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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 8 — Apr. 16, 2007
  • pp: 4953–4959
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Observation of counterclockwise, clockwise and butterfly bistabilty in 1550 nm VCSOAs

Christopher F. Marki, Douglas R. Jorgesen, Haijiang Zhang, Pengyue Wen, and Sadik C. Esener  »View Author Affiliations


Optics Express, Vol. 15, Issue 8, pp. 4953-4959 (2007)
http://dx.doi.org/10.1364/OE.15.004953


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Abstract

In this paper, we report counter-clockwise, clockwise, and, for the first time to our knowledge, butterfly bistability in 1550 nm Vertical Cavity Semiconductor Optical Amplifiers (VCSOA). Bistable operation is experimentally observed for bias currents ranging from 66–122% of threshold with switching powers as low as 2 μW. These switching powers are two orders of magnitude lower than any previous results in 1550 nm VCSOAs. These switching powers are consistent with previous reports on optical bistability in 850 nm VCSOAs and provide an important step towards the realization of small footprint, low power optical logic/switching elements in the 1550 nm wavelength band.

© 2007 Optical Society of America

1. Introduction

All-optical Boolean logic has been a heavily researched topic for several decades due to its potential impact in optical information processing (OIP) including areas such as optical signal processing (OSP), optical computing, and optical packet switching [1–3

1. A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proceedings of the IEEE 72 no.7, 758 (1984). [CrossRef]

]. Although a multitude of techniques exist which achieve OIP including cross gain modulation (XGM) and cross phase modulation (XPM) in semiconductor optical amplifiers (SOA) [4

4. N. K. Dutta and Q. Wang, Semiconductor Optical Amplifiers. (World Scientific, Hackensack, N.J., 2006). [CrossRef]

], four wave mixing (FWM) in highly nonlinear fiber [5

5. Q. Linet al, “40-gb/s optical switching and wavelength multicasting in a two-pump parametric device,” IEEE Photon. Technol. Lett. 17, no. 11 2376 (2005). [CrossRef]

], intensity bistability in Fabry-Perot laser amplifiers (FPLA) [6

6. P. Pakdeevanich and M. J. Adams, “Measurements and Modeling of Reflective Bistability in 1.55-μm Laser Diode Amplifiers,” IEEE J. Quantum Electron. 35, 1894–1903 (1999). [CrossRef]

,7

7. J. Mitchellet al, “Optical bistability in asymmetric Fabry - Perot laser-diode amplifiers,” Opt. Lett. 19, 269 (1994). [CrossRef] [PubMed]

] and polarization bistability in Vertical Cavity Surface Emitting Lasers (VCSEL) [8

8. T. Moriet al, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102 (2006). [CrossRef]

], no clear technology candidate has emerged for large-scale OIP because of shortcomings in terms of speed, power, size, large scale integrability and cost of logic elements. Over recent years, intensity bistable VCSOAs have received interest for applications in optical signal processing at 850 nm [9–13

9. P. Wenet al, “Observation of bistability in a vertical-cavity semiconductor optical amplifier (VCSOA).” Opt. Express 10, 1273 (2002). [PubMed]

]. Owing to their gain and highly nonlinear resonant structure, 850 nm VCSOAs have been shown to achieve critical functionalities such as re-amplification and reshaping (2R) [13

13. P. Wenet al, “Optical bistability in vertical-cavity semiconductor optical amplifiers,” Appl. Opt. 45, 6349 (2006). [CrossRef] [PubMed]

], optical inversion [14

14. H. Zhanget al, Optoelectronics Group, University of California, San Diego, La Jolla, CA. 92093, are preparing a manuscript to be called “Cascadable all-optical inverter based n a non-linear Vertical Cavity Semiconductor Optical Amplifier”.

], self-sustained ring oscillation [15

15. H. Zhanget al, Optoelectronics Group, University of California, San Diego, La Jolla, CA. 92093, are preparing a manuscript to be called “All-optical Oscillator based on a single bistable Vertical Cavity Semiconductor Optical Amplifier (VCSOA)”.

], and optical flip-flop [16

16. S. Esener and P. Wen, “Photonics in Computing: Interconnects and Beyond,” presented at Frontier in Optics, OSA, Rochester, NY, Oct. 2006.

]. Most importantly, as a mature technology platform, 850 nm VCSOAs offer an excellent tradeoff in terms of speed, power, size, integrability, and cost. Contrastingly, work in 1550 nm VCSOAs is still nascent as a result of the greater difficulty in fabricating 1550 nm VCSELs. Nevertheless, VCSEL/VCSOA research is ongoing in the telecom band for its potential economic impact [17

17. A. Karimet al, “Long-wavelength vertical-cavity lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 6, 1244 (2000). [CrossRef]

].

Recently, Hurtado et al. [18

18. A. Hurtadoet al, “Optical bistability and nonlinear gain in 1.55 um VCSOA,” Electron. Lett. 42, 483–484 (2006). [CrossRef]

] observed optical bistability in 1550 nm VCSOAs. The operating conditions necessary to achieve bistable switching were stringent with large switching power of 150 μW for counterclockwise and 600 μW for clockwise bistability. The narrow operating range is explained, among other factors, by the large insertion loss (20 dB) suffered when coupling into and out of the device. In order to compete with alternative technologies and to justify the use of bistable VCSOAs in commercial telecom applications, the switching power must be reduced. In this paper, we experimentally observe optical bistability with fiber pigtailed 1550 nm VCSOAs with switching powers as low as 2 μW, two orders of magnitude smaller than previously reported and comparable to that of 850 nm devices. Moreover, we observe, for the first time in VCSOAs, all three types of bistability: counterclockwise, clockwise, and butterfly. We begin by offering a physically intuitive explanation for the existence of the various forms of bistablity in reflection mode VCSOAs and then confirm that all three types can be observed experimentally by changing either the current bias of the device or the injected wavelength into the device. We find that optical bistability is readily achievable in our devices over a wide range of bias currents and wavelength detuning. These results help substantiate the claim that VCSOAs can be a key technology for future OSP applications at 1550 nm.

2. Theory

Optical bistability is the ability of a device to operate in two stable states, depending on the input history. When light is injected into the active resonant cavity carriers are consumed, resulting in gain through the process of stimulated emission. The accompanying drop in the carrier concentration leads to an increase in the refractive index of the cavity. This refractive index change, in turn, leads to a red-shift in the peak resonant wavelength of the cavity. When the injected light is detuned towards the longer wavelength side of the gain window, carrier depletion shifts the cavity resonance towards the injected wavelength causing positive feedback. The combination of this dispersive non-linearity and gain saturation within the cavity leads to a counterclockwise bistability in the transmitted intensity [2

2. H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes. (Artech House, Boston, 1994).

].

Whereas transmission mode devices only exhibit counterclockwise bistability, it has been known for some time that dispersive bistable laser diodes operated in reflection mode also exhibit two additional forms of bistability known as butterfly and clockwise bistability [3

3. M. J. Adams, “Optical amplifier bistabilty on reflection,” Opt. Quantum Electron. 19, 37 (1987). [CrossRef]

,7

7. J. Mitchellet al, “Optical bistability in asymmetric Fabry - Perot laser-diode amplifiers,” Opt. Lett. 19, 269 (1994). [CrossRef] [PubMed]

]. Butterfly and clockwise bistability are manifested through the careful balance between the incoming and outgoing intensities in the laser amplifier cavity [3

3. M. J. Adams, “Optical amplifier bistabilty on reflection,” Opt. Quantum Electron. 19, 37 (1987). [CrossRef]

,6

6. P. Pakdeevanich and M. J. Adams, “Measurements and Modeling of Reflective Bistability in 1.55-μm Laser Diode Amplifiers,” IEEE J. Quantum Electron. 35, 1894–1903 (1999). [CrossRef]

,7

7. J. Mitchellet al, “Optical bistability in asymmetric Fabry - Perot laser-diode amplifiers,” Opt. Lett. 19, 269 (1994). [CrossRef] [PubMed]

,19

19. A. Hurtadoet al, “Modeling Reflective Bistability in Vertical-Cavity Semiconductor Optical Amplifiers,” IEEE J. Quantum. Electron. 41, 376–383 (2005). [CrossRef]

].

Physical insight into the existence of butterfly and clockwise bistability is gained when one considers that, in steady state, incoming and outgoing intensities must equate [6

6. P. Pakdeevanich and M. J. Adams, “Measurements and Modeling of Reflective Bistability in 1.55-μm Laser Diode Amplifiers,” IEEE J. Quantum Electron. 35, 1894–1903 (1999). [CrossRef]

] as described by:

Iref=Iin+gL∙IavItrans
(1)

where Iin is the input intensity, Iav is the average intensity inside the cavity, gL is the single pass gain, and Itrans is the transmitted intensity. Effectively, the total intensity outside the cavity through Iref and Itrans must equal the total intensity inside the cavity (Iin and gL*Iav). As stated above, dispersive nonlinearity and gain saturation always combine to cause counterclockwise bistability for Itrans. Since Iin is a linear term, the behavior of Iref can ultimately be understood by determining gL*Iav and solving (1).

In Fig. 1, we solve (1) to demonstrate how both counterclockwise and clockwise bistability can arise by assuming gL*Iav exhibits counterclockwise bistability. Physical insight into this complex balancing of the terms in (1) can be garnered when one considers two extremes of operation: first when the current bias is high (e.g. ~99% of threshold) and the wavelength detuning is small and second when current bias is reduced (e.g. ~90% of threshold) and wavelength detuning is large. As depicted by the solid lines in Fig. 1, at high values of bias and low values of detuning, the second term in (1) dominates due to larger gain, and the reflected intensity, Iref, mimics the S shaped counterclockwise solution of gL*Iav.

Fig. 1. Illustration of (1) explaining the existence of clockwise bistability in reflection mode VCSOAs. Solid curves represent higher bias-lower detuning case which generates counterclockwise hysteresis in Iref. Dotted curves represent lower bias-higher detuning case which generates clockwise hysteresis in Iref. The transition between these two regimes generates butterfly hysteresis.

As the bias is reduced and the detuning is increased (depicted by the dotted lines), the bistable functional form of Itrans grows larger than gL*Iav due to reduced gain and thus begins to dominate the right side of (1). By summing the S-shaped -Itrans and gL*Iav terms and the linear Iin term, Fig. 1 shows that Iref results in a clockwise hysteresis loop (dashed black curve). During the transition region between counterclockwise and clockwise bistability, when gL*Iav and Itrans are of comparable magnitude, Iref exhibits butterfly bistability in which both discontinuous transitions fall from higher to lower powers.

It is worth noting that while Itrans will always exhibit counterclockwise bistability though the effects of dispersive nonlinearity and gain saturation, it is not generally true that gL*Iav is always counterclockwise bistable. As was shown in [19

19. A. Hurtadoet al, “Modeling Reflective Bistability in Vertical-Cavity Semiconductor Optical Amplifiers,” IEEE J. Quantum. Electron. 41, 376–383 (2005). [CrossRef]

], gL*Iav can also exhibit butterfly and clockwise bistability (see Fig. 5 in [19

19. A. Hurtadoet al, “Modeling Reflective Bistability in Vertical-Cavity Semiconductor Optical Amplifiers,” IEEE J. Quantum. Electron. 41, 376–383 (2005). [CrossRef]

]). Nevertheless, this fact does not distract from the physical interpretation above that it is the careful balancing of (1) which yields the complex bistability curves observed in the reflected intensity.

3. Experimental setup

The fiber-coupled experimental setup used to study the bistable switching properties of our 1550 nm devices is shown in Fig. 2.

Fig. 2. Experimental Setup to study bistabilty in 1550 nm VCSOA.

Tunable laser light is first intensity modulated using a Mach Zehnder modulator (MZM) driven by a 50 kHz sawtooth wave. This allows for real-time plotting of the input-output characteristics of the VCSOA by using the processing functionalities of the digital communication analyzer (DCA) sampling scope. After the MZM, the injected light is aligned in polarization to the strong gain axis of the VCSOA via a polarization controller (POLC1). The light is then injected into a fiber coupled 1550 nm VCSOA via a circulator. The VCSOA output is passed back through the circulator and then through POLC2 and a polarization beam splitter (PBS). The PBS helps facilitate polarization alignment to the stronger gain axis of the VCSOA and rejects the amplified spontaneous emission (ASE) in the polarization orthogonal to the signal. The input-output characteristics are plotted on the sampling scope. The current source (CS), temperature controller (TC), power meter (PM) and optical spectrum analyzer (OSA) are used to carefully control and monitor VCSOA bias current, temperature, input optical power and polarization alignment, respectively.

4. Results

As described above, Fabry-Perot bistability theory predicts that, for a given bias current (Ibias), counterclockwise bistability will onset first as the input wavelength is red-shifted with respect to the amplifiers peak resonant wavelength. Upon further detuning, the input-output characteristics will transition to butterfly and then clockwise bistability. Experimental observation of this transition can be seen in Fig. 3. Clearly, at larger detuning butterfly and clockwise bistability can be obtained at the expense of higher switching powers and wider hysteresis windows.

In a similar manner, the transition between all three bistable regimes can be observed if the wavelength detuning is kept constant and the bias current is swept as shown in Fig 4. Physically, as the bias current is decreased, the resonant peak of the amplifier blue shifts. This effectively causes the wavelength detuning to increase thereby resulting in butterfly and clockwise bistability. Consistent with Fig. 3, Fig. 4 clearly shows that counterclockwise bistability has the lowest switching powers and narrowest hysteresis windows.

Fig. 3. All three types of bistability in a 1550 nm VCSOA for constant Ibias = 0.96*Ith. Wavelength detuning is swept towards longer wavelengths. A is for no bistability. B is counterclockwise bistability. C is butterfly bistability. D is clockwise bistability.
Fig. 4. All three types of bistability for constant wavelength 1542.354 nm . Ibias is swept. 99%*Ith shows counterclockwise bistability. 94%*Ith shows butterfly bistability. 91%*Ith shows clockwise bistability.

Fig. 5. Counterclockwise Bistability for 0.99*Ith.
Fig. 6. Butterfly Bistability for 0.99*Ith.
Fig. 7. Clockwise Bistability for 0.89*Ith.

In terms of the bistable sensitivity of our devices to operating conditions, we find that all three forms of bistability manifest over an extremely wide range of bias currents and wavelength detuning. This contrasts with previously reported results which showed a relatively small range of operating conditions to achieve bistable switching [18

18. A. Hurtadoet al, “Optical bistability and nonlinear gain in 1.55 um VCSOA,” Electron. Lett. 42, 483–484 (2006). [CrossRef]

]. As we can see in Figs. 5–7, all three forms of bistability exist over tens of pm of detuning. Constrastingly, the results in [18

18. A. Hurtadoet al, “Optical bistability and nonlinear gain in 1.55 um VCSOA,” Electron. Lett. 42, 483–484 (2006). [CrossRef]

] showed very narrow hysteresis windows. We attribute the improvement primarily to the improved coupling efficiency of our fiber pigtailed devices. Additional modeling using the technique described in [9

9. P. Wenet al, “Observation of bistability in a vertical-cavity semiconductor optical amplifier (VCSOA).” Opt. Express 10, 1273 (2002). [PubMed]

] also indicates that the existence of bistability in VCSOAs in critically dependent on device properties such as top/bottom mirror reflectivity, linewidth enhancement factor, cavity confinement and overall gain. These factors may further explain why our tested devices exhibit much stronger bistability. Our measurements show counterclockwise bistability visible from 83% Ith to 122% Ith, butterfly bistability from 81% Ith to 114% Ith, and clockwise bistability from 66% Ith to 108% Ith where the upper end of the bistability for clockwise and butterfly bistability is limited by the available input power of the setup. We also obtain hysteresis windows as large as 119 μW (54–173 μW) for counterclockwise and 164 μW (89–253 μW) for clockwise bistability, only limited by the available input power of the system. The robustness and flexibility of these devices to exhibit bistable behavior over a wide range of operating conditions is of practical interest for possible future applications.

5. Conclusion

In this paper, we have observed, for the first time to our knowledge, that all three types of bistability, counter-clockwise, clockwise, and butterfly, can be achieved in VCSOAs. Moreover, we have shown that the onset of bistable action occurs at thresholds as low as 2 μW which is more than two orders of magnitude smaller than any previously reported observation in 1550 nm VCSOAs. The significance of achieving low switching thresholds is of practical concern for applications in OIP. We have also demonstrated that all three forms of bistability occur over a wide range of operating conditions indicating that these devices may offer great flexibility for future applications.

References and links

1.

A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proceedings of the IEEE 72 no.7, 758 (1984). [CrossRef]

2.

H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes. (Artech House, Boston, 1994).

3.

M. J. Adams, “Optical amplifier bistabilty on reflection,” Opt. Quantum Electron. 19, 37 (1987). [CrossRef]

4.

N. K. Dutta and Q. Wang, Semiconductor Optical Amplifiers. (World Scientific, Hackensack, N.J., 2006). [CrossRef]

5.

Q. Linet al, “40-gb/s optical switching and wavelength multicasting in a two-pump parametric device,” IEEE Photon. Technol. Lett. 17, no. 11 2376 (2005). [CrossRef]

6.

P. Pakdeevanich and M. J. Adams, “Measurements and Modeling of Reflective Bistability in 1.55-μm Laser Diode Amplifiers,” IEEE J. Quantum Electron. 35, 1894–1903 (1999). [CrossRef]

7.

J. Mitchellet al, “Optical bistability in asymmetric Fabry - Perot laser-diode amplifiers,” Opt. Lett. 19, 269 (1994). [CrossRef] [PubMed]

8.

T. Moriet al, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102 (2006). [CrossRef]

9.

P. Wenet al, “Observation of bistability in a vertical-cavity semiconductor optical amplifier (VCSOA).” Opt. Express 10, 1273 (2002). [PubMed]

10.

M. Sanchezet al, “Rate equations for modeling dispersive nonlinearity in Fabry-Perot semiconductor optical amplifiers.” Opt. Express 11, 2689 (2003). [CrossRef] [PubMed]

11.

M. Sanchezet al, “Polarization anisotropy in vertical-cavity semiconductor optical amplifiers”. Opt. Lett. 29, 1888 (2004). [CrossRef] [PubMed]

12.

H. Zhanget al, “Observation of Wavelength Bistability in 850nm Vertical-Cavity Semiconductor Optical Amplifiers,” presented at Frontier in Optics, OSA, Rochester, NY, Oct. 2006.

13.

P. Wenet al, “Optical bistability in vertical-cavity semiconductor optical amplifiers,” Appl. Opt. 45, 6349 (2006). [CrossRef] [PubMed]

14.

H. Zhanget al, Optoelectronics Group, University of California, San Diego, La Jolla, CA. 92093, are preparing a manuscript to be called “Cascadable all-optical inverter based n a non-linear Vertical Cavity Semiconductor Optical Amplifier”.

15.

H. Zhanget al, Optoelectronics Group, University of California, San Diego, La Jolla, CA. 92093, are preparing a manuscript to be called “All-optical Oscillator based on a single bistable Vertical Cavity Semiconductor Optical Amplifier (VCSOA)”.

16.

S. Esener and P. Wen, “Photonics in Computing: Interconnects and Beyond,” presented at Frontier in Optics, OSA, Rochester, NY, Oct. 2006.

17.

A. Karimet al, “Long-wavelength vertical-cavity lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 6, 1244 (2000). [CrossRef]

18.

A. Hurtadoet al, “Optical bistability and nonlinear gain in 1.55 um VCSOA,” Electron. Lett. 42, 483–484 (2006). [CrossRef]

19.

A. Hurtadoet al, “Modeling Reflective Bistability in Vertical-Cavity Semiconductor Optical Amplifiers,” IEEE J. Quantum. Electron. 41, 376–383 (2005). [CrossRef]

20.

S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers. (John Wiley & Sons, Hoboken, N. J., 2003). [CrossRef]

21.

S. F. Yu, “Theoretical analysis of polarization bistability in vertical cavity surface emitting semiconductor lasers,” IEEE J. Lightwave Technol. 15, 1032–1041 (1997). [CrossRef]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(200.4560) Optics in computing : Optical data processing
(250.5980) Optoelectronics : Semiconductor optical amplifiers

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 30, 2007
Revised Manuscript: March 12, 2007
Manuscript Accepted: March 13, 2007
Published: April 9, 2007

Citation
Christopher F. Marki, Douglas R. Jorgesen, Haijiang Zhang, Pengyue Wen, and Sadik C. Esener, "Observation of counterclockwise, clockwise and butterfly bistabilty in 1550 nm VCSOAs," Opt. Express 15, 4953-4959 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-4953


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References

  1. A. A. Sawchuk and T. C. Strand, "Digital optical computing," Proceedings of the IEEE 72no.7, 758 (1984). [CrossRef]
  2. H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes. (Artech House, Boston, 1994).
  3. M. J. Adams, "Optical amplifier bistabilty on reflection," Opt. Quantum Electron. 19, 37 (1987). [CrossRef]
  4. N. K. Dutta and Q. Wang, Semiconductor Optical Amplifiers. (World Scientific, Hackensack, N.J., 2006). [CrossRef]
  5. Q. Lin et al., "40-gb/s optical switching and wavelength multicasting in a two-pump parametric device," IEEE Photon. Technol. Lett. 17, no.112376 (2005). [CrossRef]
  6. P. Pakdeevanich and M. J. Adams, "Measurements and Modeling of Reflective Bistability in 1.55-μm Laser Diode Amplifiers," IEEE J. Quantum Electron. 35, 1894-1903 (1999). [CrossRef]
  7. J. Mitchell et al., "Optical bistability in asymmetric Fabry - Perot laser-diode amplifiers," Opt. Lett. 19, 269 (1994). [CrossRef] [PubMed]
  8. T. Mori et al., "Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser," Appl. Phys. Lett. 88, 101102 (2006). [CrossRef]
  9. P. Wen et al., "Observation of bistability in a vertical-cavity semiconductor optical amplifier (VCSOA)." Opt. Express 10, 1273 (2002). [PubMed]
  10. M. Sanchez et al., "Rate equations for modeling dispersive nonlinearity in Fabry-Perot semiconductor optical amplifiers." Opt. Express 11, 2689 (2003). [CrossRef] [PubMed]
  11. M. Sanchez et al., "Polarization anisotropy in vertical-cavity semiconductor optical amplifiers". Opt. Lett. 29, 1888 (2004). [CrossRef] [PubMed]
  12. H. Zhang et al., "Observation of Wavelength Bistability in 850nm Vertical-Cavity Semiconductor Optical Amplifiers," presented at Frontier in Optics, OSA, Rochester, NY, Oct. 2006.
  13. P. Wen et al., "Optical bistability in vertical-cavity semiconductor optical amplifiers," Appl. Opt. 45, 6349 (2006). [CrossRef] [PubMed]
  14. H. Zhang et al., Optoelectronics Group, University of California, San Diego, La Jolla, CA. 92093, are preparing a manuscript to be called "Cascadable all-optical inverter based n a non-linear Vertical Cavity Semiconductor Optical Amplifier".
  15. H. Zhang et al., Optoelectronics Group, University of California, San Diego, La Jolla, CA. 92093, are preparing a manuscript to be called "All-optical Oscillator based on a single bistable Vertical Cavity Semiconductor Optical Amplifier (VCSOA)".
  16. S. Esener and P. Wen, "Photonics in Computing: Interconnects and Beyond," presented at Frontier in Optics, OSA, Rochester, NY, Oct. 2006.
  17. A. Karim et al., "Long-wavelength vertical-cavity lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 6, 1244 (2000). [CrossRef]
  18. A. Hurtado et al., "Optical bistability and nonlinear gain in 1.55 μm VCSOA," Electron. Lett. 42, 483-484 (2006). [CrossRef]
  19. A. Hurtado et al., "Modeling Reflective Bistability in Vertical-Cavity Semiconductor Optical Amplifiers," IEEE J. Quantum. Electron. 41, 376-383 (2005). [CrossRef]
  20. S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers. (John Wiley & Sons, Hoboken, N. J., 2003). [CrossRef]
  21. S. F. Yu, "Theoretical analysis of polarization bistability in vertical cavity surface emitting semiconductor lasers," IEEE J. Lightwave Technol. 15, 1032-1041 (1997). [CrossRef]

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