Abstract

The depressed core fiber (DCF), consisting of a low-index solid core, a high-index cladding and air surrounding, is in effect a bridge between the conventional step-index fiber and the tube-type hollow-core fiber from the point of view of the index profile. In this paper the dispersion diagram of a DCF is obtained by solving the full-vector eigenvalue equations and analyzed using the theory of anti-resonant and the inhibited coupling mechanisms. While light propagation in tube-type hollow-core fibers is commonly described by the symmetric planar waveguide model, here we propose an asymmetric planar waveguide for the DCFs in an anti-resonant reflecting optical waveguide (ARROW) model. It is found that the anti-resonant core modes in the DCFs have real effective indices, compared to the anti-resonant core modes with complex effective indices in the tube-type hollow-core fibers. The anti-resonant core modes in the DCFs exhibit similar qualitative and quantitative behavior as the core modes in the conventional step-index fibers. The full-vector analytical results for the simple-structure DCFs can contribute to a better understanding of the anti-resonant and inhibited coupling guidance mechanisms in other complex inversed index fibers.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (4)

2018 (4)

S. S. Aleshkina, M. V. Yashkov, M. M. Bubnov, A. N. Guryanov, and M. E. Likhachev, “Asymptotically single-mode hybrid fiber for dispersion management near 1 µm,” IEEE J. Sel. Topics Quantum Electron 24(3), 1–8 (2018).
[Crossref]

S. F. Gao, Y. Y. Wang, W. Ding, D. L. Jiang, S. Gu, X. Zhang, and P. Wang, “Hollow-core conjoined-tube negative-curvature fibre with ultralow loss,” Nat. Commun. 9(1), 1–6 (2018).
[Crossref]

F. Tani, F. Köttig, D. Novoa, R. Keding, and P. S. Russell, “Effect of anti-crossings with cladding resonances on ultrafast nonlinear dynamics in gas-filled photonic crystal fibers,” Photonics Res. 6(2), 84–88 (2018).
[Crossref]

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[Crossref]

2017 (5)

S. Liu, Y. Ji, L. Cui, W. Sun, J. Yang, and H. Li, “Humidity-insensitive temperature sensor based on a quartz capillary anti-resonant reflection optical waveguide,” Opt. Express 25(16), 18929–18939 (2017).
[Crossref]

B. Debord, A. Amsanpally, M. Chafer, A. Baz, M. Maurel, J. M. Blondy, E. Hugonnot, F. Scol, L. Vincetti, F. Gérôme, and F. Benabid, “Ultralow transmission loss in inhibited-coupling guiding hollow fibers,” Optica 4(2), 209–217 (2017).
[Crossref]

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light: Sci. Appl. 6(12), e17124 (2017).
[Crossref]

M. Zeisberger and M. A. Schmidt, “Analytic model for the complex effective index of the leaky modes of tubetype anti-resonant hollow core fibers,” Sci. Rep. 7(1), 11761 (2017).
[Crossref]

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

2016 (3)

2014 (1)

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

2013 (3)

2012 (1)

2011 (2)

2010 (3)

2009 (1)

K. Z. Aghaie, V. Dangui, M. J. F. Digonnet, S. H. Fan, and G. S. Kino, “Classification of the core modes of hollow-core photonic-bandgap fibers,” IEEE J. Quantum Electron. 45(9), 1192–1200 (2009).
[Crossref]

2007 (1)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[Crossref]

2006 (1)

2005 (4)

2003 (1)

2002 (1)

1999 (1)

V. I. Neves and A. S. C. Fernandes, “Modal characteristics for W-type and M-type dielectric profile fibres,” Micro. & Opt. Tech. Lett. 22(6), 398–405 (1999).
[Crossref]

1997 (1)

1993 (1)

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

Abdolvand, A.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

Abeeluck, A. K.

Aghaie, K. Z.

K. Z. Aghaie, V. Dangui, M. J. F. Digonnet, S. H. Fan, and G. S. Kino, “Classification of the core modes of hollow-core photonic-bandgap fibers,” IEEE J. Quantum Electron. 45(9), 1192–1200 (2009).
[Crossref]

Ahmed, G.

Aleshkina, S. S.

S. S. Aleshkina, M. V. Yashkov, M. M. Bubnov, A. N. Guryanov, and M. E. Likhachev, “Asymptotically single-mode hybrid fiber for dispersion management near 1 µm,” IEEE J. Sel. Topics Quantum Electron 24(3), 1–8 (2018).
[Crossref]

S. S. Aleshkina, M. E. Likhachev, A. K. Senatorov, M. M. Bubnov, M. Y. Salaganskii, and A. N. Guryanov, “Low-loss hybrid fiber with zero dispersion wavelength shifted to 1 µm,” Opt. express 21(20), 23838–23843 (2013).
[Crossref]

Amsanpally, A.

Ando, R. F.

Archambault, J. L.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Arregui, F. J.

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

I. Del Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in Long Period Fiber Gratings with overlay deposition,” Opt. Express 13(1), 56–69 (2005).
[Crossref]

Ascorbe, J.

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

Astapovich, M. S.

Bache, M.

Bang, O.

D. Jain, C. Markos, T. M. Benson, A. B. Seddon, and O. Bang, “Exploiting dispersion of higher-order-modes using M-type fiber for application in mid-infrared supercontinuum generation,” Sci. Rep. 9(1), 8536 (2019).
[Crossref]

Bariain, C.

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

Baz, A.

Belanov, A. S.

A. S. Belanov and S. V. Tsvetkov, “High-index-ring three-layer fibres for mode-locked sub-1.3 µm fibre lasers,” Quantum Electron. 40(2), 160–162 (2010).
[Crossref]

Benabid, F.

B. Debord, A. Amsanpally, M. Chafer, A. Baz, M. Maurel, J. M. Blondy, E. Hugonnot, F. Scol, L. Vincetti, F. Gérôme, and F. Benabid, “Ultralow transmission loss in inhibited-coupling guiding hollow fibers,” Optica 4(2), 209–217 (2017).
[Crossref]

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[Crossref]

Benson, T. M.

D. Jain, C. Markos, T. M. Benson, A. B. Seddon, and O. Bang, “Exploiting dispersion of higher-order-modes using M-type fiber for application in mid-infrared supercontinuum generation,” Sci. Rep. 9(1), 8536 (2019).
[Crossref]

Bierlich, J.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light: Sci. Appl. 6(12), e17124 (2017).
[Crossref]

Bigot, L.

Biriukov, A. S.

Black, R. J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Blondy, J. M.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Bouwmans, G.

Bradley, T. D.

Bubnov, M. M.

S. S. Aleshkina, M. V. Yashkov, M. M. Bubnov, A. N. Guryanov, and M. E. Likhachev, “Asymptotically single-mode hybrid fiber for dispersion management near 1 µm,” IEEE J. Sel. Topics Quantum Electron 24(3), 1–8 (2018).
[Crossref]

S. S. Aleshkina, M. E. Likhachev, A. K. Senatorov, M. M. Bubnov, M. Y. Salaganskii, and A. N. Guryanov, “Low-loss hybrid fiber with zero dispersion wavelength shifted to 1 µm,” Opt. express 21(20), 23838–23843 (2013).
[Crossref]

Bures, J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Calvet, P.

Campopiano, S.

Chafer, M.

Chang, H.-C.

Chang, W.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photonics 8(4), 278–286 (2014).
[Crossref]

Chemnitz, M.

R. Sollapur, D. Kartashov, M. Zürch, A. Hoffmann, T. Grigorova, G. Sauer, A. Hartung, A. Schwuchow, J. Bierlich, J. Kobelke, M. Chemnitz, M. A. Schmidt, and C. Spielmann, “Resonance-enhanced multi-octave supercontinuum generation in antiresonant hollow-core fibers,” Light: Sci. Appl. 6(12), e17124 (2017).
[Crossref]

Chen, Y.

Churbanov, M. F.

Contessa, L.

Corres, J. M.

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

Coulombier, Q.

Couny, F.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[Crossref]

Cui, L.

Cusano, A.

Cutolo, A.

Dangui, V.

K. Z. Aghaie, V. Dangui, M. J. F. Digonnet, S. H. Fan, and G. S. Kino, “Classification of the core modes of hollow-core photonic-bandgap fibers,” IEEE J. Quantum Electron. 45(9), 1192–1200 (2009).
[Crossref]

De Acha, N.

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

de Sterke, C. M.

Debord, B.

Del Villar, I.

I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017).
[Crossref]

I. Del Villar, I. R. Matías, F. J. Arregui, and P. Lalanne, “Optimization of sensitivity in Long Period Fiber Gratings with overlay deposition,” Opt. Express 13(1), 56–69 (2005).
[Crossref]

Delplace, K.

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Figures (8)

Fig. 1.
Fig. 1. A depressed-core optical fiber and its cross section and refractive index profile.
Fig. 2.
Fig. 2. (a) and (b) show the ray trajectory of a mode with n1 < neff = n2sinθ1 < n2 in a DCF and an equivalent asymmetric planar waveguide, respectively. (c) and (d) show the ray trajectory of a mode with n3 < neff = n1sinθ1 < n1 in the DCF and the equivalent asymmetric planar waveguide, respectively.
Fig. 3.
Fig. 3. Dispersion curves (neff vs. λ) of TE modes with neff corresponding to (a) n1 < neff < n2, (b) n1-0.001 < neff < n1+0.001, n1 = 1.445, n2 = 1.51. (c) shows the modal intensity and electric field vector distributions of TE modes whose positions (neff, λ) are indicated by the black circle dots in (a) and (b). The red vertical dashed lines in (a) and (b) indicate the resonant bands.
Fig. 4.
Fig. 4. The left panel (a)-(e) shows the normalized intensity distributions along the r-coordinate for the modes shown at points C-G in Fig. 3. The right panel (a′)-(e′) shows the zoomed-in part of (a)-(e), delineated by the vertical dashed lines.
Fig. 5.
Fig. 5. Dispersion curves (neff vs. λ) of TM modes with neff corresponding to (a) n1 < neff < n2, (b) n1-0.001 < neff < n1+0.001, n1 = 1.445, n2 = 1.51. (c) shows the modal intensity and electric field vector distributions of TM modes whose positions (neff, λ) are indicated by the black squares in (a) and (b). The black vertical dashed lines in (a) and (b) indicate the resonant bands.
Fig. 6.
Fig. 6. Dispersion curves (neff vs. λ) of HE1,N (red) and EH1,N (black) modes with neff corresponding to (n1-0.001 < neff < n1+0.001, n1 = 1.445. The black and red vertical dashed lines indicate the resonant bands.
Fig. 7.
Fig. 7. Dispersion curves (neff vs. λ) of HE modes with neff corresponding to (a) n1-0.001 < neff < n1+0.001, n1 = 1.445. (b) partially enlarged image of (a), indicated by the red frame. (c) shows the modal intensity and electric field vector distributions of HE modes whose positions (neff, λ) are indicated by the circles in (b). The black and red vertical dashed lines in (a) and (b) indicate the resonant bands.
Fig. 8.
Fig. 8. (a) Dispersion curves (neff vs. λ) of a depressed core fiber. (b) partially enlarged image of (a), indicated by the black dashed frame. The text labels and the corresponding dispersion curves are of the same color. The orange solid lines in (a) and (b) are for LPm,n modes in a conventional step-index fiber (nco = 1.445, ncl = 1, rco = 62.5 um and rcl = ∞). The black and red vertical dashed lines indicate the resonant bands.

Equations (21)

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λ N , c = 2 d n 2 2 n 1 2 [ N + 1 π tan 1 ( κ n 1 2 n 3 2 n 2 2 n 1 2 ) ] , κ = { 1 , for T E N modes n 2 2 n 3 2 for T M N modes
J ^ ( K p m + r m α 2 U 2 ) = 1 U 2 ( K ^ q m + s m α 2 U 2 ) , m = 0
J ^ ( K ^ p m + s 23 r m α 2 U 2 ) = s 21 U 2 ( K ^ q m + s 23 s m α 2 U 2 ) , m = 0
p m 2 + 2 ( 2 π α 2 U 2 2 ) 2 ( n 2 2 n 1 n 3 ) x 1 x 2 + x 1 2 x 2 2 [ J ^ ( K ^ p m + r m α 2 U 2 ) 1 U 2 ( K ^ q m + s m α 2 U 2 ) ] × [ J ^ ( K ^ p m + s 23 r m α 2 U 2 ) s 21 U 2 ( K ^ q m + s 23 s m α 2 U 2 ) ] = x 1 2 ( J ^ p m q m U 2 ) ( J ^ p m s 21 q m U 2 ) + x 2 2 ( K ^ p m + r m α 2 U 2 ) ( K ^ p m + s 23 r m α 2 U 2 )
α 2 = r 2 r 1 ,
u 1 = k 0 2 n 1 2 β 2 ,
u 2 = k 0 2 n 2 2 β 2 ,
ω 3 = β 2 k 0 2 n 3 2 ,
U 1 = u 1 r 1 , U 2 = u 2 r 1 , W 3 = ω 3 r 2 ,
J ^ = J m ( U 1 ) U 1 J m ( U 1 ) ,
K ^ = K m ( W 3 ) W 3 K m ( W 3 ) ,
p m = J m ( u 2 r 2 ) Y m ( u 2 r 1 ) J m ( u 2 r 1 ) Y m ( u 2 r 2 ) ,
q m = J m ( u 2 r 2 ) Y m ( u 2 r 1 ) J m ( u 2 r 1 ) Y m ( u 2 r 2 ) ,
r m = J m ( u 2 r 2 ) Y m ( u 2 r 1 ) J m ( u 2 r 1 ) Y m ( u 2 r 2 ) ,
s n = J m ( u 2 r 2 ) Y m ( u 2 r 1 ) J m ( u 2 r 1 ) Y m ( u 2 r 2 ) ,
s 23 = n 2 2 n 3 2 , s 21 = n 2 2 n 1 2 ,
V 12 2 = k 0 2 r 1 2 ( n 1 2 n 2 2 ) , V 23 2 = k 0 2 r 2 2 ( n 2 2 n 3 2 ) ,
x 1 2 = n 1 2 U 1 4 U 2 4 σ 0 2 V 12 4 , x 2 2 = n 3 2 α 2 4 U 2 4 W 3 4 σ 0 2 V 23 4 ,
σ 0 2 = ( β m k 0 ) 2 .
u 1 = β 2 k 0 2 n 1 2
J ^ = I m ( U 1 ) U 1 I m ( U 1 ) ,