Part I Stimulated Raman Scattering (SRS) Effect in OTDR
Chapter 2 SRS Effect in 1.65 µm OTDR On-Line Monitoring 1.55 µm
3.3 Theoretical Analysis of SRS-Induced Distorted OTDR Traces
In this section, we analyze forward and backward Raman amplification schemes in single-mode fiber transmission systems with distance L. The developed theoretical models of the SRS effect can be applied in the proof of SRS-induced distorted OTDR trace for 1.31 or 1.625 µm OTDR online monitoring 1.55 µm FRA transmission system. The pump light and the signal light with the same propagating direction is called forward scheme and with opposite propagating direction is called backward scheme. Here we deal with the single-mode fiber whose core radius and attenuation constant are r (effective cross section Aeff = πr2) and α, respectively. Label S and P are used for representing the signal at the Stokes frequency and the pump frequency, respectively.
3.3.1 Forward Stimulated Raman Interaction and Amplification
Here we analyze forward stimulated Raman scattering taking account of the effect of the pump depletion. Consider the pump with a power PP(0) is injected at z = 0 and travel in the +z direction with an effective power PP(z) together with the signal whose effective power is PS(z).
The differential equations only considering SRS nonlinear interaction for forward traveling waves of the signal and the pump are given by [26]
) ( )
( } ) ( ) {
( P z
A h g z P z
A P g dz
z dP
P eff
r S S
S P
eff r
S = −α ⋅ + ν ⋅ (3.1)
and
where gr is the Raman gain coefficient, ν is the frequency of the light wave and h is Plank’s constant. We assume that and αS = αP = α to solve eq. (3.1) and eq. (3.2). The first assumption will be effective since we deal with PS(0) ≠ 0. The second assumption will be held around 1.55 µm wavelength region in low-loss fibers. Under the assumption, forward signal light power evolution PS(z) and pump power evolution PP(z) can be analytically solved and given by (see the Appendix B)
)}
We consider a dimensionless parameter F defined by
)]}
Equation (3.5) illustrates F as a function of the fiber length and F becomes larger as the fiber length increases and reaches a steady state for αz >> 1. We consider the PS(z) and PP(z) under the both F >>1 and F << 1.
)] ]}
Equation (3.6) indicates that the signal plays as if it has the input power C0(λP/λS) and merely travels in the fiber with an attenuation constant α without SRS interaction, and the signal power reaches at almost the pump power at z = 0 pulses the incident signal power. Therefore, it is important to choose parameters lest F exceed 1 when SRS is used for amplification in optical fiber transmission system.
2) F << 1: In this case, eq. (3.3) and eq. (3.4) become
Equation (3.10) is the same as the results derived by Smith [27] under assumption that pump depletion due to stimulated process is neglected.
When the theory is used in fiber Raman amplifier, the Raman gain G due to stimulated Raman amplification is defined by
}
)
3.3.2 Backward Stimulated Raman Interaction and Amplification for Strong Pump Case
In the use of backward stimulated Raman amplification in optical fiber transmission systems, it will be important that the system is designed not to induce pump depletion due to the backward stimulated process because the signal level will fluctuated while the pump depletion occurring.
Hence the pump depletion due to the backward stimulated process is neglected for stimulated Raman amplification. Let the pump with a power PP(L) be injected at z = L and travel in the -z direction with an effective power PP(z) together with the signal PS(z) which travel in +z direction. The differential equations for forward traveling waves of the signal and backward traveling waves of the pump are given by
) amplification. Using eq. (3.15) and eq. (3.16),
∫ ∫
Thus, eq. (3.15) can be analytically solved and the forward signal light power evolution PS(z) given by
The Raman gain for backward Raman amplification is obtained as
The gain given by eq. (3.19) is similar to that due to forward Raman amplification under the condition F << 1 with weak signal.
3.3.3 Backward Stimulated Raman Interaction for Weak Pump Case
In a case of backward SRS interaction, the pump light, whose power is less than the signal power, travels in opposite direction to the signal. Hence the signal depletion due to the backward stimulated process is neglected. Let the signal with a power PS(L) be injected at z = L and travel in the -z direction with an effective power PS(z) together with the pump PP(z) which travel in +z direction. The differential equations for forward traveling waves of the pump and backward traveling waves of the signal are given by
)]
Thus, eq. (3.21) can be analytically solved and the forward pump power evolution PP(z) given by
} ]
1 ) [exp(
) ) exp(
exp{ ( ) 0 ( )
( L z z
A L P P g
z
P S S P
P S S eff
S P r
P α α α
λ λ
α ⋅ − ⋅ − −
−
⋅
= (3.22)
3.4 Simulation Results for SRS-Induced OTDR Distorted Traces
In 1.625 µm OTDR on-line monitoring 1.55 µm FRA transmission system using 1.46~1.49 µm pump lights, the 1.625 µm OTDR distorted probe traces have been measured by forward and backward pumping schemes as shown in Fig. 3.2(a) and 3.2(b), respectively. The 1.625 µm OTDR probe power evolution along the fiber are calculated by eq. (3.3) and eq. (3.17) for forward and backward stimulated Raman interaction, respectively. The SRS-interaction among 1.46~1.49 µm pump lights of the 1.55 µm FRA is neglected. The 1.625 µm OTDR probe power will get the power from the 1.55 µm data channel or 1.46~1.49 µm pump lights of the 1.55 µm FRA due to the SRS effect. Figure 3.6 shows the simulated OTDR traces of (A) the pump off scheme without the 1.55 µm signal, (B) the forward- pumping scheme with the 1.55 µm signal, (C) the backward-pumping scheme with the 1.55 µm signal, and (D) the pump off scheme with the 1.55 µm signal in 1.625 µm monitoring FRA transmission system. The OTDR distorted traces mainly result from the SRS effect pumped by the 1.46~1.49 µm pumped lights of 1.55 µm FRA regardless of forward or backward pumping scheme. The 1.55 µm data channel relatively to the 1.625 µm OTDR channel gives a separation of 75 nm (about 8.93 THz), which matches higher Raman gain coefficient of about 5.7×10-14 m/W for the used fiber, but the power of 1.55 µm signal is much less than that of the 1.46~1.49 µm pumped lights which give a separation of 165~135 nm (about 20.8 ~ 16.7 THz) relatively to the 1.625 µm OTDR channel, which match the lower Raman gain coefficient of about 1×10-14 ~ 2×10-14 m/W for the used LEAF. Therefore, the 1.46~1.49 µm pumped lights of 1.55 µm FRA are mainly sources to provide Raman gain to the 1.625 µm OTDR probe light and result in distorted OTDR trace, which are higher level than the healthy OTDR trace, as shown in Fig. 3.6.
In 1.31 µm OTDR on-line monitoring 1.55 µm FRA transmission system using 1.46~1.49 µm pump lights, the 1.31 µm OTDR distorted probe traces have also been measured by forward and backward pumping schemes as shown in Fig. 3.3(a) and 3.3(b), respectively. The 1.31 µm OTDR probe power evolution along the fiber are calculated by eq. (3.4) and eq. (3.22) for forward and backward stimulated Raman interaction, respectively. The 1.31 µm OTDR probe power will deplete the power to the 1.55 µm data channel or 1.46~1.49 µm pump lights of the 1.55 µm FRA due to the SRS effect. Figure 3.7 shows the simulated OTDR traces of (A)
1.55 µm signal, (C) the forward-pumping scheme with the 1.55 µm signal , and (D) the pump off scheme with the 1.55 µm signal in 1.31 µm monitoring FRA transmission system. The distorted OTDR supervisory trace mainly results from the SRS interaction between the 1.31 µm OTDR lights and pumped lights of 1.46~1.49 µm of FRA since the 1.31 µm OTDR channel relatively to the 1.46 ~ 1.49 µm pumped lights of 1.55 µm FRA give a separation of 150 ~ 180 nm (about 23.5 ~ 27.7 THz), which match the Raman gain coefficient of about 1.7×10-14 ~ 0.4×10-14 m/W for the used fiber. The SRS effect between the 1.31 µm OTDR light and the 1.55 µm data channel can be neglected, and both trace (A) and (D) of Fig. 3.7 are the same because of a separation of 240 nm (about 35.5 THz), which matches lower Raman gain coefficient of about 0.4×10-14 m/W and lower power of 1.55 µm data channel which is less than that of the 1.46 ~ 1.49 µm pumped lights. Therefore, the power of 1.31 µm OTDR lights is depleted due to the SRS interaction with the 1.46 ~ 1.49 µm pumped light of 1.55 µm FRA along the fiber in both forward and backward pumping cases and result in distorted OTDR traces, which are lower levels than the healthy OTDR trace, as shown in Fig. 3.7. The simulated profiles of the OTDR distorted trace are in agreement to experimental profiles of that for both 1.31 µm and 1.625 µm OTDR on-line monitoring 1.55 µm FRA transmission system using forward or backward pumping schemes with 1.46~1.49 µm pump lights.
3.5. Summary
We have demonstrated the 1.625 µm and 1.31 µm OTDR on-line monitoring in forward and backward pumping distributed FRA transmission systems. In the 1.625 µm OTDR on-line monitoring 1.55 µm FRA transmission system, the gain degradation, which results from the power depletion of 1.55 µm data light due to the SRS-interaction between the 1.55 µm data channel and 1.625 µm OTDR channel, is about -0.6 dB and -0.2 dB for the forward-and backward-pumping cases, respectively. Similarly, in the 1.31 µm OTDR on-line monitoring 1.55 µm FRA transmission system, the gain improvement, which results from due to the SRS-interaction between the 1.55 µm data channel and 1.31 µm OTDR channel, is about +0.2 dB and +0.1 dB for the forward-and backward-pumping cases, respectively. However, the distorted OTDR traces are obtained regardless of forward or backward pumping scheme and give rise to an un-accurately measured fiber-loss coefficient and reflection profile along fiber link. The reflective fiber faults occurred in the fiber link can be still observed and identified.
The main reason of the distorted OTDR traces happened is the SRS effect between the OTDR probe light and the pumping lights of 1.55 µm FRA, and that is also demonstrated by
simulation in theoretical analysis. The simulated profiles of the OTDR distorted trace are in agreement to experimental profiles of that for both 1.31 µm and 1.625 µm OTDR on-line monitoring 1.55 µm FRA transmission system using forward or backward pumping schemes with 1.46~1.49 µm pump lights.
In spite of 1.31 µm or 1.625 µm OTDR on-line monitoring 1.55 µm FRA transmission system, the OTDR-monitoring induced power penalty for the BER performances of the 10 Gb/s data channel is negligible (< 0.1 dB) in spite of the pump light was on or off for a BER of 10-9 for forward-pumping and backward-pumping scheme. Therefore, the 1.55 µm signal light depleted due to SRS effect with the 1.31 µm or 1.625 µm OTDR light has trivial impact on BER performance in this system.
Part II
Broadband Erbium-Doped Fiber Sources
Chapter 4 Introduction
Incoherent broadband optical sources with low spectral ripple and high output power are desirable for various applications such as spectrum-sliced source, a light source for DWDM device characterization, optical sensor system, (e.g., fiber-optic gyroscopes (FOG)), and optical low-coherence reflectometry (OLCR) [28]-[36]. The semiconductor source such as light-emitting diodes (LED’s) and superluminescent diodes (SLD’s) can provide wide spectrum, but their low output power and poor wavelength stability for temperature will limit their usefulness. Rare-earth doped incoherent fiber sources have emerged as promising broadband sources, offering an improvement in temperature stability, as well as advantages of higher available power and improved lifetimes. Both incoherent neodymium-doped sources at 1.06 µm [37], and erbium-doped fiber (EDF) sources near 1.55 µm [38], [39], have been studied.
The EDF based amplified spontaneous emission (ASE) source is a good candidate for simultaneous offering broad spectral linewidth, high output power, and excellent mean wavelength stability to meet application requirements. Several C-band (1520 ~ 1560 nm) EDF ASE sources have been reported [40]-[42]. In general, there are four kinds of configurations to implement ASE sources: single-pass forward (SPF), single-pass backward (SPB), double-pass forward (DPF), and double-pass backward (DPB). Among them, the DPB has been demonstrated to offer the highest output power, better mean wavelength stability, and broader linewidth for C-band ASE source [43]. However, there is no work have been reported on L-band (1570 ~ 1610 nm) ASE sources and few work have been reported on broadband ASE sources, including L- and C-band (1520 ~1610 nm), [44], [45]. In this part of the thesis, the investigations in the L-band ASE fiber sources and C- plus L-band (broadband) ASE fiber source are our main works.
First, we necessarily understand what characteristics of the EDF ASE sources are needed to achieve for applications. The EDF ASE sources, applied to the FOG, OLCR and spectrum-sliced WDM system, are introduced in following sections.
4.1 Review of Fiber-Optic Gyroscopes
In 1913, Sagnac first proved that the rotation detection could be achieved by using optical
interferometer and the rotation of the system can be estimated by the phase difference of two opposite propagating lights. Figure 1 shows a rotating circular loop interferometer. When the interferometer is at rest in an inertial frame of reference the path lengths of the counterpropagating waves are equal and both waves return to the point of injection Pi in phase after a time τ = 2πR/c where R is the path radius. When the interferometer is rotating at a rate Ω and the observer is motionless in the original inertial frame, the Pi moves through an angle Ωτ during the propagating time τ. Therefore, the different time of the counterpropagating waves to the lowest order in RΩ/c is [46]
2
4 2
) 2
( ) 2
(
c R c
R c
R− −Ω = Ω
Ω
= +
∆τ π τ π τ π . (4.1)
For continuous waves of frequency ω, the corresponds to a phase shift
Ω
=
∆
=
∆ 4 22
c Rω τ π
ω
φ . (4.2)
This result remains unchanged when the interferometer is filled with a medium of refractive because the Fresnel-Fizeaudrag effect due to the movement of the medium compensates for the increased optical path lengths [47].
In 1976, Vali and Shorthill first proposed a Sagnac interferometer using fiber [48], since the single mode fiber (SMF) has low loss and the detection sensitivity of system can be improved by increasing the circles of fiber. The basic consideration of the fiber gyroscope is described by the Sagnac effect and by applying it to interferometer which makes use of a optical-fiber coil. The advantage of using an optical-fiber coil to form the interferometer is that the Sagnac phase difference increases with the number of turns or the length of the fiber. For this case it is often convenient to rewrite the above formulas (eq. (4.2)) in terms of the length of the fiber L, the diameter of the coil D, and the mean wavelength of the light source λm. Therefore, the FOG system using Sagnac interferometer gives the relationship between the Sagnac phase shift ∆Φ and the rotation rate Ω as shown in following [46].
Ω
=
∆Φ c
LD λm
π
2 (4.3)
The Sagnac phase shift ∆Φ is proportion to the rotation rate Ω and the scale factor is
2πLD/(λmc). The scalar factor stability determines the accuracy of the rotation detection. That is, the mean wavelength stability is the critical parameter of the light source for the accuracy of rotation detection with FOG. Therefore, a navigational-grade FOG requires a mean source wavelength which is stable with respect to temperature. Since temperature control of a fiber to 0.1 is easily achieved, a mean wavelength stability of 1 part per million (ppm) can be ℃ achieved by a thermal coefficient less than 10 ppm/ for the superfluorescent fiber source. ℃ The source of choice for the FOG has been the SLD. Unfortunately, a mean wavelength variation on the order of 400 ppm/℃ is exhibited for most SLD’s. It means that temperature control to 0.0025 ℃ is required to meet the stability goal of navigational-grade FOG [35].
Moreover, the power emitted by an SLD cannot be efficiently coupled into SMF. For these reasons, broadband rare-earth doped fiber ASE sources, which are inherently spectral stable and easily coupled into SMF, are developed.
To meet the stability requirements of FOG, the mean wavelength of a source must be stable not only with respect to the direct effects of temperature, but also with respect to other temperature-dependent parameters. To first order, the components of the temperature dependence of the mean wavelength of an EDF ASE source are represented by [49]
The first term is the intrinsic thermal effect which is related to the thermal behavior of the erbium-doped fiber with the population changes of the erbium level, and has a typical value of less than 10 ppm/℃. The ∂λp/∂T and ∂Pp/∂T in the second and third terms depend on the pump laser used, and only be controlled by optimize the laser’s characteristics. The ∂λm/∂λp and ∂λm
/∂ Pp take the effects of pump laser diode into account through the pump wavelength λp and the pump power Pp. The pump laser diode typically produces a wavelength coefficient of about 400 ppm/℃ and power variation on the order of -0.3 mW/℃. The EDF ASE source is desirable to have a temperature independent or insensitive mean wavelength operation. The mean wavelength should change by less 1 ppm as the FOG rotation varies over its useful range.
Therefore, the pump-power dependent mean wavelength (∂λm /∂Pp), which has an ideal amount of 0 ppm/mW, is related to the accuracy of rotation detection with FOG.
Additionally, the characteristics of broadband linewidth and high output power can be
can eliminate the coherent errors due to Rayleigh backscattering, polarization cross-coupling, and Kerr effect. The high power in SMF can improve the signal-to-noise ratio (SNR) for FOG system. Therefore, the EDF ASE source is a good choice for the light source of FOG system.
4.2 Review of Optical Low-Coherence Reflectometry
Optical low-coherence reflectometry is well known for its ability to detect, localize, and quantify weakly reflecting discontinuities and irregularities in optical waveguide and circuits. It also is powerful for diagnosing packaged modules with high resolution and high sensitivity [50]. Figure 4.2 shows the structure of OCLR based on Michelson interferometer using a 2x2 fiber coupler. One part is launched into device under test (DUT). The other part, which is optically delayed by using a mirror and a position transition, acts as a reference. The position of the mirror is adjusted appropriately and then the interference is obtained at the detector due to the Rayleigh backscattering light of the DUT and reflected light of the reference. The less coherence of light source, the higher space resolution of interferometer becomes. The measured intensity of detector is [51]
)]
cos(
) ( 2
1 )[
1
( 2 12
0K K A R A Rγ τ ωτ
P
Pd = − + + (4.5)
where P0 and K are the injecting optical power and couple-ratio of the fiber coupler, respectively. R and A are the reflectance at a measured place and loss of the DUT, respectively.
τ = t2 - t1 is the time difference between two interferometer arms (Fig. 4.2), γ12 is the level of interference and ω is the mean frequency of light source. In eq. (4.5), the latest term in square bracket corresponds to the interference signal. An oscillation achieves at the detector and its amplitude is direct proportion to the square of R. When the optical time difference between two interferometer arms exceeds the coherence time, the γ12 will drop to zero. Therefore, the interference is only achieved at a situation that the optical time difference between two interferometer arms does not exceed the coherence time. The resolution of OLCR is determined to the full-width at half-maximum (FWHM) of the broadband light source and is approximately given by [51]
ν υ
= ∆
∆ 2
x g (4.6)
where △ν is the FWHM of the broadband light source and υg is the group velocity of light
source. Therefore, the more bandwidth of light source applied in the OCLR, the smaller space resolution is achieved.
The advantage of OLCR is that the transmission loss distribution of a DUT is revealed by the micrometer-resolved Rayleigh backscattering profile. The dynamic range and space resolution of the OLCR are about 30-110 dB and 20-60 µm, respectively. The dynamic range is limited because the typical Rayleigh signal from a resolved region is much lower than the input.
The high dynamic range is necessary for diagnosing waveguides with high transmission loss such as unbiased laser diodes, and optical isolator with high isolation. High power light source used can improve the dynamic range of OLCR [30]. Therefore, a high-power broadband light source is indispensable for increasing the dynamic range.
4.3 Review of Spectrum-Sliced System
The WDM system is an attractive technique for improving the transmission capacity of optical fiber communication system. However, WDM systems are envisioned to have a multiple number of transmitter lasers operating at different wavelengths. Thus, these transmitter lasers should be wavelength-selected such as distributed feedback (DFB) laser for each channel and controlled to operate at a specific wavelength. However, the process would increase cost and complexity. There have been a few attempts to overcome this problem by using broadband LED’s or SLD’s was “spectrum-sliced” by using grating-based demultiplexers and was used in WDM systems [52], [53]. The high-power ASE from an EDFA, which is already in the single-mode fiber, can be efficiently divided into many channels by using an integrated optic WDM demultiplexer, optical filter, or long-period fiber grating (FBG). This “spectrum-sliced”
ASE can be used as light source for WDM systems rather than several wavelength-selected DFB lasers.
Figure 4.3 shows the basic structure of spectrum-slicing light source. The broadband incoherent light sources can be divided into many channels by using an integrated optic WDM demultiplexer. It is desirable to generate narrower channel bandwidth and channel spacing for
Figure 4.3 shows the basic structure of spectrum-slicing light source. The broadband incoherent light sources can be divided into many channels by using an integrated optic WDM demultiplexer. It is desirable to generate narrower channel bandwidth and channel spacing for