Abstract

An in-line interferometer based on the intermodal coupling of a multicore fiber (MCF) is proposed and experimentally demonstrated. The in-line interferometer is fabricated by adiabatically tapering the MCF. The intermodal coupling of the in-line interferometer is strongly affected by the waist diameter of the MCF, which changes the evanescent field and the pitch size. The effect of the waist diameters of the MCF on the intermodal coupling in the in-line interferometer is theoretically and experimentally investigated. The transmission oscillations of the multiple core modes resulting from the intermodal coupling and interference substantially become stronger as the waist diameter decreases. The extinction ratio and the oscillation periodicity of the transmissions oscillations are changed by the waist diameter.

© 2015 Optical Society of America

1. Introduction

Rapid traffic growth and the limitation of the transmission capacity of a single mode fiber (SMF) will cause a capacity crunch in the near future. A possible solution to increase the transmission capacity is the multicore fiber (MCF) as it has high core density and low loss [1–4 ]. The coupled waveguide array for nonlinear pulse shaping by tapering the MCF was proposed [5]. The special properties of the MCF, such as small size, well defined core separation, and good thermal stability, have led to much interest in fiber optic sensing. Fiber Bragg gratings inscribed in a four-core MCF provides a simple technique to measure the two-axis curvature [6]. It was reported that the MCF-based multimode interference device is capable of measuring temperature up to 1000°C [7, 8 ]. In previous reports [7, 8 ], the MCF with small pitch size supports multiple supermodes. Then the multimode interference between two supermodes for the condition of center core excitation can be obtained by splicing the MCF with conventional single-mode fibers (SMFs) [7, 8 ]. The interference spectrum between two supermodes could be adjusted by changing the length of the MCF. As alternative, monolithic modal interferometers using polarization [9], multimode fibers [10], twin-core fibers (TCF) [11–13 ] or a suspended multicore fiber [14] have been proposed. The modal interference can be simply generated by splicing the TCF to the SMF. In this paper, an in-line interferometer based on the MCF is proposed and experimentally demonstrated. The in-line interferometer is fabricated by adiabatically tapering the MCF. The transmission oscillation of the in-line interferometer resulting from the intermodal coupling and interference among multiple core modes is generated. The waist diameter of the MCF plays an important role in the coupling strength among multiple core modes in the in-line interferometer. The effect of the waist diameter of the MCF on the transmission characteristics of the in-line interferometer is investigated theoretically and experimentally. Since the evanescent fields of all the core modes and the pitch size of the MCF is remarkably changed by the waist diameter of the MCF, the transmission oscillations of the in-line interferometer resulting from the intermodal coupling should be changed. The waist diameter of the adiabatically tapered MCF dominantly controls the transmission characteristics of the in-line interferometer.

2. Fabrication and operation principle

Figures 1(a) and 1(b) show the structure and the scanning electron microscopy (SEM) image of the fabricated MCF, respectively. The MCF has seven Ge-doped cores surrounded by pure silica cladding. The pitch size (Λ) was measured to be ~32 μm. It is important to keep the identical size of Λ to suppress the crosstalk among the multiple cores of the MCF [15]. The core and the cladding diameters of the MCF were measured to be 10 and 125 μm, respectively. All seven cores in the MCF absolutely accommodate a single mode. Since the cladding diameter of the MCF is exactly the same as that of the conventional SMF, an ordinary fusion splicing technique is readily capable of connecting the MCF with the SMF. The micro-tapering technique was exploited to fabricate the in-line interferometer based on the MCF as seen in Fig. 2(a) [16]. During softening and melting the MCF by using a computer-controlled heater, two translation stages simultaneously elongate the MCF resulting in the formation of the adiabatically tapered MCF. The temperature of the heater and the pulling speed of the two translation stages were controlled to be ~1000°C and ~10 μm/sec, respectively. The reduction of the core diameter and the pitch size by tapering the MCF mainly induces the intermodal coupling and interference in the MCF. To control the strength of intermodal coupling and interference, it is important to investigate the effect of the waist diameter of the adiabatically tapered MCF on the optical characteristics of the in-line interferometer based on the MCF. We fabricated the various tapered MCFs with different diameters of 10, 20, 30, 50, 75, and 125 μm. The length of the uniform waist region of all tapered MCFs was ~12 mm. Figure 2(b) shows the microscopic images of the tapered MCFs with various waist diameters.

 figure: Fig. 1

Fig. 1 (a) Scheme of the MCF and (b) SEM image of the fabricated MCF.

Download Full Size | PPT Slide | PDF

 figure: Fig. 2

Fig. 2 (a) Experimental setup for the fabrication of the tapered MCF and (b) microscopic images of the tapered MCF with various waist diameters.

Download Full Size | PPT Slide | PDF

To analyze the operating principle of the intermodal coupling among the seven cores in the in-line interferometer, a coupled mode equation was employed. Among multiple core regions, the important parameters to induce the intermodal coupling among multiple core modes in the MCF are the evanescent field and the pitch size. Since the adiabatically tapering method controls the waist diameter of the MCF, the strong evanescent field and the small pitch size should be induced resulting in the intermodal coupling among the multiple core modes in the MCF. When the input light is launched into the center core ( = the 1st core) of the in-line interferometer, the coupled mode equation can be written as [17],

dAdz=CA(z),
A=[A1(z)A2(z)A3(z)A4(z)A5(z)A6(z)A7(z)]T,
where A is the column vector of the amplitude of each core mode of the in-line interferometer based on the adiabatically tapered MCF and C is a matrix of the coupling coefficient, which is composed of the elements cij . The matrix component of cij can be written as [17]
cij={jCijexp[j(βiβj)z]ij0ij,
where βi is the propagation constant of the fundamental core mode of the i th core. Since the homogenous seven cores of the MCF have the same refractive index and the diameter, their propagation constants should be the same (β 1 = β 2 = β 3 = β 4 = β 5 = β 6 = β 7) resulting in Cij = C. Therefore, the matrix C can be written as [17]
C=(0CCCCCCC0C000CCC0C000C0C0C00C00C0C0C000C0CCC000C0).
If the input light is only launched into the center core (the 1st core), the boundary condition such as A 1(0) = 1, A 2,3,4,5,6,7(0) = 0 can be achieved simply. By substituting Eqs. (2) and (3) into Eq. (1), the z-dependent amplitude of the center core mode (A 1(z)) and the six side core modes (A p(z)) can be derived as [17]
A1(z)=[cos(NCz)+jNsin(NCz)]exp(jCz),
Ap(z)=jNsin(NCz)exp(jCz)p1,
where z is the propagation direction of the fundamental core mode. N is the number of cores in the MCF. By considering Eqs. (6) and (7) , the intensities of the normalized core modes for the in-line interferometer (N = 7) can be written as [17]
|A1(z)|2=17+67cos2(7Cz),
|Ap(z)|2=17sin2(7Cz)p1.
From Eqs. (7) and (8) , it is evident that the center core mode and the p th side core modes can be oscillated periodically with a phase difference (φ) of π/2. The variation in the waist diameter changes the diameters of multiple cores and the pitch size resulting in the variation of the coupling strength among multiple core modes in the in-line interferometer. By considering the ratio (ζ) of the core diameter (a) to the waist diameter (d) of the adiabatically tapered MCF, the coupling coefficient (C) in the in-line interferometer can be derived by [18]
C=π2n12n22an1u2V2K0(wΛ/a)K12(w)=π2n12n22ζdn1u2V2K0(γ/a)K12(w),
where n 1 and n 2 are the effective refractive indices of the core and the cladding modes, respectively. a is a core diameter. K 0 and K 1 represent the first and the second order Henkel functions, respectively. V, u, and w can be defined as [18]
V=2πaλn12n22,u=a(2πn1/λ)2βp2,w=aβp2(2πn2/λ)2.
The reduction of the waist diameter simultaneously diminishes the core and the pitch size. The ratio (γ) between the core diameter and the pitch size, however, is not changed. It is clear that the coupling strength of the center core mode to the multiple side core modes in the in-line interferometer strongly depends on the waist diameter of the tapered MCF.

Figure 3 shows the theoretical results of the normalized intensity distributions of all the seven core modes in the in-line interferometer with various waist diameters obtained by using a beam propagation method (BPM). Assume that the core of a conventional SMF is connected with the center core of the MCF. When the waist diameter of the tapered MCF is larger than ~50 μm, no intermodal coupling between the center and the side core modes is observed. When the MCF is adiabatically tapered to be below 30 μm, the pitch size must be reduced and the evanescent field of the core mode should be extended simultaneously. This is sufficient to induce the intermodal coupling of the center core mode to the multiple side core modes. In Eqs. (7) and (8) , when the phase of the center core mode is π/2, its normalized intensity should be minimized to be 1/7 whereas the normalized intensities of the six side core modes should be maximized to be 1/7. Then the normalized intensities of all the core modes in the in-line interferometer must be equalized. However, the further reduction of the waist diameter degrades the extinction ratio of the oscillation transmission in the in-line interferometer and enlarges the overlap among the evanescent fields of the multiple core modes resulting in enhancement of the average normalized intensities of all the core modes. For a certain value of the waist diameter, the normalized intensities of the multiple core modes should be changed by the propagation distance because their phases are also affected by the propagation distance. When the phase difference becomes π, the normalized intensity of the center core is maximized, which can be readily understandable by considering Eqs. (7) and (8) .

 figure: Fig. 3

Fig. 3 Theoretical results for the normalized intensity distributions of all the seven core modes in the in-line interferometer with various waist diameters (d), such as 10, 20, and 30 μm.

Download Full Size | PPT Slide | PDF

3. Experimental results

To investigate the effect of the waist diameter on the intermodal coupling of the center core mode to multiple side core modes, we spliced the core of the conventional SMF with the center core of the MCF and reduced the waist diameter of the MCF. We measured the transmission spectrum based on the intermodal coupling of the proposed in-line interferometer with various waist diameters. Figure 4(a) shows the transmission spectrum of the center core mode in the in-line interferometer. After splicing the core of the SMF with the center core of the tapered MCF with versatile waist diameters, we measured the output of the in-line interferometer as seen in Fig. 4(a). When the waist diameter was larger than ~50 μm, the intermodal coupling was not exhibited in the transmission spectrum of the in-line interferometer. Since further reduction of the waist diameter improves the coupling strength of the intermodal coupling among the multiple core modes in the in-line interferometer, the periodic oscillation of the transmission spectrum was observed and the extinction ratio should be gradually increased. When the waist diameter was ~30 μm, the center core mode was sufficiently coupled to multiple side core modes. The extinction ratio of the transmission spectrum was gradually degraded by decreasing the waist diameter because the normalized intensity of the center core and multiple side core modes resulting from the intermodal coupling and interference. The oscillation periodicity of the transmission spectrum resulting from the intermodal coupling should be reduced because of the variation of the phase depending on the coupling coefficient and the waist diameter. Figure 4(b) depicts the transmission spectrum of the side core mode in the in-line interferometer. We measured the output spectrum by splicing the core of the SMF with the side core of the in-line interferometer. No transmission was measured when the waist diameter was 125 μm because no intermodal coupling exists in the in-line interferometer. Since the reduction of the waist diameter couples the center core mode to the side core modes resulting in the enhancement of coupling strength, the transmission oscillation is substantially induced. The oscillation periodicity of the output spectrum of the side core mode should be diminished in accordance with that of the center core mode.

 figure: Fig. 4

Fig. 4 Experimental results for the transmission spectra of the center core (a) and the side core modes (b), respectively, in the in-line interferometer at various waist diameters.

Download Full Size | PPT Slide | PDF

To investigate the phase difference among multiple core modes generated by the intermodal coupling, we measured the transmission spectra of the multiple side core modes coupled from the center core mode of the in-line interferometer with a waist diameter of 10 μm. Figure 5(a) shows the transmission spectra measured from the center core and the six side cores of the in-line interferometer with a waist diameter of 10 μm. The phase difference of the transmission oscillations of the center core and the side core modes was estimated to be π/2. Figures 5(b) and 5(c) shows the experimental and theoretical results for the intensity distributions of the core modes in the in-line interferometer corresponding to the phase differences and input polarization states. For a phase difference of π/2, we could achieve all the core modes coupled from the center core mode in the in-line interferometer. For a phase difference of π, no intermodal coupling was exhibited and the center core mode was only observed as seen in Fig. 5(c). Since the structure of the proposed MCF was circular symmetric, the polarization dependence of the transmission spectra of the proposed in-line interferometer was not observed. The experimental results were in good agreement with the theoretical results. Additional background losses were shown in the transmission spectra of the multiple core modes because of the misalignment of two optical fibers in the fusion-splicing process and undesirable bending in the micro-tapered MCF.

 figure: Fig. 5

Fig. 5 (a) Transmission spectra of the tapered MCF with a waist diameter of 10 μm. Experimental and theoretical results for the intensity distributions of the core modes in the in-line interferometer corresponding to the phase of π/2 (b) and π (c), respectively, depending on input polarization states.

Download Full Size | PPT Slide | PDF

4. Conclusions

In conclusion, we proposed an in-line interferometer based on the adiabatically tapered MCF. The effect of the waist diameter of the MCF on the transmission characteristics of the in-line interferometer was investigated theoretically and experimentally. The reduction of the waist diameter of the MCF efficiently improved the coupling strength of the intermodal coupling among the multiple core modes in the in-line interferometer because of the variation of the evanescent field and the pitch size. The intermodal coupling from the center core mode to the multiple side core modes of the in-line interferometer apparently generated the transmission oscillation depending on the waist diameter. The extinction ratio of the transmission oscillation was improved by diminishing the waist diameter to be ~30 μm because of the enhancement of the coupling strength of the intermodal coupling among the multiple core modes. The further reduction of the waist diameter reduced the transmission oscillation of the in-line interferometer because of the sinusoidal dependence of the normalized intensities of the center core and multiple side core modes on the coupling coefficient and the propagation distance. Depending on the phase difference between the center core mode and the multiple side core modes, the modal intensities of the multiple core or a single center core modes could be effectively controlled in the proposed in-line interferometer. Experimental results were in good agreement with the theoretical ones. We believe that the results are very useful for many applications such as optical communication systems, fiber-optic devices and sensors.

Acknowledgments

This work was supported by Korea Institute of Science and Technology (KIST) Institutional Program (2E25373) and by National Research Council of Science & Technology through the Convergence Practical Application Program (Grant 13-10-KRISS).

References

1. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]  

2. R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014). [CrossRef]  

3. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express 19(17), 16665–16671 (2011). [CrossRef]   [PubMed]  

4. B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fini, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, “Seven-core multicore fiber transmissions for passive optical network,” Opt. Express 18(11), 11117–11122 (2010). [CrossRef]   [PubMed]  

5. T. F. S. Büttner, D. D. Hudson, E. C. Mägi, A. C. Bedoya, T. Taunay, and B. J. Eggleton, “Multicore, tapered optical fiber for nonlinear pulse reshaping and saturable absorption,” Opt. Lett. 37(13), 2469–2471 (2012). [CrossRef]   [PubMed]  

6. G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett. 28(6), 387–389 (2003). [CrossRef]   [PubMed]  

7. A. Van Newkirk, E. Antonio-Lopez, G. Salceda-Delgado, R. Amezcua-Correa, and A. Schülzgen, “Optimization of multicore fiber for high-temperature sensing,” Opt. Lett. 39(16), 4812–4815 (2014). [CrossRef]   [PubMed]  

8. J. E. Antonio-Lopez, Z. S. Eznaveh, P. LiKamWa, A. Schülzgen, and R. Amezcua-Correa, “Multicore fiber sensor for high-temperature applications up to 1000°C,” Opt. Lett. 39(15), 4309–4312 (2014). [CrossRef]   [PubMed]  

9. H. J. Kim and Y. G. Han, “Polarization-dependent in-line mach-zehnder interferometer for discrimination of temperature and ambient index sensitivities,” J. Lightwave Technol. 30(8), 1037–1041 (2012). [CrossRef]  

10. C. R. Biazoli, S. Silva, M. A. R. Franco, O. Frazão, and C. M. B. Cordeiro, “Multimode interference tapered fiber refractive index sensors,” Appl. Opt. 51(24), 5941–5945 (2012). [CrossRef]   [PubMed]  

11. S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009). [CrossRef]  

12. P. Rugeland and W. Margulis, “Revisiting twin-core fiber sensors for high-temperature measurements,” Appl. Opt. 51(25), 6227–6232 (2012). [CrossRef]   [PubMed]  

13. A. Zhou, Y. Zhang, G. Li, J. Yang, Y. Wang, F. Tian, and L. Yuan, “Optical refractometer based on an asymmetrical twin-core fiber Michelson interferometer,” Opt. Lett. 36(16), 3221–3223 (2011). [CrossRef]   [PubMed]  

14. R. M. Silva, M. S. Ferreira, J. Kobelke, K. Schuster, and O. Frazão, “Simultaneous measurement of curvature and strain using a suspended multicore fiber,” Opt. Lett. 36(19), 3939–3941 (2011). [CrossRef]   [PubMed]  

15. S. Zheng, G. Ren, Z. Lin, and S. Jian, “Mode-coupling analysis and trench design for large-mode-area low-cross-talk multicore fiber,” Appl. Opt. 52(19), 4541–4548 (2013). [CrossRef]   [PubMed]  

16. M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012). [CrossRef]  

17. F. Y. Chan, A. P. T. Lau, and H.-Y. Tam, “Mode coupling dynamics and communication strategies for multi-core fiber systems,” Opt. Express 20(4), 4548–4563 (2012). [CrossRef]   [PubMed]  

18. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. 62(11), 1267–1277 (1972). [CrossRef]   [PubMed]  

References

  • View by:

  1. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
    [Crossref]
  2. R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
    [Crossref]
  3. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express 19(17), 16665–16671 (2011).
    [Crossref] [PubMed]
  4. B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fini, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, “Seven-core multicore fiber transmissions for passive optical network,” Opt. Express 18(11), 11117–11122 (2010).
    [Crossref] [PubMed]
  5. T. F. S. Büttner, D. D. Hudson, E. C. Mägi, A. C. Bedoya, T. Taunay, and B. J. Eggleton, “Multicore, tapered optical fiber for nonlinear pulse reshaping and saturable absorption,” Opt. Lett. 37(13), 2469–2471 (2012).
    [Crossref] [PubMed]
  6. G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett. 28(6), 387–389 (2003).
    [Crossref] [PubMed]
  7. A. Van Newkirk, E. Antonio-Lopez, G. Salceda-Delgado, R. Amezcua-Correa, and A. Schülzgen, “Optimization of multicore fiber for high-temperature sensing,” Opt. Lett. 39(16), 4812–4815 (2014).
    [Crossref] [PubMed]
  8. J. E. Antonio-Lopez, Z. S. Eznaveh, P. LiKamWa, A. Schülzgen, and R. Amezcua-Correa, “Multicore fiber sensor for high-temperature applications up to 1000°C,” Opt. Lett. 39(15), 4309–4312 (2014).
    [Crossref] [PubMed]
  9. H. J. Kim and Y. G. Han, “Polarization-dependent in-line mach-zehnder interferometer for discrimination of temperature and ambient index sensitivities,” J. Lightwave Technol. 30(8), 1037–1041 (2012).
    [Crossref]
  10. C. R. Biazoli, S. Silva, M. A. R. Franco, O. Frazão, and C. M. B. Cordeiro, “Multimode interference tapered fiber refractive index sensors,” Appl. Opt. 51(24), 5941–5945 (2012).
    [Crossref] [PubMed]
  11. S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
    [Crossref]
  12. P. Rugeland and W. Margulis, “Revisiting twin-core fiber sensors for high-temperature measurements,” Appl. Opt. 51(25), 6227–6232 (2012).
    [Crossref] [PubMed]
  13. A. Zhou, Y. Zhang, G. Li, J. Yang, Y. Wang, F. Tian, and L. Yuan, “Optical refractometer based on an asymmetrical twin-core fiber Michelson interferometer,” Opt. Lett. 36(16), 3221–3223 (2011).
    [Crossref] [PubMed]
  14. R. M. Silva, M. S. Ferreira, J. Kobelke, K. Schuster, and O. Frazão, “Simultaneous measurement of curvature and strain using a suspended multicore fiber,” Opt. Lett. 36(19), 3939–3941 (2011).
    [Crossref] [PubMed]
  15. S. Zheng, G. Ren, Z. Lin, and S. Jian, “Mode-coupling analysis and trench design for large-mode-area low-cross-talk multicore fiber,” Appl. Opt. 52(19), 4541–4548 (2013).
    [Crossref] [PubMed]
  16. M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012).
    [Crossref]
  17. F. Y. Chan, A. P. T. Lau, and H.-Y. Tam, “Mode coupling dynamics and communication strategies for multi-core fiber systems,” Opt. Express 20(4), 4548–4563 (2012).
    [Crossref] [PubMed]
  18. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. 62(11), 1267–1277 (1972).
    [Crossref] [PubMed]

2014 (3)

2013 (2)

S. Zheng, G. Ren, Z. Lin, and S. Jian, “Mode-coupling analysis and trench design for large-mode-area low-cross-talk multicore fiber,” Appl. Opt. 52(19), 4541–4548 (2013).
[Crossref] [PubMed]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

2012 (6)

2011 (3)

2010 (1)

2009 (1)

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

2003 (1)

1972 (1)

Amezcua Correa, R.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Amezcua-Correa, R.

Antonio-Lopez, E.

Antonio-Lopez, J. E.

Barton, J. S.

Bedoya, A. C.

Bennion, I.

Biazoli, C. R.

Brambilla, G.

M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012).
[Crossref]

Büttner, T. F. S.

Chan, F. Y.

Chandrasekhar, S.

Cordeiro, C. M. B.

de Waardt, H.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Dimarcello, F. V.

Eggleton, B. J.

Eznaveh, Z. S.

Feng, S.

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

Ferreira, M. S.

Fini, J. M.

Fishteyn, M.

Flockhart, G. M. H.

Franco, M. A. R.

Frazão, O.

Han, Y. G.

M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012).
[Crossref]

H. J. Kim and Y. G. Han, “Polarization-dependent in-line mach-zehnder interferometer for discrimination of temperature and ambient index sensitivities,” J. Lightwave Technol. 30(8), 1037–1041 (2012).
[Crossref]

Hudson, D. D.

Huijskens, F. M.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Jian, S.

S. Zheng, G. Ren, Z. Lin, and S. Jian, “Mode-coupling analysis and trench design for large-mode-area low-cross-talk multicore fiber,” Appl. Opt. 52(19), 4541–4548 (2013).
[Crossref] [PubMed]

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

Jones, J. D. C.

Kim, H. J.

H. J. Kim and Y. G. Han, “Polarization-dependent in-line mach-zehnder interferometer for discrimination of temperature and ambient index sensitivities,” J. Lightwave Technol. 30(8), 1037–1041 (2012).
[Crossref]

M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012).
[Crossref]

Kobelke, J.

Koonen, A. M. J.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Lau, A. P. T.

Li, G.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

A. Zhou, Y. Zhang, G. Li, J. Yang, Y. Wang, F. Tian, and L. Yuan, “Optical refractometer based on an asymmetrical twin-core fiber Michelson interferometer,” Opt. Lett. 36(16), 3221–3223 (2011).
[Crossref] [PubMed]

Li, H.

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

LiKamWa, P.

Lin, Z.

Liu, X.

Lopez, E. A.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Lu, S.

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

MacPherson, W. N.

Mägi, E. C.

Margulis, W.

Monberg, E. M.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Okonkwo, C. M.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Ren, G.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Rugeland, P.

Salceda-Delgado, G.

Schülzgen, A.

Schuster, K.

Silva, R. M.

Silva, S.

Snyder, A. W.

Tam, H.-Y.

Taunay, T.

Taunay, T. F.

Tian, F.

Van Newkirk, A.

van Uden, R. G. H.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Wang, Y.

Xia, C.

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Xu, O.

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

Yan, M. F.

Yang, J.

Yoon, M. S.

M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012).
[Crossref]

Yuan, L.

Zhang, L.

Zhang, Y.

Zheng, S.

Zhou, A.

Zhu, B.

Appl. Opt. (3)

J. Korean Phys. Soc. (1)

M. S. Yoon, H. J. Kim, G. Brambilla, and Y. G. Han, “Development of a small-size embedded optical microfiber coil resonator with High Q,” J. Korean Phys. Soc. 61(9), 1381–1385 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Nat. Photonics (2)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

R. G. H. van Uden, R. Amezcua Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (6)

Proc. SPIE (1)

S. Feng, H. Li, O. Xu, S. Lu, and S. Jian, “Compact in-fiber Mach-Zehnder interferometer using a twin-core fiber,” Proc. SPIE 7630, 76301R (2009).
[Crossref]

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 (a) Scheme of the MCF and (b) SEM image of the fabricated MCF.
Fig. 2
Fig. 2 (a) Experimental setup for the fabrication of the tapered MCF and (b) microscopic images of the tapered MCF with various waist diameters.
Fig. 3
Fig. 3 Theoretical results for the normalized intensity distributions of all the seven core modes in the in-line interferometer with various waist diameters (d), such as 10, 20, and 30 μm.
Fig. 4
Fig. 4 Experimental results for the transmission spectra of the center core (a) and the side core modes (b), respectively, in the in-line interferometer at various waist diameters.
Fig. 5
Fig. 5 (a) Transmission spectra of the tapered MCF with a waist diameter of 10 μm. Experimental and theoretical results for the intensity distributions of the core modes in the in-line interferometer corresponding to the phase of π/2 (b) and π (c), respectively, depending on input polarization states.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

d A d z = C A ( z ) ,
A = [ A 1 ( z ) A 2 ( z ) A 3 ( z ) A 4 ( z ) A 5 ( z ) A 6 ( z ) A 7 ( z ) ] T ,
c i j = { j C i j exp [ j ( β i β j ) z ] i j 0 i j ,
C = ( 0 C C C C C C C 0 C 0 0 0 C C C 0 C 0 0 0 C 0 C 0 C 0 0 C 0 0 C 0 C 0 C 0 0 0 C 0 C C C 0 0 0 C 0 ) .
A 1 ( z ) = [ cos ( N C z ) + j N sin ( N C z ) ] exp ( j C z ) ,
A p ( z ) = j N sin ( N C z ) exp ( j C z ) p 1 ,
| A 1 ( z ) | 2 = 1 7 + 6 7 cos 2 ( 7 C z ) ,
| A p ( z ) | 2 = 1 7 sin 2 ( 7 C z ) p 1.
C = π 2 n 1 2 n 2 2 a n 1 u 2 V 2 K 0 ( w Λ / a ) K 1 2 ( w ) = π 2 n 1 2 n 2 2 ζ d n 1 u 2 V 2 K 0 ( γ / a ) K 1 2 ( w ) ,
V = 2 π a λ n 1 2 n 2 2 , u = a ( 2 π n 1 / λ ) 2 β p 2 , w = a β p 2 ( 2 π n 2 / λ ) 2 .

Metrics