GB2236895A - Optical communications system - Google Patents

Abstract

An optical communications system has a rare earth (e.g. erbium) doped fibre amplifier coupling an optical transmitter to an optical receiver and pumped by an optical pump. The gain of the amplifier is of sufficient magnitude and distribution to overcome substantially only the distributed intrinsic absorption of the fibre amplifier. Discrete in-line amplifiers are not required. <IMAGE>

Description

An Optical Communications System Rare earth doped fibre lasers and amplifiers offer considerable potential for application to telecommunications [1,2].

Erbium-doped fibre amplifiers operating in the spectral region of 1550 nm, can be optically pumped at 800 nm [3], 980 nm [4] or 1480 nm [5] and are of special interest in the context of both trunk and local networks. To date three physical locations for fibre amplifiers have been envisaged [1] and these are power amplifiers at the transmitter end, repeaters somewhere between the transmitter and the receiver and preamplifiers prior to the receiver package. In all cases a doped fibre, typically 1 to 10 metres in length, is spliced at either one or both ends to long span undoped transmission fibre to provide gain.

According to the present invention an optical communications system comprises a transmitter and at least one receiver optically connected by an optical transmission path which includes a doped optical fibre amplifier pumped by optical pump means, the gain of the amplifier being of sufficient magnitude and distribution to overcome substantially only the distributed intrinsic absorption of the fibre amplifier. An exemplary system is shown schematically in Fig. 1. The doped fibre from which it is composed has a low concentration of erbium or other rare earth ions and can span many tens of kilometers. We term such a system a "Long-Span Fibre Amplifier". Gain, which can overcome both the distributed intrinsic host glass absorption and possibly the discrete losses associated with fibre directional couplers, is available throughout the whole system.

We show that the long-span amplifier can eliminate both the need for splicing a separate amplifier section into a transmission line and the requirement of power feed to a location remote from the transmitter end. The long-span amplifier is also of potential importance in high bit-rate systems as it offers the possibility of using insensitive but very fast receivers.

The theoretical formalism used in this analysis is described in section 2 and is applied in section 3 to study how a long-span amplifier can be produced in a point-to-point link which is longitudinally pumped with a single source located at the transmitter end. We consider the length variation of gain and show that with careful choice of the pump power and dopant density a condition can be established in which the gain exactly cancels the losses over a substantial portion of fibre.

B Nomenclature Subscriptsp, s and a designate pump, signal and amplified spontaneous emission respectively, while superscripts + and - designate propagation which is co-directional and contradirectional with respect to the pump, respectively.

a core radius (m) h Planck's constant (J/Hz) L fibrelength (m) Ni ion density of energy level i, where i = L2,3(ions/m3) Nt total ion density in all levels (ions/m3) P(z) power (W) pO power associated with the amplified spontaneous emission of one photon per mode (w) Rij(z,r) rates of pump absorption (i = 1, j = 3 ) or stimulated emission (i = 3, j = 1) (s-1) r radial coordinate (m) w fibre spot size (m) Wij(z,r) rates of signal absorption (i = 1, j = 2) or stimulated emission (i = 2, j = 1) (s-1) z fibre length coordinate; 0 < z < L (m) a intrinsic loss of host glass (m~1) ## bandwidth of gain profile (tit) v frequency (Hz) aij cross-section: absorption or stimulated emission between levels i and j; i j = 1,2, 3 (m2) #(r) normalised radial intensity variation (m-2) #ij lifetime of the spontaneous transition between energy levels I and j; i, j = 1, 5 3 (s) (r) transverse dopant distribution of ions in the fibre 2.THEORETICAL MODEL The model used describes a longitudinally pumped three level system and is derived by the use of rate equations [6,71. The theory accounts for the conversion of pump photons, the growth of both forward and backward propagating amplified spontaneous emission (ASE) and amplification of the signal. We do not restrict consideration to the small signal regime. In formulating the problem we do not assume equality of the cross-sections g13 and a3l at the pump wavelength or al2 and a2l at the signal wavelength. The inequality of the upward and downward pump cross-sections is particularly appropriate when considering pumping at 1480 nm, for example [8].When long spans are being considered the intrinsic absorption, scattering and bending losses of the glass host become important and are also included. We assume that pumping is at a wavelength which is free from excited state absorption and so the model could be applied to circumstances in which the pump is either at 980 nm or 1480 nm, for example.

When the cross sections 12, Q21, and g31 are all taken to have distinct values, the stimulated emission and absorption rates are not set to be equal (that is R13 tR31 and W12 K W21). The rate equations governing the transitions between the three levels at steady state are thus

The expressions for the transition rates R,j and W,j are

Equations (1) to (5) are used together to give equations (6) and (7) for the population densities::

In calculating N1 and N2 it is assumed that the rate of non-radiative decay from the pump band to the upper laser level, l/r32 is significantly greater than any of the rates r31, r2l, Rij or wij. When these conditions hold the population density of level 3, the pump band, is approximately zero. This explains why (6) and (7) give the result that N1 = N1 + N2. A further feature of equations (6) and (7) is that the sum of the signal and the forward and backward propagating ASE all contribute to the saturation of the population of the upper and lower laser levels. The coefficients of (P+ + P + P,), and Pp, which appear in equations (6) and (7) signity saturation of the signal and bleaching of the pump absorption, respectively [6].

When considering a 1480 nm or 980 mn pumped amplifier, the most important situation is where the fibre propagates in the fundamental mode at both the pump and signal wavelengths. We describe the fibre in terms of the usual r, ss z cylindrical coordinate scheme.

In the computations carried out for this paper the Gaussian approximation of the fibre modes was used, thus the terms ip and is are gven by:

The spot sizes, wp,5 are given in terms of the fibre v-values in reference [9] and the denominator in equation (8) is a normalisation factor to ensure that the integrated mode shape is unity.

The length variation of the of pump power in the fibre is given by equation (9):

The factor of 2r arises from integration of the symmetric fundamental modes over the ss coordinate. In practice the lifetime r32 is difficult to determine but is believed to be small (in the order of 1 pus), the consequence of which is that the coefficient of Nl(z,rK(T) in equation (9) can often be taken as a13 to a good approximation.

The power of the co- and contra-directional ASE waves at the signal wavelength are described by:

in which the term 2po accounts for the spontaneous emission power of one photon per mode over the two polarisation states. po is given by hv5Ev and Ev has a typical value in the order of 3x 1012h [10]. The signal growth, in the same direction as the pump is governed by:

The transverse distribution function of ions in the fibre, ((r), which appears in equations (9), (10) and (11), is taken to be unity in the fibre core and zero in the cladding. Armitage [8] has considered the effect of non-uniform transverse doping profiles.

The evolution of the signal can be determined from the solution to equation (11), whilst the pump propagation is described by equation (9). The level of the forward and backward propagating amplified spontaneous emission is represented by equation (10) and is included because of its contribution to gain saturation. We do not use the formulation to draw conclusions about noise performance of long span amplifiers, which is a subject that must be addressed elsewhere. Equations (9) to (11) are nonlinear coupled differential equations, which in the absence of restrictive approximations must be solved numerically.For the case of co-directional pump and signal propagation which we consider here, the boundary values are given by equations (12) to (15): ?(z=O) =?,swp (12) pa+(z=0 = 0 (13) pa(z=L) = 0 (14) P+ (z = O) = (15) The solutions of equations (9) to (11) subject to equations (12) to (15) have been found by the use of a shooting and matching technique together with numerical integration over the radial coordinate and are the subject of section 3. We have also carried out computations which omit the saturating influence of ASE and the results are reported in the Appendix.

3. SIGNAL EVOLUTION We choose as an example a fibre of length 100 km into which a low power signal and a higher power pump are injected at one end. In practice this could be achieved by means of an appropriate dichroic directional coupler as shown in Fig.l. The injected signal is 1 pW at a wavelength of 1.545 lon, as it is found that saturation behaviour is not invoked if such a value is selected. We assume that the design of fibre waveguiding properties and host materials is chosen only to satisfy the constraints imposed by attaining zero total dispersion at the signal wavelength.The relative refractive index difference of the core and the cladding is therefore taken as 0.0135 and the core diameter is 2.5 pm. The fibre is step index and the core and cladding are fabricated from appropriate levels of silica/phosphorous pentoxide/alumina composite glasses, together with erbium doping in the core in a similar manner to the fibre reported in reference [8].

Ideally, an erbium doped fibre amplifier in any form should be pumped at a wavelength which is free from excited state absorption. It would also be desirable to ensure that the pump wavelength is as close as possible to the signal wavelength to ensure firstly that the intrinsic loss of the glass host at the pump wavelength is low and secondly, that there is a good overlap of the transverse fields. We choose a pump wavelength of 1.48 cyan, but the model outlined in section 2 could also be applied to 0.98 m pumping. An additional benefit of 1.48 pm pumping is that fibre which is designed to be bend resistant at the signal wavelength can be used without excessive bending loss at the pump wavelength.

Computations using Equations (9) to (11) are most general if the cross-sections for the upward and downward transitions are not set to be equal at either the pump or signal wavelengths. Using data from reference [8], the cross-sections used are given below: l3(1.480llm) 2.2x m2 a3l(1.480p 8.0x 10-26 m2 #12(1.545 m): 2.6x 10-25 m2 a21(1.545llm} 4.3x 1t25 m2 The fluorescence lifetimes are r21 = 9.8x10-3 s [8] and r32 = 1.0x104 s. Unfortunately, r32 is not known with any certainty for the erbium-doped silicates and so will have to be revised in the light of further evidence.

The intrinsic losses of the silica-based host glass are taken as 0.4 dB/km and 0.2 dB/km at the pump and signal wavelengths, respectively. These values are not necessarily applicable to a cabled fibre, but serve to illustrate the appropriate physical principles. It would be expected that after a 100 km journey the signal in an undoped fibre would be attenuated by 20 dB. As a first estimate of the necessry ionic concentration, Nt we assume that we require a fully inverted gain which is equal to the total intrinsic loss at the signal wavelength. This requirement is satisfied when #21Nt@as@4.6X10-5m-1. Values of the ionic concentration in the order of 1.07x 102 ions/m3 would therefore be predicted.

We will examine how the signal evolves as it propagates along the fibre. We consider length dependence of the gain, defined as 10 log10 [P+ (z) /P", ]. According to such a definition, all curves will start from a zero value whenz = 0. Figs. 2A - 2D are a set of plots of the gain variation with respect to length for a number of dopant densities and pump power levels. The dopant concentration has the values of 1x 102 , 1.53x 102 , Sx 102 and 10x 1020 ions/m3 in Figs 2A, 2B, 2C and 2D, respectively. The curves marked (a) in the four graphs apply in circumstances when there is no pumping. As elected, the fibre acts as a heavily attenuating medium in which the signal reduction is most marked when the dopant density is increased.

The straight line form of these curves indicates simple exponential decay of the signal with length.

The gain variation with respect to fibre length when there is non-zero pumping will now be examined. Fig. 2A applies when there is a low dopant density of 1X1020 ions/m3 and the six curves (b) to (g) apply for launched pump powers ranging from 50 mW to 1.6 W. The curves have a negative gradient at all points and at long lengths become parallel to curve (a). The gain is negative at all points along the fibre, which indicates that, regardless of the value of the pump power, there is insufficient dopant for stimulated emission to dominate over the intrinsic silica loss at the signal wavelength. It is interesting to note, however, that at any pump power greater than 50 mW (curve (b)), the output atz = 100 km is no worse than the -20 dB level that would be obtained in the absence of any rare earth dopant.

Signal evolution with the slightly higher dopant level of 1.53x1d0 ions/m3 is shown in Fig.

2B. As can be seen, we have selected a value of the dopant density for which the gain produced by the pumped fibre very nearly compensates for the intrinsic losses of the silica host over a significant distance. Our estimate of N1 = 1.07xlO2 ions/m3, using simple considerations turned out to be close to the computed value. Fig. 2B shows that a state which can be regarded as an optical ether is established over part of the fibre length. The length over which the ether-like behaviour is available increases with pump power. However, it should be noted that high pump powers are required for the "ether length" to persist for a significant proportion of the total fibre span.Curve (g), which shows net transparency over the first 60 km, was plotted for Pp,""p = 3.2 W.

Fig. 2C shows the signal evolution when the doping level is N1 = 5x10a0 ions3. Signal growth, followed by decline is observed in all except curve (a). At points on the curves where the gradient is positive, stimulated emission dominates over the combined loss effects of the silica host and absorption from the ground state to the upper laser level. When the gradient is negative the opposite is the case. After propagating for a long distance the curves all tend to a gradient which is the same as that of the unpumped fibre.When this happens the pump power has diminished to such a level that it is incapable of promoting a significant number of ions to the upper lasing leveL It can be seen that when the fibre is pumped there is a point where the signal power returns to its value at input P"" in which case the gain is equal to zero for a second time. We designate the length at which the gain returns to its zero value as the "transparency length". Fig. 2C shows that the transparency length increases with the pump power.

The curves on Fig. 2D were plotted for the highest dopant density of N, = 1021 ions/m3.

Curves (a), (b) and (c) appear to follow the trend established in the curves of Figs 2A - 2C.

Curves (d) to (f) show a progressive flattening just after their peaks. We attribute the change of shape to the onset of gain saturation. As the pump power is increased the amplification process would be expected to become progressively nonlinear. Nevertheless, it can be seen from curves (d) to (f) that at long lengths ionic absorption dominates over stimulated emission and the gradient returns to that of the unpumped fibre.

4. DISCUSSION Figs. 2A - 2D illustrate a number of features which have important implications for a longspan erbium amplifier, which we will now consider. When there is no dopant in the fibre, the signal will be attenuated 20 dB by the intrinsic host loss. Clearly, it will not always be necessary for the overall gain, determined at z = L, to be zero. In the absence of noise considerations, it is clear that the pump power and dopant concentration must be selected so that the net loss over the fibre span is less than 20 dB.

Figures 2C and 2D indicate that provided it is acceptable for the signal power to grow and then decline over the length of the communications link, a zero net gain can be obtained for pump powers of around 500 mW. Such values of pump power are likely to be available from semiconductor laser diodes and as such may be quite practical. Alternatively, if somewhat higher pump powers can be provided a net gain over the 100 km fibre may be achieved.

Perhaps the most interesting regime of operation is that indicated in Figure 2B. We notice that in curve (g) the signal power is virtually constant over the first 60 km of the fibre. Ibis mode of operation is rather like an optical ether, the fibre forming a completely transparent link The penalty for operating in such a regime of net transparency is that the power levels required to bleach the absorption over trunk routes are rather high. Nevertheless, the optical ether mode of operation may be achieved over spans of 30 km for pump powers of only 100 mW, and as such may be of some interest in local distribution systems.

We have carried out a theoretical study of signal amplification in very long lengths of fibre which are doped with low densities of a three-level ionic species. The present invention creates an entire point-to-point link which exhibits sufficient gain to either partially or totally overcome the intrinsic loss of the host glass. The system is pumped from the transmitter end and does not require discrete in-line amplifiers with the associated splice-loss and electrical power feed problems. We have demonstrated that in principle such a link could be established and can prevent overall depletion of the signal below the launch value. Two theoretical models have been compared and we have shown in the Appendix that provided that operation invokes small signal behaviour, the contribution of ASE to gain saturation can be ignored.

APPENDIX The theoretical model presented in section 2 necessitates numerically solving four coupled differential equations for the pump, forward and backward propagating ASE and the signal respectively. These must be solved as a boundary value problem as the initial condition for the backward propagating ASE is not known. It is more time consuming to find accurate solutions in such circumstances. In this Appendix we investigate the usefulness of omitting the ASE and solving as an initial value problem.

When amplified spontaneous emission is not included signal evolution may be determined with the use of equations (9) and (11), subject to equations (12) and (15) as initial conditions.

Equations (8) are not used. Equations (6) and (7) with the terms P5+ (z) = As (z) = 0 give the population densities. Three of the curves which originally appeared in Fig. 2D have been computed by both methods of calculation and the results are plotted in Fig. 3.. Curves (a) and (b) of Fig. ; apply when there is no pumping. No ASE can be generated when the fibre is unpumped so as expected the two methods of calculation gave the same results and curves (a) and (b) lie on top of each other. Curves (c) and (d) of Fig. 3 correspond to 50 mW pumping, which is in the small signal regime. Curve (c) includes the effect of ASE and curve (d) does not. As can be seen by the close proximity of the lines, the saturating effect of the spontaneous emission is negligible. The difference between the models with and without the influence of ASE only becomes noticeable when the pumping level is increased to a level where saturation effects are apparent. Curves (e) and (f) apply when the pump power is 800 mW. The influence of ASE is included in the computation of (e) and omitted in (f). The separation between curves (e) and (f) is less than 3 dB at all points on the fibre, indicating that even with slight saturation effects the model which omits ASE gives a reasonable account of the signal evolution.

REFERENCES 1. Millar, CA; tutorial at OFC 1988.

2. Urquhart, P.; "Review of Rare Earth Doped Fibre Lasers and Amplifiers", I.E.E.

Proceedings, Part J (Optoelectronics), 135,385-407, (1988).

3. Whitley, TJ.; "Laser-Diode Pumped Operation of Er3±Doped Fibre Amplifier", Electronics Letters, 24, 1537-1539, (1988).

4. Laming, RI., Reekie, L, Payne, D.N., Scrivener, P.L, Fontana, F. and Righetti A; "Optimal Pumping of Erbium-Doped Fibre Amplifiers", in Proceedings of European Conference on Optical Communications, postdeadline paper, I.E.E. conference publication 292-part 2, 25-28, (1988).

5. Nakazawa, M., Kimura, Y. and Suzuki K; "Efficient Er3±Doped Optical Fibre Amplifier Pumped by a 1.48 jun InGaAsP Laser Diode", Applied Physics Letters, 54, 295-297, (1989).

6. Desurvire, E. and Simpson, J.R; "Amplification of Spontaneous Emission in Erbium Doped Single Mode Fibres", I.E.E.E.O.S.A. Journal of Lightwave Technology, LT-7, 835-845, (1989).

7. Milonni,P.W. and Eberly, J.H.; 'lasers", Wiley, New York, (1988), especially chapter 10.

8. Atkins, C.G., Massicott, J.F., Armitage, J.R, Wyatt, R, Ainslie, BJ. and Craig-Ryan, S.P.; "A High Gain, Broad Spectral Bandwidth Erbium Doped Fibre Amplifier Pumped Near 13m", to be published in Electronics Letters (14* July 1989).

9. Marcuse, D.; Gloss Analysis of Single-Mode Fiber Splices", Bell System Technical Journal, 56, 703-718, (1977).

10. Amiitage, J.R; Theoretical Model of a Three Level Fibre Laser Amplifier", Applied Optics, 27, 4831-4836, (1988).

FIGURE CAPTIONS Fig. 1 Schematic diagram of a Long-Span Fibre Amplifier in its most basic form.

Fig. 2A Variation of gain with respect to fibre length in a 100 km Long-Span Fibre Amplifier when the dopant density has the length-independent value of N, = 1x 102 ions3. The pump power values are (a) 0, (b) 50, (c) 100, (d) 200, (e) 400, (f) 800 and (g) 1600 mW. The values of the other parameters used are given in the text.

Fig. 2B Variation of gain with respect to fibre length in a 100 km Long-Span Fibre Amplifier when the dopant density has the length-independent value of N, = 1.53x 102 ions3. The pump power values are (a) 0, (b) 100, (c) 200, (d) 400, (e) 800, (f) 1600 and (g) 3200 mW.

The values of the other parameters used are given in the text Fig. 2C Variation of gain with respect to fibre length in a 100 km Long-Span Fibre Amplifier when the dopant density has the length-independent value of N1 = 5x 102 ions/m . The pump power values are (a) 0, (b) 54 (c) 100, (d) 200, (e) 400 and (f) 800 mW. The values of the other parameters used are given in the text.

Fig. 2D Variation of gain with respect to fibre length in a 100 km Long-Span Fibre Amplifier when the dopant density has the length-independent value of N, = 10x 102 ions/m3. The pump power values are (a) 0, (b) 50, (c) 100, (d) 200, (e) 400, and (f) 800 mW. The values of the other parameters used are given in the text.

Fig. 3 Variation of gain with respect to fibre length in a 100 km Long-Span Fibre Amplifier using two methods of computatiorL Curves (a), (c) and (e) use the formulation outlined in section 2, which incorporates ASE and curves (b), (d) and (f) use the formulation outlined in the Appendix, which omits ASE. The Dopant density is Nr = 10x 102 ions . The pump power values are (a) & (c) 0, (b) & (d) 50 and (e) & (f) 800 mW.

Claims (6)

CLAINS

1. An optical communications system comprising a transmitter and at least one receiver optically connected by an optical transmission path which includes a doped optical fibre amplifier pumped by optical pump means, the gain of the amplifier being of sufficient magnitude and distribution to overcome substantially only the distributed intrinsic absorption of the fibre amplifier.

2. A communications system as claimed in claim 1 in which the transmission path is formed entirely by the doped fibre amplifier.

3. A communications system as claimed in claim 1 or claim'2 in which the transmitter produces optical pulses capable of propagating as solitons along the fibre amplifier, the gain of the fibre amplifier being such as to provide lossless soliton propagation.

4. An optical communications systems as claimed in claim 1 comprising a plurality of receivers each optical coupled to a common unitary fibre amplifier.

5. A communications system as claimed in any preceding claim in which the fibre amplifier comprises an Erbium doped fibre amplifier.

6. A doped optical fibre amplifier including an optical pump means, the gain of the amplifier being of sufficient magnitude and distribution to overcome substantially only the distributed intrinsic absorption of a propagating optical signal of the fibre amplifier.