Modal noise due to short-wavelength (780-900-nm)transmission in single-mode fibers optimizedfor 1300 nm

Santanu K. Das

The power penalty due to modal noise has been quantified and experimentally verified for single-mode fibersystems operating above their cutoff frequency. It is shown how the modal power distribution evolves fromone connector/splice to the next and affects the degree of modal noise.

1. Introduction

Recently, considerable attention has been focusedon using inexpensive short-wavelength (780-900-nm)sources, such as compact disk (CD) player lasers foroptical fiber communication.' In the short-wave-length region, however, single-mode fibers (optimizedfor signal transmission at wavelengths of 1300 nm andbeyond) are usually multimoded (two or more modes).With coherent or partially coherent illumination, asfrom CD lasers, modal noise2 is thus generated at con-nectors/splices etc. Since this noise also depends onthe modal power distribution, two connections withidentical loss values and situated back to back gener-ate different levels of modal noise due to mode conver-sion at the first connection. This effect is investigatedin this paper. Also presented are theoretical and ex-perimental results on modal noise power penalties in adigital system.

Related work in this area includes the study of mod-al power (distribution) dependence of modal noise byWood3 and Ewell,4 the evaluation of modal amplitudecoupling coefficients by Petermann, 5 White andMettler,6 and Sakai and Kimura.7 Modal noise insingle-mode systems has been investigated by Stone,8Cheung et al.,9 Heckmann,' 0 and Sears et al."1 Re-cently Stern et al.' 2 have reported on power penaltyestimates for single-mode fiber systems operated withmultimode lasers at 800 nm.

The author is with AT&T Bell Laboratories, Whippany, NewJersey 07981-0903.

Received 16 June 1987.0003-6935/88/030552-05$02.00/0.© 1988 Optical Society of America.

Propagation characteristics of type 5-D single-modefibers (SMFs), operating at short wavelengths, are dis-cussed in the Appendix. Calculations therein suggestthat the fiber is dual moded (linearly polarized modesLPoi and LPi) around 800 nm with the possibility ofhigher-order leaky mode excitation in short fiberlengths. Also, Marcuse'3 has shown that the funda-mental mode in single-mode fibers is very nearlyGaussian in shape, especially at high V numbers.Hence, in the short-wavelength region of interest,where V 4, using modes of the infinite square lawmedium incurs little error. Assuming dual-modepropagation and Laguerre Gaussian fields for thesemodes, the dc signal-to-noise ratios (dc-SNRs) areevaluated in Sec II. It is shown how the power ratio ofthese two modes changes after an interconnection andinfluences the degree of modal noise. Section III in-cludes a description of the modal noise experiment.Good agreement has been found to exist between thefunctional form of the theory in Sec. II and the mea-sured data of Sec. III.

II. Theory

Figure 1 shows the schematic arrangement of threesingle-mode fiber sections, SMF1, SMF2, and SMF3,connected via two interconnections, C and C2.Modes LP01 and LP1 of the fibers are labeled i and j,respectively, with il and j1 referring to the modes ofSMF1 (and similarly i2 and j2 of SMF2 etc.). Theaverage coupling efficiency at any interconnectionwith an offset is given by5

(n) = F + FjjX+1 (1)

with x = PJPj = modal power ratio (MPR) of i and j,Pi = power in the ith mode,Fii = C + Q,'.,

552 APPLIED OPTICS / Vol. 27, No. 3 / 1 February 1988

SMF1 SMF2 SMF3

02 C1 (C C2 (Cx1 x2 - ~ x3

Fig. 1. Three sections of single-mode fibers SMF1, SMF2, andSMF3 connected via two connections C1 and C2. Symbol x repre-sents the mode power ratio of the fundamental to the next higher

order mode.

Fjj = C?2 + C2, andCij= amplitude coupling coefficient between

modes i and j.5-7,13The evaluation of the coupling efficiency for dual-

mode fibers has been undertaken in Ref. 7; it will beincluded here only for the sake of completeness. Thestandard deviation of iq for a partially coherent sourceis5

= GjjFj(2)X + 1 '(2

where Fij = CjjCjj + CjiCjj = interference coefficient,G(rij) = exp [-(rjj 1)/rcI for a source with Lorent-

zian spectrum,rij = delay difference between modes i and j,

andT = source coherence time.

Figure 2 illustrates the coupling efficiency () and itsstandard deviation o-(,q) as a function of the normalizedoffset (transverse offset ba/a, where ba = offset and a =fiber radius or angular offset 0/g/WA, where 0 = angularoffset in radians and A = relative index difference).'4It is assumed that the connection sustains either atransverse or an angular offset, but no longitudinaloffset since the latter yields a vanishing cross couplingcoefficient Cij for the LP0j-LPj case and hence nomodal noise. In addition, coherent illumination ( --) has been assumed while evaluating the standarddeviation of the power loss. As expected, Fig. 2 showsthat in the offset range of interest, power coupling getsbetter with increasing x. Power fluctuations are maxi-mum at x = 1 and progressively decrease on either sideof it.

A ratio of the coupling efficiency and its standarddeviation provide a measure of the SNR5:

dc - SNR = 10 lo(17)j, (3)

which assumes that spectral components of the noiseare present throoughout the signal bandwidth. Thishas been evaluated and plotted in Fig. 3 for a coherentsource; the SNRs improve by a constant factor of 10logG(rij) when partially coherent sources are used.For circuit noise-limited systems, the associated powerpenalty can be shown to be

Penalty = 10 log I _

I + E' 101'k = 1

10-'

b

A 10-2

V

1o-

lo-

x-1 x-50

x-0.5 x=10x=1

005

1 0

~~~ ~~50

0- (77)

0 .2 .4 .6NORMALIZED OFFSET

.8 1.0

Fig. 2. Coupling efficiency (77) and its standard deviation (n) as afunction of the normalized offset for dual-mode fibers. V = 4.1, a =

4.15um, and X = 780 nm.

50

40

30 30

20-x=50

0 1 00.5

0 I0 1 2 3 4 5

LOSS (dB)

Fig. 3. Direct current SNR as a function of coupling loss for acoherent source, parameter values same as in Fig. 2.

where fBk = (1/10)[SNRcct - (dc - SNR)k],SNRcct = circuit noise-limited SNR required to

achieve a given BER in decibels,(dc - SNR)k = dc - SNR of the kth connection (de-

pendent on Xk-1), andK = number of connections.

An interconnection not only generates modal noise,it disturbs the modal power distribution in the down-stream fiber also, thus influencing the behavior of thenext connection. If the input modal power ratio MPR= Pij/Pjj in SMF1 is designated x,, then due to powerloss and mode conversion at C1, the output MPR = Pi2/Pj2 in SMF 2 can be written as

2 = C2j + X1 C?.Cj + i(4)

(5)

These values have been evaluated as a function of the

1 February 1988 / Vol. 27, No. 3 / APPLIED OPTICS 553

1

I I I I I I

power loss at C1 and are plotted in Fig. 4. For largeinput MPR (x1 2 10), the output MPR decreases veryrapidly and settles to x2 0.5 beyond connection lossesof 1 dB. For intermediate values of x1, 3 < xi < 10, therate of decrease of x2 is not quite as fast. An interest-ing property is observed when x1 < 2. In this case theoutput MPR actually improves with increasing lossvalues to reach a maximum (and then decreases mono-tonically). This reinjection of power back into theLPo1 mode indicates that in a practical system theMPR never deteriorates to very low values (x << 1) butoscillates around the uniform power distribution x = 1.

Depending on the modified value of X2, C2 will nowgenerate a different level of modal noise than C1, eventhough it may be specified to be as lossy as C1. (If theoffsets at C1 and C2 are the same, C2 yields a differentloss value for x2 5z xl; however, it is assumed that theconnections are specified by power loss and not byoffsets.) Equation (5) can be used repeatedly to yieldthe evolution of the modal power ratio after K connec-tions. The associated penalty can be calculated fromEq. (4).

111. Experiment and Results

A schematic of the modal noise experiment setup isshown in Fig. 5. Three sections of single-mode fibersSMF1 (1 m), SMF2 (1 m), and SMF3 (4 km) areconnected via two variable connections C1 and C2arranged on x-y-z micropositioners. SMF3 has a cut-off wavelength of 1250 nm; for SMF1 and SMF2, vari-ous combinations of fibers with different cutoff wave-lengths in the 1150-1330-nm range were used. AMitsubishi CD laser (PO = 3 mW), emitting in a 2-Awide single longitudinal mode at 780 nm, was driven by1.5-Mbit/s, 27 - 1 NRZ PRBS. The laser and a GRINlens were aligned for maximum power coupling intoSMF1. Index matching was applied between the lensand fiber to avoid reflections back into the laser cavity.A TE cooler, which houses the laser diode, is tempera-ture cycled by +50 C about the ambient temperature.This range of source temperature excursion, leading toconditions of longitudinal mode hopping etc.,15 wasfound to be adequate to explore a wide range of specklepatterns at C1 and C2. The received power was moni-tored by the photocurrent in the receiver via the digitalvoltmeter. The receiver linear channel output provid-ed the signal eye on the oscilloscope. The power pen-alty was recorded by the BER test set.

First, the experimental value of the MPR in SMF1 isreported. This was determined to be x1 = 20 from Eq.(1) using the offset loss data at C1. Such a high valuefor the MPR in SMF1 is not surprising considering thefact that the laser, the GRIN lens, and SMF1 wereproperly aligned (i.e., without any tilt etc.) for maxi-mum power coupling into the fiber. Results from Ref.3 predict that in such a configuration, almost no powergets coupled from the laser into modes with odd azi-muthal numbers.

Measured values of power penalties (worst case) forlosses arising from transverse offsets at C1 and C2 areplotted in Fig. 6 and represent the excess optical power

10

= 0.5

10

0 1 2 3 4 5LOSS (dB)

Fig. 4. Evolution of the mode power ratio x2 as a function of theinput MPR x1 and the loss at C1.

FUNCTION DESKTOPGEN. VOLTMETER COMPUTER

TE | rDIOITALCOOLER THER. 1m l m 4 km

SMF1 SMF2 SMF3

GRIN C(ThoThfl

Cl 02 VARIALE

INDEX ATTEN.MATCHED

Fig. 5. Experimental setup for measurement of the modal noisepenalty.

4.01SYMBOLS

33.2 -

I -59 2.4

- 1.6

LOSS AT C1

0 dB 0.5 dB

1 dB EXPT.2 dB

3 dBTHEORY

, 1 dB

0.5 dB

0 dB

°°0 I ,' 1 1 ' I I

0.0 .8 1.6 2.4 3.2 4.0

LOSS (dB) OF C2

Fig. 6. Excess power penalty due to modal noise for different inputloss at C1 and C2.

required to obtain a given bit error rate, 10-5 in ourcase, in the presence of modal noise. To obtain them,the laser temperature is varied, and the linear channeloutput is simultaneously scanned for the worst caseeye pattern, i.e., one with the maximum relative eyeclosure. The penalties ranged from low values (typi-cally a few tenths of a decibel) to' their maximumvalues shown in Fig. 6. To double check that a giveneye pattern was indeed the worst, the relative modalphases in SMF1 and SMF2 were perturbed by flexing

554 APPLIED OPTICS / Vol. 27, No. 3 / 1 February 1988

0

(a)

(b)Fig. 7. Modal noise eye traces for two different loss configurationsof Cl and C2 (a) penalty = 1.85 dB (Cl = 3 dB and C2 = 2 dB) and (b)

penalty = 2.37 dB (Cl = 0.5 dB and C2 = 2 dB).

the fiber. The worst eye simply reappeared at a differ-ent temperature, its relative closure unaffected.

Theoretical values of power penalties are evaluatedaccording to Eq. (5) with various loss configuration forC1 and C2. SNRCCt = 12.5 dB(BER = 10-5), rzj = 2 ps(at 2 ns/km),16 ,r = 1.7 ps (corresponding to 2-Alinewidth at 780 nm), and x = 20. One can observeagreement between the functional form (solid curvesof Fig. 6) of the theory and the measured values. A fewdata points are -0.5 dB off the predicted values, prob-ably due to errors in the experimental measurementprocess itself. It is believed that the power penaltymeasurements are accurate to -0.5 dB. Furthermore,some discrepancy can be attributed to Eq. (3), which issomewhat underestimated on account of its rms na-ture.

In Fig. 6, it is interesting to note that for the parame-ter values considered, certain more lossy combinationsof Cl and C2 may generate less modal noise than whenCl and C2 suffer lower losses, e.g., the theoreticalpenalty of 1.3 dB for C1 = 3 dB and C2 = 2 dBcompared to a penalty of 1.6 dB when C = 0.5 dB andC2 = 2 dB. Experimental results for these cases havebeen shown in Fig. 6 by the data points; correspondingsignal eye traces can be seen in Figs. 7(a) and (b),respectively, with penalties of 1.85 dB (Cl = 3 dB andC2 = 2 dB) and 2.37 dB (Cl = 0.5 dB and C2 = 2 dB).Insofar as this behavior seems unexpected, it is entire-

ly determined by the input MPR and the power loss.For small input MPRs (x < 2) and small power losses(•1 dB) there is little change in the value of the outputMPR. In this regime, there is a negligible difference inthe modal noise values from one connection to thenext.

IV. Conclusion

Absolute values as well as functional forms of modalnoise penalties in dual-mode fibers were obtained, andtheir dependence on the mode power distribution wasalso assessed. There is agreement between the com-puted and experimental results, suggesting that onecould, based on the formalism developed in this paper,predict modal noise penalties in practical systems.

The author wishes to thank P. P. Bohn for valuablesuggestions and encouragement; some of the key modi-fications in the experiment leading to repeatable re-sults and their correct interpretation were due to him.Thanks are also due to J. Ocenasek and R. J. Lisco fortheir help with the experiment setup, R. E. Epworthand D. Marcuse for helpful discussions, C. E. Miller forproviding different fiber samples, and C. Sandahl forsupplying some optical hardware.

Appendix: Modal Properties of SMF at ShortWavelengths

Section A briefly reviews the modal properties of asingly clad step-index SMF. The propagation in W-fiber (depressed inner cladding) is discussed in Sec. B,since our experiments use this fiber type. In Sec. C,theoretical cutoff values of the test fiber are deter-mined. Discussion is limited to weakly guiding'7 fi-bers for which the refractive-index differences be-tween the core and cladding are assumed to be small;thus linearly polarized LPip modes of circumferentialorder I and radial order p are used in all calculations.

A. Singly Clad Step-Index SMF

A singly clad step-index SMF supports the LP0 1mode'8 (or HE,, in conventional notation) for normal-ized frequency V < 2.405. V is given by' 7

V=ka n1 n2, (Al)

where k = (27r)/X = vacuum wave number,X = vacuum wavelength,a = fiber core radius,

n = core refractive index, andn2 = cladding refractive index.

LP01 is the fundamental mode with a frequencycutoff V = 0. The next higher-order mode is LP11,19

which has V = 2.405. A well-defined cutoff wave-length X, corresponding to Vc = 2.405 exists, belowwhich a fiber is technically multimode. But in realitya fiber can be effectively single mode somewhat belowthe mathematical Xc, where the extra modes have highattenuation. If V is increased further, LP02 - andLP2 1- modes are guided at Vc 3.83. As Eq. (Al)indicates, SMFs that have XC around 1200 nm would

1 February 1988 / Vol. 27, No. 3 / APPLIED OPTICS 555

not guide the LP02 - or the LP21 - modes in the 780-900-nm region.

B. W-Type (Depressed Inner Cladding) SMF

For a W-type SMF with refractive-index profile,nj(r < a,),

n n(alr<a2)Ino(a2 < r),

there are two V values, V0 < V2, given by20

V = ka(A2)

V2 = kaj n2 -n 2

This fiber can be modeled as a combined system of thereference singly clad fiber of V = V2 surrounded by aperturbing outer medium. V refers to the normalizedfrequency of the W-fiber.

Modes whose propagation constant a < nok assumethe properties of leaky waves because they tunnelthrough the gap region a < r < a2. Kawakami andNishida2' have shown that the number of guidedmodes in such a fiber depends mainly on the core andouter cladding, while characteristics of guided modesare mainly determined by the core and inner cladding.The first-order approximation for cutoff of the W-fiber given by 21

2L 2E0=Oc = V2c (A3)

gets modified due to the finite gap width (a2 - a).22

Using Figs. 3 and 4 of Ref. 22 it is possible to get thecorrected values of Voc and V2c for a given gap width (a2- a,) and refractive-index difference ratio (n, - n2)/(n2 - no).

C. Theoretical Cutoff Values of the Test Fibers

In all the measurements reported in the text, de-pressed inner cladding SMFs (8.3/125 ,im) with 1130nm < Xc < 1330 nm were used. Substituting fiberparameter values23 in Eq. (A3) and then using Figs. 3and 4 of Ref. 22, one obtains for

LP11 mode:

LP02 mode:

LP21 mode:

V2, = 2.75, X, = 1180 nm,

V2, - 4.5, X, - 715 nm,

V2, -4.5, X, - 715 nm.

Cutoff values as above require that the test fibers bedual-moded from 780 to 900 nm (4.1 2 V2, > 3.57);theoretical formulations in the text are based on thisassumption.

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and Ey, the term SMF thus applies to a given polarization oflight power.

19. Due to nonzero 1, there are two orthogonal polarizations E, andEy, and two orientations coslo and sinlk.

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