW) tunable titanium-sapphire laser was used as the pump. The operational wavelength of the laser was fixed at the peak absorption of TDF, which is at μm. The setup for the ring fiber laser is shown in Fig. 3(b). Fig. 3. (a) configuration of the 1.75 μm and 1.85 μm fiber optic amplifier, and (b) fiber laser. An optical 90:10 splitter was used at the system output to direct 10% of the laser light output for sampling purposes and connect the remaining 90% to the counter-propagating suppressed ASE power generated by the near end of the TDF, followed by the PCF (90% port) in the far end of the TDF. The TDF was spliced to SMF fiber using a 45PM Fujikura splicer, with 0.8 and 1.2 dbm splice loss measured for the single and double stage respectively. The 1750 to 1850 nm wavelength region insertion loss of the WDM coupler, point-diffraction interferometer (PDI), and fiber splitter was measured as 1, 0.8, and below 0.6 db respectively. A Yokogawa AQ6375 optical spectrum analyser (OSA) was used to 2015 OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19685

6 measure the amplified spontaneous emission (ASE) and laser spectrum. Self-started mode locking was achieved using the NPR technique. This technique exploits the basic principle of intensity-dependent saturable absorption whereby light of lower intensity is absorbed while higher intensity light will continue to propagate. NPR exists in TDF due to its Kerr effect, in which two orthogonal polarization modes experience dissimilar nonlinear phase shifts. Consequently, the overall state polarization of light in the TDF will rotate, with the angle of rotation being dependent on light intensity. The center of a pulse will experience a different phase shift in comparison to that for the pulse wing. The PC is adjusted so that only a certain polarization of light corresponding to the pulse center will pass though the PDI while the pulse wing is blocked. Therefore, the polarizers inside the PDI and the PC can change the cavity loss. The resulting effect is equal to that of a fast saturable absorber, in which the pulse is slightly shortened after one round trip inside the ring cavity [29]. 4. Results and discussion 4.1 ASE Spectrum Figure 4(a) shows the ASE spectrum of a TDFA (red), TDFA with PCF (1) (blue) and TDFA with PCF(2) (black). The ASE characteristics were measured using an OSA that could detect optical signals from 1.2 μm to 2.4 μm. The μm laser power was fixed at 81 mw for the optimized fiber length of 2 m. A broadband amplification region from 1.65 μm to 2.1 μm was generated in the TDFA. In agreement with the loss spectrum of PCF, as shown in Fig. 2(a), a significant suppression of ASE can be observed above the high cut-off wavelength. Fig. 4. (a) ASE spectrum of single stage TDFA + PCF, (b) ASE spectrum of dual stages TDFA + PCF. As shown in Fig. 4(a), the amplification band changed to 1.7 μm and 1.8 μm with a peak wavelength of 1.74 μm and 1.82 μm for PCF (1) and PCF (2) respectively. In order to increase the amplification efficiency, an experimental setup of a dual stage TDFA was completed. In the dual stage setup, the μm laser power remained fixed at 181 mw while the fiber length was set to 1 m at each stage. The ASE experimental result of the 1 m TDFA, and first and second stage TDFA with PCF (2) are represented by red, blue and black curves respectively in Fig. 4(b). In comparison with the ASE spectrum of TDFA with PCF (represented by the black curve in Fig. 4(a)), a higher ASE peak power at 1.74 μm can be observed in the dual stage TDFA (black curve in Fig. 4(b)) under the same conditions of laser power. 4.2 Fiber laser Figure 5 shows the ring laser output spectra for the developed TDFL, TDFL with PCF(1), and TDFL with PCF(2). The peak emission spectrum was observed as around 1.9 μm via measuring the emission from TDFL when the μm laser power was set at 181 mw (red curve). The measured fiber laser peak wavelengths for TDFL with PCF(1) and TDFL with 2015 OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19686

7 PCF(2) were down shifted to 1.81 μm and 1.74 μm respectively. The results shown in Fig. 5 indicated that the PCF fibers provided strong electromagnetic field confinement at short wavelengths and a high loss for wavelengths higher than the cut-off wavelength. Such lowpass band filtering behavior will lead to ASE suppression in TDFL at longer wavelengths and change the lasing peak wavelength. Fig. 5. Ring laser spectra for the TDFL and developed TDFL with PCF(1) and PCF(2). The mode-locked fiber lase spectrum and pulse wide characteristic at 1.81 nm wavelength are presented at Fig. 6(a) and 6(b) respectively. The repetition rate was 3.2 MHz, as illustrated in Fig. 6(a), which exactly corresponded to the cavity round-trip frequency. Figure 6(b) illustrates the pulse-width characteristic of the pulse laser via use of an autocorrelator. By applying the function fitting, the full width at half maximum (FWHM) of the pulse was measured as 2.32 ps at 1810 nm for the TDFL with PCF(1) setup. Fig. 6. (a)rf spectrum of mode-locked at 1.81 nm wavelength, (a)pulse wide characteristic at 1.81 nm wavelength Optical conversion efficiencies of 0.42, 0.31, and 0.19 at μm, 1.81 μm, and 1.74 μm respectively were measured at room temperature. It was considered that 40 to 50% of the unconverted pump power might contribute to heating in the fiber itself. The decrease of conversion efficiency at 1.81 μm was mostly due to PCF filtering. Low conversion efficiency at 1.74 μm lasing wavelength was probably due to low thulium inversion as a result of strong absorption and emission cross-section overlap occurring at that wavelength. Higher efficiency can be achieved by optimizing the PDI and splitter components and increasing thulium concentration. Higher concentration of thulium will attributed to the 2-for-1 cross-relaxation process of the Tm ion, where one 795 nm photon can create two excited electrons in the Tm ion, and each electron generate a 2-micron photon in a subsequent process [30] OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19687

8 5. Conclusion An analysis was described for experimental results associated with an optical low-pass filter based on two PCF: PCF(1) with geometrical structure properties of Λ (lattice constant) = 3.2 µm, D (core diameter) = 3.2 µm, d (diameter of the first ring of air holes) = 2.5 µm, and d (outer ring air hole diameter) = 1.1 µm, and PCF(2) with Λ = 3.2 µm, D = 3.2 µm, d = 1.9 µm, and d = 0.70 µm. The sizes of air holes in the first ring that surrounded the central core were larger in comparison to those within the outer ring, which resulted in the n eff intersecting with n cladding beyond 1.85 μm and 1.75 μm for PCF (1) and PCF (2) respectively. This feature manifested as a long cut-off wavelength at the intersected wavelengths. A variety of PCF structures incorporated in a TDFA system were tested for low-pass filtering characteristics. It was observed that the double stage TDF had a higher ASE peak power at 1.74 μm than the single stage under the same lasing power conditions. The developed optical low-pass filter was used in the application of a fiber laser. Examination of the spectrum results indicated the fiber laser peak wavelengths for TDFL with PCF (1) and TDFL with PCF (2) were down shifted to 1.81 μm and 1.74 μm respectively. The authors anticipate these findings will be of use for further work in this research area. Acknowledgments We will like to acknowledge the financial support from University Malaya/MOHE under grant numbers UM.C/625/1/HIR/MOHE/SCI/ OSA 27 Jul 2015 Vol. 23, No. 15 DOI: /OE OPTICS EXPRESS 19688