transporting data on the orbital angular momentum of light · leslie a. rusch canada research chair...

Leslie A. RuschCanada Research ChairCommunications Systems Enabling the Cloud

Transporting Data on the Orbital Angular Momentum

of Light

FOR FURTHER READING …

2

Outline

Motivation – overcoming the Shannon limit

Space Division Multiplexing systems

Fibers for SDM• Background on fibers• Eigenmodes & Few mode fibers

Linearly polarized (LP) modes solution• Multiple input, multiple output (MIMO) processing

Orbital angular momentum modes (OAM) solution• OAM fibers – why we like them & how we design them• OAM at UL• OAM transmission experiments

Conclusion

3

Squeezing Shannon

Coaxial cable to fiber optics• Increased distance & bandwidth

Squeezing Shannon


Fast electronics

A. Erik, et al., "Roadmap of optical communications," Journal of Optics, vol. 18, p. 063002, 2016.

Squeezing Shannon


Fast electronics

Wavelength Multiplexing


Squeezing Shannon


Fast electronics


Advanced modulation• polarization and I/Q


Squeezing Shannon


Fast electronics


Advanced modulation• polarization and I/Q


capa

city

Nonlinear Effects

Optical fibers are pretty thin …• 8 micron cores• Many wavelengths means high power

• Megawatts per square centimeter• Nonlinear effects

Sending more power makes performance worse• Not part of Shannon’s limit

9A. D. Ellis, et al., "Performance limits in optical communications due to fiber nonlinearity," Advances in Optics and Photonics, vol. 9, pp. 429-503, 2017/09/30.

Nonlinear Effects

Optical fibers are pretty thin …• 8 micron cores• Many wavelengths means high power

• Megawatts per square centimeter• Nonlinear effects

Sending more power makes performance worse• Not part of Shannon’s limit

10A. D. Ellis, et al., "Performance limits in optical communications due to fiber nonlinearity," Advances in Optics and Photonics, vol. 9, pp. 429-503, 2017/09/30.

Bandwidth growth and demand

11Winzer, P.J., "Spatial Multiplexing in Fiber Optics: The 10X Scaling of Metro/Core Capacities," Bell Labs Tech. J. , vol.19, pp.22-30, 2014

Bandwidth growth and demand

12

Global IP Forcast

Winzer, P.J., "Spatial Multiplexing in Fiber Optics: The 10X Scaling of Metro/Core Capacities," Bell Labs Tech. J. , vol.19, pp.22-30, 2014

Next wave of capacity increase

D. J. Richardson, J. M. Fini, and L. E. Nelson, "Space-division multiplexing in optical fibres," Nature Photonics, vol. 7, p. 354, 04/29/online.

Next wave of capacity increase

D. J. Richardson, J. M. Fini, and L. E. Nelson, "Space-division multiplexing in optical fibres," Nature Photonics, vol. 7, p. 354, 04/29/online.

space division multiplexing

Outline






Conclusion

18

Fiber bundles ?

Instead of electronic regeneration

Use parallel fiber systems

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Fiber bundles ?

Instead of electronic regeneration

Use parallel fiber systems

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Increased capacity, but• not greener• not cheaper

Integration drives down price per bit

Fiber bundles vs. fiber w/multiple channels

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Requirements• Fiber with multiple channels

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Requirements• Fiber with multiple channels• Integrate transceivers to higher capacity

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Requirements• Fiber with multiple channels• Integrate transceivers to higher capacity• Amplifiers

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Requirements• Fiber with multiple channels• Integrate transceivers to higher capacity• Amplifiers• Switches

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Requirements• Fiber with multiple channels• Integrate transceivers to higher capacity• Amplifiers• Switches

SDM offers • higher capacity • path to lower cost and power per bit

26

Spatial Multiplexing in New Fibers

a single core, a single mode56 Gbaud, 80 λs, DP-16QAM

27


a single core, a single mode

multiple cores, each a single mode

28



a single core, multiple modes


29





ring core fiber

30





and eventually ….multiple cores, multiple modes

ring core fiber

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32

What kind of fiber can support the most modes?



33

What kind of fiber can support the most modes?

What kind of modes?

Outline






Conclusion

34

Single mode vs. multimode

Fibers used to come in two types…• Small core (single mode)• Large core (multimode)

35

high performance, long distanceeasy to couple, cheap

Spatial division multiplexing

A new kind of fiber• Larger distances & bit rate of SMF• Avoid the modal dispersion of MMF• Modes as independent, separate channels

Need to control the modal interactions• Play with dimensions to limit the number of modes • Few mode fiber – not hundreds, not thousands

36

Few mode fibers

Modes in fibers: solutions of Maxwell's equations

Eigenmodes• Building blocks of derivative modes• Some solutions of Maxwell’s equation “flock” together

• mode groups that are interrelated and that interact

All depends on physical parameters of the fiber

37

SINGLE-MODE OPTICAL FIBER (SMF)

Even in single mode fiber – two polarizations

Gaussian shaped intensity profile

38

SINGLE-MODE OPTICAL FIBER (SMF)

Even in single mode fiber – two polarizations

Gaussian shaped intensity profile

39

arrows are polarization

Few-mode-fiber (FMF)

40

Six spatial and polarization modes to place information.

FEW-MODE

8 micron core

Few-mode-fiber (FMF)

41

Six spatial and polarization modes to place information.

Eigenmodes

FEW-MODE

8 micron core

Few mode fibers

Modes in fibers

Eigenmodes• Building blocks of derivative modes• Some solutions of Maxwell’s equation “flock” together

• mode groups that are interrelated and that interact

All depends on physical parameters of the fiber

Typical fibers have solutions called scalar modes• Solution of a simplified version of Maxwell’s equation• Called the “weakly guiding” solution

42

Refractive index of cladding ≈Refractive index of core

Linear-Polarized (LP) Modes

43

Scalar approximation to vector modes

Six spatial and polarization paths

Boxes indicate near-degenerate modes – expect strong coupling

Linear-Polarized (LP) Modes Scalar

approximation to vector modes



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45

LP01 LP11a LP11b





46

Y-pol

LP01 LP11a LP11b

X-pol

Outline






Conclusion

47

LP modes or scalar modes

Studied for a long time

Intensity profiles of light for each mode

Degenerate modes … • Same propagation speed in the fiber• Similar geometry to intensity profiles

48

LP modes or scalar modes

LP for Spatial division multiplexing

Modal interactions mix transmitted signals

Digital signal processing at RX can undo this• Multiple input Multiple output (MIMO) processing

50

Electronic MIMO Demultiplexing

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53

I1 = h11O1 + h12O2 + h13O3 + h14O4 + … + h1NON


Need the complex filter (time varying amplitudes/phases) for each mode output

54

I1 = h11O1 + h12O2 + h13O3 + h14O4 + … + h1NON


Number of filters scales with the square of number of modes

55

DSP requirements for LP mode multiplexing

57


58


59

Different markets

Long haul• Spectral efficiency being maxed out• DSP complexity high for dispersion compensation• MIMO complexity not significant

Data centers• MIMO complexity would dominate

60

Different markets

Long haul• Spectral efficiency being maxed out• DSP complexity high for dispersion compensation• MIMO complexity not significant

Data centers• MIMO complexity would dominate

Opportunities for NEW version of spatial multiplexing

61

Outline






Conclusion

62

LP vs. OAM

Linearly polarized modes (LP)

• Well known & studied• First solution for SDM• Perturbations cause coupling

Orbital angular momentum modes (OAM)

• Recent subject of research• New solution for SDM• Robust to perturbations

63

Eigenmodes of a fiber

64

Linearly polarized (LP) Modes

LP11x LP11yLP01

65

Linear combination of fiber eigenmodes

LP21


HE11 EH11 + HE31TE01 + HE21

LP11x

TM01 + HE21

LP11yLP01

66


LP21


HE11 EH11 + HE31TE01 + HE21

LP11x

TM01 + HE21

LP11yLP01

67


LP21

crosstalk


HE11

β1 β2 , β3 β5, β6

EH11 + HE31TE01 + HE21

LP11x

TM01 + HE21

β4 , β3

LP11yLP01

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Different eigenmodes travel at different speeds

LP21


HE11

β1 β2 , β3 β5, β6

EH11 + HE31TE01 + HE21

LP11x

TM01 + HE21

β4 , β3

LP11yLP01

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Different eigenmodes travel at different speeds

LP21

modal birefringence & crosstalk


HE11

β1 β2 , β3 β5, β6

EH11 + HE31

LP11x

TM01 + HE21

β4 , β3

LP11yLP01

OAM(1)OAM(0) OAM(-2) OAM(+2)

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Eigenmodes combined differently for OAM …

LP21

TE01 + HE21

OAM Modes

HE11

β1 β3 β6

LP01

OAM(1)OAM(0) OAM(-2) OAM(+2)

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Eigenmodes combined differently for OAM …

𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐𝐞𝐞𝐞𝐞𝐞𝐞𝐞𝐞 + 𝐣𝐣𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐𝐨𝐨𝐨𝐨𝐨𝐨 𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐𝐞𝐞𝐞𝐞𝐞𝐞𝐞𝐞 + 𝐣𝐣𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐

𝐨𝐨𝐨𝐨𝐨𝐨 𝐇𝐇𝐇𝐇𝟑𝟑𝟐𝟐𝐞𝐞𝐞𝐞𝐞𝐞𝐞𝐞 + 𝐣𝐣𝐇𝐇𝐇𝐇𝟑𝟑𝟐𝟐𝐨𝐨𝐨𝐨𝐨𝐨

β5

OAM0 OAM1 OAM-2 OAM2

OAM Modes

neff1 neff3 neff6

LP11x LP11yLP01

OAM(1) OAM(-2) OAM(+2)

72

Instead of propagation constant, consider mode effective index …

LP21

𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐𝐞𝐞𝐞𝐞𝐞𝐞𝐞𝐞 + 𝐣𝐣𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐


neff5

𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐𝐞𝐞𝐞𝐞𝐞𝐞𝐞𝐞 + 𝐣𝐣𝐇𝐇𝐇𝐇𝟐𝟐𝟐𝟐𝐨𝐨𝐨𝐨𝐨𝐨

OAM0 OAM1 OAM-2 OAM2

HE11

OAM(0)

Avoid LP modes and favor OAM modes

neff3 neff6


73



neff5

“Fence off” modes

Keep effective index separation high to avoid coupling in the fiber…

Instead of propagation constant, consider mode effective index…

neff1

HE11

OAM(0)

Avoid LP modes and favor OAM modes

neff3 neff6


74

Instead of group velocity, think of effective index for the mode



neff5

“Fence off” modes

Keep effective index separation high to avoid coupling in the fiber…

410effn −∆ >

neff1

HE11

OAM(0)

FMF for LP modes cannot support OAM modes

75

FMF designed for LP modes violate this condition …

410effn −∆ >

Recap

OAM modes can be fenced off from one another

LP modes formed from overlapping eigenmodes

• effective index cannot be shaped to avoid coupling

76

OAM characteristics

Phase varies in time

along propagation

axis

77Yao, Alison M., and Miles J. Padgett. "Orbital angular momentum: origins, behavior and applications." Advances in Optics and Photonics 3, no. 2 (2011): 161-204.

OAM characteristics

Phase varies in time

along propagation

axis

78Yao, Alison M., and Miles J. Padgett. "Orbital angular momentum: origins, behavior and applications." Advances in Optics and Photonics 3, no. 2 (2011): 161-204.

OAM example – 3rd order mode Annular field intensity profile (m=1)

Helical phase front

Circular Polarization (±)

79OAM3,1

( )ie ϕ± l

Why do we call it OAM?

80

Why do we call it OAM?

81

conservation of momentum effect

OAM fibers

Index profile matches OAM mode field intensity profile

(ring shaped)

Vector modes with well separated effective indices

⇒ avoid degeneracy into LP modes

(i.e. at least 10−4)

Effective index separation ⇒ high refractive index contrast

(violates the weakly guiding approximation)

82

Designing a fiber for OAM

Ring shaped

Large effective index separation

83

OAM fibers

84

"Vortex fiber" (2 OAM states)∆neff ≈ 1.8×10-4

S. Ramanchandran et al., “Generation and propagation of radially polarized beams in optical fiber,” Optics Letters 34, p.2525 (2009)

N. Bozinovic et al., “Terabit-Scale Orbital Angular Momentum Mode Division multiplexing in Fibers,” Science 340, p. 1545 (2013)

Ring core fibers at UL

Inverse Parabolic Graded Index Fiber (IPGIF)• Smooth gradient profile• Gradient varied to achieve

Hollow core fiber• Hollow core to maximize index contrast• Probe maximum number of modes

Ring core fiber• Analytical tools for designing step index OAM fiber

85

𝛥𝛥𝑛𝑛𝑒𝑒𝑒𝑒𝑒𝑒 > 10−4

waveguide


6µm IPGIF

23.2µm

2.4µmHollow core

5.6µm

1.8µmRing core

87

N < 0 : curvature parameter

Inverse Parabolic Graded Index Fiber (IPGIF)

Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch and S. LaRochelle, “Few-mode fiber with inverse-parabolic graded-index profile for transmission of OAM-carrying modes,” Optics Express 22, no. 15, pp. 18044-18055 (July 2014).

6µm IPGIF

88

N < 0 : curvature parameter

Inverse Parabolic Graded Index Fiber (IPGIF)

∆nmax=na-n2

N: curvature

a: core radius

a

Ung, P. Vaity, L. Wang, Y. Messaddeq, L. A. Rusch and S. LaRochelle, “Few-mode fiber with inverse-parabolic graded-index profile for transmission of OAM-carrying modes,” Optics Express 22, no. 15, pp. 18044-18055 (July 2014).

6µm IPGIF

IPGIF: Design

89

∆neff = 2×10-4

(a=3 µm)

IPGIF: Design

90

(a=3 µm)

∆neff = 2×10-4

Average loss : 8.6 dB/kmLP01 loss : 6.5 dB/km





91


OAM fibers

92

Air-core fiber (12 OAM states)∆neff ≈ 1.0×10-4

P. Gregg et al., “Stable Transmission of 12 OAM States in an Air-Core Fiber,” CLEO 2013, paper CTu2K2.

Ring-core and trench indices • dictated by material constraints • highest possible index contrast

Optimize• ∆𝑛𝑛eff > 10−4

• Number of supported modes (≥ 16 OAM states)

93

Hollow-Center Ring-Core Fiber: design

C. Brunet, P. Vaity, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Design, fabrication and validation of an OAM fiber supporting 36 states,” Optics Express 22, no 21, pp. 26117-26127 (2014).

23.2µm

2.4µm

Hollow core

Hollow-Center Ring-Core Fiber

94


95


96


97

9 OAM orders17 OAM modes36 information channels


98[ ] 4min 1.1 10effn −∆ = ×

99

Right circularpolarization

Left circularpolarization

Hollow-Center Ring-Core Fiber : 1 m transmission

loss few dB/m


100

cut-off





101


Ring Core Fiber – design tools

102

Simple geometry

fiber cross section

refractive index


103

Simple geometry

Analytical tools to choose dimensions


104

Simple geometry

Analytical tools to choose dimensions• OAM modes supported• Type• Number

410effn −∆ >

RCF Family – analytical tools for cutoff

105


106

scalar equations


107

scalar equations

vectorequations


108

scalar equations

vectorequations

C. Brunet, B. Ung, P.-A. Bélanger, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, "Vector mode analysis of ring-core fibers: design tools for spatial division multiplexing," Journal of Lightwave Technology 32.23 (2014): 4046-4057.

RCF Family – modal maps

Geometry

Normalized propagation constant

Normalized frequency

109

Modal map

110

Modal map

111

SCF fiber ρ→0

Modal map

112LP mode group

Modal map

113OAM mode “group”

Predicting ∆neff

114C. Brunet, B. Ung, L. Wang, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, "Design of a family of ring-core fibres for OAM transmission studies," Optics Express 23.8 (2015): 10553-10563.

Predicting ∆neff

115

SCF fiber ρ→0

no “fence” ⇒vector modes mix

to form LP

RCF family

116

5.6µm

1.8µm

Ring core

Outline






Conclusion

117

First proof of concept

Optical control of polarization Mode separation facilitated by this control No MIMO processing required

118N. Bozinovic, et al., "Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers," Science, vol. 340, pp. 1545-1548, June 28, 2013.

Electronic polarization demultiplexing

Single port reception

1.4 km transmission

Standard 2×2 MIMO

No polarization tuning

119R. Mirzaei Nejad, et al., "Mode Division Multiplexing using Orbital Angular Momentum Modes over 1.4 km Ring Core Fiber," IEEE/OSAJournal of Lightwave Technology, vol. 34, pp. 4252-4258, 15 Sep 2016.

5.6µm

1.8µm

Ring core

Commercial Receivers & OAM Fiber

Heterogeneous transmission (OOK/QPSK)

OAM states separated by commercial 2x2

MIMO

120L. A. Rusch, M. M. Rad, K. Allahverdyan, I. Fazal, and E. Bernier, "Carrying data on the orbital angular momentum of light," IEEE Communications Magazine, vol. 56, pp. 219 - 224, February 2018.

5.6µm

1.8µm

Ring core

Second order OAM

OAM2 in IPGIF fiber

121J. Zhu, et al., "3.36-Tbit/s OAM and Wavelength Multiplexed Transmission over an Inverse-Parabolic Graded Index Fiber," in CLEO 2017, San Jose, p. SW4I.3, May 2017.

6µm IPGIF

Higher order OAM

122

G. Zhu, et al., "Scalable mode division multiplexed transmission over a 10-km ring-core fiber using high-order orbital angular momentum modes," Optics Express, vol. 26, pp. 594-604, 2018/01/22.

4×4 MIMO over one OAM |order|

8 channelsOAM |4| OAM |5|

Higher order OAM

123

L. Zhu, et al., "18 km low-crosstalk OAM+WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation," Optics Letters, vol. 43, pp. 1890-1893, 2018/04/15.

Higher order OAM

124

no MIMO; but mode groups, ¼ of channels exploited


Higher order OAM

125


K. Ingerslev, et al., "12 Mode, MIMO-Free OAM Transmission," in OFC 2017, Los Angeles, p. M2D.1, 2017/03/19.

Higher order OAM

126

K. Ingerslev, et al., "12 Mode, MIMO-Free OAM Transmission," in OFC 2017, Los Angeles, p. M2D.1, 2017/03/19.

no MIMO; stability once modes adjusted for TX

12 channelsOAM |5| OAM |6|OAM |7|

LP vs. OAM

• Rich set of components• coupling and muxing

• LP modes from eigenmodes that necessarily interact

• high crosstalk• limited channel count

• Requires MIMO processing and multiplexed receivers

• Early stages of research• coupling issues still open

• OAM modes from eigenmodes that can be designed to avoid interaction

• low crosstalk• better channel count

• DSP & RX simpler• No MIMO processing needed• Standard 2×2

127

LP vs. OAM

• Rich set of components• coupling and muxing

• LP modes from eigenmodes that necessarily interact

• high crosstalk• limited channel count

• Requires MIMO processing and multiplexed receivers

• Early stages of research• coupling issues still open

• OAM modes from eigenmodes that can be designed to avoid interaction

• low crosstalk• better channel count

• DSP & RX simpler• No MIMO processing needed• Standard 2×2

128

target very low fiber interactions, but what about splices, etc.?; avoid MIMO

Different Strategiesembrace strong fiber interactions

to simplify components; exploit MIMO

Some other promising directions



ring core fiber

129

Some other promising directions



elliptical core fibers

linearly polarized VECTOR modes hold promise

ring core fiber

130

Conclusion

131

• Transmission of OAM modes still very new

• Design and fabrication of optical fibers is challenging

• Need to better understand mode-coupling and cross-talk mechanisms

- optimize designs

- target most appropriate OAM modes

• Integrated components are needed as well as fibers

Acknowledgments

Alessandro CorsiDr. Charles BrunetDr. Reza NejadDr. Karen AllahverdyanDr. Pravin VaityDr. Lixian WangProf. Sophie LaRochelleProf. Younès Messaddeq

Canada Research Chairs

Prof. Bora UngIrfan FazalMohammad RadEric Bernier

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transporting data on the orbital angular momentum of light · leslie a. rusch canada research chair...

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