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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 22 — Oct. 30, 2006
  • pp: 10693–10698

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All-optical half adder using cross gain modulation in semiconductor optical amplifiers

Sang Hun Kim, Jae Hun Kim, Jae Won Choi, Chang Wan Son, Young Tae Byun, Young Min Jhon, Seok Lee, Deck Ha Woo, and Sun Ho Kim  »View Author Affiliations


Optics Express, Vol. 14, Issue 22, pp. 10693-10698 (2006)
http://dx.doi.org/10.1364/OE.14.010693


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Abstract

By using the gain nonlinearity characteristics of semiconductor optical amplifier, an all-optical binary half adder at 10 Gbps is demonstrated. The half adder operates in a single mechanism, which is cross gain modulation. The half adder utilizes two logic functions of SUM and CARRY, which can be demonstrated by using XOR and AND gates, respectively. The extinction ratios of both XOR and AND gates are about 6.1 dB. By achieving this experiment, we also explored the possibilities for the enhanced complex logic operation and higher chances for multiple logic integration.

© 2006 Optical Society of America

1. Introduction

A binary half adder [1

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical half adder using Semiconductor Optical Amplifier based devices,” Opt. Commun. 218, 345–349 (2003). [CrossRef]

] is a well known function in electronic gates and is a basis for enhanced complex processing circuits such as a full adder, a binary decoder, and a binary counter. As electronic circuits are anticipated to confront the speed limitation, efforts on the realization of all-optical logic systems are eventually increasing. Therefore, all-optical binary logic gates are expected to become a key technique in future communication networks. All-optical binary half adders have been reported by using many optical designs such as terahertz optical asymmetric demultiplexers (TOAD) [2

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical binary half-adder,” Opt. Commun. 156, 22–26 (1998). [CrossRef]

] and ultra-fast nonlinear interferometer [3

D. Tsiokos, E. Kehayas, K. Vyrsokinos, T. Houbavlis, L. Stampoulidis, G. T. Kanellos, N. Pleros, G. Guekos, and H. Avramopoulos, “10-Gb/s all-optical half-adder with interferometric SOA gates”, ” IEEE Photon. Technol. Lett. 16, 284–286 (2004). [CrossRef]

]. All-optical logic device can be classified into several types such as the nonlinearity based on fibers [4–8

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A Terahertz optical asymmetric demultiplexer (TOAD),” IEEE Phot. Technol. Lett. 5, 787–790 (1993). [CrossRef]

], wavelength conversion based on a semiconductor optical amplifier, and so on. Comparing to techniques based on a fiber, wavelength conversion techniques based semiconductor optical amplifiers (SOA) [9–13

B. K. Kang, J. H. Kim, Y. T. Byun, S. Lee, Y. M. Jhon, D. H. Woo, J. S. Yang, S. H. Kim, Y. H. Park, and B. G. Yu, “All-optical AND gate using probe and pump signals as the multiple binary points in cross phase modulation,” Jpn. J. Appl. Phys. 41, 568–570 (2002). [CrossRef]

] are attractive because of their high-gain, high-saturation output power, wide-gain bandwidth, compactness, and integratibility with other photonic devices. The cross gain modulation (XGM) [14–18

X. Jin, T. Keating, and S. L. Chuang, “Theory and Experiment of High-Speed Cross-Gain Modulation in Semiconductor Lasers,” IEEE J. Quantum Electron. 36, 1485–1493 (2000). [CrossRef]

], one of several wavelength conversion techniques based on SOAs, is simple to implement and has shown impressive operation for a high bit rate. Moreover, the XGM shows a high conversion efficiency as well as insensitivity to the polarization of input signals. Our first binary half adder has been demonstrated previously [1

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical half adder using Semiconductor Optical Amplifier based devices,” Opt. Commun. 218, 345–349 (2003). [CrossRef]

]. However, past work utilizes two different mechanisms that are the XGM and cross-phase modulation (XPM) for XOR and AND operations, respectively. It is needless to mention that the system operating in a single mechanism has the definite advantages of high compactness and integration possibility over multiple mechanisms. In this paper, we experimentally demonstrate an all-optical half adder consisted of four SOAs using a single mechanism, which is the XGM.

2. Operational principle

The half adder utilizes two logic functions of SUM and CARRY, which can be demonstrated by using XOR and AND gates, respectively. An SOA is basically similar to a semiconductor laser diode except that there is no end mirror facet for resonance. To prevent internal feedback at the end, the facet reflectivity of less than 10-4 is necessary. When electrical current is applied to an SOA, electrons in the SOA are placed in the excited states. The excited electrons are stimulated by an incoming optical signal, and settled to the ground states after the signal is amplified. This stimulated emission continues as the input signal travels through the SOA until the photons exit together as an amplified signal. However, the amplification of the input signal consumes carriers thereby transiently reducing a gain, which is called gain saturation. The carrier density changes in an SOA will affect all of the input signals, so it is possible that a signal at one wavelength affect the gain of signal at another wavelength. This nonlinearity property is called XGM based on an SOA and the most basic operating principle of XGM is shown in Fig. 1.

Fig. 1. Schematic and principle of operation for wavelength conversion based on XGM in SOA.

When a pulse exists for the pump signal passing through an SOA, it causes carrier depletion in the SOA. The carrier depletion leads to gain saturation in the SOA causing the marked intensity reduction of an incoming probe signal. Therefore, the marked intensity reduction of the probe signal in the SOA leads to no pulse existence for output signal. When a pulse does not exist for the pump signal, there is no effect on the gain of probe signal in the SOA. Therefore, output signal has the same pulse as the probe signal. When signal A as a probe signal and signal B as a pump signal pass through the SOA, the output signal X can be defined as Boolean A•B̄.

Figure 2 shows the general concept of an optical half adder based on the XGM. In an XOR (A B̄+ ĀB) gate, Boolean A B̄ is obtained by using signal A as a probe beam and signal B as a pump beam in SOA-1. Also, Boolean ĀB is obtained by using signal B as a probe beam and signal A as a pump beam in SOA-2. By adding two outputs from SOA-1 and SOA-2, Boolean A B̄+ ĀB (logic XOR) can be obtained. In an AND (AB) gate, Boolean B̄ is firstly obtained by using signal B as a pump beam and clock signal as a probe beam in SOA-3. By passing signal A as a probe beam and B̄ as a pump beam through SOA-4, Boolean AB is acquired. The combination of the XOR and AND gates as SUM and CARRY gives the operation of a half adder.

Fig. 2. Operational principle for all-optical binary half adder. The half adder utilizes two logic functions of (a) SUM and (b) CARRY, which can be demonstrated by using the XOR gate and the AND gate, respectively.

3. Experimental setups and results

An experimental setup for an all-optical half adder operating at 10Gbps using the XGM is shown in Fig. 3. For realizing SUM and CARRY, signals A and B, and clock signal are required.

Fig. 3. Schematic diagram of the experimental setup for all-optical binary half adder. The adjustable bit synchronization between probe and pump signal is controlled by variable optical delayer; FRL: fiber ring laser, PC: polarization controller, Att.: optical attenuator, 1×2:1×2 optical splitter, EDFA: erbium doped fiber amplifier, OC: optical circulator, SOA: semiconductor optical amplifier, SA: signal analyzer

The Return-to-Zero (RZ) pulse with the repetition rate of 400ps (2.5Gbps) is generated from a fiber-ring laser at 1550nm. To acquire signal A having bit stream 1100, the RZ pulse is divided into two arms by a 1×2 coupler and coupled back into one channel by a 2×1 coupler after the optical delay of 100ps is applied to one of two arms. The optical delay of 100ps to signal A is applied to generate signal B with bit stream 0110. To acquire clock signal having bit stream 1111, signal A is divided into two arms by a 1×2 coupler and recombined into one channel by a 2×1 coupler after the optical delay of 200ps is applied.

In an XOR, signal A is divided into two channels by using a 1×2 coupler and inserted into SOA-1 in forward- and SOA-2 in reverse-direction. Identically, signal B is fed into SOA-1 and SOA-2, but in different directions. Signals A and B, used for pump signal, are inserted into SOA-1 and SOA-2 through optical circulators so as to counter-propagate against each probe signal. It should be noted that the optical power of pump signal is controlled to be larger than the optical power of probe signal for enough gain saturation in an SOA. Therefore, the use of an erbium doped fiber amplifier (EDFA) before entering an SOA is essential to obtain the enough amplified gain power of pump signal. The probe and pump signals in an SOA are synchronized by using a variable optical delay line. The output signals from SOA-1 and SOA-2 are combined by using 2×1 optical coupler to form an XOR gate. In an AND gate, signal B as pump signal and clock signal as probe signal are transmitted into SOA-4 in opposite directions. Then, the output signal from SOA-4 as pump signal and signal A as probe signal are inserted into SOA-3 in opposite directions. The output signal from SOA-3 is an AND gate.

Fig. 4. Inputs and outputs for (a) XOR operation, (b) AND operation and (c) half adder. (200ps/div.)

Experimental results for all-optical half adder operating at 10Gbps using XGM are shown in Fig. 4. When the pattern 1100 of signal A as probe signal and the pattern 0110 of signal B as pump signal are passed into SOA-2 in opposite directions, the second pulse of 1100 is disappeared because of gain saturation caused by second pulse of 0110 in SOA-2. Therefore, pattern 1000(A B̄) as output signal is obtained. The powers of the probe, pump, and output signals in SOA-2 are -32.4, 3.4, and 0.2dBm. Similarly, pattern 0010 (ĀB) is obtained when the pattern 0110 of signal B as probe and the pattern 1100 of signal B as pump are inserted into SOA-1. The powers of the probe, pump, and output signals in SOA-1 are -33.6, 3.7, and 0.1dBm. Pattern 1010 as an XOR operation is performed by using addition of pattern 0010 and 1000 emitted from SOA-1 and SOA-2, respectively. The pumping current in EDFA-1, EDFA-2 and injected current in SOA-1, SOA-2 to perform an XOR operation are measured in 120mA, 85mA and 95mA, 110mA, respectively. Figure 4(a) shows the oscilloscope traces of input signals A and B, Boolean A B̄, ĀB, and XOR operation. When signals A and B have different logic values, an output is logic 1. Otherwise, an output is logic 0. This result coincides with Boolean table of logic XOR.

In an AND gate, Boolean B̄ is obtained by using signal B as pump beam and clock signal as probe beam in SOA-4. By passing signal A as probe beam and B̄ as pump beam through SOA-3, Boolean AB is acquired. Figure 4(b) shows the oscilloscope traces of input signals A, B, clock, Boolean B̄ and AND operation. When both signals A and B have logic 1, an output signal is logic 1. Otherwise, an output is logic 0. This result coincides with Boolean table of logic AND. Figure 4(c) shows the oscilloscope traces of the simultaneous half adder operation. The powers of the probe, pump and output signals in SOA-3 are −4.6, 5.7, and 2.4dBm, respectively. Also, the powers of the probe, pump and output signals in SOA-4 are -16.4, 5.4 and -4.3dBm, respectively. The pumping current in EDFA-3, EDFA-4 and injected current in SOA-3, SOA-4 to perform AND operation are measured as 105mA, 130mA and 100mA, 125mA, respectively. The extinction ratios of both XOR and AND are about 6.1 dB.

To achieve the high rate of optical logic gates, it is important to consider recovery time in an SOA. SOAs used for this experiment has the cavity length of about 600um and the recovery time of approximately 150 ps. To avoid the distortion of a signal, the recovery time of gain must be shorter than the bit–period between two pulses, generally. However, 100ps is a sufficient time to recover most carriers in an SOA. If the following signal after gain saturation has logic 1, its intensity can be slightly smaller than other logic 1 levels because of insufficient recovery time as shown in Fig. 4(b). Even though there is logic level difference, it is still convincible that all-optical half adder can be successfully operated at 10Gbps, as shown in Fig. 4(b). However, if the speed of the logic gates is more than 10 Gbps, output signal may be distorted due to insufficient recovery time. To minimize the recovery time of an SOA, many researches including 2mm long SOA and Quantum dots SOA have been conducted [19

A. D. Ellies, A. E. Kelly, D. Nesset, D. Pitcher, D. G. Moodle, and R. Kashyap, “Error free 100Gbit/s wavelength conversion using grating assisted cross-gain modulation in 2mm long semiconductor optical amplifier,” IEE Electron. Lett. 34, 1958–1959 (1998). [CrossRef]

,20

T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and M. Sugawara, “Pattern-effect-free semiconductor optical amplifier achieved using quantum dots,” IEE Electron. Lett. 38, 1139–1140(2004). [CrossRef]

].

4. Conclusions

By using the gain nonlinearity characteristics of cross gain modulation (XGM) in a semiconductor optical amplifier (SOA), we successfully demonstrated an all-optical binary half-adder at 10Gbps. This half adder comprises two logic functions of SUM and CARRY, which can be demonstrated by using XOR and AND gates, respectively. By achieving this experiment, we also explored the possibilities for the enhanced complex logic operation and higher chances for multiple logic integration.

References and links

1.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical half adder using Semiconductor Optical Amplifier based devices,” Opt. Commun. 218, 345–349 (2003). [CrossRef]

2.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical binary half-adder,” Opt. Commun. 156, 22–26 (1998). [CrossRef]

3.

D. Tsiokos, E. Kehayas, K. Vyrsokinos, T. Houbavlis, L. Stampoulidis, G. T. Kanellos, N. Pleros, G. Guekos, and H. Avramopoulos, “10-Gb/s all-optical half-adder with interferometric SOA gates”, ” IEEE Photon. Technol. Lett. 16, 284–286 (2004). [CrossRef]

4.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A Terahertz optical asymmetric demultiplexer (TOAD),” IEEE Phot. Technol. Lett. 5, 787–790 (1993). [CrossRef]

5.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical parity checker with bit-differential delay,” Opt. Commun. 162, 37–43 (1999). [CrossRef]

6.

E. Jahn, N. Agrawal, W. Peiper, H. J. Ehrke, D. Franke, W. Furst, and C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexer,” IEE Electron. Lett. 32, 782–784 (1996). [CrossRef]

7.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical full adder with bit-differential delay,” Opt. Commun. 168, 89–93 (1999). [CrossRef]

8.

A. Poustie, R. Manning, A. Kelly, and K. Blow, “All-optical binary counter,” Opt. Express 6, 69–74 (2000). [CrossRef] [PubMed]

9.

B. K. Kang, J. H. Kim, Y. T. Byun, S. Lee, Y. M. Jhon, D. H. Woo, J. S. Yang, S. H. Kim, Y. H. Park, and B. G. Yu, “All-optical AND gate using probe and pump signals as the multiple binary points in cross phase modulation,” Jpn. J. Appl. Phys. 41, 568–570 (2002). [CrossRef]

10.

S. Lee, J. Park, K. Lee, D. Eom, S. Lee, and J. H. Kim, “All-optical exclusive NOR logic gate using Mach-Zender Interferometer,” Jpn. J. Appl. Phys. 41, 1155–1157 (2002). [CrossRef]

11.

H. Lee, H. Yoon, Y. Kim, and J. Jeong, “Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s,” IEEE J. Quantum Electron. 35, 1213–1219 (1999). [CrossRef]

12.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, “All-Optical Wavelength Conversion by Semiconductor Optical Amplifiers,” J. Lightwave Technol. 14, 942–954 (1996). [CrossRef]

13.

K. E. Stubkjaer, “Semiconductor Optical Amplifier-Based All-Optical Gates for High-Speed Optical Processing,” IEEE J. Sel. Top. Quantum Electron 6, 1428–1435 (2000). [CrossRef]

14.

X. Jin, T. Keating, and S. L. Chuang, “Theory and Experiment of High-Speed Cross-Gain Modulation in Semiconductor Lasers,” IEEE J. Quantum Electron. 36, 1485–1493 (2000). [CrossRef]

15.

X. Zhang, Y. Wang, J. Sun, D. Liu, and D. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12, 361–366 (2004). [CrossRef] [PubMed]

16.

J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photon. Technol. Lett. 14, 1436–1438 (2002). [CrossRef]

17.

J. H. Kim, B. C. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical AND gate using cross-gain modulation in semiconductor optical amplifiers,” Jpn. J. Appl. Phys. 43, 608–610 (2004). [CrossRef]

18.

S. H. Kim, J. H. Kim, J. W. Choi, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, “All-optical NAND Gate using cross gain modulation in Semiconductor Optical Amplifiers,” IEE Electron. Lett. 41, 1027–1028 (2005). [CrossRef]

19.

A. D. Ellies, A. E. Kelly, D. Nesset, D. Pitcher, D. G. Moodle, and R. Kashyap, “Error free 100Gbit/s wavelength conversion using grating assisted cross-gain modulation in 2mm long semiconductor optical amplifier,” IEE Electron. Lett. 34, 1958–1959 (1998). [CrossRef]

20.

T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and M. Sugawara, “Pattern-effect-free semiconductor optical amplifier achieved using quantum dots,” IEE Electron. Lett. 38, 1139–1140(2004). [CrossRef]

OCIS Codes
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(200.3760) Optics in computing : Logic-based optical processing
(200.4660) Optics in computing : Optical logic

ToC Category:
Optical Computing

History
Original Manuscript: July 24, 2006
Revised Manuscript: October 9, 2006
Manuscript Accepted: October 10, 2006
Published: October 30, 2006

Citation
Sang Hun Kim, Jae Hun Kim, Jae Won Choi, Chang Wan Son, Young Tae Byun, Young Min Jhon, Seok Lee, Deck Ha Woo, and Sun Ho Kim, "All-optical half adder using cross gain modulation in semiconductor optical amplifiers," Opt. Express 14, 10693-10698 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-22-10693


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References

  1. J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using Semiconductor Optical Amplifier based devices," Opt. Commun. 218, 345-349 (2003). [CrossRef]
  2. A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998). [CrossRef]
  3. D. Tsiokos, E. Kehayas, K. Vyrsokinos, T. Houbavlis, L. Stampoulidis, G. T. Kanellos, N. Pleros, G. Guekos, and H. Avramopoulos, "10-Gb/s all-optical half-adder with interferometric SOA gates," IEEE Photon. Technol. Lett. 16, 284-286 (2004). [CrossRef]
  4. J. P. Sokoloff, P. R. Prucnal, I. Glesk and M. Kane, "A Terahertz optical asymmetric demultiplexer (TOAD)," IEEE Photon. Technol. Lett. 5, 787-790 (1993). [CrossRef]
  5. A. J. Poustie, K. J. Blow, A. E. Kelly and R. J. Manning, "All-optical parity checker with bit-differential delay," Opt. Commun. 162, 37-43 (1999). [CrossRef]
  6. E. Jahn, N. Agrawal, W. Peiper, H. J. Ehrke, D. Franke, W. Furst and C. M. Weinert, "Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexer," Electron. Lett. 32, 782-784 (1996). [CrossRef]
  7. A. J. Poustie, K. J. Blow, A. E. Kelly and R. J. Manning, "All-optical full adder with bit-differential delay," Opt. Commun. 168, 89-93 (1999). [CrossRef]
  8. A. Poustie, R. Manning, A. Kelly, and K. Blow, "All-optical binary counter," Opt. Express 6, 69-74 (2000). [CrossRef] [PubMed]
  9. B. K. Kang, J. H. Kim, Y. T. Byun, S. Lee, Y. M. Jhon, D. H. Woo, J. S. Yang, S. H. Kim, Y. H. Park and B. G. Yu, "All-optical AND gate using probe and pump signals as the multiple binary points in cross phase modulation," Jpn. J. Appl. Phys. 41, 568 - 570 (2002). [CrossRef]
  10. S. Lee, J. Park, K. Lee, D. Eom, S. Lee, and J. H. Kim, " All-optical exclusive NOR logic gate using Mach-Zender Interferometer," Jpn. J. Appl. Phys. 41, 1155-1157 (2002). [CrossRef]
  11. H. Lee, H. Yoon, Y. Kim, and J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999). [CrossRef]
  12. T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, "All-optical wavelength conversion by Semiconductor Optical Amplifiers," J. Lightwave Technol. 14, 942-954 (1996). [CrossRef]
  13. K. E. Stubkjaer, "Semiconductor optical amplifier-based All-Optical Gates for high-speed optical processing," IEEE J. Sel. Top. Quantum Electron 6, 1428-1435 (2000). [CrossRef]
  14. X. Jin, T. Keating, and S. L. Chuang, "Theory and Experiment of high-speed cross-gain modulation in Semiconductor Lasers," IEEE J. Quantum Electron. 36,1485-1493 (2000). [CrossRef]
  15. X. Zhang, Y. Wang, J. Sun, D. Liu, and D. Huang, "All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs," Opt. Express 12, 361-366 (2004). [CrossRef] [PubMed]
  16. J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo and S. H. Kim, "All-optical XOR gate using semiconductor optical amplifiers without additional input beam," IEEE Photon. Technol. Lett. 14, 1436-1438 (2002). [CrossRef]
  17. J. H. Kim, B. C. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo and S. H. Kim, "All-optical AND gate using cross-gain modulation in semiconductor optical amplifiers," Jpn. J. Appl. Phys. 43, 608-610 (2004). [CrossRef]
  18. S. H. Kim, J. H. Kim, J. W. Choi, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical NAND Gate using cross gain modulation in Semiconductor Optical Amplifiers," Electron. Lett. 41, 1027-1028 (2005). [CrossRef]
  19. A. D. Ellies, A. E. Kelly, D. Nesset, D. Pitcher, D. G. Moodle and R. Kashyap, "Error free 100Gbit/s wavelength conversion using grating assisted cross-gain modulation in 2mm long semiconductor optical amplifier," Electron. Lett. 34,1958-1959 (1998). [CrossRef]
  20. T. Akiyama. N. Hatori, Y. Nakata, H. Ebe, and M. Sugawara, "Pattern-effect-free semiconductor optical amplifier achieved using quantum dots," Electron. Lett. 38, 1139-1140(2004). [CrossRef]

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