國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture 11.3.3 EDFA Power-Conversion Efficiency and Gain  11.4 AMPLIFIER NOISE  11.5 SYSTEM APPLICATIONS 11.5.1 Power Amplifiers 11.5.2 In-Line Amplifiers 11.5.3 Preamplifiers 11.5.4 Multichannel Operation 11.5.5 In-Line Amplifier Gain Control

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.6 WAVELENGTH CONVERTERS 11.6.1 Optical-Gating Wavelength Converters 11.6.2 Wave-Mixing Wavelength Converters

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3 ERBIUM-DOPED FIBER AMPLIFIERS  The active medium in an optical fiber amplifier consists of a nominally 10- to 30-m length of optical fiber that has been lightly doped (e.g., 1000 parts per million weight) with a rare-earth element, such as erbium (Er), ytterbium (Yb), neodymium (Nd), or praseodymium (Pr).  The host fiber material can be either standard silica, a fluoride-based glass, or a multi-component glass.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3 ERBIUM-DOPED FIBER AMPLIFIERS  The operating regions of these devices depend on the host material and the doping elements.  The most popular material for long-haul telecommunication applications is a silica fiber doped with erbium, which is known as an erbium- doped fiber amplifier or EDFA.  In some cases, Yb is added to increase the pumping efficiency and the amplifier gain.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3 ERBIUM-DOPED FIBER AMPLIFIERS  The operation of an EDFA by itself normally is limited to the 1530-to-1560-nm region.  However, when combined with a Raman fiber amplifier that boosts the gain at higher wavelengths, a 3-dB gain bandwidth of 75-nm has been achieved over the 1531 ~ 1616-nm region.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3 ERBIUM-DOPED FIBER AMPLIFIERS Figure 11-3. Typical dependence of the single-pass gain on optical input power for a small-signal gain of G 0 = 30 dB (a gain of 1000).

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism  Whereas semiconductor optical amplifiers use external current injection to excite electrons to higher energy levels, optical fiber amplifiers use optical pumping.  The optical pumping process requires the use of three energy levels. The top energy level to which the electron is elevated must lie energetically above the desired lasing level.  After reaching its excited state, the electron must release some of its energy and drop to the desired lasing level.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism  From this level, a signal photon can then trigger it into stimulated emission, whereby it releases its remaining energy in the form of a new photon with a wavelength identical to that of the signal photon.  Since the pump photon must have a higher energy than the signal photon, the pump wavelength is shorter than the signal wavelength.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism  The erbium atoms in silica are actual Er 3+ ions. In describing the transitions of the outer electrons in these ions to higher energy states, it is common to refer to the process as "raising the ions to higher energy levels."  Figure 11-4 shows a simplified energy-level diagram and various energy-level transition processes of these Er 3+ ions in silica glass.  The two principal levels for telecommunication applications are a metastable level (the so-called 4 I 13/2 level) and the 4 I 11/2 pump level.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism  A pump laser emitting 980-nm photons is used to excite ions from the ground state to the pump level, as shown by transition process 1 in Fig. 11-4.  The excited ions decay (relax) very quickly (in about 1-  s) from the pump band to the metastable band, shown as transition process 2.  During the decay, the excess energy is released as phonons or, equivalently, mechanical vibrations in the fiber.  Within the metastable band, the electrons of the excited ions tend to populate the lower end of the band. Here, they are characterized by a very long fluorescence time of about 10 ms

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism Figure 11-4. Simplified energy-level diagrams and various transition processes of Er 3+ ions in silica.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism  Another possible pump wavelength is 1480 nm. The absorption of a 1480-nm pump photon excites an electron from the ground state directly to the lightly populated top of the metastable level, as indicated by transition process 3 in Fig. 11-4.  These electrons then tend to move down to the more populated lower end of the metastable level (transition 4).  Some of the ions sitting at the metastable level can decay back to the ground state in the absence of an externally stimulating photon flux, as shown by transition process 5.  This decay phenomenon is known as spontaneous emission and adds to the amplifier noise.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.1 Amplification Mechanism  Two more types of transitions occur when a flux of signal photons that have energies corresponding to the band-gap energy between the ground state and the metastable level passes through the device.  First, a small portion of the external photons will be absorbed by ions in the ground state, which raises these ions to the metastable level, as shown by transition process 6.  Second, in the stimulated emission process (transition process 7) a signal photon triggers an excited ion to drop to the ground state, thereby emitting a new photon of the same energy, wave vector, and polarization as the incoming signal photon.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The widths of the metastable and ground-state levels allow high levels of stimulated emissions to occur in the 1530-to-1560-nm range.  Beyond 1560 nm, the gain decreases steadily until it reaches 0 dB (unity gain) at around 1616 nm. 11.3.1 Amplification Mechanism

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.2 EDFA Architecture  An optical fiber amplifier consists of a doped fiber, one or more pump lasers, a passive wavelength coupler, optical isolators, and tap couplers, as shown in Fig. 11-5.  The dichroic (two-wavelength) coupler handles either 980/1550-nm or 1480/1550-nm wavelength combinations to couple both the pump and signal optical powers efficiently into the fiber amplifier.  The tap couplers are wavelength-insensitive with typical splitting ratios ranging from 99:1 to 95:5. They are generally used on both sides of the amplifier to compare the incoming signal with the amplified output.  The optical isolators prevent the amplified signal from reflecting back into the device, where it could increase the amplifier noise and decrease its efficiency.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.2 EDFA Architecture  The pump light is usually injected from the same direction as the signal flow. This is known as codirectional pumping.  It is also possible to inject the pump power in the opposite direction to the signal flow, which is known as counter-directional pumping.  As shown in Fig. 11-5, one can employ either a single pump source or use dual-pump schemes, with the resultant gains typically being +17 dB and +35 dB, respectively.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.2 EDFA Architecture Figure 11-5. Three possible configurations of an EDFA: (a). co-directional pumping, (b). counter-directional pumping, (c). dual pumping.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Counter-directional pumping allows higher gains, but codirectional pumping gives better noise performance.  In addition, pumping at 980 nm is preferred, since it produces less noise and achieves larger population inversions than pumping at 1480 nm. 11.3.2 EDFA Architecture

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  As is the case with any amplifier, as the magnitude of the output signal from an EDFA increases, the amplifier gain eventually starts to saturate.  The reduction of gain in an EDFA occurs when the population inversion is reduced significantly by a large signal, thereby yielding the typical gain-power performance curve shown in Fig. 11-3.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  The input and output powers of an EDFA can be expressed in terms of the principle of energy conservational: P s,out < P s,in + ( p / s )P p,in (11-16) where P p,in is the input pump power, and p and s are the pump and signal wavelengths, respectively.  The inequality in Eq. (11-16) reflects the possibility of effects such as pump photons being lost due to various causes (such as interactions with impurities) or pump energy lost due to spontaneous emission.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  From Eq. (11- 16), we see that for the pumping scheme to work, we need to have p < s, and, to have an appropriate gain, it is necessary that P s,in << P p,in.  Thus, the power conversion efficiency (PCE), defined as (11-17) is less than unity.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  The maximum theoretical value of the PCE is p / s.  For absolute reference purposes, it is helpful to use the quantum conversion efficiency (QCE), which is wavelength-independent and is defined by QCE = ( s / p )PCE (11-18)  The maximum value of QCE is unity, in which case all the pump photons are converted to signal photons.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  We can also rewrite Eq. (11- 16) in terms of the amplifier gain G. Assuming there is no spontaneous emission, then G = P s,out /P s,in < 1 + ( p / s )(P p,in /P s,in ) (11-19)  This shows an important relationship between signal input power and gain.  When the input signal power is very large so that P s,in >> ( p / s )P p,in, then the maximum amplifier gain is unity.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  From Eq. (11-19), we also see that in order to achieve a specific maximum gain G, the input signal power cannot exceed a value given by P s,in < ( p / s )P p,in /(G-1) (11-20)

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain Example 11-3.  Consider an EDFA being pumped at 980 nm with a 30-mW pump power.  If the gain at 1550 nm is 20 dB, then, from Eq. (11- 20), the maximum input power is  From Eq. (11- 16), the maximum output power is

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  In addition to pump power, the gain also depends on the fiber length.  The maximum gain in a three-level laser medium of length L, such as an EDFA, is given by G max = exp(  e L) (11-21)  where  e is the signal-emission cross section and  is the rare-earth element concentration.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  The maximum possible EDFA gain is given by the lowest of the two gain expressions of Eqs. (11-19) and (11-21): (11-22)  Since G = P s,out /P s,in = exp(  e L), it follows similarly that the maximum possible EDFA output power is given by the minimum of the two expressions of Eqs. (11-19) and (11-21) : (11-23)

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  Figure 11-6 illustrates the onset of gain saturation for various doped-fiber lengths as the pumping power increases.  As the fiber length increases for low pumping powers, the gain starts to decrease after a certain length because the pump does not have enough energy to create a complete population inversion in the downward portion of the amplifier.  In this case, the unpumped region of the fiber absorbs the signal, thus resulting in signal loss rather than gain in that section.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain Figure 11-6. Calculation of the dependence of EDFA gain on fiber length and pump power for a 1480-nm pump and a 1550-nm signal. Example 11-4 : From Fig. 11-6 we see that for 1480-nm pumping, a 35-dB gain can be achieved with a pump power of 5-mW for an amplifier length of 30-m.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain  Since the metastable level in an EDFA has a relatively long lifetime, it is possible to obtain very high saturated output powers.  The saturated output power, (the power at which gain saturation occurs) is defined as the 3-dB compression point of the small-signal gain.  For large signal operation, the saturated gain increases linearly with pump power, as can be inferred from Fig. 11-7.  This figure shows that as the input power increases for a given pump level, the amplifier gain remains constant until saturation occurs.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.3.3 EDFA Power-Conversion Efficiency and Gain Figure 11-7. Gain behavior of an EDFA as a function of output signal power for various pump levels.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The dominant noise generated in an optical amplifier is amplified spontaneous emission (ASE). The origin of this is the spontaneous recombination of electrons and holes in the amplifier medium (transition 5 in Fig. 11-4).  This recombination gives rise to a broad spectral background of photons that get amplified along with the optical signal. This effect is shown in Fig. 11-8 for an EDFA amplifying a signal at 1540 nm.  The spontaneous noise can be modeled as a stream of random infinitely short pulses that are distributed all along the amplifying medium. Such a random process is characterized by a noise power spectrum that is flat with frequency. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Figure 11-8. Representative 1480-nm pump spectrum and a typical output signal at 1540nm with the associated amplified-spontaneous-emission (ASE) noise. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The power spectral density of the ASE noise is S ASE (f) = h  n sp [G(f) – 1] = P ASE /  v opt (11-24) where P ASE is the ASE noise power in an optical bandwidth  v opt  and n sp is the spontaneous-emission or population- inversion factor, defined as n sp = n 2 / (n 2 – n 1 ) (11-25) where n 1 and n 2 are the fractional densities or populations of electrons in states 1 and 2, respectively. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Thus, n sp denotes how complete the population inversion is between two energy levels. From Eq. (11.25), n sp > 1, with equality holding for an ideal amplifier when the population inversion is complete.  Typical values of n sp range from 1.4 to 4, depending on the wavelength and the pumping rate.  The ASE noise level depends on whether codirectional or counterdirectional pumping is used.  Figure 11-9 shows experimental and calculated data on ASE noise versus pump power for different EDFA lengths. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Figure 11-9. Experimental and theoretical ASE noise powers input pump power for various EDFA lengths arising from (a) codirectional (forward) pumping and (b) counter- directional (backward) pumping. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The photo-current consists of a number of beat signals between the signal and the optical noise fields, in addition to the squares of the signal field and the spontaneous-emission field.  The total photo-detector current i tot is proportional to the square of the electric field of the optical signal: i tot ~ (E s + E n ) 2 = E s 2 + E n 2 + 2E s E n. Here the first two terms arise purely from the signal and spontaneous-emission noise, respectively.  The 3rd term is a beat mixing component between the signal and noise, which can fall within the bandwidth of the receiver and degrade the signal-to-noise ratio. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Taking the ASE photons into account, the optical power incident on the photo-detector becomes P o = GP s,in + S ASE  opt. Note that  v opt can be reduced significantly if an optical filter precedes the photo-detector.  Substituting the expression for P o into Eq. (6-6) then yields the total mean-square shot-noise current =  2 shot =  2 shot-s +  2 shot-ASE = 2qRGP s,in B + 2qRS ASE  opt (11-26) where B is the front-end receiver electrical bandwidth. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The other two noises arise from the mixing of the different optical frequencies contained in the light signal and the ASE, which generates two sets of beat frequencies.  Since the signal and the ASE have different optical frequencies, the beat noise of the signal with the ASE is  2 s-ASE = 4(RGP s,in )(RS ASE B) (11-27) 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Since the ASE spans a wide optical frequency range, it can beat against itself giving rise to the noise current  2 ASE-ASE = R 2 S 2 ASE (2  opt - B) (11-28)  The total mean-square receiver noise current then becomes =  2 total =  T 2 +  2 shot-s +  2 shot-ASE +  2 s-ASE =  2 ASE-ASE (11-29) where the thermal noise variance  T 2 is given by Eq. (6-17). 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The last four terms in Eq. (11-29) tend to be of similar magnitudes when the optical bandwidth  v opt is taken to be the optical bandwidth of the spontaneous emission noise, which covers a 30-nm spectrum.  However, one generally uses a narrow optical filter at the receiver, so that  v opt is on the order of 125 GHz (a 1-nm spectral width at 1550 nm) or less.  In that case, we can simplify Eq. (11-29) by examining the magnitudes of the various noise components. First, the thermal noise can generally be neglected when the amplifier gain is large enough. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Since the amplified signal power GP s,in is much larger than the ASE noise power S ASE  v opt,  the ASE-ASE beat noise given by Eq. (11-28) is significantly smaller than the signal-ASE beat noise.  This observation reduces Eq. (11-26) to  2 shot = 2qRGP s,in B (11-30) 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Using these results together with the expression for S ASE from Eq. (11-24) yields the following approximate signal-to-noise ratio (S/N) at the photo-detector output: (S/N)out = (  2 ph /  2 total ) = (R 2 G 2 P 2 s,in /  2 total ) = (RP s,in /2qB){G/[1+2  n sp (G-1)]} (11-31)  where  is the quantum efficiency of the photo- detector and, from Eq. (6-11), the mean-square input photo-current is  i ph 2  ph 2 = R 2 G 2 P 2 s,in (11-32) 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Note that the term (S/N) in = RP s,in /2qB (11-33) in Eq. (11-31) is the signal-to-noise ratio of an ideal photo-detector at the input to the optical amplifier.  From Eq. (11-31) we can then find the noise figure of the optical amplifier, which is a measure of the S/N degradation experienced by a signal after passing through the amplifier.  Using the standard definition of noise figure as the ratio between the S/N at the input and the S/N at the amplifier output, we have Noise figure = F = (11-34) 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  When G is large, this becomes 2  n sp. A perfect amplifier would have n sp =1, yielding a noise figure of 2 (or 3 dB), assuming  = 1.  That is, using an ideal receiver with a perfect amplifier would degrade the S/N by a factor of 2.  In a real EDFA, for example, n sp is around 2, so the input S/N gets reduced by a factor of about 4. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.4 Amplifier Noise Example 11-5 :  Figure 11-10 shows measured values of the noise figure for an EDFA under gain saturation for both codirectional and counter-directional pumping.  The pump wavelength was 1480 nm and the signal wavelength was 1558 nm with an input power to the amplifier of -60 dBm.  Under small-signal conditions, the codirectional pumping noise was about 5.5 dB, which included a 1.5- dB input coupling loss.  The noise figure of the optical amplifier itself was thus 4 dB, compared with the theoretical minimum of 3 dB with complete population inversion. The noise figure in the counter-directional pumping case was about 1 dB higher.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Figure 11-10. Measured EDFA noise figure under gain saturation for codirectional pumping and counter- directional pumping at 1480-nm. The gain was similar for both pumping directions. 11.4 Amplifier Noise

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.1 Power Amplifiers  For the power amplifier, the input power is high, since the device immediately follows an optical transmitter. High pump powers are normally required for this applications.  The amplifier inputs are generally -8 dBm or greater, and the power amplifier gain must be greater than 5 dB in order for it to be more advantageous than using a preamplifier at the receiver.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Example 11-6 :  Consider an EDFA which is used as a power amplifier with a 10-dB gain. Assume the amplifier input is a 0-dBm level from a laser diode transmitter.  If the pump wavelength is 980nm, then from Eq.(11-16), for a 10-dBm output at 1540nm, the pump power must be at least P p,in > ( s / p )(P s,out - P s,in ) = (1540/980)(10mW - 1mW) =14mW 11.5.1 Power Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.2 In-Line Amplifiers  In a long transmission system, optical amplifiers are needed to periodically restore the power level after it has decreased due to attenuation in the fiber.  The gain of each EDFA in this amplifier chain is chosen to compensate exactly for the signal loss incurred in the preceding fiber section of length L, that is, G = exp(-  L).  The accumulated ASE noise is the dominant degradation factor in such a cascaded chain of amplifiers.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Example 11-7 :  Consider Fig.11-11, which shows the values of the per-channel signal power, the per-channel ASE noise, and the SNR along a chain of seven optical amplifiers in a WDM link.  The input signal level starts out at 6-dBm and decays due to fiber attenuation as it travels along the link.  When its power level has dropped to dB, it gets boosted back to 6-dBm by an optical amplifier. 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Figure 11-11. SNR degradation as a function of link distance over which the ASE noise increases with the number of amplifiers. The curves show the signal level (solid lines), the ASE noise level (dashed lines), and the SNR (dotted lines) for a signal channel in a WDM link. 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  For a given channel transmitted over the link, the SNR starts out at a high level and then decreases at each amplifier as the ASE noise accumulates through the length of the link.  For example, following amplifier number 1, the SNR is 28 dB for a 6-dBm amplified signal level and a -22-dBm ASE noise level.  After amplifier number 4, the SNR is 22 dB for a 6-dBm amplified signal level and a -16-dBm ASE noise level.  The higher the gain in the amplifier, the faster the ASE noise builds up. 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Although the SNR decreases quickly in the first few amplifications, the incremental effect of adding another EDFA diminishes rapidly with an increasing number of amplifiers.  As a consequence, although the SNR drops by 3 dB when the number of EDFAs increases from one to two, it also drops by 3 dB when the number of amplifiers is increased from two to four, and by another 3 dB when the number of amplifiers is further increased to eight. 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  To compensate for the accumulated ASE noise, the signal power must increase at least linearly with the length of the link in order to keep a constant SNR.  If the total system length is L tot = NL and the system contains N optical amplifiers each having a gain G = exp(-dL), then, using Eq.(11-24), the path-averaged ASE power along a chain of optical amplifiers is (11-35)  where  is the fiber attenuation and F path (G) is a penalty factor defined as F path (G) = (1/G)[(G-1)/lnG] 2 (11-36) 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Basically, F path (G) gives the factor by which the path-average signal energy must be increased (as G increases) in a chain of N cascaded optical amplifiers to maintain a fixed S/N.  These optical amplifiers should be placed uniformly along the transmission path to yield the best combination of overall gain and final S/N.  The input power levels for these in-line amplifiers nominally ranges from -26 dBm (2.5  W) to -9 dBm (125  W), with gains generally greater than 15 dB. 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Example 11-8 :  Consider an optical transmission path containing N cascaded optical amplifiers, each having a 30-dB gain.  If the fiber has a loss of 0.2dB/km, then the span between optical amplifiers is 150km if there are no other system impairments.  As an example, for a 900-km link we would need five amplifiers. From Eq. (11-36), the noise penalty factor over the total path is (in decibels) 10.log F path (G) = 10.log{(1/1000)[(1000-1)/ln 1000] 2 } = 10.log 20.9 = 13.2 dB 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  If we reduce the gain to 20dB, then the impairment-free transmission distance is 100km for which we need eight amplifiers.  In this case, the noise-penalty factor is 10.log F path (G) = 10.log{(1/100)[(100-1)/ln 100] 2 } = 10.log 4.62 = 6.6 dB 11.5.2 In-Line Amplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.3 Preamplifiers  An optical amplifier can be used as a preamplifier to improve the sensitivity of direct-detection receivers that are limited by thermal noise.  First, assume the receiver noise is represented by the electrical power level N.  Let S min be the minimum value of the electrical signal power S that is required for the receiver to perform with a specific acceptable bit-error rate.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  The acceptable signal-to-noise ratio then is S min /N.  If we now use an optical preamplifier with gain G, the electrical received signal power is G 2 S' and the signal-to-noise ratio is (S/N) preamp = G 2 S' / (N + N') (11-37)  where the noise term N' is the spontaneous emission from the optical preamplifier that gets converted by the photodiode in the receiver to an additional background noise. 11.5.3 Preamplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  If S' min is the new minimum detectable electrical signal level needed to maintain the same signal-to- noise ratio, then we need to have G 2 S' min /(N + N') = S min /N (11-38)  For an optical preamplifier to enhance the received signal level, we must have S' min < S min, so that S min /S' min = G 2 N/(N + N') > 1 (11-39)  This ratio of S min to S' min represents the improvement of minimum detectable signal or detector sensitivity. 11.5.3 Preamplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Example 11-9 :  Consider an EDFA used as an optical preamplifier. Assume that N is due to thermal noise and that the noise N' introduced by the preamplifier is dominated by signal-ASE beat noise.  We want to see under what conditions Eq. (11-39) holds. For sufficiently high gain G, Equ. (11-39) becomes G 2 –1 = G 2 > N'/N =  2 s-ASE /  T 2 11.5.3 Preamplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  Substituting Eqs.(6-17) and (11-27) into this expression, using Eq. (11-24) for S ASE, and solving for P s,in yields P s,in < k B T. h /(Rn sp  2 q 2 )  If T= 300 o K, R= 50 , = 1550-nm, n sp =2, and  = 0.65, then P s,in < 490  W. This is much higher than any expected received signal, so the condition in Eq. (11-39) is always satisfied.  The above does not mean that by making G sufficiently high, the improvement in sensitivity can be made arbitrarily large, since there is a minimum received power level that is needed to achieve a specific BER. 11.5.3 Preamplifiers

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.4 Multichannel Operation  An advantage of both semiconductor optical amplifiers and EDFAs is their ability to amplify multiple optical channels, provided the bandwidth of the multichannel signal is smaller than the amplifier bandwidths.  For both SOAs and EDFAs, this bandwidth ranges from 1 to 5 THz.  A disadvantage of SOAs is their sensitivity to interchannel crosstalk arising from carrier-density modulation due to beating of signals from adjacent optical channels.  For SOAs, this beating occurs whenever the channel spacing is less than 10 GHz.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.4 Multichannel Operation  This crosstalk does not occur in EDFAs, as long as the channel spacing is greater than 10 kHz, which holds in practice.  For multichannel operation in an EDFA, the signal power for N channels is given by P s =  N i=1 P s,i (11-40) where P s,i is the signal power in channel i; that is, at the optical carrier frequency v i.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.4 Multichannel Operation  EDFA gain is wavelength-dependent in the normal operating window of 1530-1560 nm. If it is not equalized over the spectral range of operation in a multichannel system, the gain variation will create a large SNR differential among the channels after passing through a cascade of EDFAs.  Numerous techniques, such as the use of gain compensating fiber gratings, have been tried for this equalization. In addition, when combined with a Raman fiber amplifier, a gain that is flat to within 3 dB can be extended to 1616 nm.  Figure 11-12 shows typical results for two commercially available EDFAs that have been gain-compensated in the 1528-to-1563-nm and the 1568-to-1603-nm spectral bands, respectively.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.5 In-Line Amplifier Gain Control Figure 11-12(a). A commercially available EDFA that has a gain flattened over the 1528- to-1563-nm spectral band. Figure 11-12(b). A commercially available EDFA that has a gain flattened over the 1568- to-1603-nm spectral band.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.5 In-Line Amplifier Gain Control  In a long-distance fiber transmission system using optical amplifiers, it is desirable to keep the output power of the in-line amplifiers constant when there are fluctuations in the input power level.  For example, such fluctuations could occur from loss variations in the optical cable or from degradation in a preceding optical amplifier.  Changes in the number of channels caused by network reconfiguration will also produce a power transition in the optical amplifier output.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.5 In-Line Amplifier Gain Control  A practical way to keep the output power constant is to operate the optical amplifier in the gain- saturation region, as shown in Fig. 11-13.  In this signal-controlled automatic gain control (AGC) method, when the input power to the amplifier decreases, the gain becomes higher to yield a higher output power.  Conversely, if the input power increases, the gain drops to compensate for this variation.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.5 In-Line Amplifier Gain Control Figure 11-13. A passive signal-controlled gain control method in which a decrease in the input power will raise the gain toward G 2, whereas an input-power increase will lower the gain toward G 2.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.5 In-Line Amplifier Gain Control  The exact amount of compensation depends on the relationship between the gain and the input power (as given by the slope of the curve in the saturation region).  In a cascaded chain of optical amplifiers, if the span loss between amplifiers happens to increase somewhere so that the input power to an optical amplifier is reduced,  the signal power is largely restored in the following several amplifiers. This is known as a self-healing effect in optically amplified communication systems.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.5.5 In-Line Amplifier Gain Control  The limitation of the signal-controlled AGC scheme is that the gain is low, since the amplifier operates in the saturation region.  More versatile dynamic gain control methods that keep the per-wavelength output power constant when the number of channels changes have also been demonstrated.  For example, in one dynamic AGC implementation, when a channel is suddenly dropped, the amplifier output power is restored to its original level within 1 ms with the transient level change being less than 0.5 dB.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.6 Wavelength Converters  An optical wavelength converter is a device that can directly translate information contained on an incoming wavelength to a new wavelength without entering the electrical domain.  This is an important component in all-optical networks, since the wavelength of the incoming signal may already be in use by another information channel residing on the destined outgoing path.  Converting the incoming signal to a new wavelength will allow both information channels to traverse the same fiber simultaneously.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.6.1 Optical-Gating Wavelength Converters  A wide variety of optical-gating techniques using devices such as SOAs, semiconductor lasers, or nonlinear optical-loop mirrors have been investigated to achieve wavelength conversion.  The use of a SOA in a cross-phase modulation (XPM) mode has been one of the most successful techniques for implementing single-wavelength conversion.  The configurations for implementing this scheme include the Mach-Zehnder or the Michelson interferometer setups shown in Fig. 11-14.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Figure 11-14. (a). Mach-Zehnder interferometer and (b). Michelson interferometer setups using a pair of SOAs for implementing the XPM wavelength-conversion scheme. 11.6.1 Optical-Gating Wavelength Converters

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  As depicted in Fig. 11-14, the basic concept is that an information-carrying signal at wavelength s and a continuous-wave (CW) signal at the desired new wavelength c (called the probe beam) are simultaneously coupled into the SOA device.  The signal beam modulates the gain of the SOA by depleting the carriers, which produces a modulation of the refractive index.  When the CW beam encounters the modulated gain and refractive index, its amplitude and phase are changed, so that it now carries the same information as the input signal. 11.6.1 Optical-Gating Wavelength Converters

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  As shown in Fig. 11-14, the CW light is modulated according to the phase difference in the two amplifiers. A typical splitting ratio is 69:31%. This type of converters readily handle data rates of at least 10-Gb/s.  A limitation of the XPM architecture is that it only converts one wavelength at a time. In addition, it has limited transparency in terms of the data format.  Any information in the form of phase, frequency, or analog amplitude is lost during the wavelength conversion process. Consequently, this scheme is restricted to converting digital signal streams. 11.6.1 Optical-Gating Wavelength Converters

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.6.2 Wave-Mixing Wavelength Converters  Wavelength conversion based on nonlinear optical wave mixing offers the generation of another wave whose intensity is proportional to the product of the intensities of the interacting waves.  The phase and frequency of the generated wave are a linear combination of those of the interacting waves.  The wave mixing preserves both amplitude and phase information, and is the only wavelength- conversion category that offers strict transparency to the modulation format.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.6.2 Wave-Mixing Wavelength Converters  Two successful schemes are four-wave mixing (FWM) in either passive waveguides or SOAs, and difference-frequency generation in waveguides.  For wavelength conversion, the FWM scheme employs the mixing of three distinct input waves to generate a fourth distinct output wave.  In this method, an intensity pattern resulting from two input waves interacting in a nonlinear material forms a grating.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰  For example, in SOAs there are three physical mechanisms that can form a grating. These are carrier-density modulation, dynamic carrier heating, and spectral hole burning.  The third input wave in the material gets scattered by this grating, thereby generating an output wave. The generated output wave is offset from that of the third wave by the frequency difference between the first two waves.  If one of the three incident waves contains amplitude, phase, or frequency information, and the other two waves are constant, then the generated wave will contain the same information. 11.6.2 Wave-Mixing Wavelength Converters

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 11.6.2 Wave-Mixing Wavelength Converters  Difference-frequency generation in waveguides is based on the mixing of two input waves. Here, the nonlinear interaction of the material is with a pump and a signal wave.  Figure 11-15 gives an example of the simultaneous conversion of eight input wavelengths in the 1546-to- 1560-nm region to a set of eight output wavelengths in the 1524-to-1538-nm region.

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Figure 11-15. Simultaneous conversion of eight input wavelengths (1546~1560 nm) to a set of eight output wavelengths (1538~1524 nm) using difference-frequency generation. The 1542 nm spike is a 2 nd -order spectrometer response to the pump wave at 771 nm. 11.6.2 Wave-Mixing Wavelength Converters

國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture.

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Presentation on theme: "國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture."— Presentation transcript:

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國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture.

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Presentation on theme: "國立成功大學 電機工程學系 光纖通訊實驗室 黃振發教授 編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture."— Presentation transcript:

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國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture.

Presentation on theme: "國立成功大學電機工程學系光纖通訊實驗室黃振發教授編撰 Chapter 11 Optical Amplifiers  11.3 ERBIUM-DOPED FIBER AMPLIFIERS 11.3.1 Amplification Mechanism 11.3.2 EDFA Architecture."— Presentation transcript: