Effects of inhomogeneous distribution of Si–Nc and Er ions on optical amplification in Si–Nc Er doped fiber

Optik 123 (2012) 1140–1145

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Optik journal homepage: www.elsevier.de/ijleo

Effects of inhomogeneous distribution of Si–Nc and Er ions on optical amplification in Si–Nc Er doped fiber A. Meidanchi a , A. SalmanOgli b,∗ a b

Department of Physics, Payame Noor University, Tehran, Iran Photonics and Nanocrystal Research Lab, University of Tabriz, Tabriz, Iran

a r t i c l e

i n f o

Article history: Received 12 February 2011 Accepted 11 July 2011

Keywords: Confined carrier absorption cross-section (CCa) Silicon nanocrystal (Si–Nc) Er-doped optical amplifier (EDFA) Wavelength division multiplexing (WDM)

a b s t r a c t In this article, the effects of Si–Nc and Er3+ ions distribution parameters including inhomogeneous and homogeneous distribution profile are studied on the optical parameters such as gain, population inversion and Si–Nc induced losses. We have shown that by increasing of the concentration of Si–Nc particles the net gain and induced Si–Nc losses increased in homogeneous and inhomogeneous distributions. In practice, the homogeneous distribution of Er ions and Si–Nc is hard to be realized. Therefore, the inhomogeneous distributions of ions cased to perturb state in mode shape of optical signal then the investigations of those effects are important for high speed optical communications. In this article, a method for evaluation of the effects of inhomogeneous distribution of impurities on performance of optical amplifier is developed and the managing of the gain with use of suitable distribution functions is proposed. © 2011 Elsevier GmbH. All rights reserved.

1. Introduction Optical amplifiers are one of key elements in optical communications and related links. Traditional erbium doped fiber amplifiers (EDFA) and semiconductor optical amplifiers (SOA) [1,2] are popular element and are widely used in WDM and dense WDM (DWDM). These amplifiers have advantage to avoid making multiple optoelectronic conversions since they amplify all signals simultaneously in the optical domain without depending for demultiplex. However, in spite of those noticeable advantages, the modern optical communication can have multiple components such as expensive laser, optical isolators and filters. Moreover, in order to achieve sufficient optical gain, the traditional EDFA usually requires several meters of Er-doped fiber length. So that, for elimination of these disadvantages, Si–Nc is doped to the optical fiber. In such system, the input signals at 1.55 ␮m are amplified through indirect excitation of Er ions by silicon nanocrystal [3]. Therefore, by indirectly pumping Er ions in presence of nanocrystals, the length of fiber amplifier is drastically reduced for achieving of positive high gain. Also, bandwidth of amplification is broadened due to doping of Si–Nc. This is mainly due to broad absorption band and high absorption cross-section of Si–Nc. For description of operation of Si–Nc Er doped fiber amplifier there are so interesting published papers which we are going to review some of them.

∗ Corresponding author. E-mail address: [email protected] (A. SalmanOgli). 0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.07.041

One of important idea, as it is discussed above, is using nanotechnology for improving amplification process. It was shown that the adding silicon nanocrystals to Er doped SiO2 strongly enhances the effective Er absorption cross-section [4–6]. Also, it was shown that nanocrystals doped into fiber causes the excitations of Er ions compared traditional EDFA through a strong coupling mechanism. This energy transfer process could enable the fabrication of an optical amplifier operating at 1.55 ␮m that is optically excited at pump intensities as low as a few mW/cm2 . We think that beside of the reported results, adding Si–Ncs into Er-doped optical fiber can decrease fiber length for given gain. Also, Si–Ncs have large absorption cross-section area which is so interesting property for increasing the absorption coefficient of the pump wave, concluding to decrease of pump loss or increase of quantum efficiency. Also, because of large quantum confinement of Si–Nc the appeared band gap is increased compared bulk SiO2 matrix. This property concludes to absorption of visible light. Due to this effect, the amplifier bandwidth also can be increased [7–10]. In [11–13] the authors concentrated on Si–Nc–Er doped fiber amplifier generally and in these references main focusing done on quantum dot and optical properties of Si–Nc. The using of those ideas some features of optical amplifier was extracted and distinguished properties were illustrated. Also, a traditional EDFA and Si–Nc Er-doped fiber amplifier were compared. But, the effects of maximum number of excitons in Si–Nc on amplification process did not discuss. In [14] modeling of experimentally realized Si–Nc and Er doped fiber amplifier was done. In this paper, a phenomenological model based on an energy level scheme was presented. Also, the strong

A. Meidanchi, A. SalmanOgli / Optik 123 (2012) 1140–1145

coupling between each Si nanocrystal and the neighboring Er ions and considering the interactions between pairs of Er ions, such as the concentration quenching effect and the cooperative upconversion mechanism were investigated. This is an interesting paper, but some critical points such as inhomogeneous distribution of Er-ions did not address. In practice inhomogeneous distribution usually occurred and complete description of experimental results should be considered. Optical for Si–Nc Er doped fiber amplifiers were discussed in [15,16,20–22]. In these papers, the scattering losses and optical losses due to inhomogeneity in manufacturing step of waveguide were discussed. Moreover, the effects of optical amplifier parameters are studied on dispersion curve. Results of those papers can be used for modeling of optical amplifier precisely. Energy transfer between Si–Nc and Er ions and time constant of energy coupling was discussed in [17]. This paper presented experimental result of silica thin films containing Si nanocrystals and Er ions prepared by ion implementation. Results of this paper can be used for transient analysis of optical amplifier in presence of nanocrystals. Finally, the gain limiting factors in Si–Nc Er doped fiber amplifier was discussed and addressed in [15]. Presented materials in this paper is interested for finding the root of gain limitation in this structure. In [18] excitation mechanism of Er ions by Si–Nc was discussed and based on the developed method rate of energy exchange between nanocrystal and Er ions is calculated and shown that microsecond time is attainable. One of assumption of this paper is each Si–Nc can support 1–2 Er ions and based on this assumption, they shown that maximum optical gain will be 0.6 dB cm−1 . All calculations are based on homogeneous distributions for Er and Si–Nc particles. Effect of concentration quenching in Er implanted alkali silicate glasses was presented in [19]. They have shown that by increasing concentration of Er ions the population of level two is decreased. In all of those papers, there is no information about inhomogeneous distribution of Si–Nc and Er ions. Inhomogeneous distributions of these particles have significant effect on propagating mode shape and concluding to distortion of energy propagating shape. For this reason, we consider this subject. In this paper, we consider effects of inhomogeneous distributions of Si–Nc and Er ions on optical amplification process in fiber. For this purpose, the Gaussian distributions are assumed. Two critical cases including same and different center and peak of distributions for nanocrystals and Er ions are studied. For simulation of effects of inhomogeneous distributions the numerical solution of the rate equations is used. We observed that the using of suitable distribution profiles can be managed the shape and intensity of gain. Also, the important assumptions for the Gaussian distribution of Si–Nc particles and Er ions are  Si–Nc <  Er and same distribution peaks. The organization of this paper is as follows. Mathematical background is presented in Section 2. In Section 3 simulated results and discussion is illustrated. Finally the paper ends with a short conclusion.

1141

Fig. 1. Schematic of inhomogeneous Si–Nc Er doped fiber amplifier. Table 1 Physical parameter taken from Ref. [14] that used in rate equations. Symbol

Value

exc  abs  dir Wb W21 W32 W43 W54 Cb1 Cup1 Cb2 Cb3 Cbt Ca C3 Wer

488 nm 2 × 10−16 cm2 1 × 10−20 cm2 2 × 104 s−1 4.2 × 102 s−1 4.2 × 105 s−1 1 × 107 s−1 <1 × 107 s−1 3 × 10−15 cm3 s−1 7 × 10−17 cm3 s−1 <3 × 10−19 cm3 s−1 <3 × 10−19 cm3 s−1 <3 × 10−19 cm3 s−1 <3 × 10−19 cm3 s−1 7 × 10−17 cm3 s−1 8.1 × 10−19 NTotaler s−1

In this section, the basic principle of operation and mathematical formulation of inhomogeneous distribution by using of rate equations are discussed and presented. Fig. 1 shows the Gaussian distributions for Si–Nc and Er ions. Based on this figure, it is obvious that in the central part of the fiber the concentrations of particles are high and so optical gain will be high, then the central part of the input pulse more than other parts is amplified and introduces signal distortion in mode shape. In the following, we study the effect of this type of distribution on optical amplification process and try to improve gain and other interesting parameters of optical amplifier. Moreover, two cases including similar distribution of Er ions and Si–Ncs (Gaussian profiles with same position of peak values) and shifted Gaussian profiles with same parameters in first case are explored. According to presented papers and experimental results twoand five-level models for Si–Nc and Er ions can be used. The following rate equations based on these models can be expressed (Table 1).

 dNb (z) = abs (N0 (z) − Nb (z))−(Wb Nb (z))− Cbi Nb (z)Ni (z) dt 3

i=1

(1)

 dNa (z) = abs (−N0 (z) + Nb (z)) + (Wb Nb (z)) + Cbi Nb (z)Ni (z) dt i=1

2. Mathematical background and principles of operation of Si–Nc optical amplifier Si–Nc and Er doped fiber amplifier is a suitable alternative for decreasing of the fiber length for given gain. In this amplifier, the Er ions excited indirectly through Si–Nc and because of high absorption cross-section of Si–Nc, the efficiency of pumping is increased too. Also, in this case, the large optical bandwidth can be supported and the need for precise laser diode is lighten.

3

(2)

dN5 (z) = (Cdir dir N3 (z)) + (C3 N3 (z)2 ) − (W54 N5 (z)) dt +

3  i=2

Cbi Nb (z)Ni (z)

(3)

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dN4 (z) = (W54 N5 (z)) + (Cup N2 (z)2 ) − (W43 N4 (z)) + (Cb1 N1 (z)Nb (z)) dt (4)

1 2 3 4

9 8

2

− (2C3 N3 (z) ) − (Cb3 Nb (z)N3 (z)) − (Ca Nb (z)N3 (z))

(5)

Si-Nc Loss

7

dN3 (z) = (W43 N4 (z)) − (W32 + W31 )N3 (z) dt

6 5 4 3 2

dN2 (z) = (W32 N3 (z)) − (W21 + Wer )N2 (z) dt 2

− (2Cup N2 (z) ) − (Cb2 Nb (z)N2 (z)) − (Ca Nb (z)N2 (z))

1 0 17 10

(6)

18

10

10

19

10

20

10

21

10

22

10

23

Er Concentration Fig. 2. Si–Nc loss vs. Er concentration (cm−3 ). 1. Pump = 1 × 1017 photon cm−2 s−1 , 2. Pump = 1 × 1020 photon cm−2 s−1 , 3. Pump = 1 × 1021 photon cm−2 s−1 , and 4. Pump = 5 × 1022 photon cm−2 s−1 .

+ N3 (z))Ca Nb (z) + (W31 N3 (z)) + (C3 N3 (z)2 ) − (Cbt Nb (z)N1 (z)) − (dir N1 (z))

(7)

where the following parameters are used which is defined as: N0 , total density of silicon nanocrystal; Na,b , population of level a and b in silicon nanocrystal; Ni , population in different levels (i) of Er(3+) ions;  abs , Si–Nc absorption cross-section; , photon flux;  dir , direction absorption cross-section; Wer , the concentration quenching effect (due to the energy migration all over the sample introduced by the energy transfer between two nearby Er(3+) ions occurred between ground and first excited states); Wb , the exciton total recombination rate; Wij , the total transition rate from level i to level j(i > j); Cup , co-operative up-conversion coefficient; Cbt , backward transfer energy from Er to Si–Nc; Cbi (i > 2) , excited state excitation (ESA) from level i(i > 2); Cbi (i = 1) , the coupling between the silicon nanocrystal and the ground state of Er(3+) . In the next section, we consider numerical analysis of Eqs. (1)–(7) and effects of inhomogeneous distribution on performance of optical amplifier. It is shown that by tuning of the distribution profiles interesting results can be obtained. 3. Results and discussion In this section, presented idea is simulated in different category as (1) Uniform distribution for Er ions and Si–Nc. (2) Gaussian distribution for Si–Nc and uniform distribution for Er ions ( Si–Nc = 3 ␮m). (3) Gaussian distribution for Er ions and uniform distribution for Si–Nc ( Er = 4 ␮m). (4) Gaussian distribution for both Si–Nc and Er ions with different mean position ( Si–Nc = 3 ␮m,  Er = 4 ␮m). And results are illustrated and discussed in the following. In simulation process, we need for insert confined carrier absorption loss which is defined by ˛CCa =  CCa Nb and parameter ( CCa ) is the confined carrier absorption cross-section and in the all simulation “Z” introduce position in the fiber diameter across. 3.1. Uniform distribution for Er ions and Si–Nc: in this part uniform distributions are supposed and depending results are extracted and discussed

pair dissociates and finally electron moves to the excited state of Si–Nc so the number of photons in optical signal output (1.55 ␮m) is decreased. Considering Fig. 2, it is observed that by the increasing of concentration of Er(3+) ions, the introduced confined carrier optical loss is decreased because of strong coupling of Si–Nc and Er(3+) ions. Thus possibility of absorption of optical signal by excitons by increasing of the concentration of Er(3+) ions is decreased. Also, as a final result of this simulation, it is considerable to discuss about effect of pump on confined carrier absorption. It is shown that by increasing of the pump power the number of generated exciton is increased so the confined carrier absorption will be increased. The Effects of Er(3+) ions concentration and pump power on optical gain are illustrated in Fig. 3 by increasing of the Er(3+) ions concentration, the optical gain begins to increase and finally in the case of high concentrations it goes to decrease because of increasing in interaction between Er(3+) ions. It should be mention that in this simulation, the emission cross-section of Er(3+) ions assumed to be 1 × 10−19 cm2 . Also, by increasing pump power, optical gain is increased. Moreover, the maximum gain in this simulation is reached to 12 dB cm−1 . In this part, the effect of concentration of Er(3+) ions with regarding the different confined carrier absorption loss are discussed and illustrated in Fig. 4. In this figure, for confined carrier cross-section  CCa = 1 × 10−17 cm2 , the effect of pump power is noticeable on the net gain. By increasing of the pump power, because of high level confined carrier cross-section, induced optical loss due to Si–Nc is

1 2 3 4

10 8 6

Gain

dN1 (z) = (W21 + Wer )N2 (z) + (Cup N2 (z)2 ) + (N2 (z) dt

4 2 0

10

18

10

19

10

20

10

21

Er Concentration

Fig. 2 shows confined carrier absorption loss as a function of Er(3+) ions concentration. The introduced optical loss comes back to absorption of optical signal by exciton in Si–Nc and electron-hole

Fig. 3. Gain vs. Er concentration (cm−3 ). 1. Pump = 1 × 1017 photon cm−2 s−1 , 2. Pump = 1 × 1020 photon cm−2 s−1 , 3. Pump = 1 × 1021 photon cm−2 s−1 , and 4. Pump = 5 × 1022 photon cm−2 s−1 .

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1 2 3 4

100

1143

1 2 3 4

5

50

Net Gain

Net Gain

4 0

-50

-100

0 18

19

10

20

10

10

21

10

-1 0

Er Concentration Fig. 4. Net gain vs. Er concentration (cm−3 ). 1. Pump = 1 × 1017 photon cm−2 s−1 , Pump = 1 × 1020 photon cm−2 s−1 , 3. Pump = 1 × 1021 photon cm−2 s−1 , 2. and 4. Pump = 5 × 1022 photon cm−2 s−1 . Confined carrier absorption crosssection = 1 × 10−17 cm2 .

increased more than increasing of optical gain. Therefore, the optical net gain will be decreased by increasing of pump power. Based on simulated figures, it is observed that the proposed optical amplifier may have negative gain for  CCa = 1 × 10−17 cm2 in whole pump power. 3.2. Gaussian distribution for Si–Nc and uniform distribution for Er ions ( Si–Nc = 3 m, Pump = 5 × 1022 photon cm−2 s−1 ) In this section, the effect of the Si–Nc and Er ions concentration on the population inversion is investigated. In Fig. 5 the effect is illustrated at constant concentration of Er ions in the case of Gaussian distribution for Si–Nc particles. This figure shows that for low level of Er ions, by increasing of the Si–Ncs density, the population inversion is increased. This event comes back to increase of the coupling between Er ions and Si–Nc particles. But in the large amount of Er ions concentration distribution the interaction between ions at first excited state have dominant effect and conclude to considerable decreasing in the population inversion. In Figs. 6 and 7, the effect of concentration of Si–Nc on Net gain at the fixed Er ions population is illustrated. In Fig. 6, with maximum peak (Mp = 1 × 1020 cm−3 ) it is shown that the positive and approximately flat gain (concentration of Er ions near to 1 × 1020 cm−3 can be achieved in broad range for large peak of Er ions distribution. Since distribution functions for Si–Nc and Er ions are same (considering the upper limit of Er ions) the induced population

20

40

60

80

100

120

140

Z Fig. 6. Net gain vs. Z. 1. Er concentration = 1.57 × 1019 cm−3 , 2. Er concentration = 4.47 × 1019 cm−3 , 3. Er concentration = 8.5 × 1019 cm−3 and 4. Er concentration = 1 × 1020 cm−3 . Confined carrier absorption cross-section = 1 × 10−19 cm2 .

inversion within core is uniform and optical gain will be constant approximately. In Fig. 7 the situation is same as previous figure but the concentration of Er ions is increased. In this situation because of high level of concentration of Er ions especially far from central part of the Gaussian distribution, the Si–Ncs particle do not excite Er ions and induced population inversion do not sufficient and positive gain cannot be obtained. In central part, because of high Si–Nc particle concentration, the positive gain and is obtained.

3.3. Gaussian distribution for Er ions and uniform distribution for Si–Nc ( Si–Nc = 4 m, Pump = 5 × 1022 photon cm−2 s−1 ) Fig. 8 shows that the effect of Er ions on population inversion at the fixed concentration of Si–Nc particles. We have shown that by increasing of the Er ions, the population inversion decreased because the strongly coupling between Er ions concludes to depletion of first excited state. Moreover, by increasing of the Si–Ncs, the population inversion is increased that is comes back to the increasing of the coupling between the Si–Nc and Er ions and consequently large population in first excited state to appear.

20

1

1 2 3 4

10

0.5 0

0

-0.5

-10

-1

Net Gain

Population Inversion

2 1

-150

-1.5 -2 -2.5

-20 -30 -40

-3 -3.5 -4

3

0

20

40

60

80

100

120

1 2 3 4 140

Z Fig. 5. Population inversion vs. Z. 1. Er concentration = 1.57 × 1019 cm−3 , 2. Er concentration = 8.5 × 1019 cm−3 , 3. Er concentration = 1.57 × 1021 cm−3 and 4. Er concentration = 8.5 × 1021 cm−3 .

-50 -60

0

20

40

60

80

100

120

140

Z Fig. 7. Net gain vs. Z. 1. Er concentration = 1.57 × 1020 cm−3 , 2. Er concentration = 4.47 × 1020 cm−3 , 3. Er concentration = 8.5 × 1020 cm−3 and 4. Er concentration = 1 × 1021 cm−3 . Confined carrier absorption cross-section = 1 × 10−19 cm2 .

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1.2

19.5

Mp1

1

N1si-nc

0.6

Si-Nc Loss

Population Inversion

Mp1

18.5

0.8 N2si-nc

0.4

Mp2

18 17.5 N2si-nc

17

16.5 0.2

16 15.5

0 -0.2

0

40

0

20

40

60

80

100

120

20

140

1 2 2 1

15

10 Mp2

5

60

80

120

140

ShL1 ShL2 ShL3 ShL4

Mp1

40

100

by increasing of the Si–Nc density the Si–Nc excited particle is increased. This is related to increase of amount of excitons due to increase of the density of the Si–Nc. Now, with displacement of the center of distributions, it is observed that the excited of Si–Nc is increased due to decrease of the coupling between Er ions and Si–Nc. Effects of the concentration of the Si–Nc and Er ions on net gain are investigated and illustrated for the Gaussian distributions in Fig. 13. In the case of centered distributions of Si–Nc and Er ions, 1

20

80

Fig. 10. Net gain vs. Z. Mp1 (maximum Er concentration) = 1 × 1020 cm−3 , Mp2 (maximum Er concentration) = 1 × 1021 cm−3 N2si-nc (Si–Nc concentration) = 1 × 1019 cm−3 , and N1si-nc (Si–Nc concentration) = 2 × 1019 cm−3 .

0

0

60

Z

Fig. 8. Population inversion vs. Z. Mp1 (maximum Er concentration) = 1 × 1020 cm−3 , Mp2 (maximum Er concentration) = 1 × 1021 cm−3 , N1si-nc (Si–Nc concentration) = 2 × 1019 cm−3 , and N2si-nc (Si–Nc concentration) = 1 × 1019 cm−3 .

-5

20

Mp2

Z

Net Gain

N1si-nc

19

100

120

140

Z

In Fig. 11 the effect of concentration of Si–Nc and Er ions on the population inversion is investigated. Our simulations show that by increasing of the density of Si–Nc and Er ions the population inversion goes to decrease; this reduction increases when the Si–Nc peak shifts to right. But by increasing of the coupling between Si–Nc and Er ions (near to the peak of Si–Nc) the population inversion is increased. In this case it is observed that for displaced Gaussian distributions of Si–Nc and Er ions the population inversion tolerate strong variation inside core. In Fig. 9 we consider the effects of concentration of Si–Nc and Er ions on net gain. It is shown that for small concentration of Er ions, the variation of concentration of Si–Nc does not considerable perturb the optical net gain. But with large concentration of Er ions, the variation of concentration of Si–Nc has considerable affect on flat gain. In Fig. 10, the effect of concentration of Si–Nc on induced Si–Nc optical loss is considered and the density of Er ions as essential parameter is studied. It is shown that by increasing of the Si–Nc density, the induced loss is increased. By supposing of uniform distribution for Si–Nc, by increasing of the Er ions the induced optical loss is decreased because of increasing of the coupling between Er ions and Si–Ncs. The effects of the concentration of Si–Nc and Er ions on Si–Nc excited particle are illustrated in Fig. 12. For case one, where the Si–Nc and Er ions distributions are centered, it is observed that

Population Inversion

3.4. Gaussian distribution for both Si–Nc and Er ions with different mean position ( Er = 4 m,  Si–Nc = 3 m, Pump = 5 × 1022 photon cm−2 s−1 )

0.5

0

-0.5

0

20

40

60

80

100

120

Z Fig. 11. Population inversion vs. Z. ShL1 (shifted length) = 0, ShL1 (shifted length) = 2.5 ␮m, ShL1 (shifted length) = 5 ␮m, ShL1 (shifted length) = 7.5 ␮m, and Mp (maximam Er concentration) = 1 × 1021 cm−3 . 19

2

x 10

ShL1 ShL2 ShL3 ShL4

1.8 1.6 1.4

Excited Si-Nc

Fig. 9. Net gain vs. Z. 1. Nsi-nc = 1 × 1019 cm−3 , 2. Nsi-nc = 2 × 1019 cm−3 , Confined carrier absorption cross-section = 1 × 10−19 cm2 . Mp1 (maximum Er concentration) = 1 × 1020 cm−3 and Mp2 (maximum Er concentration) = 1 × 1021 cm−3 .

1.2 1 0.8 0.6 0.4 0.2 0

0

20

40

60

80

100

120

Z Fig. 12. Excited Si–Nc vs. Z. ShL1 (shifted length) = 0, ShL1 (shifted length) = 2.5 ␮m, ShL1 (shifted length) = 5 ␮m, ShL1 (shifted length) = 7.5 ␮m, ShL1 (shifted length) = 750 nm, and Mp (maximam Er concentration) = 1 × 1021 cm−3 .

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0

Net Gain

1145

-10 -20 -30 -40 -50

0

20

40

60

80

100

ShL1 ShL2 ShL3 ShL4 120

Z

Fig. 13. Net gain vs. Z. ShL1 (shifted length) = 0, ShL1 (shifted length) = 2.5 ␮m, ShL1 (shifted length) = 5 ␮m, ShL1 (shifted length) = 7.5 ␮m, and Mp (maximam Er concentration) = 1 × 1021 cm−3 .

the optical net gain has maximum amount around the center of distributions profile because maximum coupling is occurred in that position. By increasing of displacement between centers of distributions because of weak coupling the net gain is decreased first and with approaching to center of Si–Nc distribution profile the net gain is increased. The intensity of optical net gain in this case, is larger than other cases. This increasing of gain is related to weak interaction between Er ions in first excited state. But in case of large displacement between centers of the distributions, the described situation is observed but the intensity of maximum gain are decreased compared to small displacements due to ultra small coupling between Si–Nc and Er ions. 4. Conclusion In practice, ions doped in fiber distribution profile are not homogeneous so that we assumed Gaussian profile for this work. We have shown that by increasing of Si–Nc density the net gain in both profiles is increased. Moreover by increasing of Si–Nc particles and Er ions, the excited concentration at the Gaussian profile distribution are increased because of Si–Nc induced loss decreasing and increasing of coupling between Er ions and excited Si–Nc. Furthermore, the results of simulations of this article shown that by increasing of Er ions, the population inversion, gain and Si–Nc induced loss are decreased. Finally, we have shown that the positive and approximately flat gain can be achieved in broad range for large peak of Er ions distribution.