A new approach for filtering an optical band-pass in optical amplifier is proposed using a macro bending. The proposed filter leverages the bending loss of higher order modes at shorter wavelengths. At longer wavelengths, the filter increases fiber’s bending loss as the fundamental mode ‘tail’ is leak out from the cladding. The combination of wavelength dependent loss at longer and shorter wavelength gives rise to the optical band-pass filter characteristic inside the fiber. The simulated spectral response of the filter is found to be in good agreement with the experimental results. Subsequently, the proposed optical band-pass filter is applied in Thulium-doped fiber amplifiers (TDFA) system for gain and noise figure enhancements. The filter functions to suppress both the amplified spontaneous emission (ASE) at 800 nm and 1800 nm wavelength regions and thus improves both gain and noise figure performances in S-band region. By bending of the gain medium, gain and noise figure of the TDFA are improved by about 2 dB and 0.5 dB respectively, within a wavelength region from 1440 and 1500 nm when the 1050 nm pump power is fixed at 250 mW.
© 2012 OSA
Researches on optical band pass filters are recently attracted tremendous interest due to its importance applications in optical wavelength division multiplexing (WDM) network , optical measurements  and optical amplifiers . Various all-fiber band pass filters have been reported using fused taper coupler , dissimilar core fiber coupler , dual-core , and triple-fiber couplers  which are based on the mode coupling phenomenon. Other types of all-fiber optical filters are based on grating, which is written directly onto the fibers . Exchange Bragg reflection between two strongly coupled dissimilar waveguides, lead to tunable and narrow pass band fiber Bragg grating (FBG) filter, was proposed by . The acousto-optic tunable filters (ATOF)  utilizes interaction of optical waves and acoustic waves. Microfiber loop resonator, is another method for tunable band-pass all-fiber filter, reported by . Despite the advantages of all-fiber, tunable and narrow pass-band, these filters are somewhat complex and localized.
In this paper, we report a distributed and continuous optical band-pass filtering mechanism along the fiber using macro bending. The main advantages of the proposed filter include distributed and continuous optical band-pass filtering, filtering without additional components, broadband filtering, flexible band-pass wavelength, easy implementation and ability to be incorporated in active fibers. The spectral response of this filter is numerically and experimentally investigated. A comprehensive, spectrally and spatially resolved numerical model is developed to simulate the effect of macro bending on the fundamental mode and higher order modes. Finally, the proposed optical band-pass filter is applied in Thulium-doped fiber amplifiers (TDFA) system for gain and noise figure enhancements in S-band region.
2. Working principle of the macro-bending based optical band-pass filter
An optical band pass filter is designed to pass a specific range of wavelength. It can be accomplished by combining the properties of optical low pass and high pass filter into a single filter. The bandwidth of the filter is simply the difference between the upper (λu) and lower (λL) 3-dB cut-off wavelengths as shown in Fig. 1 . The dashed line in Fig. 1 indicates the transmission profile of an optical band pass filter while the solid line indicates the loss profile of the filter. The proposed filter leverages the bending loss of higher order modes at shorter wavelengths . A larger mode filed diameter in longer wavelengths leads to a loose confinement in the fiber core and causes higher bending loss. For shorter wavelengths below the cut-off wavelength, higher order modes will be excited. Since the higher order modes’ peak power distribution is closer to the core-cladding border, results in higher bending loss. This results in a wavelength dependent loss that realizes high loss at wavelengths shorter than λL. Subsequently, results in high loss for wavelengths longer than λu. The characteristics of the proposed optical band-pass filter can be tuned according to bending radius, fiber numerical aperture and fiber core diameter .
To understand the band pass filter mechanism using macro bending, the transversal mode field distribution of the fundamental mode and higher order modes is investigated. The transversal mode filed distributions for both straight and bent fiber are investigated for 3 different wavelengths (1800 nm, 1460 nm and 800 nm) and the result is depicted in Fig. 2 . The fiber used has a core diameter of 7.3 μm and NA of 0.0927. The bent fiber has an effective bending radius of 20 mm. Figures 2(a) and 2(b) show the mode field distribution for LP01 mode at 1800 nm for the straight and bent fiber, respectively. Figures 2(c) and 2(d) show the same distribution for 1400 nm operation. It is found that the LP01 mode at shorter wavelength region of 1460 nm is not significantly affected as compared to 1800 nm region. This is attributed to the 1460 nm signal, which has a smaller MFD, calculated to be 13.971 µm, and thus the propagating light is tightly confined in the core. At 1800 nm, the MFD is 22.461 µm, which leads to poor light confinement [12, 14]. Higher MFD at longer wavelength leads to higher bending loss  as the fiber bending radius reduces.
Figure 2(e) and 2(f) show the mode field distribution of LP11 at 800 nm for a straight and a bent fiber respectively. The LP11 mode at shorter wavelength of 800 nm is highly affected compared to other two wavelengths of 1460 nm and 1800 nm. At 800 nm, the LP11 modes’ peak power distribution is closer to the core-cladding border, resulting in poor confinement and subsequently higher bending loss [13, 15] as the fiber bending radius reduces.
Various mathematical models have been suggested to calculate the bending effects in optical waveguide. Earlier references for bending loss at single mode fibers with step index profiles were developed by Marcuse . According to Marcuse, the total loss of a macro bent fiber includes the pure bending loss and transition loss caused by mismatching between the quasi-mode of the bending fiber and the fundamental mode of the straight fiber . The analytical expression for fiber bend loss α is expressed as follow :18]:
Equation (1) agrees well with our earlier experimental results for macro-bent single-mode fiber [19, 20]. However, Eq. (3) does not consider the bending loss for higher order modes. An alternative to analytical formulae for predicting higher order modes bend loss use the beam propagation method (BPM) in conjunction with the conformal mapping technique . In BPM technique, the bent fiber is defined as straight fiber with modified reflective index distribution along the core axis x as follow:Eq. (4) and (5), the modified refractive index of the bent fiber becomes:Eq. (6) can then be used in Eq. (3) to quantify the bending loss for higher order modes. This expression can physically be explained from the perspective of mode intensity distribution, which is influenced by the fiber refractive index profile and the intermediate components such as connectors and couplers. We assume all modes carry equal power, so more portion of power distribution goes to LP11 (2xHE11 for LP01 and 2xHE21, TM01 and TE01 for LP11). Since the mode intensity distribution includes LP01 and LP11, as shown in Fig. 3(a) and 3(b) macrobending brings about the effect of mode stripping as reported in . Mode stripping causes LP01 and LP11mode to be suppressed as parts of the fundamental and higher order modes are coupled into the cladding and lost. This results in wavelength dependent bending loss for shorter wavelengths as higher modes are excited .
Figure 4 shows the calculated fiber bending loss at different wavelengths of 800nm, 1460 nm and 1800 nm in a standard single mode fiber with a core diameter of 7.3 μm and NA of 0.0927. As expected, there is a significant bending loss effect on LP11 mode compared to the LP01 mode. It also shows an exponential relationship between the bending loss, fiber bending radius and wavelength. Bending the fiber causes the guided modes to be partially coupled into the cladding layer, which in turn results in losses as earlier reported .
3. Optical band pass filter design
By utilizing the effect of macro-bending, one can then design the optical band-pass filter accordingly. The filter was designed as follows;
- I. The loss at lower cut-off wavelength λA should be 20 dB. This loss is provided by fiber bending loss of higher order modes. The value λA is influenced by fiber numerical aperture (NA), core diameter and bending radius .
- II. The loss at upper cut-off wavelength λC should also be 20 dB. The loss at this region is provided by fiber bending loss of the fundamental mode. At longer wavelengths, higher MFD leads to higher bending loss. Again, the value λC is influenced by fiber NA, core diameter and bending radius .
- III. At band-pass peak wavalength λB , the signal should propagate in fundamental mode with minimal loss.
These critiria can be achieved by designing the fiber to have higher order modes at λA and fundamental mode at λC with higher MFD. In order to determine the number of modes at specific wavelength in a step-index fiber, the normalized frequency V, is determined. When V is below 2.405, only one mode (LP01) can be guided. For V higher than 2.405, higher order modes are excited in the fiber. Figures 5(a) and 5(b) show the mapping of V versus NA for fibers in various fiber diameters for higher order mode operations at λA and single mode operations at λB.
In order to achieve higher loss at λA, the fiber’s physical parameters such as NA and core diameter are chosen to position λA as the cutoff wavelength. Criteria map for multimode at λA is shown in Fig. 5(a). A criteria map for single mode operation at λC is shown in Fig. 5(b). The fiber’s physical parameters such as NA and core diameter are chosen to position the cut-off wavelength at λC and the band-pass peak wavalength. Figure 5(c) shows the criteria mapping for both the conditions (single mode at λC and multimode at λA). The colored area denotes the NA and core diameter value pairs that allow for both the criteria.
The sample point was selected from the criteria map that fulfills both the conditions discussed above. For high pass, the cut-off wavelength was chosen at 800 nm. For low pass, the cut-off wavelength was chosen at 1000 nm. The choice of the parameter values is made in accordance with the fabrication abilities of our MCVD facilities where the core diameter is set between 4 μm and 10 μm and the NA is set between 0.02 and 0.17. The criteria mapping for high pass wavelength ranges from 700 nm to 1000 nm wavelength is demonstrated in Fig. 6(a) . Selected values in this range have the common characteristic at wavelength lower than 700 nm. Selecting the high pass wavelength ranges instead of single cut off value is due to MCVD fabrication restriction on choosing the exact NA value. Besides selecting the suitable bending loss and V parameter for choosing the high pass wavelength, the appropriate values of NA must also be considered. Smaller value of NA reduces the acceptance angle, hence reduces the coupling of incident light into the fiber . Therefore to improve the coupling efficiency, the NA of the two fibers must match. This ensures a match of the mode field diameter of light from the feed fiber and the incident fiber. NA also affects the nature of light propagation in the fiber where higher NA leads to strongly guided light. Considering above matters, the choice of NA for selected points are close to 0.16. Fiber loss spectrum for selected point at NA = 0.14 and core diameter = 5.5 nm is presented at Fig. 6(b). The bending diameter is set at 14 mm. As expected from criteria mapping diagram there is a very high loss at wavelength lower than 700 nm and zero loss at 1000 nm wavelength. Fiber loss spectrum at longer wavelength for three different bending diameters between 10 mm to 16 mm is demonstrated in inset Fig. 6(b). For bending diameters of 10mm, 12 mm, 14 mm and 16 mm the high pass wavelength (λU) of 1000 nm, 1050 nm, 1100 and 1200 nm are achieved respectively. Higher bending diameter causes higher portion of guided modes coupled into the cladding layer, which in turn increase the losses and change the high pass wavelength (λU) values. In order toshow accuracy of our hypothesis, the spectral response of Corning HI1060 fiber with specification of NA = 0.14 and cutoff wavelength 920 nm 50 nm  in bent and unbent condition was demonstrated in Fig. 6(c). In order to get spectral response, the white light source with −40 dBm input power was injected to the fiber. As expected from fiber loss spectrum, there is a high loss of −30 dbm at wavelengths shorter than the cut-off wavelength 910 nm. At wavelengths longer than 950 nm for 10 mm bending diameter, bigger MFD leads to exponential decrease in the spectral response. At bending radius of 14 mm, the same decrease is observed at wavelengths longer than 1100 nm. This is in agreement with fiber loss spectrum as shown in Fig. 6(c).
4. Optical band pass filter application on doped fiber amplifiers
Significant effort have been made in recent years to improve the doped fiber amplifier gain and noise figure. Suppression of ASE in optical amplifier at certain region is one of the effective ways to improve the gain in the other regions [22, 23]. In order to suppress ASE at certain region, different approach has been suggested. In particular, it has been demonstrated that the amplified spontaneous emission (ASE) of erbium doped fibers amplifier (EDFA) can be suppressed in the C-band region, to the advantage of the S-band region amplification [24, 25]. The suppression of ASE in the C band was achieved by exploiting the fundamental mode cutoff of the depressed cladding Erbium doped fiber or by inserting multiple filters within the amplifier module thus increasing its complexity and cost . Later on it was shown that ASE can also be suppressed by manupulating a bending loss profile in a fiber instead of adding new component in the amplifier module . For instance, a macro-bending approach was demonstrated to increase a gain and noise figure at shorter wavelength region of EDFA . The macro-bending suppresses the ASE at longer wavelength to achieve a higher population inversion at shorter wavelengths. Without the bending, the ASE peaks at 1530 nm, which is a few times higher than the ASE at the shorter wavelength, would deplete the population inversion and suppresses the gain in this region .
Thulium doped fibers has one of the emission peaks at 1470nm , which falls within the S-band. TDFA has shown good performance, especially in Fluoride host . However, there are problems of fusion splicing the fluoride based TDFA with telecommunication-grade silica fibers used for transmission and efforts have been made to develop silica based Thulium-doped fiber (TDF) . However, due to high phonon energy of silica host, the radiative lifetime at 3H4 level is very short. This produces very low gain in the S-band region. Efforts have also been made to study multi-component silica host such as aluminum to reduce the phonon energy [29, 30]. Since TDF has significant spontaneous emission at both 8 μm, and 1.8 μm wavelength bands, gain improvement in the S-band region can also be achieved by suppressing the amplified spontaneous emission (ASE) at both 8 μm and 1.8 μm bands , however no suitable method of the ASE suppression have been proposed. Figure 7 shows the normalized excited state absorption, ground state absorption and emission spectra of Tm3+ doped silica fiber. The spectral emission at S-band of Thulium ion  can be estimated by the modified McCumber’s relation from the measured absorption values .The normalized emission was demonstrated for four emission bands at 0.46 μm, 0.8 μm, 1.46 μm and 1.82 μm. These four bands were assigned to the 3H6 → 1G4, 3H6 → 3H4, 3H4 → 3F4, and 3H6 → 3F4 transitions. The spectra have been normalized to the peak at 795 nm from 3H6 → 3H4, The measured normalized emission cross section rate at 0.46 μm, 0.8 μm, 1.46 μm and 1.82 μm bands are 0.31, 0.98, 0.27 and 0.72, respectively. Poor branching ratio of transitions from 3H6 to ground has led to higher emission at 800 nm. Furthermore, the emission at 1800 nm is also significantly higher than 1400 nm. These result in stronger ASEs at 800 nm and 1800 nm compared to the intended amplification region at 1400 nm.
For lasing and amplification at telecommunication band of 1470 nm, there is a wide choice of available pump wavelengths that is available including 14xx nm, 1050 nm and etc . In some cases, pumping at two wavelengths such as 14xx nm + 1560 nm, 1050 nm + 1560 nm, 14xx nm + 800 nm and 1050 nm + 800 nm can be used to increase the performance of the laser and amplifier . Figures 8(a) , 8(b) and 8(c) show the pump mechanism of 1420 nm, 1050 nm and 1560 nm respectively. The emission transitions of trivalent Thulium ions in silica glass shows in Fig. 8(d) . As shown in Fig. 8(d), the main transition used for S-band amplification is between 3H4 and 3F4 levels, which emit photons at 1460 nm region. This amplification is made possible by an up-conversion pumping method, which forms a population inversion between 3H4 and 3F4 levels. 1050 nm and 1420 nm pump alone can provide both the ground-state and excited-state absorptions . However, excited state absorption from 3H4 to 1G4 energy level reduces the population of the 3H4 energy level. Therefore, an auxiliary pump source at 1560 nm is used to excite the 3H6 energy level ions and increase the population of 3F4 energy level.
The performance of TDFA can be improved by suppressing the ASE, both at 1800 nm and 800 nm . The macro-bending introduced in the TDF can behave as a distributed filter to suppress ASE both at 1800 nm and 800 nm. In order for macro bending to be utilized effectively as an ASE filter, the fiber’s physical dimensions will have to be optimized first. The objective of this optimization is to suppress the ASE by the following criteria:
- I. The pump at 1050 nm, 1420 nm and 1560 nm has to be propagating in fundamental mode in order to maximize the overlap factor and Thulium absorption.
- II. The 1460 nm signals will be propagating in fundamental mode with zero loss.
- III. The 800 nm ASE has to be propagating with higher order modes.
- IV. The 1800 nm ASE has higher bending loss.
In order to design the filter to address the above criteria, the filter should have the specification as λA = 800 nm, λB = 1050 nm~1550 and λC = 1800 nm. Figure 9(a) shows the criteria mapping for both single mode at 1050 nm and multi-mode at 800 nm. The shaded area denotes the NA and core diameter value pairs that allow for both multi-mode operations at 800 nm and single-mode operations at 1050 nm. The cut-off wavelength is set for 1000 nm. In order to further optimize the bending loss at 1460 nm and 1800 nm, six points from different parts of the shaded area in Fig. 9(a) are selected.
The bending loss as a function of wavelength with bending radius of 10 mm at the six selected points is shown in Fig. 9(b). The main objective of this figure is to find the optimized fiber radius and NA for high suppression of ASE at 1800 nm and minimal suppression at 1460 nm S-band region. As shown in Fig. 9(b), for Selected Point A, D and F at bending radius 10 mm, there is a high loss at 1460 nm wavelength and it is sensitive to bending diameter sit is not a good choice for fiber fabrication. At the selected bending diameter there is zero loss at 1800 nm wavelength for selected point B and C. Therefore, area near selected point E is the optimized fiber radius and NA for high suppression of ASE at 1800 nm and minimal suppression at 1460 nm S-band region. In optimizing the TDFA, besides bending loss and V parameter, the appropriate values of NA must also be considered. Smaller value of NA reduces the acceptance angle, hence reduces the coupling of incident light into the TDF . Subsequently, to improve the coupling efficiency, the NA of the two fibers must match. This ensures a match of the mode field diameter of the light from the feed fiber and the incident fiber. The NA also affects the nature of light propagation in the fiber where higher NA leads to strongly guided light. Besides this, the NA also affects the overlap factor  that subsequently affects the performance of the TDFA. Considering above matters the choice of NA should be close to 0.14.
In the proposed TDF, 800 nm amplified spontaneous emission (ASE) is distributed over LP01 and LP11 modes, which are influenced by the fiber refractive index profile and the intermediate components such as connectors and couplers. The ASE power dynamics are related to different factors such as, overlap factor, doping concentration and doping profile of Thulium. We assume all modes carry equal power, so more portion of power distribution goes to LP11. (2xHE11 for LP01 and 2xHE21,TM01 and TE01 for LP11). In the case of using 790 nm auxiliary pump, the pump power is distributed over LP01 and LP11 modes. Bending of the fiber causes high bending loss in the LP11 modes. This makes pumping at 790 nm in the bent fiber less effective unless the fiber cut-off wavelength is designed at less than 790 nm. Hence, using 790 nm auxiliary pump in the bent fiber is not recommended in this TDFA design.
Figure 8(c) shows the configuration of the TDFA, which consists of a silica-based TDF co-doped with aluminum, a WDM coupler, a pump laser and two optical isolators. The pump light and the input signal are combined using the WDM coupler. A 1050 nm laser diode is used as the pump. Thulium concentration is 1.68 × 1025 1/m3, core diameter is 7.3 μm and NA is 0.115. Figure 10 shows the experimental ASE spectrum at normal and bent conditions for different wavelength ranges. It also shows the bending loss spectrum. The fiber length is fixed at 5 m and 1050 nm pump power is 150 mW. Bending radius is 3 cm. As shown at Fig. 10, the bending loss starts to be significant at around 1600 nm wavelength and increases exponentially with wavelength. Due to high loss at 800 nm even in normal bending diameter and high connection loss, ASE value is measured to be very low compared to the real value. The suppression of 800 nm and 1800 nm ASE results in the increased ASE power at 1400 nm band.
Figure 11 shows the experimental variation of the gain and noise figure across the input signal wavelength for the TDFA with and without macro-bending. The input signal and 1050-nm pump powers are fixed at −30 dBm and 250 mW, respectively. The bending radius is set at 12 mm in the case of the amplifier with macro-bending. As shown in the figure, gain enhancements of about 2 dB are obtained with macro-bending at a wavelength region between 1440 and 1500 nm. This enhancement is attributed to the macro bending effect, which suppresses the ASE at 800nm and 1800 nm. On the other hand, the noise figure is also improved by about 0.5 dB with the macro-bending as also shown in Fig. 11. This is attributed to the increase in the gain with micro bending, which affects the noise figure as described in the standard noise figure Eq . Increasing the pump power lead to more gain and noise improve due to higher ASE suppression rates at 800nm and 1800 nm.
A new optical band pass filtering technique has been demonstrated using macro bending approach. The filter characteristics of λA, λB, λC wavelengths have been defined and manipulated to achieve a desired filtering profile. The high loss at shorter wavelength of λA and zero loss at wavelength of λB in high pass filter is provided by fiber bending of multimode propagation of light which is optimized by fiber numerical aperture and fiber core diammeter. The loss at longer wavelength of λC is provided by fiber bending loss of single mode propagation of light due to higher signal mode field diameter (MFD) lead to higher loss at bending situation. A smaller filed diameter in shorter wavelength indicates that ligth more tightly confined to the fiber center and therfore, is less prone to leakage when power is bent. In order to show the filter flexibility, the optical band pass filter for four different ranges of wavelengths has been demonstrated. The sample point was selected from criteria map of wavelength ranges λA and λB and the bending diameter have been optimized to achieve the desirable λc. The application of proposed filter on gain enhancement in S-band Thulium-doped fiber amplifier (TDFA) has been demonstrated using a macro-bending approach. Macro-bending the doped fiber in a small radius suppresses both the amplified spontaneous emissions (ASEs) at 800nm and 1800 nm band and thus increases the population inversion in the S-band region. The NA and core radius of the doped fiber are optimized so that 800 nm ASE propagates with higher order modes to achieve a significant suppression while the loss is maintained at a minimum level in the S-band region. Meanwhile, the 1050 nm, 14xx nm and 1550 nm main Thulium pump wavelengths propagate in the fundamental mode to maximize the overlap factor and Thulium ion absorption so that the ASE loss is significant at 1800 nm region. Gain enhancements of about 2~3 dB are obtained with macro bending at the wavelength region between 1420 and 1480 nm. Concurrently, the macro-bending also improves the noise figure by about 0.5 to 2 dB within this wavelength region.
We will like to acknowledge the financial support from University Malaya/MOHE under grant number UM.C/HIR/MOHE/SC/01.
References and links
1. N. A. Riza and S. Sumriddetchkajorn, “Fault-tolerant dense multiwavelength add-drop filter with a two-dimensional digital micromirror device,” Appl. Opt. 37(27), 6355–6361 (1998). [CrossRef]
2. D. S. Ferreira, J. Mirkovic, R. F. Wolffenbuttel, J. H. Correia, M. S. Feld, and G. Minas, “Narrow-band pass filter array for integrated opto-electronic spectroscopy detectors to assess esophageal tissue,” Biomed. Opt. Express 2(6), 1703–1716 (2011). [CrossRef]
3. S. H. Yun, B. W. Lee, H. K. Kim, and B. Y. Kim, “Dynamic erbium-doped fiber amplifier based on active gain flattening with fiber acoustooptic tunable filters,” IEEE Photon. Technol. Lett. 11(10), 1229–1231 (1999). [CrossRef]
4. M. S. Yataki, D. N. Payne, and M. P. Varnham, “All-fiber wavelength filters using concatenated fused-taper couplers,” Electron. Lett. 21(6), 248–249 (1985). [CrossRef]
5. R. Zengerle and O. G. Leminger, “Wavelength-selective directional coupler made of nonidentical single-mode fibers,” J. Lightwave Technol. 4(7), 823–827 (1986). [CrossRef]
6. K. Okamoto and J. Noda, “Fiber-optic spectral filter consisting of concatenated dual-core fibers,” Optical Fiber Communication Conference (OFC), Atlanta, Georgia (February 24, 1986).
7. A. Safaai-Jazi and J. C. Mckeeman, “All-fiber spectral filters with nonperiodic bandpass characteristics and high extinction ratios in the wavelength range 0.8 Mu-M Less-Than Lambda Less-Than 1.6 Mu-M,” J. Lightwave Technol. 9, 959–963 (1991). [CrossRef]
8. N. Imoto, “An analysis for contradirectional-coupler-type optical grating filters,” J. Lightwave Technol. 3(4), 895–900 (1985). [CrossRef]
9. W. P. Huang and J. Hong, “A coupled-waveguide grating resonator filter,” IEEE Photon. Technol. Lett. 4(8), 884–886 (1992). [CrossRef]
10. K. W. Cheung, D. A. Smith, J. E. Baran, and J. J. Johnson, “1 Gb/S System performance of an integrated, polarization-independent, acoustically-tunable optical filter,” IEEE Photon. Technol. Lett. 2(4), 271–273 (1990). [CrossRef]
11. Y. Wu, X. Zeng, C. L. Hou, J. Bai, and G. G. Yang, “A tunable all-fiber filter based on microfiber loop resonator,” Appl. Phys. Lett. 92(19), 191112 (2008). [CrossRef]
12. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–717 (1977).
14. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, NY, 1997).
15. R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007). [CrossRef]
16. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. B 66(3), 216–220 (1976). [CrossRef]
17. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66(4), 311–320 (1976). [CrossRef]
18. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, NY, 1982).
19. J. J. R., “Optical fiber communication system comprising mode-stripping means,” US patent (1990).
20. M. Bigot-Astruc, D. Molin, P. Nouchi, P. Matthijsse, L. De Montmorillon, Y. Lumineau, I. Flammer, P. Sillard, and F. Gooijer, “Single mode optical fiber with low bending losses,” European Patent (2006).
21. C. HI1060, “Single-mode component fiber for high performance photonic applications,” (2003).
22. S. A. Daud, S. D. Emami, K. S. Mohamed, N. M. Yusoff, L. Aminudin, H. H. Abdul-Rashid, S. W. Harun, H. Ahmad, M. R. Mokhtar, Z. Yusoff, and F. A. Rahman, “Gain and noise figure improvements in a shorter wavelength region of EDFA using a macrobending approach,” Laser Phys. 18(11), 1362–1364 (2008). [CrossRef]
23. S. A. Daud, S. D. Emami, K. S. Mohamed, H. A. Abdul-Rashid, S. W. Harun, H. Ahmad, M. R. Mokhtar, Z. Yusoff, and F. A. Rahman, “Shorter wavelength gain shift In EDFA Using a macro-bending approach,” 2008 IEEE Photonicsglobal@Singapore (Ipgc), Vols 1 and 2, 412–414 (2008).
24. M. Z. Zulkifli, M. H. Jemangin, S. W. Harun, and H. Ahmad, “Gain-flattened S-band depressed cladding erbium doped fiber amplifier with a flat bandwidth of 12 nm using a Tunable Mach-Zehnder Filter,” Laser Phys. 21(9), 1633–1637 (2011). [CrossRef]
26. P. R. Watekar, S. Ju, and W. T. Han, “A small-signal power model for Tm-doped silica-glass optical fiber amplifier,” IEEE Photon. Technol. Lett. 18(19), 2035–2037 (2006). [CrossRef]
27. R. M. Percival, “Highly efficient 1.064 μm upconversion pumped 1.47 μm thulium doped fluoride fibre laser,” Electron. Lett. 30, 1684–1685 (1994). [CrossRef]
28. P. R. Watekar, S. Ju, and W. T. Han, “Analysis of 1064-nm pumped Tm-doped silica glass fiber amplifier operating at 1470 nm,” J. Lightwave Technol. 25(4), 1045–1052 (2007). [CrossRef]
29. B. Faure, W. Blanc, B. Dussardier, and G. Monnom, “Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy,” J. Non-Cryst. Solids 353(29), 2767–2773 (2007). [CrossRef]
30. B. Faure, W. Blanc, B. Dussardier, G. Monnom, and P. Peterka, “Thulium-doped silica-fiber based S-band amplifier with increased efficiency by aluminum co-doping,” Optical Amplifiers and Their Applications Conference, San Francisco, California (2004).
31. P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, “Theoretical modelling of S-band thulium-doped silica fibre amplifiers,” Opt. Quantum Electron. 36(1-3), 201–212 (2004). [CrossRef]
32. J. Michael and F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers (CRC Press, 2001).
33. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (John Wiley & Sons, NY, 1994).
34. S. S. H. Yam and J. Kim, “Ground state absorption in thulium-doped fiber amplifier: Experiment and modeling,” IEEE J. Sel. Top. Quantum Electron. 12(4), 797–803 (2006). [CrossRef]
35. Y. Yano and T. Ono, “1.49-μm-band gain-shifted thulium-doped fiber amplifier for WDM transmission systems,” J. Lightwave Technol. 20(10), 1826–1838 (2002). [CrossRef]