Detailed theoretical investigation on relative intensity noise reduction enhancement based on reflective SOAs

Optics & Laser Technology 44 (2012) 1240–1246

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Detailed theoretical investigation on relative intensity noise reduction enhancement based on reflective SOAs Xin-Hong Jia a,n, Zheng-Mao Wu b, Guang-Qiong Xia b a b

School of Physics & Electronic Engineering, Sichuan Normal University, Chengdu 610068, People’s Republic of China School of Physics, Southwest University, Chongqing 400715, People’s Republic of China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 November 2011 Received in revised form 4 January 2012 Accepted 4 January 2012 Available online 24 January 2012

The enhanced performance for relative intensity noise (RIN) reduction based on reflective semiconductor optical amplifiers (R-SOA) has been investigated theoretically by comparison with conventional transmission SOA. The results show that, by selecting appropriate input optical power, as large as 420 dB RIN suppression improvement can be achieved for R-SOA, without sacrificing the noise rejection bandwidth. With increased injection current, the optimized input signal power is decreased and the operation region is extended for the best RIN reduction. For RIN suppression in WDM spectrum slicing, the bandwidth optimization of receiver filter should be performed to avoid the spectral broadening induced by self-phase modulation (SPM) and four wave mixing (FWM). Our derived result is helpful for designing and optimizing the R-SOA in application of noise suppression enhancement. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Reflective semiconductor optical amplifiers (R-SOA) Relative intensity noise (RIN) suppression

1. Introduction In optical communication system, intensity noise is harmful to optical signal transmission and processing. For an instance, in wavelength-division-multiplexing (WDM) systems or passive optical network (PON), spectrum slicing is an attractive way as they use the cost-effective available incoherent optical source, such as the light-emitting diodes, super-luminescent diodes, and fiberbased amplified spontaneous emission (ASE) sources [1,2]. By spectrum slicing, only one broadband optical source is needed to form many channels by dividing the spectral slice to each channel. However, the optical signal-noise ratio (OSNR) suffers from the severe intensity noise of the broadband optical source [3]. Another typical example is the super-mode noise (SN) in harmonically mode-locked fiber lasers (HML-FL). For HML-FL, the phase of modes with frequency multiple to the cavity fundamental frequency is locked each other to form a set of super-mode. There exist many such super-modes with random phase, which would lead to strong amplitude fluctuation for output optical pulse via beating among these super-modes [4–10]. Thus, the noise suppression is essential to produce the high quality mode-locked pulse strain. Among many noise suppression schemes [4–18], the utilization of saturated semiconductor optical amplifier (SOA) provides an economic, simple, and efficient approach without excess devices [4–6,13–18]. For conventional transmission SOA, the relative intensity noise (RIN) suppression is determined by the injection current and input optical power. Although the RIN suppression is improved

n

Corresponding author. Tel.: þ86 15882380655. E-mail address: [email protected] (X.-H. Jia).

0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2012.01.003

by increasing the injection current, the improvement is limited due to the thermal penalty and non-radiative recombination in active region. The RIN suppression improvement is also limited by increasing the input power owing to saturation characteristic [14]. For the RIN suppression, earlier studies mainly focus on the conventional transmission SOA [4–6,13–18]. To the best of our knowledge, the complete theoretical analysis for the RIN suppression based on reflective SOA (R-SOA), has not yet been published. In this paper, the enhanced RIN reduction characteristics based on R-SOA is investigated theoretically. We use the perturbation analysis to optical transmission and carrier rate equations to calculate the modulation transfer function (MTF). The RIN suppression comparisons between conventional transmission SOA and R-SOA are performed. The results show that, as large as 420 dB RIN suppression improvement can be achieved for R-SOA, without sacrificing the noise rejection bandwidth. With increased injection current, the optimum input signal power is decreased and the operation region is extended for the best RIN reduction. The derived results may provide an instructive insight and is helpful for designing and optimizing the R-SOA based RIN suppression enhancement.

2. Theoretical model The schematic diagram of RIN suppression based on R-SOA is shown in Fig. 1. The signal light with noise is launched into R-SOA via an optical circulator (OC). The tunable optical band-pass filter (BPF) is applied to exclude the ASE of R-SOA. The signal input power into R-SOA can be adjusted using a variable optical attenuator (VOA) to reach the optimized RIN suppression.

X.-H. Jia et al. / Optics & Laser Technology 44 (2012) 1240–1246

z ¼ L : P b ðL,tÞ ¼ R2 Pf ðL,tÞ

R2 R-SOA

P t ðtÞ ¼ ð1R2 ÞP f ðL,tÞ

VOA

ð5bÞ

where L is the active region length, Pin, Pr and Pt are the optical powers of input signal, reflected and transmitted lights, respectively. R1 and R2 are the power reflectivity for AR and HR facets, respectively.

R1

Optical Source with Noise

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OC

BPF

Output

Fig. 1. Schematic diagram of RIN suppression based on R-SOA.

In presence of input modulation perturbation, the optical power, carrier density, and gain coefficient can be decomposed of steady and dynamic components, expressed by

2.1. Time-domain traveling and carrier rate equations The facets of R-SOA consist of high-reflective (HR) and antireflective (AR) coatings at the back and front ends, respectively. Since the reflectivity of AR end is typically smaller than 1  10  4, the resonance effect between the input light and R-SOA cavity is negligible. For this reason, the influence of phase variation of optical field on RIN through carrier induced refractive index change can be omitted. The evolution of forward and backward optical powers inside the R-SOA active region obeys the following time-domain traveling equations: @P f 1 @P f þ ¼ ½GgðN, lÞaP f vg @t @z

ð1aÞ

@P b 1 @P b  ¼ ½GgðN, lÞaP b @z vg @t

ð1bÞ

where Pf and Pb are the forward and backward optical powers, respectively, vg is group velocity in the medium, G is the confinement factor, l is the signal wavelength, g and a account for the power gain and loss coefficients, respectively. The carrier rate equation for N can be described by [19] @N I N GgðPf þ Pb Þ ¼   @t qV ts ðNÞ Across E

ð2aÞ

where I is the injection current, q is electron charge, V is activelayer volume, Across is cross sectional area of active-layer, E is the photon energy, the carrier lifetime ts (N) is defined as [19]

ts ðNÞ ¼ ðA þBN þ CN2 Þ1

2.2. Modulation transfer function for RIN suppression using smallsignal analysis

Pf ðz,tÞ ¼ Pf ðzÞ þRe½DPf ðz, OÞexpðiOtÞ

ð6aÞ

Pb ðz,tÞ ¼ Pb ðzÞ þ Re½DP b ðz, OÞexpðiOtÞ

ð6bÞ

Pin ðtÞ ¼ Pin þ Re½DP in expðiOtÞ

ð6cÞ

Pr ðtÞ ¼ Pr þ Re½DP r expðiOtÞ

ð6dÞ

Pt ðtÞ ¼ Pt þRe½DPt expðiOtÞ

ð6eÞ

Nðz,tÞ ¼ NðzÞ þRe½DNðz, OÞexpðiOtÞ

ð6fÞ

gðz,tÞ ¼ g ðzÞ þ Re½Dgðz, OÞ expðiOtÞ

ð6gÞ

where O is the modulation angular frequency, DPf, DPb, DPin, DPr, DPt, are the power modulation amplitudes for forward, backward, input, reflective, and transmitted waves, respectively. Similarly, DN and Dg are the carrier and gain modulation amplitudes. Substituting Eqs. (6a) and (6b) into Eqs. (1) and (2), the modulation amplitudes for forward and backward optical powers are written as   dDP f iO ¼ Gg a DP f þ GP f DDN ð7aÞ dz vg   dDP b iO ¼  Gg a DPb GP b DDN dz vg

ð7bÞ

ð2bÞ

where A, B, C are the non-radiative, radiative and Auger recombination coefficients. Similar to Refs. [14,15], the influence of ASE noise on carrier density is neglected. The dependence of material gain coefficient g on carrier density and wavelength can be approximated to [20,21] 2

gðN, lÞ ¼ a0 ðNN0 Þa1 ðllN Þ þa3 ðllN Þ

3

ð3aÞ

where a0, a1 and a3 are gain constants, N0 is carrier density at transparency, lN is gain peak wavelength, which is assumed to shift linearly with carrier density

lN ¼ l0 a2 ðNN0 Þ

ð3bÞ

where l0 is the gain peak wavelength at transparency. The loss coefficient a is calculated by

a ¼ Gaa þð1GÞac þ ascat

ð4Þ

where aa, ac and ascat are the active-layer, cladding and scattering losses, respectively. The boundary conditions of forward and backward waves are given by z ¼ 0 : P f ð0,tÞ ¼ ð1R1 ÞPin ðtÞ þ R1 P b ð0,tÞ Pr ðtÞ ¼ R1 P in ðtÞ þ ð1R1 ÞP b ð0,tÞ

ð5aÞ

Table 1 Device structure and material parameters used in calculations. Symbol

Parameter

Value

L Across V

Active layer length Active layer cross-sectional area Active layer volume Confinement factor Signal wavelength Peak gain wavelength at transparency Group velocity Carrier density at transparency Loss in active layer Loss in cladding Scatting loss Material gain constant Material gain constant Material gain constant Material gain constant Non-radiative recombination coefficient Bimolecular radiative recombination coefficient Auger recombination coefficient Reflectivity of front end Reflectivity of back end

1000 mm 2.7  10–13 m2 2.7  10–16 m3 0.3 1550 nm 1595 nm 7.5  107 m/s 1.5  1024 m  3 1.4  104 m  1 2  103 m  1 1  103 m-1 2.5  10–20 m2 7.4  1018 m  3 3  10–32 m4 3.155  1025 m  4 1.5  108 s  1 2.5  10–17 m3s  1 9.4  10–41 m6s  1 1  10  4 0.9

G l l0 vg N0

aa ac ascat a0 a1 a2 a3 A B C R1 R2

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where D is used to represent the derivative of Dg to DN, defined as

Dg ¼ DDN

ð8aÞ

The boundary conditions for forward and backward optical power modulation amplitudes are described by z ¼ 0 : DP f ð0Þ ¼ ð1R1 ÞDPin þ R1 DPb ð0Þ

With 

 D ¼ a0 2a1 a2 ll0 þ a2 ðNN0 Þ þ 3a2 a3 ½ll0 þ a2 ðN N0 Þ2

ð8bÞ

DP r ¼ R1 DP in þ ð1R1 ÞDPb ð0Þ

ð10aÞ

The carrier modulation amplitude is expressed by

DN ¼

Gg =Across EðDPf þ DP b Þ 2

iO þ A þ 2BN þ 3CN þ ðGD=Across EÞðPf þ Pb Þ

z ¼ L : DP b ðLÞ ¼ R2 DPf ðLÞ ð9Þ

DP t ¼ ð1R2 ÞDPf ðLÞ

ð10bÞ

Fig. 2. Comparisons on MTF ((a) and (b)), carrier density distribution ((c) and (d)), and optical power distribution ((e) and (f)) between R-SOA ((a), (c), and (e)) and convention transmission SOA((b), (d), and (f)) for various signal input powers. In (e), the solid and dotted lines represent the forward and back-ward optical powers, respectively.

X.-H. Jia et al. / Optics & Laser Technology 44 (2012) 1240–1246

The reflective modulation transfer function (MTFr) is used to evaluate the RIN suppression of R-SOA, defined as MTF r ðOÞ ¼

2

2

2

2

9DP in ðOÞ9 =P in 9DP r ðOÞ9 =P r

ð11aÞ

For conventional transmission SOA, both of amplifier’s ends have AR coatings, the transmitted modulation transfer function (MTFt) is given by 2

MTF t ðOÞ ¼

2

9DP in ðOÞ9 =P in 2

9DPt ðOÞ9

2 =P t

ð11bÞ

2.3. Numerical simulation method Setting the derivative to t in Eqs. (1) and (2) to zero, the steadystate distribution for forward and backward optical powers and carrier density can be obtained using iteration method. Specifically, the backward optical power is assumed to be zero at first, the initial distribution for forward optical power and carrier density is obtained by integrating Eqs. (1) and (2) based on fourth-order Runge–Kutta method. The backward optical power at HR end is obtained using boundary condition Eqs. (5b). Repeating this integration process, the optical power and carrier distribution is renewed. The converged steady-state solution is reached after few iteration steps. As to the MTF, we can derive a transfer-matrix from Eqs. (7)–(9), the modulation amplitude is simulated by solving the linear equations combining the transfer matrix and boundary

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condition (Eqs. (10a) and (10b)). It should be stressed that, the precision and validity can be improved by increasing the grid number. Our simulation results have shown that for typical active section length ( 1000 mm), if the grid number closes to 50 or more, the solutions remain unchanged.

3. Results and discussions The device structure and material parameters used in simulation are listed in Table 1. In the following discussions, RIN suppression comparisons between convention transmission SOA and R-SOA will be discussed in detail. The parameters’ optimization for the best RIN reduction is also shown. Fig.2 shows the comparisons on MTF ((a) and (b)), carrier density distribution ((c) and (d)), and optical power distribution ((e) and (f)) between R-SOA((a), (c) and (e)) and conventional transmission SOA ((b), (d) and (f)) for various signal input powers. In Fig. 2(e), the solid and dotted lines represent the forward and backward optical powers, respectively. The injection current is set to be 150 mA. For conventional SOA, R1 ¼R2 ¼1  10  4. By comparing Fig. 2(a) and (b), with the increased signal optical power from  20 dBm to 10 dBm, the low-frequency RIN suppression is firstly increased from 23 dB to 436 dB, then decreased to  2 dB for R-SOA. Note that the best RIN reduction is not shown in Fig. 2(a).On the contrary, for conventional SOA, the lowfrequency RIN suppression is monotonically increased from  3 dB to 32.5 dB. It is found from Fig. 2(b) that, for conventional SOA, it is difficult to further improve the RIN suppression

Fig. 3. Comparisons on low-frequency RIN reduction (a), output power (b), and gain (c) as functions of input power for conventional and R-SOA.

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by increasing the input optical power due to the power saturation characteristics. The RIN suppression is mainly determined by the carrier density distribution. From Fig. 2(c) and (d), we can see that, the mean carrier density for R-SOA is smaller than the conventional SOA, showing the deeply carrier depletion feature. The strong carrier depletion for R-SOA could be further identified in Fig. 2(e) and (f). The signal light experiences second amplification after the HR facet, thus extending the effective cavity length, and more visible small-signal gain and carrier depletion are found in R-SOA. On the other hand, for conventional SOA, the signal only experiences the forward amplification, thus the small-signal gain is smaller, leading to the weaker carrier depletion and RIN reduction. From Fig. 2(a) and (b), both of R-SOA and conventional SOA exhibit similar noise rejection bandwidth with magnitude of 1–5 GHz, depending on the input power and biasing current. The noise bandwidth depends on the effective carrier lifetime, which is determined by the non-radiative, radiative, Auger recombination speed and stimulated recombination speed. The former is dependent of carrier density, and the latter is related to the total power of active region (see Eq. (9)). As mentioned above, for R-SOA, due to the fact that deeply carrier depletion is accompanied by enhanced small-signal optical power amplification, the difference of total noise suppression bandwidth is slight between R-SOA and conventional SOA. To further explore the RIN suppression enhancement by R-SOA, the comparisons on low-frequency RIN reduction (a), output power (b), and gain (c) as functions of input power for conventional and

R-SOA are depicted in Fig. 3. The injection current is set to be 150 mA. From Fig. 3(a), there exists an optimization input power range for RIN suppression. Under the given parameters, the best RIN suppression is reached at  8 dBm and 12 dBm for R-SOA and conventional SOA, respectively. As large as 450 dB (the maximum is  72 dB) RIN reduction is achieved for R-SOA near optimization range, far greater than conventional SOA ( 32.5 dB). The MTF depends on the optical gain and derivative of optical output power to input power for R-SOA and conventional SOA (see Eqs. (11a) and (11b)). From Fig. 3(b), we can clearly observe a stationary point for R-SOA, at which the reflective power reveals the minimum variation with increased input power (see curve a). This point corresponds to the optimized operation point. However, for conventional SOA, the stationary point can only be realized asymptotically for sufficiently large input power (see curve b), which is difficult to be fully reached from the viewpoint of available optical power in practice. Although the small-signal gain is larger for R-SOA, the RIN suppression is poor when input power deviating from its optimization range due to intensified gain saturation (see Fig. 3(c)). Fig. 4 shows the Low-frequency RIN suppression (a), reflective power (b), and gain (c) as function of signal input power for various injection currents. From Fig. 4(a), the optimized input power is decreased from  4 dBm to   10 dBm for increased injection current from 100 mA to 250 mA. This attributes to the strengthened gain saturation effect for larger current (see Fig. 4(c)). Up to 460 dB low-frequency RIN reduction is achieved for 250 mA injection current. Additionally, the input power operation range for optimized

Fig. 4. Low-frequency RIN suppression (a), reflective power (b), and gain (c) as function of signal input power for various injection currents.

X.-H. Jia et al. / Optics & Laser Technology 44 (2012) 1240–1246

RIN suppression is greatly extended by increasing injection current from Fig. 4(a), which is also confirmed by the extended flatten region in Fig. 4(b). As a typical example, we consider the RIN suppression in WDM spectrum splicing technology based on R-SOA. Although the influence of phase variation of optical field on RIN at R-SOA output is negligible, however, the RIN after receiver filter is sensitive to optical spectrum distortion and broadening because of four wave mixing (FWM) and frequency chirping induced by self-phase modulation (SPM) [14,18]. Thus, to simulate the RIN after receiver filter, the phase variation should be included as follows [14,18]:   @Af 1 @Af GgðN, lÞð1ibÞa þ ¼ Af ð12aÞ vg @t @z 2   @Ab 1 @Ab GgðN, lÞð1ibÞa  ¼ Ab @z vg @t 2

1245

Fig. 6 shows the RIN at R-SOA input (blue squares) and output (red triangles) as function of 3 dB bandwidth of input slicing filter. No received filter is used. The RIN corresponds to the component at 100 MHz.The noise floor of detector is neglected. It can be seen that, the RIN at R-SOA input is reduced gradually with increased input slicing filter bandwidth. Although the excess beating noise is proportional to Bo (Bo is the bandwidth of slicing filter), the direct current (DC) power of incoherent light after slicing filter is proportional to B2o, resulting in the smaller RIN for larger Bo [2]. The estimated RIN suppression of R-SOA is  36 dB, which is consistent with the preceding discussions based on modulation transfer function analysis.

ð12bÞ

where Af and Ab (in unit of W1/2) are the slowly varying amplitudes of forward and backward waves, respectively. b is the line-width enhancement factor. The incoherent optical source is simulated based on thermal light statistical model. Eqs. (12a) and (12b) combined with boundary condition (Eqs. (5a) and (5b)) can be solved using time-domain transfer matrix method [21]. The optical filter takes the form of 3 order super-Gaussian shape. Fig. 5 depicts the normalized optical spectrum before and after R-SOA. The 3 dB bandwidth of input slicing filter is 0.25 nm (a), 0.5 nm (b), 0.75 nm (c), and 1 nm (d). The injection current and averaged input power of R-SOA is 300 mA and  15 dBm, respectively. Additionally, b ¼5. From this figure, the obvious optical spectrum distortion and broadening are observed. The wavelength redshift is caused by frequency chirping. The optical spectrum broadening is more pronounced for larger bandwidth of input slicing filter.

Fig. 6. RIN at R-SOA input (blue squares) and output (red triangles) as function of 3 dB bandwidth of input slicing filter. No receiver filter is used. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Normalized optical spectrum before and after R-SOA. The 3 dB bandwidth of input slicing filter is 0.25 nm (a), 0.5 nm (b), 0.75 nm (c), and 1 nm (d), respectively.

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References

Fig. 7. RIN after receiver filter as function of 3 dB bandwidth of receiver filter. The input slicing filter bandwidth is 0.25 nm.

Fig. 7 gives the RIN after receiver filter as function of 3 dB bandwidth of receiver filter. The input slicing filter bandwidth is 0.25 nm, and the RIN at R-SOA input is  106 dBc/Hz (see Fig. 6 (blue square)). It is found that the RIN after receiver filter is decreased from  106 dBc/Hz to  142 dBc/Hz with increased receiver filter bandwidth from 0.25 nm to 3 nm. Due to the optical spectrum broadening (see Fig. 5(a)) and the intensity correlation between different wavelength components [14,18], the receiver filter bandwidth should be large enough to cover the broadened optical spectrum after R-SOA.

4. Conclusions In summary, the enhanced RIN suppression characteristic analysis of R-SOA has been carried out in detail by comparisons with conventional transmission SOA. The modulation transfer function is investigated to characterize the RIN suppression based on small-signal analysis. The numerical simulation shows that, by selecting appropriate input optical power, as large as 420 dB RIN suppression improvement can be achieved for R-SOA, without sacrificing the noise rejection bandwidth. With increased injection current, the optimized input signal power is decreased and the operation region is extended for the best RIN reduction. For RIN suppression in WDM spectrum slicing, the bandwidth optimization of receiver filter should be performed to avoid the spectral broadening induced by SPM and FWM. Our derived result is helpful for designing and optimizing the R-SOA in application of noise suppression enhancement.

Acknowledgment This work is supported by Scientific Research Fund of Sichuan Provincial Education Department No. 09ZB060. The author thanks the reviewers for their helpful comments.

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