Digital Mirror Devices for Mode Selective Excitation in Multimode

Fibers

Andreas Ahrens, Steffen Lochmann and Peter Bartmann

Hochschule Wismar, University of Technology, Business and Design, Philipp-Müller-Straße 14, 23966 Wismar, Germany

Keywords:

Optical MIMO, Space Division Multiplexing, Digital Mirror Devices (DMDs), Digital Light Processor

(DLP), Mode Combining.

Abstract:

Space division multiplex (SDM) in optical communications became an attractive research topic in recent years.

A tremendous increase of data rates was exposed. In optical multiple-input multiple-output (OMIMO) SDM

can be achieved by using separated ﬁber cores or several modes in multimode ﬁbers (MMF). This paper tackles

the task of mode selective excitation in MMFs. A completely new approach is shown utilizing digital mirror

devices (DMDs) in this ﬁeld. However, ﬁnding the optimal coupling conditions is a complex task due to the

blazed grated structure of the micromirror array (MMA). A possible and intuitive solution for that problem is

shown. Still, the beneﬁts of such DMDs lies in the ﬂexibility of mode excitation and the low insertion loss of

around ´1.27dB. This paper shows that the mode separation is comparative to mode excitation achieved with

offset splices.

1 INTRODUCTION

Time division, wavelength and polarization multi-

plexing as well as high order modulation schemes

have been developed coping with the exponential

grow of data trafﬁc in optical networks and have

reached a state of maturity. Therefore, there exists

an increasing interest in optical space division multi-

plexing (SDM). Adapting well-known wireless com-

munications multiple-input multiple-output (MIMO)

techniques to optical multiple-input multiple-output

(OMIMO) transmission has been discussed in sev-

eral papers like (Hsu et al., 2004; Hsu et al., 2006).

In analogy to wireless communications, where spa-

tial diversity gained by separated antennas is sufﬁ-

cient for a MIMO channel, OMIMO exploits mode

diversity in multimode ﬁbers (MMFs) among others.

However, the ﬁrst experiment for modal multiplex-

ing dates back to 1982, where it was demonstrated

in a 10-m long MMF (Berdagué and Facq, 1982).

Newer publications show the feasibility of 2 ˆ 2 up

to 12 ˆ 12 OMIMO systems in longer optical links of

km-domain (Shah et al., 2005; Ryf et al., 2012). How-

ever, efﬁcient excitation of speciﬁc modes in a MMF

and their respective coupling and splitting is an open

question.

This paper tackles the problem of mode selective

excitation into conventional MMFs. Conventional ap-

proaches use centric and eccentric splices of a sin-

glemode ﬁber (SMF) to a MMF (Schollmann et al.,

2008). Due to the offset launching condition different

modegroups are excited within the MMF depending

on the eccentricity of the splice. Afterwards two or

more modegroups in different MMFs are combined

using fusion couplers. The hard reproducibility as

well as the low ﬂexibility are two drawbacks of this

method. Another approach is to utilize spatial light

modulators (SLMs). With SLMs as described in (Gu

et al., 2013), for instance, individual modes can be

excited with high contrast. Nevertheless, the atten-

uation due to the serial mode combining with semi-

permeable mirror couplers, which has to be used for a

concatenation of SLMs, leads to an exponential grow-

ing power loss of 3dB in each step.

Addressing these problems this paper shows a new

approach utilizing Digital Light Processor

(DLP)

chips as coupling devices. The use of digital mirror

devices (DMDs) in optical networks is described for

one source in (Yoder et al., 2001), where the DMD

has been used as a signal level controlling or network

switching device. However, this paper extends its us-

ability for SDM. The micromirror array (MMA) of

a DMD has to be considered as a diffraction grating

with blazed condition. Hence, the reﬂection of an in-

citing laser beam produces multiple diffraction maxi-

mums. Finding the global maximum in a mechanical

Ahrens, A., Lochmann, S. and Bartmann, P.

Digital Mirror Devices for Mode Selective Excitation in Multimode Fibers.

DOI: 10.5220/0005948500190024

In Proceedings of the 13th International Joint Conference on e-Business and Telecommunications (ICETE 2016) - Volume 3: OPTICS, pages 19-24

ISBN: 978-989-758-196-0

setup becomes a complex task. To avoid possible side

effects of this in the OMIMO ﬁeld new technology

this paper concentrates on 2 ˆ 2 OMIMO. This con-

tribution is structured as follows: Sec. II starts with

a short description of the coupling system. More in

detail Sec. III deﬁnes parameters as well as the coor-

dinate systems used to determine the diffraction be-

haviour of the DLP in Sec. IV. The mathematical de-

scription is then used in Sec. V ﬁnding optimal cou-

pling conditions for the experimental setup. Sec. VI

shows how the theory is realized and the ﬁrst results

achieved with visible light. They are compared to pre-

vious results from (Sandmann et al., 2014). The paper

closes with a conclusion-section in VII.

2 UTILIZING DMDS IN OPTICAL

MIMO

The breakthrough of the DLP technology can be

traced back to efforts made by Texas Instruments (TI)

at the beginning of the eighties, more precisely to

Larry J. Hornbeck. The heart of a DLP projector is

the DMD, which is patented by TI in 1986. The DMD

consists of thousand of small mirrors having sizes in

micrometer domain. The micromirrors are synony-

mously referred as pixels. The principle of a DMD

is quite simple: each mirror can be tilted such that a

light source is reﬂected to either an optical output sys-

tem or an absorber. Hence, each pixel can be switched

into so called ’on’- and ’off’-states. This principle is

adapted for OMIMO as depicted in Fig. 1.

Fig. 1 shows the principle for the coupling pro-

cess. Utilizing the property that each single mirror

can be addressed to two opposite states, two inde-

pendent sources can be arranged in front of the DLP

Figure 1: DMD supported optical space division multiplex-

ing.

such that the main output direction of both reﬂected

laser beam patterns is equal for both sources. The

light sources are simply two SMF at which ends are

collimating lenses to widen the light into collimated

laser beams. These beams are reﬂected by the MMA

where mirrors in ’on’-state reﬂect only one source to

the output direction, for the other source mirrors in

’off’-state do. In this output direction an optic focuses

the reﬂected laser beams onto a MMF. Thus, the tilt

pattern on the MMA performs SDM. A ﬂexible so-

lution for a parallel excitation of low and high order

modes can be designed.

3 DEFINITIONS

This section deﬁnes in a ﬁrst step two different coor-

dinate systems: one aligned with the DLP, the other

one with the setup as well as their mathematical con-

nectedness. In a second step the coupling parameters

are deﬁned in the second space.

The whole mathematical description is made in

the direction cosine space (DCS) (Tang, 2007) whose

axes are orientated with the micromirror vertices. Fig.

2 illustrates its orientation. The origin lies in the

MMAs center. The tilt axes of each micromirror is

parallel to α “ ´β. This means in other words that

the normal of each mirror lies parallel to the plane

spanned by the γ-axis and the line α “ β. In the ’on’-

or ’off’-state of a pixel the angle between the normal

of the mirror and the γ-axis is either `ρ or ´ρ, re-

spectively.

Figure 2: Experimental setup and its coordinates of the di-

rection cosine space.

The second DCS is motivated by the aim that the

experimental setup is symmetric related to the vertical

plane on an optical breadboard. Considering that it is

deﬁned as depicted in Fig. 2 b) and 2 c). The DMD is

rotated in the α

-plane by ε such each normal of a

micromirror is parallel to the α

-plane independent

on the state of the mirror. Hence, mirrors in ’on’-state

can be used by one source, mirrors in ’off’-state by

OPTICS 2016 - International Conference on Optical Communication Systems

the other source. The two DCSs are connected by

“ R

(1)

and

“ γ , (2)

where R is a simple two dimensional rotation matrix.

There are two coupling parameters for each direc-

tion deﬁned, where Fig. 2 exemplary shows them for

the ﬁrst input direction. The angle between the pro-

jection of the location vector of a source onto the α

plane and the γ

-axis is called θ and the angle between

the location vector and the β

-axis is ϕ. The two an-

gles are orthogonal to each other. Subscripts like i1,

i2 and o denotes the connection of an parameter to

the ﬁrst or second input or the output direction. By

applying simple vector calculation as well as the con-

nection between a Cartesian space and the DCS one

can easily derive the association between coupling pa-

rameters and the DCS.

“ cospθqsinpϕq (3)

“ cospϕq (4)

4 DIFFRACTION BEHAVIOUR OF

THE MMA

Due to the physical structure of the MMA, the DMD

has to be considered as a two dimensional blazed grat-

ing. If the mirrors are not tilted, the MMA reacts as

a common diffraction grating with the difference that

the light is reﬂected instead of passing a two dimen-

sional lattice. In the case of one dimension the macro-

scopic equation of diffraction is given by

sinξ

˘ sin ξ

“ m

, (5)

where ξ

is the incident angle, ξ

the output an-

gle, λ the used wavelength and g the grating con-

stant (Goodman, 2005). Note that the angles ξ are

measured to the array normal, which is different to

the deﬁnition of θ. The variable m gives the order

of the grating which is an integer limited by physical

possible directions. In the setup corresponding angles

of zeroth order are given by

“ π ´ θ

(6)

and

“ π ´ ϕ

. (7)

In (Harvey and Vernold, 1998) the derivation of (5) to

the appropriate DCS representation is presented. By

extending these equations to the two dimensional case

the grating behaviour can be described by

` α

“

(8)

and

` β

“

. (9)

The transition from the macroscopic equation to

the real intensity distribution of the reﬂected light has

to be taken in order to ﬁnd optimal coupling param-

eters. By neglecting the faceted proﬁle of the MMA

(Hayat, ), i.e., the blazed structure, and by utilizing

the same mathematical tools as in (Harvey and Ver-

nold, 1998), the full intensity distribution is deﬁned

pα, βq “ I

sinpP

πpg{λqpα ´α

sinpπpg{λq pα ´ α

sin

πpg{λqpβ ´β

sinpπpg{λq pβ ´ β

. (10)

The number of micromirrors (pixels) in α- and β-

direction is denoted by P

and P

. Under the con-

dition that (8) and (9) hold, (10) becomes the normal-

ization constant I

which is a multiple occurred global

maximum.

By considering the proﬁle of the MMA one takes

the step into the blazed grated structure. Due to the

symmetric setup the blazed behaviour inﬂuences the

output parameter θ

whereas the ϕ

stays unchanged

compared to (7). Due to the tilt of the mirror ρ the

angle θ

o,b

becomes

o,b

“

π ´ 2ρ ´θ

for ε “ ´π{4

π ` 2ρ ´θ

for ε “ `3π{4 ,

(11)

where the subscript o,b denotes the blazed output di-

rection. From (Instruments, 2008) it is known that

the faceted proﬁle creates a sinc

p¨q-envelope on the

intensity distribution (10) in each direction. By con-

sidering the rotation (1) and applying (3) to (11) to get

the blazed parameters α

o,b

and β

o,b

one ends up with

Ipα, βq “I

pα, βq sinc

α ´ α

o,b

sinc

pβ ´ β

o,b

(12)

being the complete description of the intensity distri-

bution of the MMA reﬂected laser beam, where s is

the length of an edge of a micromirror.

Digital Mirror Devices for Mode Selective Excitation in Multimode Fibers

5 OPTIMAL CONDITIONS FOR

OPTICAL MIMO COUPLING

Using this equation one can deﬁne an optimization

program whose result gives the coupling parameters

one has to apply in the experimental setup. A simpli-

ﬁed program is evaluated as follows:

pθ

, ϕ

q “ argmax

0ăθ

ăπ{2

pi{2ăϕ

ăπ

max

α“0

ρ“`π{15

ε“´π{4

Ipα, βq . (13)

This program considers the symmetric setup achieved

by the DMD rotation by ε. The optimization returns

the coupling parameters of the ﬁrst source i1. Note

that α “ 0 assumes θ

“ π. The missing parameters

of the second source i2 as well as for the output o are

deﬁned by the symmetry.

“ π ´ θ

(14)

“ ϕ

(15)

“ π ´ ϕ

(16)

However, the program (13) is of highly non-convex

structure. For a few selected wavelengths the found

results were obtained by exhaustive searches over a

predeﬁned subset of optimization parameters. The

subset is chosen to 61{180 ¨ π ď θ

ď 71{180 ¨ π and

0{180 ¨ π ď ϕ

ď 90{180 ¨π with steps of 0.025{180 ¨

π in each direction. The results are given in Tab. 1.

The coupling loss at this point, which is deﬁned

by the ratio between the energy located within output

direction and its ´3dB cut-off and the overall energy,

for the selected wavelength is L

DMD

« ´1.27dB. This

loss neglects the window attached in front of the

MMA, which has to be passed twice, as well as the

refelctivity of the mirrors. However, by intuition the

angles θ

and θ

are around π˘2ρ which is expected

by (11) because the output direction is demanded to

“ π. By presuming this condition to the program

(13) an evaluation was made using a wider range of

wavelength. To these results regressions on the previ-

ously sorted sets were made assuming analytic func-

tions of quadratic form

λ “ f

pθ

“ 11{30 ¨ π, ϕ

q “

”

pϕ

´ π{2q

` λ

¨ 10

´9

(17)

The results for the regression parameters λ

and λ

are given in Tab. 2. The family of curves is given in

Fig. 3.

With this result one can directly determine op-

timal coupling parameters for an operating wave-

length. The choice, which curve has to be chosen,

is a trade off between stability around this operating

Figure 3: Illustration of Tab. 2.

wavelength, e.g., for wavelength division multiplex-

ing systems, and the mechanical stability of the setup.

The ﬂatter the slope of the curve in a chosen working

point the more stable is the mechanical setup against

variations of the positioning. In contrast, the steeper

the curve the higher is the stability for wavelengths

around this point.

6 REALIZATION AND RESULTS

Fig. 4 shows the ﬁrst version of the experimental

setup. Two collimating lenses

widen the signal

carrying light at the end of two SMFs to two colli-

mated laser beams. These two beams are reﬂected at

the DLP

, where a previously assigned bit map de-

termines the tilt pattern of the underlying MMA. This

consequently decides which source later activates low

and which source high order modes, respectively. The

camera UI-1240LE

measures the reﬂected laser

beam pattern at the main output direction, which will

be later replaced by an optic focusing the light pattern

onto an attached MMF.

Figure 4: Experimental setup.

The ﬁrst proof of concept has been made using

visible light with wavelength λ “ 675nm. Therefore,

the camera gives a more detailed and intuitive insight

OPTICS 2016 - International Conference on Optical Communication Systems

Table 1: Optimal coupling parameters of two sources arranged in front of the DLP.

λ ϕ

i1{i2

¨ 180{π θ

¨ 180{π

675nm 36.025 66.025 113.975

778nm 44.600 65.650 114.350

1326nm 38.000 66.375 113.625

1576nm 46.125 66.000 114.000

into the mechanical structure and its optimization pa-

rameters. The setup has two orthogonal degrees of

freedom for each source as previously mentioned:

i1{i2

and ϕ

i1{i2

. As the experiment is realized using

standard optical adjustment components, the param-

eters, which can be varied, are not orthogonalized to

each other. The adjustment becomes an iterative pro-

cess, which is easier achievable for visible light. The

optimized parameters ϕ

“ ϕ

« 0.62π, θ

« 0.37π

and θ

« 0.63π which are chosen from Tab. 2 curve

j “ 2.

The DLP was programmed with a bitmap with

an inner circle of ones and zeros around this circle.

Hence, one source is seen as a circle on the MMA

from the camera, the other one as the corresponding

annulus. For the evaluation process the camera took

pictures from each source while the parallel source

was switched off. Through these pictures a vertical

cut was taken to look at the light intensity as a func-

tion of the radius. By looking at the orthogonality of

the curves generated by the different sources one can

conclude to the capability of SDM of this setup. To

have a better reference, these curves are compared to

light intensity distributions measured at the end sur-

face of a 1.4km MMF. The different distributions are

obtained by splices of SMFs to MMFs with centred

and offset launching conditions and a subsequent fu-

sion coupler for the mode combining process into that

MMF as used in the OMIMO testbed in (Sandmann

et al., 2014). Fig. 5 and 6 show the ﬁeld pattern of the

measurements.

Fig. 5 shows the intensity distribution over a ver-

tical cut through a surface of a MMF. The red dashed

curve is the distribution produced by a centric splice

as described and the blue solid curve produced by an

18µm eccentric splice. The graph shows well sepa-

Table 2: Analytic functions of shape (17) to obtain optimal

coupling parameters using the DLP.

j λ

rnms λ

rnms

1 ´311.0 624.5

2 ´354.9 728.1

3 ´415.1 872.3

4 ´507.5 1088.0

5 ´666.7 1448.0

6 ´994.0 2167.0

7 ´1604.0 3886.0

Figure 5: Cut through light intensity measurements: Mode

ﬁeld pattern realized by a fusion coupler with center and

offset launch condition.

Figure 6: Cut through light intensity measurements: Mea-

sured DLP-controlled output pattern.

rated low and high order modes as expected. In con-

trast to Fig. 5, Fig. 6 represents vertical cut through

pictures acquired by the camera. For the red dashed

curve a centred circle pattern is set to the DLP, for

the blue solid curve the corresponding annulus. Note

that the parameters I

0,1{0,2

as well as r

0,1{0,2

are nor-

malizing constants taken from the measured bit map

acquired by different sensors, which only allows a

conclusion about relative power distribution within

one graph rather than absolute power distribution or

a comparison between both graphs with respect to the

Digital Mirror Devices for Mode Selective Excitation in Multimode Fibers

measured power.

In Fig. 6, the proﬁle is disturbed by fridges. They

originate from a non-optimal anti-reﬂection coating

of the protection window attached to the DLP. An ad-

ditional difﬁculty appears if one compares the left and

right maximum of the annulus which are different in

their intensity. The differences is related to the me-

chanical setup which was not able to match the opti-

mal coupling conditions as described in Sec. 5, per-

fectly. Nevertheless, a clear separation of both curves

can be seen as good as in Fig. 5. This meets the re-

quirement such that the inner source excites low order

modes and the outer source high order modes if both

sources are concurrently stimulated and the reﬂected

pattern is focused onto a MMF. An advantage of the

mode coupling technique utilizing the DLP compared

to the splices concatenated with fusion coupler is that

the ratio between the inner circle and the outer one

can be freely chosen by the tilt pattern of the MMA

and is not ﬁxed. Moreover, the achievable theoretical

power loss of L

DLP

« ´1.27dB of our setup is far less

than L

SLM

« ´3dB for a two step serial concatenation

of SLMs.

7 CONCLUSION

This paper shows how mode group speciﬁc excitation

in a MMF can be realized using a DMD. The under-

lying MMA combines two different mode groups si-

multaneously. Therefore, the DMD features advan-

tages of SLM techniques and fusion couplers while

avoiding their speciﬁc drawbacks – a controllable

mode speciﬁc and parallel excitation while having a

low insertion loss. Since the MMA is a blazed grat-

ing ﬁnding the optimal incident angles to the DMD is

a complex task. A ﬁrst proof of the concept is done

with visible light. The ﬁeld pattern of the reﬂected

light of each was captured by a camera to evaluate

their orthogonality. Similar to the mode ﬁeld pat-

tern achieved by offset splices of SMF and MMF the

curves of the light intensity distribution generated by

different sources are well separated. Hence, the po-

tential of using DMDs for mode selective excitation

in a MMF has been demonstrated.

REFERENCES

Berdagué, S. and Facq, P. (1982). Mode division multiplex-

ing in optical ﬁbers. Appl. Opt., 21(11):1950–1955.

Goodman, J. W. (2005). Introduction to Fourier Optics. The

McGraw-Hill Companies, Inc., 2nd edition.

Gu, R. Y., Ip, E., Li, M.-J., Huang, Y.-K., and Kahn, J. M.

(2013). Experimental demonstration of a spatial light

modulator few-mode ﬁber switch for space-division

multiplexing. In Frontiers in Optics 2013 Postdead-

line. Optical Society of America.

Harvey, J. E. and Vernold, C. L. (1998). Description of

diffraction grating behavior in direction cosine space.

Appl. Opt., 37(34):8158–8159.

Hayat, G. S. Handbook of diffraction gratings - ruled and

holographic. JOBIN-YVON S.A.

Hsu, R., Tarighat, A., Shah, A., Sayed, A., and Jalali, B.

(2006). Capacity enhancement in coherent optical

MIMO (COMIMO) multimode ﬁber links. Commu-

nications Letters, IEEE, 10(3):195–197.

Hsu, R. C. J., Shah, A., and Jalali, B. (2004). Coherent op-

tical multiple-input multiple-output communication.

IEICE Electronics Express, 1(13):392–397.

Instruments, T. (2008). Using lasers with DLP DMD tech-

nology. Technical report, Texas Instruments.

Ryf, R., Fontaine, N. K., Mestre, M. A., Randel, S., Palou,

X., Bolle, C., Gnauck, A. H., Chandrasekhar, S., Liu,

X., Guan, B., Essiambre, R.-J., Winzer, P. J., Leon-

Saval, S., Bland-Hawthorn, J., Delbue, R., Pupalaikis,

P., Sureka, A., Sun, Y., Grüner-Nielsen, L., Jensen,

R. V., and Lingle, R. (2012). 12 ˆ 12 MIMO trans-

mission over 130-km few-mode ﬁber. In Frontiers

in Optics 2012/Laser Science XXVIII, page FW6C.4.

Optical Society of America.

Sandmann, A., Ahrens, A., and Lochmann, S. (2014). Ex-

perimental description of multimode mimo channels

utilizing optical couplers. In Photonic Networks; 15.

ITG Symposium; Proceedings of, pages 1–6.

Schollmann, S., Schrammar, N., and Rosenkranz, W.

(2008). Experimental realisation of 3 ˆ 3 MIMO sys-

tem with mode group diversity multiplexing limited

by modal noise. In Optical Fiber communication/-

National Fiber Optic Engineers Conference, 2008.

OFC/NFOEC 2008. Conference on, pages 1–3.

Shah, A., Hsu, R., Tarighat, A., Sayed, A., and Jalali, B.

(2005). Coherent optical MIMO (COMIMO). Light-

wave Technology, Journal of, 23(8):2410–2419.

Tang, K.-T. (2007). Mathematical Methods for Engineers

and Scientists 2. Springer-Verlag Berlin.

Yoder, L. A., Duncan, W. M., Koontz, E. M., So, J., Bartlett,

T. A., Lee, B. L., Sawyers, B. D., Powell, D., and Ran-

curet, P. (2001). DLP technolgy: applications in op-

tical networking. In SPI Proceedings, volume 4457,

pages 54–61.

OPTICS 2016 - International Conference on Optical Communication Systems