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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9624–9635
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Controllable mode multistability in microring lasers

Guohui Yuan and Zhuoran Wang  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9624-9635 (2013)
http://dx.doi.org/10.1364/OE.21.009624


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Abstract

We investigate mode multistability, i.e. coexistence of direction bistability and wavelength bi/multistability in microring lasers (MRLs) theoretically and numerically. We derive the expressions for conditions required for mode multistable operation in microring lasers based on a nonlinear multimode model with nonlinear effects stemming from carrier density pulsation, carrier heating and spectral hole burning included. We find theoretically that lasing mode can be selected from the multistable modes by external optical injection through gain saturation, and removal of the external optical injection will not affect the stability of the established lasing mode. Numerical results on all-optical multistate flip-flop function demonstrate that switching between multistable modes can be induced by trigger signals with each states self-sustained after the removal of the trigger signals in a 50µm-radius microring laser.

© 2013 OSA

1. Introduction

All optical technology is very attractive because of its potential to overcome the electronic bottleneck limits for processing ultra-wideband and ultra-fast signals. Plenty of schemes have been proposed and investigated in these years for the implementation of the photonic counterparts of conventional electronic systems, such as the memory [1

1. K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012). [CrossRef]

], logic [2

2. Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-3-924. [CrossRef] [PubMed]

] and switch [3

3. K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010). [CrossRef]

]. Semiconductor disk or ring lasers, offering advantages of high speed, robustness, small size, low power consumption, have been investigated as an attractive candidate for this long-term dream [4

4. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]

6

6. Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010). [CrossRef]

]. Especially they have been realized on silicon platform recently for the purpose of optical sources and memory showing a great potential to integrate both optical and electronic functionalities on a common platform [7

7. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]

,8

8. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010). [CrossRef]

].

Recently, a unique feature of microring lases has been observed and experimentally demonstrated that stable unidirectional, single mode oscillation at set wavelength from both directions can be achieved without the requirement of any injection power to keep the laser locked in the desired mode, which is also known as mode multistability [9

9. C. Born, S. Yu, M. Sorel, and P. J. R. Laybourn, “Controllable and stable mode selection in a semiconductor ring laser by injection locking,” in CLEO Proceedings, paper CWK4, (2003).

,10

10. Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008). [CrossRef]

]. It shows a great future that a single photonics building block with multiple stable states capable of handling multiple wavelength information can be utilized to achieve lower power consumption, higher functional and integration densities.

Despite its interesting potential applications, the coexistence of directional bistability and wavelength bi/multistability in microring lasers has not been well understood. Mechanisms behind selection of lasing mode from multistable modes and switching between multistable modes are also still unclear. The direction bistable modes share the same wavelength but propagate in the opposite direction. Directional bistability in microring lasers is believed to be caused by mode competition between the counter propagating modes through nonlinear gain saturation which is described in a phenomenological way [11

11. G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008). [CrossRef]

]. Wavelength bi/multistability in microring lasers refers to stable unidirectional, single mode oscillation at two or a set of wavelengths propagating in the same direction. Wavelength bi/multistability is investigated both analytically and numerically based on a nonlinear multimode model [12

12. G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011). [CrossRef]

]. The results indicate that coupling and saturation between modes of different wavelengths through nonlinear gain leads to wavelength bi/multistability in microring lasers [12

12. G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011). [CrossRef]

]. Later theoretical study on longitudinal mode multistability in ring and Fabry-Perot lasers [13

13. A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19(4), 3284–3289 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-4-3284. [CrossRef] [PubMed]

] suggests that configuration is important for mode multistability, but the effects of nonlinear gain are not taken into account.

Actually, nonlinear effects are vital for understanding mode multistability which occurs as a result of mode competition in microring lasers. Resonant modes propagating in counter clock-wise (CCW) and clock-wise (CW) directions in microring cavity are travelling waves. Beating of modes at different cavity resonances in both directions modulates carrier density in the cavity at the beat frequency and leads to dynamic grating through nonlinear mechanisms. The dynamic grating results in a change of the gain of modes and coupling between modes both of which have great impact in mode competition.

In this paper, we investigate the mode multistability theoretically and numerically based on a time domain multi-mode nonlinear model with nonlinear effects from carrier density pulsation (CDP), carrier heating (CH) and spectral hole burning (SHB) considered. The theoretical and numerical methods used in this paper are similar to those used in studying wavelength bi/multistability in Ref [12

12. G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011). [CrossRef]

]. The wavelength bi/multistable modes discussed in [12

12. G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011). [CrossRef]

] have different wavelengths but propagate in the same direction. However, the mode multistable modes studied in this manuscript can either have different wavelengths but propagate in the same direction or share the same wavelength but propagate in different directions or have different wavelengths and propagate in different directions. We analyze the stability of potential multistable cavity modes and the condition required for mode multistable operation in microring lasers. Furthermore, we investigate the selection of lasing mode from multistable modes by external optical injection and the stability of the selected mode after the removal of injection theoretically. Numerical simulation of multistate all optical flip-flop function is then carried out to verify our theoretical results.

2. Theory

The dynamics of a multistable microring laser can be modeled by a couple of differential rate equations for the carrier density and the time evolution of the slowly varying envelop of the mode electric fields. The deviation of the carrier density from its threshold value is denoted byΔN:
dΔNdt=IItheVcΔNτN2ε0ngn0ωpkvgaga|Ea|2
(1)
Where I is the injection current, Ith is the threshold current, e for the elementary charge, Vc for the volume of active region containing carriers, τN for differential carrier lifetime, ε0 for permittivity of free space, ng for group index, n0 for the effective mode index, ωpk for frequency of the linear gain peak, vg for group velocity, ga for material gain of mode a, Ea for the complex slowly varying electric field of mode a. Equation (1) takes into account the static carrier density change due to the intensity of modes, i.e., beating of the same modes.

The total electric field E in the laser is expressed as a sum of complex field of both lasing and nonlasing modes in terms of Ea as
E(z,t)=aEa(t)exp(ikaz)exp(iωat)+c.c.
(2)
where z is the field propagation direction, with CCW as positive z direction and CW as negative z direction, and
ka={ωan0c,+zdirectionωan0c,zdirection
(3)
where ωa accounts for the optical frequency of mode a.

The dynamics of mode a is described by:
dEadt=[0.5vgΓ(ga+ΔNdgdN(1iαN)1Γvgτp)iΔωadis]Ea(t)+i0.5vgωacnΓbcdχbcd3Eb(t)Ec*(t)Ed(t)ζabcd+Fa(t)
(4)
where Г accounts for confinement factor, dg/dN for differential gain coefficient, αN for linewidth enhancement factor associated with carrier density pulsation, τp for photon lifetime, Δωadisfor total frequency shift of lasing mode frequency from the cold grid frequency. Equation (4) takes into account the effect of the carrier density beating due to beating of different modes and the nonlinear gain saturation effects which are described by the nonlinear susceptibility derived using density matrix method. χbcd3 for 3rd order material susceptibility including effects of CDP, CH and SHB for the interaction between modes b, c and d [14

14. C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008). [CrossRef]

], with

χbcd3=χbcdCDP+χbcdSHB+χbcdCH
(5)
χbcdCDP=2ε0nngωpkεCDPηcdCDP(αCDP+i)1(1iΩτCDPηcdCDP)(1iΩτSHBηcdSHB)χpk1''
(6)
χbcdCH=2ε0nngωpkεCHηcdCH(αCH+i)1(1iΩτCHηcdCH)(1iΩτSHBηcdSHB)χpk1''
(7)
χbcdSHB=2ε0nngωpkεSHBηcdSHBi(1iΩτSHBηcdSHB)(1i(ωaωc)τdp/2)χpk1''
(8)

ζabcd=1L0Lexp[i(kakb+kckd)z]dz
(9)

ζabcd would be very small for integration over many wavelengths long unless resonant coupling condition i.e. kak+bkckd=0 is satisfied.

We refer to the lasing established mode which is closest to the material gain peak as mode Lp (p = 1,2) and one of the competing multistable modes as mode Mq (q = 1,2), where 1 and 2 represent the CCW and CW directions for wavelengths L and M respectively. We are interested in the dynamics and stability of the established mode and the competing multistable modes so we concentrate our theoretical analyses on the coupling between these modes. Assuming the laser is biased high above threshold current with quasi-single mode operation with mode Lp as the dominant mode, we consider the situation illustrated in Fig. 1
Fig. 1 Illustration of modes Lp and Mq in both directions of a microring laser.
, where both wavelength L and wavelength M can propagate in either CCW or CW direction.

We approximate the linear material gain as parabolic around ωpk with gain peak equals togpk, and find the gain of each mode as:
ga=gpk[1(ωaωpkΔωHG)2]
(10)
where ΔωHG is the half width of the gain bandwidth. The lasing mode Lp is assumed to be the one that is closest to the linear material gain peak with frequency ωL=ωpk+lΔω (l=0,±1,...) and wavelength λL, and the potential multistable Mq is assumed to be farther away from the linear gain peak than mode Lp with frequency ωM=ωpk+mΔω (m=±1,±2,...), |m|>|l| and wavelength λMwhere Δω is the free spectral range (FSR). Because modes L and M have different wavelengths, 1 and 2 are used to represent two modes with the same wavelength but different propagation directions, i.e. 1 for CCW and 2 for CW direction of L or M respectively.

We find the following Eqs. for modes Lp and Mq by evaluating Eq. (4):

dELpdt=[0.5vg(ΓgLp+ΔNΓdgdN(1iαN)1vgτp)iΔωLpdis]ELp(t)+FLp+i0.5vgωpkcnΓbcdχbcd3Eb(t)Ec*(t)Ed(t)ζLpbcd
(11)
dEMqdt=[0.5vg(ΓgMq+ΔNΓdgdN(1iαN)1vgτp)iΔωMqdis]EMq(t)+FMq+i0.5vgωpkcnΓbcdχbcd3Eb(t)Ec*(t)Ed(t)ζMqbcd
(12)

If modes Lp and Mq are co-propagating with p = q, which is the case discussed in [12

12. G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011). [CrossRef]

], the time evolutions of the normalized intensities of modes Lp and Mq are given by:
dSL,Mdt=Γvg(gL,M+ΔNdgdN1ΓvgτpωpkcnχLLL,MMM3''SL,Mωpkcn(χLMM,MLL3''+χMML,LLM3'')SM,L)SL,M
(13)
where noise is neglected because the device is biased high above the threshold current, and the operating point is chosen to be in the middle of a robust unidirectional region. Notations p and q are removed for simplicity.

If modes Lp and Mq are counter-propagating with p≠q, nonlinear coupling between modes Lp and Mq through four wave mixing does not exist because phase matching condition is not satisfied. We find in this case:
bcdχbcd3Eb(t)Ec*(t)Ed(t)ζLbcd=χLLL3ζLLLL|EL|2EL+(χLMM3ζLLMM+χMML3ζLMML)|EM|2ELbcdχbcd3Eb(t)Ec*(t)Ed(t)ζMbcd=χMMM3ζMMMM|EM|2EM+(χMLL3ζMMLL+χLLM3ζMLLM)|EL|2EM
(14)
where notations p and q are also removed for simplicity.

Consequently, if modes Lp and Mq are counter-propagating, the time evolutions of the normalized intensities of Lp and Mq, which are derived based on Eqs. (11) and (12) and Eq. (14), possess the same form as Eq. (13).

Similarly, we find the time evolutions of the normalized intensities of modes with the same wavelength in the CCW and CW directions (i.e. modes L1 and L2 or modes M1 and M2) by evaluating Eq. (4) as:
dS1,2dt=Γvg(gL,M+ΔNdgdN1Γvgτpωpkcnχ111,2223''S1,2ωpkcn(χ122,2113''+χ221,1123'')S2,1)S1,2
(15)
Where notations L and M are removed for simplicity.

3. Analytical analysis and numerical results

3.1 Mode multistability analysis

From the analyses and discussions above, we find that modes Lp and Mq degenerate into L and M since the time evolutions of their normalized intensities can all be described by Eq. (13) with whatever combination of p and q. Consequently, the notation p and q are removed in the following analyses for simplicity.

The stability of modes L and M described by Eq. (13) can be studied by phase plane analysis. As shown in Fig. 2
Fig. 2 Illustration of transient behaviour of the intensities of modes L and M in the phase plane. Dashed straight line for dSL/dSM=0, and dotted straight line fordSM/dSL=0.
, two straight lines representing dSL/dSM=0 and dSM/dSL=0 intersect with axes L and M at (Ll,m, 0) and (0, Ml,m) respectively. Multistable operation of modes L and M can be achieved if Ll>Lm and Ml<Mm, i.e. the following conditions are satisfied:

Ll>Lm>0gL+ΔNdgdN1ΓvgτpχLLL3''>gM+ΔNdgdN1ΓvgτpχMLL3''+χLLM3''>0
(16)
0<Ml<Mm0<gL+ΔNdgdN1ΓvgτpχLMM3''+χMML3''<gM+ΔNdgdN1ΓvgτpχMMM3''
(17)

Here each of modes L and M has a mode degeneracy of two including CW and CCW directions as indicated by Eq. (13), which means that two multistable states are of the same wavelength. The stability of modes with the same wavelength but different propagation directions is analyzed in the same way. As shown in Fig. 3
Fig. 3 Illustration of transient behaviour of the intensities of modes in the CCW and CW directions in the phase plane. Dashed straight line fordS1/dS2=0, and dotted straight line for dS2/dS1=0.
, two straight lines representing dS1/dS2=0and dS2/dS1=0 intersect with axes CCW and CW at (CCW1,2, 0) and (0, CW1,2) respectively. We find that direction bistability can be achieved if CCW1>CCW2 and CW1<CW2, i.e. the following conditions have to be satisfied:

CCW1>CCW2>01χ1113''>1χ2113''+χ1123''>0
(18)
0<CW1<CW20<1χ1223''+χ2213''<1χ2223''
(19)

Because modes considered in In Eqs. (18) and (19) propagate in different directions but share the same wavelength, it is obvious that In Eqs. (18) and (19) hold for any resonant mode in a normal ring laser.

Therefore, we find that the laser is mode multistable with at least four multistable modes if conditions described by In Eqs. (16) and (17) are satisfied. As indicated by In Eqs. (16) and (17), the coupling and saturation between resonant travelling modes through nonlinear mechanisms such as CDP, CH and SHB lead to mode multistability in semiconductor microring lasers.

dSL,Mdt=Γvg(gL,M+ΔNdgdN1ΓvgτpωpkcnχLLL,MMM3''SL,Mωpkcn(χLMM,MLL3''+χMML,LLM3'')SM,L)SL,M+κSL,MSinjL,M
(20)

We find that the lasing mode of a multistable microring laser can be selected from the multistable modes with appropriate external optical injection through gain saturation as shown in Fig. 4
Fig. 4 Illustration of transient behaviour of the intensities of modes L and M in the phase plane with appropriate external optical injections. Dashed line fordSL/dSM=0, and dotted line for dSM/dSL=0. (a) an external optical injection is added to mode L; (b) an external optical injection is added to mode M.
. As shown in Fig. 4(a), dSL/dSM=0is distorted by the external optical injection added to mode L, flows are all attracted to the solution of SM = 0, therefore mode L is selected to be the lasing mode. Whereas Fig. 4(b) shows that dSM/dSL=0 is distorted by the external optical injection added to mode M, flows are all attracted to the solution of SL = 0, and therefore mode M is selected to be the lasing mode. Furthermore, because both modes L and M are multistable, the lasing mode will remain stable even after removal of the external optical injection signal as indicated by Fig. 2.

As shown in Fig. 5(a)
Fig. 5 Illustration of transient behaviour of the intensities of modes in the CCW and CW directions in the phase plane with appropriate external optical injections. Dashed line for dS1/dS2=0, and dotted line for dS2/dS1=0. (a) an external optical injection is added to the CCW direction of mode L or M; (b) an external optical injection is added to CW direction of mode L or M.
, with external optical injection added to the CCW direction of mode L or M, dS1/dS2=0 is distorted and flows are all attracted to the solution of S2 = 0, therefore CCW direction of mode L or M is selected to be the lasing direction. Whereas Fig. 5(b) shows that dS2/dS1=0 is distorted by the external optical injection added to the CW direction of mode L or M, flows are all attracted to the solution of S1 = 0, and therefore CW direction of mode L or M is selected to be the lasing direction. The lasing direction will remain stable even after the removal of the injection signal since the microring laser is directional bistable as shown in Fig. 3.

3.2 Numerical results

Numerical simulations are carried out based on a nonlinear multimode model including effects from CDP, CH and SHB. The model is described by Eqs. (1) and (4) with 30 modes from both CW and CCW directions considered. We assume that a multiple quantum-well material system is used to fabricate the device which is a ridge waveguide circular laser with a straight output waveguide coupled to the ring via a directional coupler. Main parameters for the device are given in Table 1

Table 1. Main parameters

table-icon
View This Table
.

We find that the microring laser can support ten different multistable modes by simulation, i.e. modes m0,CCW ~m4,CCW in CCW direction and modes m0,CW ~m4,CW in the CW direction where modes m0,CCW and m0,CW are the free running modes whereas m4,CCW and m4,CW are on the long wavelength side of the free running modes.

Figure 6(a)
Fig. 6 Illustrations of the external trigger pulse signals. (a) external trigger pulse signals with 10ns pulse width and 20ns time slot; (b) zone A with 10 pulses included; (c) zone B with 15 pulses included.
shows the external trigger pulse signals with 10ns pulse width and 20ns time slot. Each trigger pulse signal representing one random number ranging from 0 to 9 will set the mode state to the corresponding multistable mode. We then carried out numerical study to verify the switching operations between different multistable modes by randomly selecting two zones (A and B) in the external injection pulse stream.

The mode states of the 10 selected input pulses in zone A appear as follows: m0,CCW, m3,CCW, m3,CW, m2,CW, m4,CCW, m2,CCW, m1,CCW, m4,CW, m1,CW, and m0,CW (Fig. 6(b)), which cover all the supported multistable modes in the device. Triggered by the pulse stream, the oscillating mode switches from m0,CCW in the CCW direction to modes m3,CCW, m3,CW, m2,CW, m4,CCW, m2,CCW, m1,CCW, m4,CW, and m1,CW consecutively and finally switches to mode m0,CW in the CW direction. Each state is self-sustained which means that the selected multistable mode is stable after the removal of the trigger signal as shown in Fig. 7(a)
Fig. 7 (a) Simulated switching dynamics between multistable modes. (a) switching induced by the trigger pulse stream shown in Fig. 6(b); (b) Switching induced by the trigger signals illustrated in Fig. 6(c).
.

The order for the injected trigger pulse stream in zone B is m0,CCW, m0,CW, m0,CCW, m4,CCW, m2,CW, m4,CCW, m4,CW, m2,CCW, m1,CW, m3,CCW, m1,CCW, m3,CW, m2,CW, m3,CW, and m1,CCW and shown in Fig. 6(c). The combination includes not only switching between all the supported multistable modes, but also several set-reset operations between a few pairs of modes such as m0,CCW, m0,CW, and m0,CCW. As shown by Fig. 7(b), the lasing mode is successfully switched to the selected states by the trigger pulse signals and self-sustained flip-flop operations are achieved after the removal of the signals.

Figure 8
Fig. 8 Optical spectra for CCW direction (a) and for CW direction (b) show the power of resonant modes at different self-sustained states after the removal of trigger signals in multistate flip-flop operations.
shows the corresponding optical spectra of resonant modes in CCW (Fig. 8(a)) and CW (Fig. 8(b)) directions at different self-sustained states after the removal of trigger signals with reference to Fig. 7. It is clear that unidirectional single mode operation at the multistable mode is achieved as a result of an injection of a trigger signal to select the lasing mode.

4. Conclusions

Acknowledgments

References and links

1.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012). [CrossRef]

2.

Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-3-924. [CrossRef] [PubMed]

3.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010). [CrossRef]

4.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]

5.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003). [CrossRef]

6.

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010). [CrossRef]

7.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]

8.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010). [CrossRef]

9.

C. Born, S. Yu, M. Sorel, and P. J. R. Laybourn, “Controllable and stable mode selection in a semiconductor ring laser by injection locking,” in CLEO Proceedings, paper CWK4, (2003).

10.

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008). [CrossRef]

11.

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008). [CrossRef]

12.

G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011). [CrossRef]

13.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19(4), 3284–3289 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-4-3284. [CrossRef] [PubMed]

14.

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008). [CrossRef]

OCIS Codes
(140.3560) Lasers and laser optics : Lasers, ring
(140.5960) Lasers and laser optics : Semiconductor lasers
(190.1450) Nonlinear optics : Bistability
(140.3948) Lasers and laser optics : Microcavity devices
(130.4815) Integrated optics : Optical switching devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 6, 2012
Revised Manuscript: February 15, 2013
Manuscript Accepted: March 17, 2013
Published: April 10, 2013

Citation
Guohui Yuan and Zhuoran Wang, "Controllable mode multistability in microring lasers," Opt. Express 21, 9624-9635 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9624


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References

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