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Optical Amplified Recirculating Delay Lines Transient Response Effect on Hybrid Fiber Buses
OPTICAL FIBER TECHNOLOGY ARTICLE NO.
3, 65]71 Ž1997.
OF970201
Optical Amplified Recirculating Delay Lines Transient Response Effect on Hybrid Fiber Buses B. Vizoso Departamento de Tecnologıa E. T. S. I. Telecomunicacion ´ Fotonica, ´ ´ Ciudad Uni¨ ersitaria, 28040-Madrid, Spain
C. Vazquez ´ Area de Tecnologıa E. T. S. Uni¨ ersidad Carlos III, Butarque 15, Leganes ´ Electronica, ´ ´ 28911, Madrid, Spain
and M. Lopez-Amo and M. A. Muriel ´ Departamento de Tecnologıa E. T. S. I. Telecomunicacion ´ Fotonica, ´ ´ Ciudad Uni¨ ersitaria, 28040-Madrid, Spain Received August 15, 1996
rules that must be considered to obtain both equalized sensor signals and undistorted amplified data. Experimental results are shown utilizing commercially available light sources, optical amplifiers, and detectors. The paper is organized as follows. Section II briefly describes the hybrid fiber buses topology and optical equalizing principle. Section III surveys the parameters and the behavior of single amplified recirculating delay lines in the time domain. The basic concept behind the transient response limitation on the bit rate is first introduced by means of an example in this section. A similar study is devoted to double parallel amplified recirculating delay lines in Section IV. Finally Section V includes a summary and concluding remarks.
This paper presents novel theoretical and experimental results of the temporal response of optical amplified recirculating delay lines. These optical amplified recirculating delay lines have been used for equalizing sensor signals from hybrid fiber buses. To assure nondistortion of telecommunication data in these fiber buses, optical equalizer high transient times must be avoided. The time analysis carried out in this work allows the development of equalizer design rules to overcome the transient time limitations and fulfil the steady-state equalizing scheme. Q 1997 Academic Press
I. INTRODUCTION
Signal-processing functions in high-capacity optical fiber networks such as filtering, TV decoding without optoelectronics or electro-optic conversions have been performed with single amplified recirculating delay lines w1]4x. A higher degree of design flexibility has been achieved with more complex structures such as double parallel amplified recirculating optical delay lines w5, 6x. These double structures have been used in the development of sensor networks w7x. Their characteristic frequency response allows the equalization of sensor signals which have different attenuations depending on the number of couplers they have crossed in hybrid fiber buses. However, the influence of the equalizer on the data traffic involved Žtelephony, video, and computer interconnections. has not yet been analyzed. A temporal analysis focused on the transient response and on the output signal amplitude reveals the design
II. HYBRID FIBER BUS EQUALIZATION
Bus architectures for both sensing and transmitting data are particularly appealing. They allow the exploitation of the huge bandwidth of optical fiber networks. The advent of optical fiber amplifiers solved the problem of attenuation on signals addressing remote sensors which pass through numerous directional couplers. However, this amplification must be different depending on the number of couplers each sensor signal has crossed Žwhich means a different attenuation factor.. This equalization can be realized with a double recirculating ring structure. Figure 1 shows a wavelength division multiplexed, equalized, hybrid fiber bus network. The electrical subcarriers are modulated by sensor and data signals w7x. 65 1068-5200r97 $25.00 Copyright Q 1997 by Academic Press All rights of reproduction in any form reserved.
66
VIZOSO ET AL.
FIG. 1.
Wavelength multiplexed, equalized, amplified hybrid fiber bus network for sensors.
This bus was constructed with a section of 2 km of single mode fiber, a section of 2 km of multimode fiber, six couplers that exhibited extinctions ratios of 10%, a 1.3r1.55 m m WDM, a double amplified ring structure, and sensor elements that measure temperature and light intensity. The light intensity sensors are integrated circuits TSL 220 from Texas Instruments and the temperature sensors are integrated circuits LM35. The electrical subcarriers f 1 and f 2 modulate a 1.55-m m laser source, f 3 modulates a 1.3-m m laser source, and f 4 , f5 , f6 modulate three 820-nm LED sources. For this fiber bus, the output power of the ith sensor Ž before the double ring structure and ignoring the insertion loss of the couplers. is Pi0 s Ž 1 y K .
ny i
KPi I ,
i s 1, . . . , 6,
Ž 1.
where n is the number of sensors Ž n s 6., K is the coupling ratio of the couplers; and Pi I is the launched signal power in sensor i. So, the output power of sensor 1 is 5 dB lower than the output power from sensor 2, due to the pass though a greater number of couplers. The double ring structure equalized and amplified signals from sensor 1 and sensor 2. III. SINGLE AMPLIFIED RECIRCULATING RING STRUCTURE
Single amplified recirculating ring is one of the simplest optical processors. Thus, it has been used to describe bit rate limitations related to the transient response in hybrid fiber buses.
A schematic diagram of the optical amplified recirculating ring w2, 3x is shown in Fig. 2. The signals to be processed are modulated as intensity variations on optical carriers whose coherence time is less than the shortest relevant time in the system w1x. For the structure shown in Fig. 2, V is the electrical frequency modulating the optical carrier; l 0 is the length of the unamplified fiberŽm., while l a is the length of the erbium-doped fiber, so l s Ž l a q l 0 . is the total loop length; a is the propagation loss per unit length, expressed in dBrm; K and g are the coupling ratio and the fractional losses of the directional coupler; G is the gain introduced by the optical amplifier, and GU s 10yl 0 r10 GŽ1 y g . is the gain factor in each recirculation; t is the propagation time delay introduced by the loop line, t s nlrc with n the refractive index of the fiber and c the speed of light in vacuum w5x. A. Time Analysis The impulsive response of the system is given by w5x hŽ t . s Ž 1 y K . d Ž t . q
`
Ý
K 2 GU n Ž 1 y K .
ny 1
d Ž t y nt . .
Ž 2.
ns1
Although hŽ t . consists of an infinite sum of terms, there is a value of n s Np beyond which the terms of the summation can be neglected. This is only certain when the system is stable. The stability condition is given by
67
OPTICAL AMPLIFIED RECIRCULATING DELAY LINES
FIG. 2.
Simple recirculating fiber-optic processor, introducing an erbium-doped fiber amplifier acting as delay-line.
z p - 1, where z p s GU Ž1 y K . is the expression of the pole of the transfer function w3x. When the system follows this stability condition, it responds to any signal through a finite transient time prior to its steady state. The closer the pole system is to the positive real axe Žwhich means an increment of G or a decrement of K ., the higher the transient time is. Figure 3 shows measurements of transient response of a single recirculating fiber-optic processor with K s 0.74, l s 254 m, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 3.54. They are obtained with the setup of Fig. 2, excited by a CW LD at 1.55 m m modulated in frequency by a sinusoidal input signal with a period T s 0.92t . This setup
utilizes a 2 = 2 k-variable fiber coupler with 2-m-long pigtails. The pigtails of ports 4 and 3 are connected using an erbium-doped fiber amplifier pumped at 980 nm and single mode fiber. A sinusoidal carrier is used to selectively translate the signal spectrum to a maximum of the fiber-optic processor transfer function, as otherwise the signal will be distorted. B. System Response to an Amplitude Modulated Bit Train Digital transmission can be analyzed considering a digital signal modulating the amplitude of a sinusoidal carrier wave. An amplitude modulated bit train, with a k amplitude and a bit duration T b , can be represented as w8x xŽ t. s
Ý ak , p Ž t y kTb . , k
and 1 pŽ t . s 0
½
ts0 t s "T b , "2T b . . . .
Ž 3.
The output of the single ring structure y Ž t . is the convolution y Ž t . s hŽ t .) x Ž t .. If the system is stable, only a finite number of terms of the summation of hŽ t ., previously defined as Np , contribute to the output signal. The negligible amplitude of the Npq 1 term can be calculated from Ž2.: K 2 GU N pq 1 Ž 1 y K .
FIG. 3. Simple recirculating fiber-optic processor time response to a sinusoidal input signal of period T related to the delay time t of the loop by the relation 0.92. System parameters: K s 0.74, l s 254 m, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 3.54.
Np
< 1.
Ž 4.
This expression reveals a compromise between Np , GU , and K. The product Npt corresponds to the transient time. On the other hand, the minimum bit duration T b , which means the maximum bit rate r s 1rT b , depends on this negligible term Np and the delay of the system t . This is
68
VIZOSO ET AL.
because T b must be high enough to allow the output of the system to reach the steady state. This can be accomplished by the expression T b Žminimum. s Npt .
Ž 5.
From Ž5. we infer that the length of the loop line limits the bit rate. Integration of these signal processors will overcome that limitation. The value of T b also depends on the selection made in Ž4., which must be based on the desired characteristics of the structure. There is a decrement in the bit rate proportional to the increment of Np Žwhich means an increment in G .. So there is a compromise between r and G. The output signal can be sampled in the bit period after a guard time, which is also dependent on Np . In Fig. 4, two different situations are shown. The input signal is an amplitude modulated bit train 1010 with a sinusoidal carrier, so each sinusoidal output corresponds to each recirculation in the loop, the a k value being labeled below each bit. As mentioned, the sinusoidal carrier corresponds to a maximum of the fiber-optic processor transfer function. From Fig. 4Ža. and Fig. 4Žb. it can be inferred that by changing the parameters K and G, the integer Np increases. Although Np is greater in Fig. 4Žb., the guard time is lower because the time delay of the loop in Fig. 4Ža. is higher than in Fig. 4Žb.. IV. DOUBLE AMPLIFIED RECIRCULATING RING STRUCTURE
h2 Ž t . s
K 12 Ž 1 y g 1 .
Ž 1 y K1 . n
=
Ý cs0
`
Ý w GU1
ž nc / Ž 1 y K .
`
Ý
m1s1
ny c
2
???
n
n
n
ns1
=K 22 c Ž 1 y g 2 . =
GU2 x Ž 1 y K 1 . Ž 1 y g 1 .
`
Ý
m c s1
Ž1 y g2 .
nyc
Ž2 c .
GU3 Ý is 1 m i Ž 1 y g 2 . c
=Ž 1 y g 2 .
Ý cis m1iyc
Ý cis m1iyc
d c
= t y nŽ t 1 q t 2 . y
ž
Ý m it 3 is1
/
;
Ž 7.
here GUi s Gi 10yl i r10 . Although hŽ t . is constituted by an infinite sum of terms, there is a value of n s Ne and m i s Me beyond which the terms of the summation can be neglected. This is only certain when the system is stable. So, Ž7. would be used to analyze the transient time of this structure. B. System Response to an Amplitude Modulated Bit Train
A. Time Analysis A schematic diagram of the double amplified recirculating ring structure is shown in Fig. 5 w1, 4x. This structure is also supposed to be excited by an incoherent source. For the structure shown in Fig. 5, in addition to parameters given in Section II, l i is the fiber length of each of the loop lines; g 1 , K 1 are the coupler fractional losses and the coupling ratio of the first directional coupler; g 2 , K 2 are the coupler fractional losses and the coupling ratio of the second directional coupler; G1 , G 2 , G 3 are the gain introduced in each one of the fiber loop lines; t 1 , t 2 , t 3 are the propagation delay times introduced by the loop lines. In the transfer function of the double structure, there is one frequency in each repetition period where there is an absolute maximum. However, in each repetition period, there can be more than one frequency with a secondary maxima w4x Žsee the measurement results of Fig. 6.. The impulsive response of the system is given by h Ž t . s h1 Ž t . q h 2 Ž t . ,
ated to l 1 q l 2 , without entering into the ring associated to l 3 , the recirculations that cross c times the coupler K 2 , and all the possible recirculations along the ring associated to l 3 for each c:
Ž 6.
where h1Ž t . s Ž1 y K 1 .Ž1 y g 1 . d Ž t . is the direct term, h 2 Ž t . includes all the recirculations along the ring associ-
The analysis carried out for the single ring can be utilized also for the double parallel ring. In order to deal with sequences of bits, it will also be considered an amplitude modulation with a sinusoidal carrier and bit train modulator signal. The carrier frequency has to fit with the frequency of an absolute maximum of the transfer function or with the frequency of a secondary maximum Žonly when secondary maxima have a similar amplitude. w7x. In order to analyze the frequency response of the double parallel ring, it is useful to utilize a method that consists of splitting up the system into three single independent rings w5, 6x. The first ring is constituted with l 1 and l 2 . The second ring corresponds to l 3 . In this ring the transfer function is multiplied by the factor K 12 G1G 2 due to the first and last crossing through coupler 1 in each turn. The last ring includes l 1 , l 2 , and l 3 , and a factor of K 22 from crossing through coupler 2 is added to overall gain of the loop. To obtain the number of terms that should be considered on the summation of hŽ t . and then the limitations imposed on r, this method is utilized. From Eq. Ž4. applied to each ring of the decomposition, the following
OPTICAL AMPLIFIED RECIRCULATING DELAY LINES
69
FIG. 4. Output intensity versus time for different amplitude modulated bit trains. Ža. f carrier s 159 KHz, r s 3.97 Kbps. The parameters of the structure are K s 0.85, l s 13.33 km, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 0.55 Žwhich means Np s 2.. Žb. f carrier s 350 KHz, r s 7 Kbps. The parameters of the structure are: K s 0.7, l s 4.166 km, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 0.8 Žwhich means Np s 3..
70
VIZOSO ET AL.
FIG. 5. Configuration of double recirculating fiber-optic processor, introducing an erbium-doped fiber amplifier which may be placed within l 1 , l 2 or l 3 .
expressions are obtained: RING 1:
G 1G 2 Ž 1 y K 2 . Ž 1 y K 1 .
RING 2: RING 3:
G3 Ž 1 y K 2 .
N a 2 q1
G 1G 2 G 3 K 2 2 Ž 1 y K 1 .
N a1 q1
<1
N a 3 q1
< 1 Ž 8.
Ž 9.
< 1; Ž 10 .
here Na1 , Na2 , and Na3 are integers. The other inequality to relate r and the transient time must be also established for each ring T bŽm inimum. s t 1 Na1
Ž 11.
T bŽm inimum. s t 2 Na2
Ž 12.
T bŽm inimum. s t 3 Na3
Ž 13.
For a certain set of values K 1 , K 2 , G1 , G 2 , and G 3 , when there is one ring which has more influence than the rest of the rings, only the expressions that correspond to that ring have to be taken into account. When the influence of the three rings is fairly similar, the last six expressions have to be considered. In Fig. 7, two different situations are shown. From Figs. 7a and 7b it can be inferred that by changing the parameter G 3 , the time guard to sample the signal increases, because in this case the time delays do not change. V. CONCLUSIONS
Time analysis of optical amplified recirculating delay lines has been carried out showing the transient time prior to steady state, that is reached when the systems are stable. As the amplitude of transfer functions increases,
FIG. 6. Experimental results of the transfer function of the doubleparallel structure for K 1 s 0.94, K 2 s 0.84, l 1 s 252 m, l 2 s 2 m, l 3 s 4166.6 m, G1 s G 2 s 0.7, G 3 s 1, g 1 s g 2 s g 3 s 0.05, a 1 s a 2 s a 3 s 0.3 dBrkm.
the systems are closer to the instability condition and the transient time of the output signal increases. Design rules are derived from the temporal analysis in order to avoid high transient times, related to lower bit rates. These recirculating structures are useful for processing all kinds of periodical signals if the propagation delay time introduced by the loop is proportional to the period of the signal. In the double amplified ring, the frequency of the data input signal must be the frequency of an absolute maxima or the frequency of a secondary maxima. To equalize sensor signals without distorting the digital data streams in hybrid fiber buses, special rules must be considered in the design process. The relation between the maximum bit rate and the parameters of the double ring was derived. This factor corresponds to the maximum number of times that the signal can feedback before getting a negligible amplitude. Integration of these structures will lead to higher rates w8x. ASK modulation have been demonstrated for optical amplified recirculating delay lines. The sampling of the output signal must be done after a time guard, which is also dependent on the mentioned factor. In conclusion, time analysis allows us to study the dynamic behavior of these structures, including the transient time and the distortion in the steady state of the output signals. ACKNOWLEDGMENTS We thank J. M. Lopez Higuera, P. Datta, I. Matıas, and ´ ´ F. J. Lopez, ´ J. M. Oton ´ for their help. This work was supported by the Spanish CICYT ŽTIC95-631-C04. and CICYT ŽTIC95-025-CO2-01..
OPTICAL AMPLIFIED RECIRCULATING DELAY LINES
71
FIG. 7. Output intensity versus time for different amplitude modulated bit trains. Ža. f carrier s 150 KHz, r s 9.25 Kbps. The parameters of the double structure are: K 1 s 0.94, K 2 s 0.84, l 1 s 252 m, l 2 s 2 m, l 3 s 4166.6 m, G1 s G 2 s 0.7, G 3 s 1, g 1 s g 2 s g 3 s 0.05, a 1 s a 2 s a 3 s 0.3 dBrkm. Žb. f carrier s 150 KHz, r s 8.33 Kbps. The parameters of the double structure are: K 1 s 0.4, K 2 s 0.84, l 1 s 252 m, l 2 s 2 m, l 3 s 4166.6 m, G1 s G 2 s 0.7, G 3 s 1.1, g 1 s g 2 s g 3 s 0.05, a 1 s a 2 s a 3 s 0.3 dBrkm.
REFERENCES w1x K. P. Jackson and H. J. Shaw, ‘‘Fiber optic delay line signal processors,’’ in Optical Signal Processing, J. L. Horner, Ed. Chap. 7.1, p. 431, Academic Press, New York, 1987. w2x M. C. Vazquez, B. Vizoso, M. Lopez-Amo, and M. A. Muriel, ‘‘Single ´ ´ and double recirculating delay lines as fibre-optic filters,’’ Electron. Lett., vol. 28, no. 11, 1017, 1992. w3x B. Mosheli, ‘‘Fibre-optic filters employing optical amplifiers to provide design flexibility,’’ Electron. Lett., vol. 28, no. 3, 226, 1992. w4x C. Vazquez, M. Lopez-Amo, J. R. Montegjo-Garai, and J. M. Lopez´ ´ ´ Higuera, ‘‘Amplified recirculating delay line as fiber-optic decoders in TV systems,’’ Opt. Fiber Technol., vol. 2, 369, 1995. w5x B. Vizoso, M. C. Vazquez, R. Civera, M. Lopez-Amo, and M. A. ´ ´
Muriel, ‘‘Amplified fiber-optic recirculating delay lines,’’ IEEE J. Lightwa¨ e Technol., vol. 12, no. 2, 294, 1994. w6x M. C. Vazquez, R. Civera, M. Lopez-Amo, and M. A. Muriel, ´ ‘‘Analysis of double-parallel amplified recirculating optical-delay lines,’’ Appl. Opt., vol. 33, no. 6, 1015, 1994. w7x B. Vizoso, I. R. Matıas, and M. A. Muriel, ‘‘Design ´ M. Lopez-Amo, ´ and application of double amplified recirculating ring structure for hybrid fibre buses,’’ Opt. Quantum Electron., vol. 27, 847, 1995. w8x K. Oda, N. Takato, and h. Toba, ‘‘A wide FSR waveguide double ring resonator for optical FDM transmission systems,’’ IEEE J. Lightwa¨ e Technol., vol. 9, 728, 1991. w9x A. B. Carlson, Communication Systems, McGraw]Hill, New York, 1986.
3, 65]71 Ž1997.
OF970201
Optical Amplified Recirculating Delay Lines Transient Response Effect on Hybrid Fiber Buses B. Vizoso Departamento de Tecnologıa E. T. S. I. Telecomunicacion ´ Fotonica, ´ ´ Ciudad Uni¨ ersitaria, 28040-Madrid, Spain
C. Vazquez ´ Area de Tecnologıa E. T. S. Uni¨ ersidad Carlos III, Butarque 15, Leganes ´ Electronica, ´ ´ 28911, Madrid, Spain
and M. Lopez-Amo and M. A. Muriel ´ Departamento de Tecnologıa E. T. S. I. Telecomunicacion ´ Fotonica, ´ ´ Ciudad Uni¨ ersitaria, 28040-Madrid, Spain Received August 15, 1996
rules that must be considered to obtain both equalized sensor signals and undistorted amplified data. Experimental results are shown utilizing commercially available light sources, optical amplifiers, and detectors. The paper is organized as follows. Section II briefly describes the hybrid fiber buses topology and optical equalizing principle. Section III surveys the parameters and the behavior of single amplified recirculating delay lines in the time domain. The basic concept behind the transient response limitation on the bit rate is first introduced by means of an example in this section. A similar study is devoted to double parallel amplified recirculating delay lines in Section IV. Finally Section V includes a summary and concluding remarks.
This paper presents novel theoretical and experimental results of the temporal response of optical amplified recirculating delay lines. These optical amplified recirculating delay lines have been used for equalizing sensor signals from hybrid fiber buses. To assure nondistortion of telecommunication data in these fiber buses, optical equalizer high transient times must be avoided. The time analysis carried out in this work allows the development of equalizer design rules to overcome the transient time limitations and fulfil the steady-state equalizing scheme. Q 1997 Academic Press
I. INTRODUCTION
Signal-processing functions in high-capacity optical fiber networks such as filtering, TV decoding without optoelectronics or electro-optic conversions have been performed with single amplified recirculating delay lines w1]4x. A higher degree of design flexibility has been achieved with more complex structures such as double parallel amplified recirculating optical delay lines w5, 6x. These double structures have been used in the development of sensor networks w7x. Their characteristic frequency response allows the equalization of sensor signals which have different attenuations depending on the number of couplers they have crossed in hybrid fiber buses. However, the influence of the equalizer on the data traffic involved Žtelephony, video, and computer interconnections. has not yet been analyzed. A temporal analysis focused on the transient response and on the output signal amplitude reveals the design
II. HYBRID FIBER BUS EQUALIZATION
Bus architectures for both sensing and transmitting data are particularly appealing. They allow the exploitation of the huge bandwidth of optical fiber networks. The advent of optical fiber amplifiers solved the problem of attenuation on signals addressing remote sensors which pass through numerous directional couplers. However, this amplification must be different depending on the number of couplers each sensor signal has crossed Žwhich means a different attenuation factor.. This equalization can be realized with a double recirculating ring structure. Figure 1 shows a wavelength division multiplexed, equalized, hybrid fiber bus network. The electrical subcarriers are modulated by sensor and data signals w7x. 65 1068-5200r97 $25.00 Copyright Q 1997 by Academic Press All rights of reproduction in any form reserved.
66
VIZOSO ET AL.
FIG. 1.
Wavelength multiplexed, equalized, amplified hybrid fiber bus network for sensors.
This bus was constructed with a section of 2 km of single mode fiber, a section of 2 km of multimode fiber, six couplers that exhibited extinctions ratios of 10%, a 1.3r1.55 m m WDM, a double amplified ring structure, and sensor elements that measure temperature and light intensity. The light intensity sensors are integrated circuits TSL 220 from Texas Instruments and the temperature sensors are integrated circuits LM35. The electrical subcarriers f 1 and f 2 modulate a 1.55-m m laser source, f 3 modulates a 1.3-m m laser source, and f 4 , f5 , f6 modulate three 820-nm LED sources. For this fiber bus, the output power of the ith sensor Ž before the double ring structure and ignoring the insertion loss of the couplers. is Pi0 s Ž 1 y K .
ny i
KPi I ,
i s 1, . . . , 6,
Ž 1.
where n is the number of sensors Ž n s 6., K is the coupling ratio of the couplers; and Pi I is the launched signal power in sensor i. So, the output power of sensor 1 is 5 dB lower than the output power from sensor 2, due to the pass though a greater number of couplers. The double ring structure equalized and amplified signals from sensor 1 and sensor 2. III. SINGLE AMPLIFIED RECIRCULATING RING STRUCTURE
Single amplified recirculating ring is one of the simplest optical processors. Thus, it has been used to describe bit rate limitations related to the transient response in hybrid fiber buses.
A schematic diagram of the optical amplified recirculating ring w2, 3x is shown in Fig. 2. The signals to be processed are modulated as intensity variations on optical carriers whose coherence time is less than the shortest relevant time in the system w1x. For the structure shown in Fig. 2, V is the electrical frequency modulating the optical carrier; l 0 is the length of the unamplified fiberŽm., while l a is the length of the erbium-doped fiber, so l s Ž l a q l 0 . is the total loop length; a is the propagation loss per unit length, expressed in dBrm; K and g are the coupling ratio and the fractional losses of the directional coupler; G is the gain introduced by the optical amplifier, and GU s 10yl 0 r10 GŽ1 y g . is the gain factor in each recirculation; t is the propagation time delay introduced by the loop line, t s nlrc with n the refractive index of the fiber and c the speed of light in vacuum w5x. A. Time Analysis The impulsive response of the system is given by w5x hŽ t . s Ž 1 y K . d Ž t . q
`
Ý
K 2 GU n Ž 1 y K .
ny 1
d Ž t y nt . .
Ž 2.
ns1
Although hŽ t . consists of an infinite sum of terms, there is a value of n s Np beyond which the terms of the summation can be neglected. This is only certain when the system is stable. The stability condition is given by
67
OPTICAL AMPLIFIED RECIRCULATING DELAY LINES
FIG. 2.
Simple recirculating fiber-optic processor, introducing an erbium-doped fiber amplifier acting as delay-line.
z p - 1, where z p s GU Ž1 y K . is the expression of the pole of the transfer function w3x. When the system follows this stability condition, it responds to any signal through a finite transient time prior to its steady state. The closer the pole system is to the positive real axe Žwhich means an increment of G or a decrement of K ., the higher the transient time is. Figure 3 shows measurements of transient response of a single recirculating fiber-optic processor with K s 0.74, l s 254 m, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 3.54. They are obtained with the setup of Fig. 2, excited by a CW LD at 1.55 m m modulated in frequency by a sinusoidal input signal with a period T s 0.92t . This setup
utilizes a 2 = 2 k-variable fiber coupler with 2-m-long pigtails. The pigtails of ports 4 and 3 are connected using an erbium-doped fiber amplifier pumped at 980 nm and single mode fiber. A sinusoidal carrier is used to selectively translate the signal spectrum to a maximum of the fiber-optic processor transfer function, as otherwise the signal will be distorted. B. System Response to an Amplitude Modulated Bit Train Digital transmission can be analyzed considering a digital signal modulating the amplitude of a sinusoidal carrier wave. An amplitude modulated bit train, with a k amplitude and a bit duration T b , can be represented as w8x xŽ t. s
Ý ak , p Ž t y kTb . , k
and 1 pŽ t . s 0
½
ts0 t s "T b , "2T b . . . .
Ž 3.
The output of the single ring structure y Ž t . is the convolution y Ž t . s hŽ t .) x Ž t .. If the system is stable, only a finite number of terms of the summation of hŽ t ., previously defined as Np , contribute to the output signal. The negligible amplitude of the Npq 1 term can be calculated from Ž2.: K 2 GU N pq 1 Ž 1 y K .
FIG. 3. Simple recirculating fiber-optic processor time response to a sinusoidal input signal of period T related to the delay time t of the loop by the relation 0.92. System parameters: K s 0.74, l s 254 m, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 3.54.
Np
< 1.
Ž 4.
This expression reveals a compromise between Np , GU , and K. The product Npt corresponds to the transient time. On the other hand, the minimum bit duration T b , which means the maximum bit rate r s 1rT b , depends on this negligible term Np and the delay of the system t . This is
68
VIZOSO ET AL.
because T b must be high enough to allow the output of the system to reach the steady state. This can be accomplished by the expression T b Žminimum. s Npt .
Ž 5.
From Ž5. we infer that the length of the loop line limits the bit rate. Integration of these signal processors will overcome that limitation. The value of T b also depends on the selection made in Ž4., which must be based on the desired characteristics of the structure. There is a decrement in the bit rate proportional to the increment of Np Žwhich means an increment in G .. So there is a compromise between r and G. The output signal can be sampled in the bit period after a guard time, which is also dependent on Np . In Fig. 4, two different situations are shown. The input signal is an amplitude modulated bit train 1010 with a sinusoidal carrier, so each sinusoidal output corresponds to each recirculation in the loop, the a k value being labeled below each bit. As mentioned, the sinusoidal carrier corresponds to a maximum of the fiber-optic processor transfer function. From Fig. 4Ža. and Fig. 4Žb. it can be inferred that by changing the parameters K and G, the integer Np increases. Although Np is greater in Fig. 4Žb., the guard time is lower because the time delay of the loop in Fig. 4Ža. is higher than in Fig. 4Žb.. IV. DOUBLE AMPLIFIED RECIRCULATING RING STRUCTURE
h2 Ž t . s
K 12 Ž 1 y g 1 .
Ž 1 y K1 . n
=
Ý cs0
`
Ý w GU1
ž nc / Ž 1 y K .
`
Ý
m1s1
ny c
2
???
n
n
n
ns1
=K 22 c Ž 1 y g 2 . =
GU2 x Ž 1 y K 1 . Ž 1 y g 1 .
`
Ý
m c s1
Ž1 y g2 .
nyc
Ž2 c .
GU3 Ý is 1 m i Ž 1 y g 2 . c
=Ž 1 y g 2 .
Ý cis m1iyc
Ý cis m1iyc
d c
= t y nŽ t 1 q t 2 . y
ž
Ý m it 3 is1
/
;
Ž 7.
here GUi s Gi 10yl i r10 . Although hŽ t . is constituted by an infinite sum of terms, there is a value of n s Ne and m i s Me beyond which the terms of the summation can be neglected. This is only certain when the system is stable. So, Ž7. would be used to analyze the transient time of this structure. B. System Response to an Amplitude Modulated Bit Train
A. Time Analysis A schematic diagram of the double amplified recirculating ring structure is shown in Fig. 5 w1, 4x. This structure is also supposed to be excited by an incoherent source. For the structure shown in Fig. 5, in addition to parameters given in Section II, l i is the fiber length of each of the loop lines; g 1 , K 1 are the coupler fractional losses and the coupling ratio of the first directional coupler; g 2 , K 2 are the coupler fractional losses and the coupling ratio of the second directional coupler; G1 , G 2 , G 3 are the gain introduced in each one of the fiber loop lines; t 1 , t 2 , t 3 are the propagation delay times introduced by the loop lines. In the transfer function of the double structure, there is one frequency in each repetition period where there is an absolute maximum. However, in each repetition period, there can be more than one frequency with a secondary maxima w4x Žsee the measurement results of Fig. 6.. The impulsive response of the system is given by h Ž t . s h1 Ž t . q h 2 Ž t . ,
ated to l 1 q l 2 , without entering into the ring associated to l 3 , the recirculations that cross c times the coupler K 2 , and all the possible recirculations along the ring associated to l 3 for each c:
Ž 6.
where h1Ž t . s Ž1 y K 1 .Ž1 y g 1 . d Ž t . is the direct term, h 2 Ž t . includes all the recirculations along the ring associ-
The analysis carried out for the single ring can be utilized also for the double parallel ring. In order to deal with sequences of bits, it will also be considered an amplitude modulation with a sinusoidal carrier and bit train modulator signal. The carrier frequency has to fit with the frequency of an absolute maximum of the transfer function or with the frequency of a secondary maximum Žonly when secondary maxima have a similar amplitude. w7x. In order to analyze the frequency response of the double parallel ring, it is useful to utilize a method that consists of splitting up the system into three single independent rings w5, 6x. The first ring is constituted with l 1 and l 2 . The second ring corresponds to l 3 . In this ring the transfer function is multiplied by the factor K 12 G1G 2 due to the first and last crossing through coupler 1 in each turn. The last ring includes l 1 , l 2 , and l 3 , and a factor of K 22 from crossing through coupler 2 is added to overall gain of the loop. To obtain the number of terms that should be considered on the summation of hŽ t . and then the limitations imposed on r, this method is utilized. From Eq. Ž4. applied to each ring of the decomposition, the following
OPTICAL AMPLIFIED RECIRCULATING DELAY LINES
69
FIG. 4. Output intensity versus time for different amplitude modulated bit trains. Ža. f carrier s 159 KHz, r s 3.97 Kbps. The parameters of the structure are K s 0.85, l s 13.33 km, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 0.55 Žwhich means Np s 2.. Žb. f carrier s 350 KHz, r s 7 Kbps. The parameters of the structure are: K s 0.7, l s 4.166 km, g s 0.05, a s 0.3 dBrkm, n s 1.44, G s 0.8 Žwhich means Np s 3..
70
VIZOSO ET AL.
FIG. 5. Configuration of double recirculating fiber-optic processor, introducing an erbium-doped fiber amplifier which may be placed within l 1 , l 2 or l 3 .
expressions are obtained: RING 1:
G 1G 2 Ž 1 y K 2 . Ž 1 y K 1 .
RING 2: RING 3:
G3 Ž 1 y K 2 .
N a 2 q1
G 1G 2 G 3 K 2 2 Ž 1 y K 1 .
N a1 q1
<1
N a 3 q1
< 1 Ž 8.
Ž 9.
< 1; Ž 10 .
here Na1 , Na2 , and Na3 are integers. The other inequality to relate r and the transient time must be also established for each ring T bŽm inimum. s t 1 Na1
Ž 11.
T bŽm inimum. s t 2 Na2
Ž 12.
T bŽm inimum. s t 3 Na3
Ž 13.
For a certain set of values K 1 , K 2 , G1 , G 2 , and G 3 , when there is one ring which has more influence than the rest of the rings, only the expressions that correspond to that ring have to be taken into account. When the influence of the three rings is fairly similar, the last six expressions have to be considered. In Fig. 7, two different situations are shown. From Figs. 7a and 7b it can be inferred that by changing the parameter G 3 , the time guard to sample the signal increases, because in this case the time delays do not change. V. CONCLUSIONS
Time analysis of optical amplified recirculating delay lines has been carried out showing the transient time prior to steady state, that is reached when the systems are stable. As the amplitude of transfer functions increases,
FIG. 6. Experimental results of the transfer function of the doubleparallel structure for K 1 s 0.94, K 2 s 0.84, l 1 s 252 m, l 2 s 2 m, l 3 s 4166.6 m, G1 s G 2 s 0.7, G 3 s 1, g 1 s g 2 s g 3 s 0.05, a 1 s a 2 s a 3 s 0.3 dBrkm.
the systems are closer to the instability condition and the transient time of the output signal increases. Design rules are derived from the temporal analysis in order to avoid high transient times, related to lower bit rates. These recirculating structures are useful for processing all kinds of periodical signals if the propagation delay time introduced by the loop is proportional to the period of the signal. In the double amplified ring, the frequency of the data input signal must be the frequency of an absolute maxima or the frequency of a secondary maxima. To equalize sensor signals without distorting the digital data streams in hybrid fiber buses, special rules must be considered in the design process. The relation between the maximum bit rate and the parameters of the double ring was derived. This factor corresponds to the maximum number of times that the signal can feedback before getting a negligible amplitude. Integration of these structures will lead to higher rates w8x. ASK modulation have been demonstrated for optical amplified recirculating delay lines. The sampling of the output signal must be done after a time guard, which is also dependent on the mentioned factor. In conclusion, time analysis allows us to study the dynamic behavior of these structures, including the transient time and the distortion in the steady state of the output signals. ACKNOWLEDGMENTS We thank J. M. Lopez Higuera, P. Datta, I. Matıas, and ´ ´ F. J. Lopez, ´ J. M. Oton ´ for their help. This work was supported by the Spanish CICYT ŽTIC95-631-C04. and CICYT ŽTIC95-025-CO2-01..
OPTICAL AMPLIFIED RECIRCULATING DELAY LINES
71
FIG. 7. Output intensity versus time for different amplitude modulated bit trains. Ža. f carrier s 150 KHz, r s 9.25 Kbps. The parameters of the double structure are: K 1 s 0.94, K 2 s 0.84, l 1 s 252 m, l 2 s 2 m, l 3 s 4166.6 m, G1 s G 2 s 0.7, G 3 s 1, g 1 s g 2 s g 3 s 0.05, a 1 s a 2 s a 3 s 0.3 dBrkm. Žb. f carrier s 150 KHz, r s 8.33 Kbps. The parameters of the double structure are: K 1 s 0.4, K 2 s 0.84, l 1 s 252 m, l 2 s 2 m, l 3 s 4166.6 m, G1 s G 2 s 0.7, G 3 s 1.1, g 1 s g 2 s g 3 s 0.05, a 1 s a 2 s a 3 s 0.3 dBrkm.
REFERENCES w1x K. P. Jackson and H. J. Shaw, ‘‘Fiber optic delay line signal processors,’’ in Optical Signal Processing, J. L. Horner, Ed. Chap. 7.1, p. 431, Academic Press, New York, 1987. w2x M. C. Vazquez, B. Vizoso, M. Lopez-Amo, and M. A. Muriel, ‘‘Single ´ ´ and double recirculating delay lines as fibre-optic filters,’’ Electron. Lett., vol. 28, no. 11, 1017, 1992. w3x B. Mosheli, ‘‘Fibre-optic filters employing optical amplifiers to provide design flexibility,’’ Electron. Lett., vol. 28, no. 3, 226, 1992. w4x C. Vazquez, M. Lopez-Amo, J. R. Montegjo-Garai, and J. M. Lopez´ ´ ´ Higuera, ‘‘Amplified recirculating delay line as fiber-optic decoders in TV systems,’’ Opt. Fiber Technol., vol. 2, 369, 1995. w5x B. Vizoso, M. C. Vazquez, R. Civera, M. Lopez-Amo, and M. A. ´ ´
Muriel, ‘‘Amplified fiber-optic recirculating delay lines,’’ IEEE J. Lightwa¨ e Technol., vol. 12, no. 2, 294, 1994. w6x M. C. Vazquez, R. Civera, M. Lopez-Amo, and M. A. Muriel, ´ ‘‘Analysis of double-parallel amplified recirculating optical-delay lines,’’ Appl. Opt., vol. 33, no. 6, 1015, 1994. w7x B. Vizoso, I. R. Matıas, and M. A. Muriel, ‘‘Design ´ M. Lopez-Amo, ´ and application of double amplified recirculating ring structure for hybrid fibre buses,’’ Opt. Quantum Electron., vol. 27, 847, 1995. w8x K. Oda, N. Takato, and h. Toba, ‘‘A wide FSR waveguide double ring resonator for optical FDM transmission systems,’’ IEEE J. Lightwa¨ e Technol., vol. 9, 728, 1991. w9x A. B. Carlson, Communication Systems, McGraw]Hill, New York, 1986.