Abstract

We report on a measurement method for the effective area of the few-mode fiber. We derived a transform equation between a near-field pattern and a far-field pattern generalized for circularly-asymmetric higher-order modes of a cylindrical core, and enabled effective area measurement of the higher-order modes using high-dynamic-range far-field scan technique and low-crosstalk mode multiplexer. The measured effective area values agreed well with the values that were numerically predicted using a finite-element method from the refractive index profile, when the modal crosstalk was suppressed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  4. T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
    [Crossref]
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    [Crossref]
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2016 (1)

2015 (1)

P. J. Winzer, “Scaling Optical Fiber Networks: Challenges and Solutions,” Opt. Photon.News 26(3), 28–35 (2015).
[Crossref]

2014 (1)

2009 (1)

2008 (1)

1989 (1)

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[Crossref]

1979 (2)

Abe, Y.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Aikawa, K.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Aozasa, S.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Artiglia, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[Crossref]

Awaji, Y.

Baddour, N.

Coppa, G.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[Crossref]

Denolle, B.

Di Vita, P.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[Crossref]

Genevaux, P.

Ghalmi, S.

Hayashi, T.

J. Sakaguchi, W. Klaus, J.-M. D. Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Large spatial channel (36-core × 3 mode) heterogeneous few-mode multi-core fiber,” J. Lightwave Technol. 34(1), 93–103 (2016).
[Crossref]

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Hotate, K.

Igarashi, K.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Jian, P.

Klaus, W.

Kobayashi, T.

Kokubun, Y.

Labroille, G.

Lgarashi, K.

Y. Wakayama, H. Taga, K. Lgarashi, and T. Tsuritani, “DMD measurement of 114-SDM transmission fibre using low-coherence interferometry with digital holographic processing,” in Eur. Conf. Opt. Commun. (ECOC) (2015), p. 1.
[Crossref]

Luis, R. S.

Matsui, T.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Matsuo, S.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Mendinueta, J.-M. D.

Miyamoto, Y.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Mizuno, T.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Morizur, J.-F.

Nagashima, T.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Nakajima, K.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Nakanishi, T.

Nicholson, J. W.

Okamoto, K.

Okoshi, T.

Potenza, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[Crossref]

Puttnam, B. J.

Ramachandran, S.

Saitoh, K.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Saitoh, S.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Sakaguchi, J.

Sakamoto, T.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Sasaki, T.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Sharma, A.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7(8), 1139–1152 (1989).
[Crossref]

Shibahara, K.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Sillard, P.

P. Sillard, “Few-Mode Fibers for Space Division Multiplexing,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th1J.1.

Soma, D.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Taga, H.

Y. Wakayama, H. Taga, K. Lgarashi, and T. Tsuritani, “DMD measurement of 114-SDM transmission fibre using low-coherence interferometry with digital holographic processing,” in Eur. Conf. Opt. Commun. (ECOC) (2015), p. 1.
[Crossref]

Takahata, T.

Takenaga, K.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Tobita, Y.

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Treps, N.

Tsuritani, T.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Y. Wakayama, H. Taga, K. Lgarashi, and T. Tsuritani, “DMD measurement of 114-SDM transmission fibre using low-coherence interferometry with digital holographic processing,” in Eur. Conf. Opt. Commun. (ECOC) (2015), p. 1.
[Crossref]

Wada, N.

Wakayama, Y.

Y. Wakayama, H. Taga, K. Lgarashi, and T. Tsuritani, “DMD measurement of 114-SDM transmission fibre using low-coherence interferometry with digital holographic processing,” in Eur. Conf. Opt. Commun. (ECOC) (2015), p. 1.
[Crossref]

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Watanabe, T.

Winzer, P. J.

P. J. Winzer, “Scaling Optical Fiber Networks: Challenges and Solutions,” Opt. Photon.News 26(3), 28–35 (2015).
[Crossref]

Yablon, A. D.

Yonezawa, K.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

Appl. Opt. (2)

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Opt. Photon.News (1)

P. J. Winzer, “Scaling Optical Fiber Networks: Challenges and Solutions,” Opt. Photon.News 26(3), 28–35 (2015).
[Crossref]

Other (8)

P. Sillard, “Few-Mode Fibers for Space Division Multiplexing,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th1J.1.

T. Hayashi, T. Nagashima, K. Yonezawa, Y. Wakayama, D. Soma, K. Igarashi, T. Tsuritani, and T. Sasaki, “6-mode 19-core fiber for weakly-coupled mode-multiplexed transmission over uncoupled cores,” in Opt. Fiber Commun. Conf. (OFC) (2016), p. W1F.4.
[Crossref]

T. Sakamoto, T. Matsui, K. Saitoh, S. Saitoh, K. Takenaga, T. Mizuno, Y. Abe, K. Shibahara, Y. Tobita, S. Matsuo, K. Aikawa, S. Aozasa, K. Nakajima, and Y. Miyamoto, “Low-loss and Low-DMD Few-mode Multi-core Fiber with Highest Core Multiplicity Factor,” in Opt. Fiber Commun. Conf. (OFC) (Optical Society of America, 2016), p. Th5A.2.
[Crossref]

Y. Wakayama, H. Taga, K. Lgarashi, and T. Tsuritani, “DMD measurement of 114-SDM transmission fibre using low-coherence interferometry with digital holographic processing,” in Eur. Conf. Opt. Commun. (ECOC) (2015), p. 1.
[Crossref]

ITU-T G.650.2, “Definitions and test methods for statistical and non-linear related attributes of single-mode fibre and cable,” (2015).

T. Hayashi, Y. Tamura, T. Nagashima, K. Yonezawa, T. Taru, K. Igarashi, D. Soma, Y. Wakayama, and T. Tsuritani, “Effective area measurement of few-mode fiber using far field scan technique with Hankel transform generalized for circularly-asymmetric mode,” in Frontiers in Optics (2016), p. FTh5E.3.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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Figures (3)

Fig. 1
Fig. 1 Comparison between the FFP intensity profiles calculated using 2D FT from the LP11 and LP21 even modes, and those converted using 1D HT of zeroth order.
Fig. 2
Fig. 2 Comparison between the FFP intensity profiles calculated using 2D FT and those converted using 1D HT of the order of the AMN.
Fig. 3
Fig. 3 The measured FFPs (Meas.) and the numerically predicted FFPs (FEM) of the 4LPMF. The numerically predicted FFPs were converted from the FEM-calculated NFPs using Eq. (6)with an appropriate value of n. The descriptions (a), (b), and (a + b) in the legends represent the measurement results when the light was launched into LPn1a, LPn1b, and both of LPn1a and LPn1b, respectively. The description (a, Θ’-deg rot.) represents the measurement result when the 4LPMF was rotated by Θ’ degrees from the measurement state of (a).

Tables (1)

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Table 1 Effective area of the vector modes of 4LPMF

Equations (26)

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{ F φ ( φ ) 0 E r ( r ) J 0 ( rksinφ )rdr, E r ( r ) 0 F φ ( φ ) J 0 ( rksinφ )sin2φdφ,
F( φ x , φ y ) E( x,y )exp[ jk( xsin φ x +ysin φ y ) ]dxdy ,
F ω ( ω x , ω y ) E( x,y )exp[ j( ω x x+ ω y y ) ]dxdy , [ ω x =ksin φ x , ω y =ksin φ y ]
F ω,polar ( ρ,Θ ) 0 0 2π E polar ( r,θ )exp[ jρrcos( Θθ ) ]dθ rdr ,
Case E polar = E r ( r )cos( nθ ): { F polar ( φ,Θ ) H n [ E r ]( φ )cos( nΘ ), E polar ( r,θ ) H n 1 [ F φ ]( r )cos( nθ ), Case E polar = E r ( r )sin( nθ ): { F polar ( φ,Θ ) H n [ E r ]( φ )sin( nΘ ), E polar ( r,θ ) H n 1 [ F φ ]( r )sin( nθ ),
{ F φ ( φ )= H n [ E r ]( φ )= 0 E r ( r ) J n ( rksinφ )rdr , E r ( r )= H n 1 [ F φ ]( r )= k 2 2 0 F φ ( φ ) J n ( rksinφ )sin2φdφ
MFD1=2 2 [ 0 | E r ( r ) | 2 r 3 dr 0 | E r ( r ) | 2 rdr ] 1/2 ,
MFD=2 2 [ 0 | F ρ ( ρ ) | 2 ρdρ 0 | F ρ ( ρ ) | 2 ρ 3 dρ ] 1/2 , = 2 λ π [ 0 π/2 | F φ ( φ ) | 2 sinφcosφdφ 0 π/2 | F φ ( φ ) | 2 sin 3 φcosφdφ ] 1/2 .
A eff = ( | E | 2 dxdy ) 2 | E | 4 dxdy = ( 0 0 2π | E | 2 dθrdr ) 2 0 0 2π | E | 4 dθrdr ,
A eff,EM = ( 0 | E r | 2 rdr 0 2π dθ ) 2 0 | E r | 4 rdr 0 2π dθ =2π ( 0 | E r | 2 rdr ) 2 0 | E r | 4 rdr .
A eff,LP = ( 0 | E r | 2 rdr 0 2π cos 2 nθdθ ) 2 0 | E r | 4 rdr 0 2π cos 4 nθdθ , = ( π 0 | E r | 2 rdr ) 2 3π 4 0 | E r | 4 rdr = 4π 3 ( 0 | E r | 2 rdr ) 2 0 | E r | 4 rdr , = 2 3 A eff,EM ,
E polar ( r,θ )= k= E k ( r )exp( jkθ ) ,
E k ( r )= 1 2π 0 2π E( r,θ )exp( jkθ )dθ ,
E ±n ( r )= E r ( r ) 2 , E k ( r )| k±n =0,( Even mode ), E ±n ( r )=± E r ( r ) 2j , E k ( r )| k±n =0,( Odd mode ).
F polar = k= F k ( ρ )exp( jkΘ ),
F k ( ρ )=2π j k H k [ E k ( r ) ],
H n [ f( r ) ]= 0 f( r ) J n ( ρr )rdr ,
J n ( x )= ( 1 ) n J n ( x ),
H n [ f( r ) ]= ( 1 ) n H n [ f( r ) ]
F polar | j n H n [ E n ]exp( jnΘ )+ j n H n [ E n ]exp( jnΘ ) |, | j n H n [ E r 2 ]exp( jnΘ )+ j n H n [ E r 2 ]exp( jnΘ ) |, | j n H n [ E r 2 ]exp( jnΘ )+ j n ( 1 ) n H n [ E r 2 ]exp( jnΘ ) |, | j n H n [ E r ] exp( jnΘ )+exp( jnΘ ) 2 |, H n [ E r ]cosnΘ,
F polar | j n H n [ E r 2j ]exp( jnΘ )+ j n H n [ E r 2j ]exp( jnΘ ) |, | j n H n [ E r 2 ]exp( jnΘ )+ j n ( 1 ) n H n [ E r 2j ]exp( jnΘ ) |, | j n H n [ E r ] exp( jnΘ )exp( jnΘ ) 2j |, H n [ E r ]sinnΘ,
E k ( r )= j k 2π H k 1 [ F k ( ρ ) ],
H n 1 [ F( ρ ) ]= 0 F( ρ ) J n ( ρr )ρdρ , = 0 F( ρ ) J n ( rksinφ ) k 2 sinφcosφdφ , = k 2 2 0 F( ρ ) J n ( rksinφ )sin2φdφ .
F ±n ( ρ )= F ρ ( ρ ) 2 , F k ( ρ )| k±n =0,( Even mode ), F ±n ( ρ )=± F ρ ( ρ ) 2j , F k ( ρ )| k±n =0,( Odd mode ).
E polar | j n H n [ F n ]exp( jnθ )+ j n H n [ F n ]exp( jnθ ) |, | j n H n [ F ρ 2 ]exp( jnθ )+ j n H n [ F ρ 2 ]exp( jnθ ) |, | j n H n [ F ρ 2 ]exp( jnθ )+ j n ( 1 ) n H n [ F ρ 2 ]exp( jnθ ) |, | j n H n [ F ρ ] exp( jnθ )+exp( jnθ ) 2 |, H n [ F ρ ]cosnθ,
E polar | j n H n [ F ρ 2j ]exp( jnθ )+ j n H n [ F ρ 2j ]exp( jnθ ) |, | j n H n [ F ρ 2 ]exp( jnθ )+ j n H n [ F ρ 2j ]exp( jnθ ) |, | j n H n [ F ρ ] exp( jnθ )exp( jnθ ) 2j |, H n [ F ρ ]sinnθ,

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