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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 8 — Apr. 9, 2012
  • pp: 8568–8574
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A self-coupling multi-port microcoil resonator

Rand Ismaeel, Timothy Lee, Feras Al-Saab, Yongmin Jung, and Gilberto Brambilla  »View Author Affiliations


Optics Express, Vol. 20, Issue 8, pp. 8568-8574 (2012)
http://dx.doi.org/10.1364/OE.20.008568


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Abstract

A new type of self-coupling multi-port microcoil resonator using a microfiber coupler is presented. The microresonators, a simple combination of a microfiber coupler and microcoil resonator, were fabricated by coiling a four port microfiber coupler around a low index support rod to induce optical resonance via coupling between adjacent turns. Light propagates along the coil whilst the beating between the supermodes of the coupler is still present, giving an increased extinction ratio and an output spectrum strongly dependent on the microfiber coupler diameter. The multiport microcoil resonator was embedded in a low refractive index polymer to improve its robustness and the polarization dependence was further analyzed.

© 2012 OSA

1. Introduction

Optical microfiber resonators [1

1. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7(6), 288–290 (1982). [CrossRef] [PubMed]

4

4. G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

] have gained a great interest in a variety of fields, due to their easy configurability with fiberized components, low-cost, ease of manufacture, strong evanescent fields and relatively high quality factor (Q-factor up to 2.2 × 105) [5

5. Y. Jung, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high-Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

]. Microfibers with a diameter of a few micrometers are particularly suited for fabricating such compact devices due to their flexibility and ease of bending without any measurable losses [2

2. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

,4

4. G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

]. Three different types of micro-resonators have been demonstrated from a single strand of microfiber to date, including loop resonators [1

1. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7(6), 288–290 (1982). [CrossRef] [PubMed]

], knot resonators [2

2. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

] and microcoil resonators (MCRs) [3

3. M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004). [CrossRef] [PubMed]

]. In particular, MCRs were first proposed theoretically in ref. 3

3. M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004). [CrossRef] [PubMed]

and then implemented experimentally in ref. 6

6. F. Xu and G. Brambilla, “Manufacture of 3-D microfiber coil resonators,” IEEE Photon. Technol. Lett. 19(19), 1481–1483 (2007). [CrossRef]

, with subsequent research introducing a new pack of applications in optical sensing [7

7. F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett. 92(10), 101126 (2008). [CrossRef]

, 8

8. M. Belal, Z. Song, Y. Jung, G. Brambilla, and T. P. Newson, “Optical fiber microwire current sensor,” Opt. Lett. 35(18), 3045–3047 (2010). [CrossRef] [PubMed]

], fast/slow light [9

9. N. G. Broderick, “Optical snakes and ladders: dispersion and nonlinearity in microcoil resonators,” Opt. Express 16(20), 16247–16254 (2008). [CrossRef] [PubMed]

] and optical delay lines [10

10. M. Sumetsky, “Optical microfiber coil delay line,” Opt. Express 17(9), 7196–7205 (2009). [CrossRef] [PubMed]

]. However, some applications in this area (mostly sensors) require multi-port channels and attempts for achieving four port micro-resonators included a reef knot (multiport equivalent of the knot resonator) [11

11. G. Vienne, A. Coillet, P. Grelu, M. El Amraoui, J. C. Jules, F. Smektala, and L. Tong, “Demonstration of a reef knot microfiber resonator,” Opt. Express 17(8), 6224–6229 (2009). [CrossRef] [PubMed]

] and racetrack resonators (equivalent of the loop resonator) [12

12. Y. Jung, G. Brambilla, G. S. Murugan, and D. J. Richardson, “Optical racetrack ring-resonator based on two U-bent microfibers,” Appl. Phys. Lett. 98(2), 021109 (2011). [CrossRef]

]. In this paper, we propose a new type of multi-port microcoil resonator (MMCR), which is the multiport equivalent of the MCR. The MMCR is based on a microfiber coupler (MC) wrapped around a low index support rod, thus offering the potential benefits of both the MCR and the fiber coupler. This resonator promises to serve all the applications that utilize the MCR; however the interesting features of MMCR such as the high polarization dependent extinction ratio and/or the physical separation between the output ports could be exploited in applications such as optical sensing, integrated optical switches and modulators.

2. MMCR fabrication

The proposed MMCRs as shown in Fig. 1
Fig. 1 Schematic of the MMCR: two microfibers are fused together at high temperature and later coiled around a low-index support rod. Ports 1 and 2 are the inputs whilst ports 3 and 4 are the outputs.
were fabricated in three steps: first, a MC was fabricated from two 125 μm diameter standard telecom fibers (Corning SMF-28) using the microheater brushing technique [4

4. G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

]; then, the MC was wrapped around a low refractive-index support rod in a self-coupling coil; finally, the coiled MC was embedded in a low refractive index polymer matrix which was cured to enhance sturdiness. ~100 mm long sections of two single mode fibers were stripped of their coating and twisted 1.5 turns around each other to ensure the two fibers were in close contact before being fused together using a ceramic heater at an estimated fusing temperature of ~1450 °C. In our experiment, two different microfiber couplers were fabricated with waist diameters of d~3.2 µm (MC1) and d~0.7 µm (MC2) respectively. In both MCs, the lengths of the uniform waist region were 4 mm and the adjacent transition regions were ~3 cm. These dimensions were chosen to facilitate handling and simultaneously provide a large distance (~40 nm) between two consecutive maxima in the output ports spectra, so the coupler’s spectral features can be easily distinguished from the resonator resonances.

First of all, we investigated the output spectra of the microfiber coupler using an optical spectrum analyzer (Yokogawa, AQ6370) while the input port was connected to an incoherent white light source (Bentham, WLS100). Figure 2(a)
Fig. 2 Output spectra of two microfiber couplers; the taper waist diameters were d~3.2 µm for MC1 (a) and d~0.7 µm for MC2 (b). An incoherent white light source was connected to input port 1 and the output ports 3 and 4 were analyzed using optical spectrum analyzer.
clearly shows the oscillation pattern typical of beating between supermodes [13

13. B. S. Kawasaki, K. O. Hill, and R. G. Lamont, “Biconical-taper single-mode fiber coupler,” Opt. Lett. 6(7), 327–328 (1981). [CrossRef] [PubMed]

] over the whole investigated spectral range [14

14. Y. Jung, G. Brambilla, and D. J. Richardson, “Optical microfiber coupler for broadband single-mode operation,” Opt. Express 17(7), 5273–5278 (2009). [CrossRef] [PubMed]

], while Fig. 2(b) presents high frequency oscillations only at wavelengths smaller than λ<1.05 μm, due to higher order mode filtering [14

14. Y. Jung, G. Brambilla, and D. J. Richardson, “Optical microfiber coupler for broadband single-mode operation,” Opt. Express 17(7), 5273–5278 (2009). [CrossRef] [PubMed]

]. The fabricated MCs were coiled around a 1 mm diameter glass rod coated with Teflon (refractive index n~1.31 at λ = 1.55 μm) using a computer controlled set of rotation and linear stages [4

4. G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

]. The distance between adjacent turns was about 3.5 μm and coiling was carried out until sharp resonance peaks appeared (typically after 720°).

Figure 3(a)
Fig. 3 (a) Microscope image of the coupler (MC1) coiled on the support rod coated with Teflon; spacing between adjacent loops in the coil is ~3.5µm. (b) SEM image of the microcoupler cross section.
shows an optical microscope image of the coiled MC1 and a cross sectional scanning electron microscope (SEM) image at the microfiber waist is shown in Fig. (b). In fact, because of the low fabrication temperature, the MC exhibits a dumbbell cross section and longitudinal rotations considerably complicate the overall interloop coupling properties. The final microresonator was packaged with ultra-violet (UV) curable polymer (Luvantix PC-373) to enhance their stability. Normally, a resonance shift and optical loss increase are introduced as a result of the large index difference between the air and polymer, but the latter effect can be minimized using techniques explained in Ref. 5

5. Y. Jung, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high-Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

.

3. Experimental MMCR spectral characterization

Figure 4
Fig. 4 The power spectra of MMCR1 (a,b) and MMCR2 (c,d) when light is injected into port 1. (a,c) report spectral changes during MMCR fabrication, while (b, d) show the spectra in final devices.
shows the optical resonance spectra for both output ports in two MMCRs, all exhibiting sharp resonances similar to those previously well-reported MCR [6

6. F. Xu and G. Brambilla, “Manufacture of 3-D microfiber coil resonators,” IEEE Photon. Technol. Lett. 19(19), 1481–1483 (2007). [CrossRef]

]. However, the additional degree of coupling present in the MC complicates the MMCR spectra; in fact, the output ports seem to be complementary to each other in sample MC1 Fig. 4(b) and similar in MC2 (Fig. 4(d).The explanation behind the different behaviour may lie in the different number of supermodes supported by the MC used to make the different MMCRs. MMCR1 Fig. (4b) has a relatively large waist diameter; thus it supports several supermodes which beat and give the complementary output characteristic of couplers.

At resonances, light simply traverses a longer optical path within the MMCR and the output spectra depend on the relative phase difference between the two supermodes. For this reason, the maxima of port 3 coincide to the minima of port 4 and vice versa. On the other hand, in MMCR2 Fig. 4(d) output spectra maxima and minima of port 3 and 4 coincide; i.e. no complimentary behaviour was noticed. This could be attributed to the fact that the narrower waist of this coupler can support only one supermode, which makes the spectra of the MMCR2 very similar to the well-known MCR, and power is simply split at the output ports in a similar ratio. However, this device still shows some modulation in the resonance extinction ratio as shown in Fig. 4(c); these oscillations are believed to arise in the transition region of the coupler, where beating between the supermodes could still exist. MMCR2 has considerably higher losses than that of MMCR1 and its fabrication is also more challenging. Similar to loop and knot resonators, MMCRs are expected to be polarization dependent and therefore we investigated the transmission of MMCR1 for linearly polarized light with different polarization angles. As shown in Fig. 5(a)
Fig. 5 Polarization effects in the MMCR1. (a) Output spectra of MMCR1 port 3 when linearly polarized light is injected in port 1. (b) Dependence of the extinction ratio on the polarization azimuthal angle.
, the change in polarization azimuth results in a small shift in the resonance wavelength (0.0616 nm), accompanied by an enhancement in the extinction ratio, which can reach values >20 dB as shown in Fig. 5(b). Compared to a standard MCR, the MMCR extinction ratio at port 3 is relatively high because power injected in port 1 is reduced both by loss and by power exchange into port 4.

4. Modelling

Numerical modelling has been carried out to prove that the secondary resonance peaks and the complimentary behaviour of the resonance peaks in different output ports are an intrinsic feature of the MMCR1 and that they do not arise from external experimental factors such as fabrication tolerances and/or polarization. Simulations focus on MMCR1, as MMCR2 behaves like an MCR, which has been modelled in [3

3. M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004). [CrossRef] [PubMed]

, 6

6. F. Xu and G. Brambilla, “Manufacture of 3-D microfiber coil resonators,” IEEE Photon. Technol. Lett. 19(19), 1481–1483 (2007). [CrossRef]

-7

7. F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett. 92(10), 101126 (2008). [CrossRef]

, 9

9. N. G. Broderick, “Optical snakes and ladders: dispersion and nonlinearity in microcoil resonators,” Opt. Express 16(20), 16247–16254 (2008). [CrossRef] [PubMed]

-10

10. M. Sumetsky, “Optical microfiber coil delay line,” Opt. Express 17(9), 7196–7205 (2009). [CrossRef] [PubMed]

]: while in a common MCR resonances arise from interloop coupling of the fundamental mode propagating in a single microfiber, in MMCR2 they are created by a single supermode propagating in the coupler. In a coupler, light exchange between the two arms is due to beating between supermodes excited by a single mode at the input port. MMCR1 was modelled using the schematic shown in Fig. 6
Fig. 6 Cross section of the multiport microcoil resonator; two types of coupling exist in this resonator: the first one (κ1) between the fibres composing the coupler, the second (κ2) between different turns of the coil.
.

Equations that describe light propagation/coupling inside an MCR [3

3. M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004). [CrossRef] [PubMed]

] were adapted to include coupling between different fibres composing the coupler [6

6. F. Xu and G. Brambilla, “Manufacture of 3-D microfiber coil resonators,” IEEE Photon. Technol. Lett. 19(19), 1481–1483 (2007). [CrossRef]

, 15

15. K. Okamoto, “Fundamentals of optical waveguides,” Academic Press, (2006).

] in addition to the conventional coupling to the next/previous turn, as given by Eqs. (1-2):

dA2j1ds=iκ1A2j+ik2A2j2
(1)
dA2jds=iκ1A2j1+ik2A2j+1
(2)

Here Aj(s)represents the amplitude of the electric field component in the jthturn of the coil at a distances along the turn which has a total lengthL. Note that each arm of the coupler is assigned a separate field amplitude. βrepresents the propagation constant of the mode β=2πneff/λ . The transmissivity T=An(L)exp(iβL)/A1(0) was calculated from numerical solution of Eqs. (1-2) subject to the boundary conditions of field continuity between turns as in [3

3. M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004). [CrossRef] [PubMed]

]. The coupling κ2between neighboring turns of a microcoil is typically of the order of 103 m−1 [9

9. N. G. Broderick, “Optical snakes and ladders: dispersion and nonlinearity in microcoil resonators,” Opt. Express 16(20), 16247–16254 (2008). [CrossRef] [PubMed]

]; to ensure sharp resonances, κ2was chosen to be 5600 m−1 (i.e. near to critical coupling). The internal coupling κ1of the MC was evaluated from SEM pictures of the MC1 cross section (Fig. 3b). The image of the cross section of the coupler was imported to COMSOL to calculate the effective index of the supermodes and thereby calculate the value ofκ1, which resulted to be κ1 = 36140 m−1. Figure 7
Fig. 7 Simulated mode profiles at the center of MC1. (a) The odd supermode neff = 1.404. (b) The even supermode neff = 1.427. (c) The electric field amplitude of the modes.
Shows the odd and even supermode profiles in the MC1 waist. The even supermode in Fig. 7(a) and green line in Fig. 7(c) is similar to the fundamental mode in single mode fibers.

Although κ1could vary considerably with any change in geometry, its value nonetheless remains in the range of 104 m−1. Simulation results are shown in Fig. 8(a)
Fig. 8 (a) Simulated transmissivity of the MMCR1. Light is injected from port 1 and collected at ports 3 and 4. (b) The output power spectrum for port 3 and 4 of MMCR1 when light is injected in port 1 andκ1is varied. The complimentary behavior is noticed between the two output ports.
and clearly resemble experimental results: in both experiments and simulations the output power of the output ports are complementary and show closely spaced multiple peaks. This can be ascribed to more light coupling at resonance and less coupling off resonance, as a result of the different effective optical paths experienced by light propagating inside the resonator.

Note that an equivalent MCR with the same κ2and geometry would only show one resonance per free spectral range (FSR), whereas Fig. 8a clearly shows several resonances per FSR. MMCR can therefore exhibit certain traits normally found in MCRs with higher number of turns (N = 6). Figure 8(b) shows the effects of the coupler coupling coefficient on the output over one free spectral range. It is clear that the transmission is strongly dependent on even small variations ofκ1. In particular, for κ1 near the critical coupling (κc~3.6 × 104 m−1), the spectrum contains two resonances per FSR, in agreement with Fig. 4(b), whereas further away from κceach resonance undergoes splitting.

6. Conclusions

In summary, a new type of a four port micro-resonator (the MMCR) has been fabricated by coiling a micro-coupler with specific dimensions around a support rod. By varying the diameter of the coupler minimum waist, it has been possible to control the output spectra: at a small coupler diameter ~700nm the MMCR behaves exactly as an ordinary MCR. This device can have high extinction ratios (~20 dB) and it is highly polarization dependent. These properties make the MMCR a promising device for microfiber devices and sensors, where sharp resonances and physical separation between output signals are important.

References and links

1.

L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7(6), 288–290 (1982). [CrossRef] [PubMed]

2.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

3.

M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004). [CrossRef] [PubMed]

4.

G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

5.

Y. Jung, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high-Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

6.

F. Xu and G. Brambilla, “Manufacture of 3-D microfiber coil resonators,” IEEE Photon. Technol. Lett. 19(19), 1481–1483 (2007). [CrossRef]

7.

F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett. 92(10), 101126 (2008). [CrossRef]

8.

M. Belal, Z. Song, Y. Jung, G. Brambilla, and T. P. Newson, “Optical fiber microwire current sensor,” Opt. Lett. 35(18), 3045–3047 (2010). [CrossRef] [PubMed]

9.

N. G. Broderick, “Optical snakes and ladders: dispersion and nonlinearity in microcoil resonators,” Opt. Express 16(20), 16247–16254 (2008). [CrossRef] [PubMed]

10.

M. Sumetsky, “Optical microfiber coil delay line,” Opt. Express 17(9), 7196–7205 (2009). [CrossRef] [PubMed]

11.

G. Vienne, A. Coillet, P. Grelu, M. El Amraoui, J. C. Jules, F. Smektala, and L. Tong, “Demonstration of a reef knot microfiber resonator,” Opt. Express 17(8), 6224–6229 (2009). [CrossRef] [PubMed]

12.

Y. Jung, G. Brambilla, G. S. Murugan, and D. J. Richardson, “Optical racetrack ring-resonator based on two U-bent microfibers,” Appl. Phys. Lett. 98(2), 021109 (2011). [CrossRef]

13.

B. S. Kawasaki, K. O. Hill, and R. G. Lamont, “Biconical-taper single-mode fiber coupler,” Opt. Lett. 6(7), 327–328 (1981). [CrossRef] [PubMed]

14.

Y. Jung, G. Brambilla, and D. J. Richardson, “Optical microfiber coupler for broadband single-mode operation,” Opt. Express 17(7), 5273–5278 (2009). [CrossRef] [PubMed]

15.

K. Okamoto, “Fundamentals of optical waveguides,” Academic Press, (2006).

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(140.4780) Lasers and laser optics : Optical resonators
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Integrated Optics

History
Original Manuscript: January 18, 2012
Revised Manuscript: February 14, 2012
Manuscript Accepted: February 14, 2012
Published: March 28, 2012

Citation
Rand Ismaeel, Timothy Lee, Feras Al-Saab, Yongmin Jung, and Gilberto Brambilla, "A self-coupling multi-port microcoil resonator," Opt. Express 20, 8568-8574 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8568


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References

  1. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett.7(6), 288–290 (1982). [CrossRef] [PubMed]
  2. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003). [CrossRef] [PubMed]
  3. M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express12(10), 2303–2316 (2004). [CrossRef] [PubMed]
  4. G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt.12(4), 043001 (2010). [CrossRef]
  5. Y. Jung, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high-Q,” IEEE Photon. Technol. Lett.22, 1638–1640 (2010).
  6. F. Xu and G. Brambilla, “Manufacture of 3-D microfiber coil resonators,” IEEE Photon. Technol. Lett.19(19), 1481–1483 (2007). [CrossRef]
  7. F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett.92(10), 101126 (2008). [CrossRef]
  8. M. Belal, Z. Song, Y. Jung, G. Brambilla, and T. P. Newson, “Optical fiber microwire current sensor,” Opt. Lett.35(18), 3045–3047 (2010). [CrossRef] [PubMed]
  9. N. G. Broderick, “Optical snakes and ladders: dispersion and nonlinearity in microcoil resonators,” Opt. Express16(20), 16247–16254 (2008). [CrossRef] [PubMed]
  10. M. Sumetsky, “Optical microfiber coil delay line,” Opt. Express17(9), 7196–7205 (2009). [CrossRef] [PubMed]
  11. G. Vienne, A. Coillet, P. Grelu, M. El Amraoui, J. C. Jules, F. Smektala, and L. Tong, “Demonstration of a reef knot microfiber resonator,” Opt. Express17(8), 6224–6229 (2009). [CrossRef] [PubMed]
  12. Y. Jung, G. Brambilla, G. S. Murugan, and D. J. Richardson, “Optical racetrack ring-resonator based on two U-bent microfibers,” Appl. Phys. Lett.98(2), 021109 (2011). [CrossRef]
  13. B. S. Kawasaki, K. O. Hill, and R. G. Lamont, “Biconical-taper single-mode fiber coupler,” Opt. Lett.6(7), 327–328 (1981). [CrossRef] [PubMed]
  14. Y. Jung, G. Brambilla, and D. J. Richardson, “Optical microfiber coupler for broadband single-mode operation,” Opt. Express17(7), 5273–5278 (2009). [CrossRef] [PubMed]
  15. K. Okamoto, “Fundamentals of optical waveguides,” Academic Press, (2006).

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