Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit

doi:10.1364/OE.17.012835

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Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit

Yunhong Ding, Xiaobei Zhang, Xinliang Zhang, and Dexiu Huang »View Author Affiliations

Optics Express, Vol. 17, Issue 15, pp. 12835-12848 (2009)
http://dx.doi.org/10.1364/OE.17.012835

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▸ Article Outline
– Abstract
1. Introduction
2. Principle and simulation model
3. Numerical results
4. Conclusion
– References and links

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Abstract

We propose and analyze a novel loadable and erasable optical memory unit based on an active microring optical integrator associated with electroabsorption modulators (EAM) on III-V material system. The gain of the active microring is characterized by the two energy band model with amplified spontaneous emission noises taken into account. Based on the light field propagation equation in the active microring waveguide and the transfer function of the EAM-MZI switch, the step function performances of the optical memory under the gain matching condition are discussed for different injection light powers. After that, the memory operation of the novel optical memory unit is analyzed in detail. Simulations show that, the step function response and memory performances are affected by the carrier consumption. However, such influence will be released, and the memory operates well for the low light power injection case. The novel optical memory unit is promising to be cascaded connected and densely integrated for high speed low power optical data stream storage and buffer.

1. Introduction

Optical memory or buffer is critical for all-optical network, and considerable efforts have been made to realize optical data buffering. Most of the optical buffering schemes produce a delay time of the data stream, such as slowing light [1

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002). [CrossRef]

–4

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007). [CrossRef]

], optical fiber loop [5

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004). [CrossRef]

–7

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007). [CrossRef]

] and so on. Another scheme is based on optical memory unit and similar to memory in the field of micro-electronics, it solves single bit storage problem. If the single optical data bit storage is solved successfully, the optical data steam storage can be easily solved just by cascading the memory units. A semiconductor optical memory unit controlled by a comb-like electrode has been realized [8

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999). [CrossRef] [PubMed]

]. However, ultra-low temperature is required. Another approach for optical memory unit is the injection-locked optical memory unit realized by single [9

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

] or dual microring lasers [10

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. 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]

]. But they are still inconvenient for cascading, because that the two operating laser modes are clockwise and anti-clockwise, and there will be influences between neighborhoods for cascaded connection.

Optical integrator performs the function of time integral of the intensity [11

N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995). [CrossRef]

] or the complex envelope [12

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006). [CrossRef] [PubMed]

–16

Y. P. R. Slavík, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic Temporal Integrator,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), CPDB3 http://www.opticsinfobase.org/abstract.cfm?URI=URI=CLEO-2008-CPDB2003.

] of an arbitrary optical input signal. Theoretical study in optical integrator has been comprehensively carried out [17

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006). [CrossRef]

], and recently it has been realized by passive filters based on fiber Bragg gratings (FBGs) [13

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007). [CrossRef] [PubMed]

–15

M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett. 33(12), 1348–1350 (2008). [CrossRef] [PubMed]

] and a distributed active Fabry-Perot (FP) filter based on FBGs [16

]. An active microring whose gain just compensates the waveguide and coupling losses also plays a role of an optical integrator [12

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006). [CrossRef] [PubMed]

,18

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008). [CrossRef]

] for the light on resonation. For the time integral function of the complex envelope, if the injected light pulse is coherent, the optical integrator performs a light step function. Such a characteristic has been noticed for optical memory [18

] based on dual coupled active microring resonators, however, it is still lack of analysis with gain dynamics and noises influences considered in detail. What’s more, it is difficult to be fabricated for the dual-coupled active microring resonator system is relative complicated. Another promising optical ring-resonator memory cell scheme has also been proposed [19

R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008). [CrossRef]

], whose storing state also performs the integral of the input light pulse. However, to eliminate the leakage pulse during the write operation, a time dependent coupling coefficient with specific shape related to the input light pulse is required, which is hard to be controlled and realized in practice.

In this paper, we propose another novel scheme of loadable and erasable optical memory unit based on single active microring resonator associated with EAM on III-V material system, which is different from the previously reported memory units. The gain dynamics is characterized by the two energy band model, and the noises of the side lasing modes are also considered. We first analyze the step function response performance of the optical memory unit, since the step function is essential for the optical integrator based memory unit. After that, the memory operation is analyzed in detail. Simulations show that the step function response and memory performance are impacted by carrier consumption. However, such impaction can be released for the low light power injection case. The proposed novel memory scheme has many advantages. Firstly, it is convenient for write operation without requirement of specific time dependent write control signal related to input light pulse, and can work with negligible leakage light if designed properly. Secondly, the configuration is simple, and it is compact for optical integration and convenient for cascaded connection for optical digital register and random-access memory as in [18

] and [19

R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008). [CrossRef]

]. What’s more, it supports fabrication though the current planar process, can work with ultra-fast response and so on. It has the potential for densely integration for large scale data stream storage with high speed and low light power.

2. Principle and simulation model

2.1 Principle

The scheme of the proposed memory unit is shown in Fig. 1 . It consists of a microring optical integrator with an embedded EAM-MZI switch. The two EAMs of the EAM-MZI switch are designed symmetrically. An optical pulse

E_{i n}

is injected into the active microring optical integrator from the input port. The red solid arrows represent the signal propagation, and the blue dashed arrows represent the clockwise noises

E_{n o i s e}^{C W}

and counter-clockwise noises

E_{n o i s e}^{C C W}

propagation. In the EAM-MZI switch, the signal light

E_{1}^{s i g n a l}

is injected from the right-down port. Based on the light propagation equation of the EAM [20

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef]

] and coupling equation of the 2 × 2 coupler of the EAM-MZI switch, the output from the EAM-MZI switch fed back into the microring

E_{2}^{s i g n a l}

and read out signal

E_{o u t}

from the output port satisfy

\begin{array}{l} E_{2}^{s i g n a l} = - j κ_{0} τ_{0} [e^{- \frac{1}{2} Γ_{E A M} a_{u} (1 - j α_{u}) L_{E A M}} + e^{- \frac{1}{2} Γ_{E A M} a_{d} (V_{r e a d}) (1 - j α_{d} (V_{r e a d})) L_{E A M}}] E_{1}^{s i g n a l} \\ = r_{E A M - M Z I} (V_{r e a d}) E_{1}^{s i g n a l} \end{array}

(1a)

\begin{array}{l} E_{o u t} = [- κ_{0}^{2} e^{- \frac{1}{2} Γ_{E A M} a_{u} (1 - j α_{u}) L_{E A M}} + τ_{0}^{2} e^{- \frac{1}{2} Γ_{E A M} a_{d} (V_{r e a d}) (1 - j α_{d} (V_{r e a d})) L_{E A M}}] E_{1}^{s i g n a l} \\ = κ_{E A M - M Z I} (V_{r e a d}) E_{1}^{s i g n a l} \end{array}

(1b)

r_{E A M - M Z I} (V_{r e a d})

and

κ_{E A M - M Z I} (V_{r e a d})

are transfer functions for

E_{2}^{s i g n a l}

and

E_{o u t}

of the EAM-MZI switch.

κ_{0}

and

τ_{0}

are coupling and transmission coefficient of the 2 × 2 coupler of the EAM-MZI switch respectively, and related by

κ_{0}^{2} + τ_{0}^{2} = 1

for lossless coupling.

Γ_{E A M}

is the optical confinement factor of the EAM.

a_{u (d)}

and

α_{u (d)}

are loss coefficient and linewidth enhancement factor respectively for the upper and lower EAMs of the EAM-MZI switch, and

L_{E A M}

is the length of the EAMs. The EAM-MZI switch plays a critical role of read operation controlled by the read voltage pulse

V_{r e a d}

loaded on the lower EAM. Initially,

V_{r e a d} = 0

, then

a_{u} = a_{d} = a_{0}

and

α_{u} = α_{d} = α_{0}

, with

a_{0}

and

α_{0}

as the loss coefficient and linewidth enhancement factor of the two EAMs when reversely biased voltage is not loaded. Then we can obtain from Eq. (1)a) and Eq. (1)b) that

r_{E A M - M Z I} (0) = - j 2 κ_{0} τ_{0} e^{- \frac{1}{2} Γ_{E A M} a_{0} (1 - j α_{0}) L_{E A M}}

and

κ_{E A M - M Z I} (0) = (τ_{0}^{2} - κ_{0}^{2}) e^{- \frac{1}{2} Γ_{E A M} a_{0} (1 - j α_{0}) L_{E A M}}

. For memory operation, there must be no readout light before read operation. Hence,

E_{o u t} = 0

when

V_{r e a d} = 0

, then we obtain that

τ_{0} = κ_{0} = \sqrt{0.5}

, and

E_{2}^{s i g n a l} = - j e^{- \frac{1}{2} Γ_{E A M} a_{0} (1 - j α_{0}) L_{E A M}} E_{1}^{s i g n a l}

. If

τ_{0} \neq κ_{0}

, then

E_{o u t} \neq 0

, there will be leakage light output before read operation, and the extinction ratio (ER) of the read out data will be deteriorated. Additionally, we can obtain that

| r_{E A M - M Z I} (0) | = 2 κ_{0} τ_{0} e^{- \frac{1}{2} Γ_{E A M} a_{0} L_{E A M}} < e^{- \frac{1}{2} Γ_{E A M} a_{0} L_{E A M}}

, and

| r_{E A M - M Z I} (0) |

reaches its maximum of

e^{- \frac{1}{2} Γ_{E A M} a_{0} L_{E A M}}

only when

τ_{0} = κ_{0} = \sqrt{0.5}

. Hence, if

τ_{0} \neq κ_{0}

, the required roundtrip gain for gain matching condition will increase, leading to higher bias current and energy consumption. Hence, it is important to design

τ_{0} = κ_{0}

to obtain better performances of the device.

Fig. 1 Scheme of the novel optical memory unit.

Considering a light

E_{i n} (ω)

with angular frequency of ω is injected into the memory unit, the transfer function of light is found as

H (ω) = \frac{E_{1}^{s i g n a l} (ω)}{E_{i n} (ω)} = \frac{- j κ \exp (- j β L_{1}) \exp (- \frac{1}{2} a_{R} L_{1})}{1 - {[G (1 - κ^{2}) \exp (- Γ_{E A M} a_{0} L_{E A M}) \exp (- a_{R} L_{R})]}^{1 / 2} \exp (- j ω T)}

(2)

where

ω T = β L_{R} - Γ_{E A M} a_{0} α_{0} L_{E A M} / 2 - π / 2

. G is the roundtrip optical intensity gain,

a_{R}

and

L_{R} = L_{1} + L_{2}

are the loss coefficient and the length of the ring waveguide except the EAM-MZI switch length,

L_{1}

and

L_{2}

is the length of the right and left parts of the ring waveguide, and T is the roundtrip propagating time of the light. For an optical integral function, the required optical intensity gain G will be

G = \frac{1}{(1 - κ^{2}) \exp (- Γ_{E A M} a_{0} L_{E A M}) \exp (- a_{R} L_{R})}

(3)

Equation (3) is also the gain matching condition for the memory unit acting as an optical integrator element. For the gain matching condition, the roundtrip net gain is

G (1 - κ^{2}) \exp (- Γ_{E A M} a_{0} L_{E A M}) \exp (- a_{R} L_{R}) = 1

. Under the gain matching condition, if an optical pulse is injected into the memory unit, there will be a light step function generated in the memory unit, without light output from the read port. If we need to read out the information from the memory unit, we need to load a read voltage pulse

V_{r e a d} (t)

on the lower EAM of the EAM-MZI switch. Then from Eq. (1)b) we can see

E_{o u t} \neq 0

, hence light will be read out from the output port. Additionally,

\begin{array}{l} | r_{E A M - M Z I} (V_{r e a d}) | = \frac{1}{2} e^{- \frac{1}{2} Γ_{E A M} a_{0} L_{E A M}} | 1 + e^{- \frac{1}{2} Γ_{E A M} [a_{d} (V_{r e a d}) - a_{0}] L_{E A M}} e^{j Γ_{E A M} [a_{d} (V_{r e a d}) α_{d} (V_{r e a d}) - a_{0} α_{0}] L_{E A M}} | \\ < e^{- \frac{1}{2} Γ_{E A M} a_{0} L_{E A M}} = | r_{E A M - M Z I} (0) | \end{array}

(4)

hence, the gain matching condition is destroyed, and the light stored in the memory unit will be erased. Fabrications of the device can be carried out since active microring lasers have been successfully demonstrated [21

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]

,22

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005). [CrossRef]

] and EAMs have been successfully integrated with semiconductor optical amplifiers (SOA) [23

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005). [CrossRef]

] and distributed feedback (DFB) lasers [24

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001). [CrossRef]

Attentions should be paied that the traveling wave effects induced by modulating the EAM to the read output signal are not rigorously considered in our model, but such neglect does not affect the correction of the operation principle and following analysis because such effects are weak and do not impact the main characteristics of the EAM-MZI switch. However, it may slightly influence the dynamics of the EAM-MZI switch, and will further slightly impact the quality of the read out pulses, because for read operation, the memory unit works as a ring resonator modulator with coupling modulation [25

W. D. Sacher and J. K. S. Poon, “Dynamics of microring resonator modulators,” Opt. Express 16(20), 15741–15753 (2008). [CrossRef] [PubMed]

] which determines the quality of the modulated output light pulse.

2.2 Simulation model

The active ring waveguide with multiple quantum wells (MQW) can offer the required gain for the gain matching by a bias current I. To realize the integral function, the active ring resonator must work slightly under the lasing threshold [16

], and the injected light must be also on resonation [18

]. Regarding the noises, only the noises which are on resonation will be amplified and should be considered. Then the resonance light fields propagating along the active ring waveguide with MQW can be described by [26

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001). [CrossRef]

]

\frac{1}{v_{g}} \frac{\partial E_{p}^{C W, C C W}}{\partial t} \pm \frac{\partial E_{p}^{C W, C C W}}{\partial z} = {- j \frac{2 π}{λ_{p}} Δ n + \frac{1}{2} (Γ g (z, t, N, λ_{p}) - α_{s})} \times E_{p}^{C W, C C W} + s_{p}^{C W, C C W}

(5)

Attentions should be paid that the considered noises are lasing modes, hence initially they are on resonation and their round-trip phase shifts will be integer multiple of

2 π

, hence, the propagating term of

- j (2 π / λ_{p}) n_{e q 0} E_{p}^{C W, C C W}

in the light field propagating Eq. (26) is degenerated, with

n_{e q 0}

as the initial mode effective refractive index without noises.

p = 0, \pm 1, \pm 2, \dots \dots

is the mode number, and

p = 0

is assumed to be at the peak lasing mode of the lasing spectral profile where the integral operation should work on. The spectrum is discretized by FSR of

Δ υ = c / [n_{g} (L_{R} + L_{E A M})]

with

n_{g}

as the group refractive index. Here we consider the 2 × 2 couplers as a point for their length can be amounted to the total length of the ring waveguide

L_{R}

, then does not affect the following results.

E_{p}^{C W, C C W}

(m^-3/2) is the traveling optical light field wave propagating in the clockwise (CW) and counterclockwise (CCW) direction,

v_{g}

(m/s) denotes the group velocity,

λ_{p}

is the wavelength of the light field, Γ is the light field confinement factor, N is the carrier density, g (m⁻¹) is the material gain coefficient,

α_{s}

(m⁻¹) is the total losses coefficient and

Δ n

is the refractive index change relative to the initial state and can be evaluated by

Δ n = (d n / d N) Δ N

, where

d n / d N

is the differential of equivalent refractive index with respect to carrier density change

Δ N

s_{p}^{C W, C C W}

represents the amplified spontaneous emission noises propagating in the clockwise (CW) and counterclockwise (CCW) directions.

The ASE noise contribution can be evaluated by a Gaussian-distributed random number generator with a self-correlation function as follows [27

J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed]

]

〈 s_{(C W, C C W)} (z, t, λ_{k}) s^{*}_{(C W, C C W)} (z, t, λ_{k}) 〉 = γ \frac{R_{s p} (z, t, λ_{k})}{d_{z} v_{g}} δ (z - z') δ (t - t') δ (λ_{k} - λ_{k'})

(6)

where γ is spontaneous emission coupling coefficient,

R_{s p}

(s⁻¹m⁻³) is the spontaneous emission rate, and d_z is the length of each subsection introduced by the spatial discretization of the active zone. The material gain g and spontaneous emission rate

R_{s p}

can be evaluated by the two energy band model [28

E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007). [CrossRef] [PubMed]

]

g (ω_{p}) = \frac{c^{2}}{2 n_{1}^{2} ω_{p}^{2} τ} {(\frac{2 m_{e} m_{h h}}{ℏ (m_{e} + m_{h h})})}^{3 / 2} \times {(ω_{p} - \frac{E_{g}}{ℏ})}^{1 / 2} [f_{c} (ω_{p}) - f_{v} (ω_{p})]

(7)

R_{s p} (ω_{p}) = \frac{Δ υ}{π τ} {(\frac{2 m_{e} m_{h h}}{ℏ (m_{e} + m_{h h})})}^{3 / 2} \times {(ω_{p} - \frac{E_{g}}{ℏ})}^{1 / 2} f_{c} (ω_{p}) [1 - f_{v} (ω_{p})]

(8)

where c is velocity of propagation of light in vacuum,

n_{1}

is active region refractive index,

τ = {(A_{r a d} + B_{r a d} N)}^{- 1}

is the radiative carrier recombination lifetime with A_rad and B_rad as the linear and bimolecular radiative recombination coefficient respectively, ℏ is the normalized Planck’s constant,

m_{e}

and

m_{h h}

are the effective mass of an electron in conduction band and a heavy hole in valence band respectively,

f_{c} (ω_{p})

and

f_{v} (ω_{p})

are the Fermi-Dirac distributions which determine the occupation probabilities for the electrons in the conduction band and the valence band respectively.

E_{g}

is the bandgap energy.

The carrier rate equation is described by

\frac{d N (z, t)}{d t} = \frac{I}{e V} - [R_{r a d} (N) + R_{n r a d} (N)] - {\sum_{k = 1}^{N_{d}} Γ v_{g} g (z, t, λ_{k}) | E_{C W} (z, t, λ_{k}) + E_{C C W} (z, t, λ_{k}) |}^{2}

(9)

where I is the bias current,

V = L_{R} w d

is the active layer volume, with w and d as the ring waveguide width and height of active region respectively,

R_{r a d} (N) = A_{r a d} N + B_{r a d} N^{2}

and

R_{n r a d} (N) = A_{n r a d} N + B_{n r a d} N^{2} + C N^{3}

with

A_{n r a d}

B_{n r a d}

and C as the linear nonradiative, bimolecular nonradiative and Auger recombination coefficient respectively.

For the light propagating in the EAM, the loss coefficient

a_{d} (V_{r e a d})

of EAM is assumed to be Lorentzian function depends on wavelength and driving voltage [20

] due to quantum-confined Stark effect. The linewidth enhancement factor is defined by

α_{d} (λ_{p}, V_{r e a d}) = (4 π / λ_{p}) [Δ n (λ_{p}, V_{r e a d}) / Δ a (λ_{p}, V_{r e a d})]

, with

Δ n (λ_{p}, V_{r e a d})

and

Δ a (λ_{p}, V_{r e a d})

as the refractive index and absorption change respect to that when the EAM is zero biased. And

Δ n (λ_{p}, V_{r e a d})

can be evaluated by the Kramers-Kronig relation.

Finally, light field in the input 2 × 2 coupling region is governed by

[\begin{array}{c} E_{R 2} \\ E_{t} \end{array}] = [\begin{array}{c} τ & - j κ \\ - j κ & τ \end{array}] [\begin{array}{c} E_{R 1} \\ E_{i n} \end{array}]

(10)

where κ is the coupling coefficient and τ is the transmittance related to κ by

τ^{2} + κ^{2} = 1

for lossless coupling.

3. Numerical results

3.1. Step function response performances of the optical memory unit

A light step function is basic for the memory unit based on the optical integrator [18

]. The performances of the light step function response to the input data pulse directly impacts the storage performances of the memory unit. A memory unit based on the optical integrator with an ideal light step function can obtain infinite storage time, with invariable readout power for read operation at different read time. As the light step function of the optical integrator based memory is deteriorated, the ability of storage time will be greatly affected as analyzed below. Hence, we first analyze the step function response performances of the memory unit under gain matching condition, i.e. slightly under lasing threshold. Based on the input 2 × 2 coupling equation Eq. (10), light propagation equation Eq. (5), and transfer function Eq. (1) of the EAM-MZI switch, a spatial discretization and time-dependent transfer matrix method (TMM) is applied to calculate the dynamics of the memory unit. The parameters referred above are shown in Table 1 . below.

Table 1 Parameters used in the simulation.

Symbol	Parameter	Value
Parameters of the ring waveguide
L_R	Length of the total ring waveguide	200μm
w	Waveguide width of the active region	1.8μm [29 I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef] ]
d	Waveguide height of the active region	0.3μm [29 I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef] ]
n_g	Waveguide group index	3.5 [29 I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef] ]
n₁	Active region refractive index	3.17
$α_{s}$	Material loss	2 × 10³m⁻¹ [29 I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef] ]
Γ	Optical field confinement factor of the active region	0.226 [30 G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007). [CrossRef] ]
$d n / d N$	Differential of equivalent refractive index with respect to carrier density change	−1.34 × 10⁻²⁶m⁻³ [28 E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007). [CrossRef] [PubMed] ]
κ	Field coupling coefficient of the input 2 × 2 coupler	0.2
γ	Spontaneous emission coupling coefficient	10⁻⁴ [31 Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000). [CrossRef] ]
A_rad	Linear radiative recombination coefficient	1 × 10⁷s⁻¹ [27 J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed] ]
B_rad	Bimolecular radiative recombination coefficient	5.6 × 10⁻¹⁶ m³s⁻¹ [27 J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed] ]
A_nrad	Linear nonradiative recombination coefficient	3.5 × 10⁸s⁻¹ [27 J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed] ]
B_nrad	Bimolecular nonradiative recombination coefficient	0.0 × 10⁻¹⁶ m³s⁻¹ [27 J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed] ]
C	Auger recombination coefficient	3.0 × 10⁻⁴¹ m⁶s⁻¹ [27 J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed] ]

Parameters of EAM-MZI switch
L_EAM	Length of the EAM	100μm
Γ_EAM	Optical field confinement factor of EAM	0.075 [20 K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef] ]
$a_{p 0}$	Peak absorption coefficient	3.0 × 10⁵ m⁻¹ [20 K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef] ]
$λ_{p 0}$	Wavelength with the peak absorption	1.52μm
n_g	Waveguide group index	3.5
P	Cauchy principal value	1 [20 K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef] ]
V_on	On state voltage for the EAM	0V

The system is chosen to work at

λ_{0} = 1.55 μ m

by adjusting the bandgap energy. The peak wavelength of the gain spectrum is adjusted slightly blue shifted from

1.55 μ m

. As the noises are amplified, carriers will be consumed, leading to red shift of the gain spectrum [26

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001). [CrossRef]

]. To calculate the threshold current I_th , the noises of

E_{p}^{C W}

and

E_{p}^{C C W}

are neglected. The gain matching condition gives the required gain, and further associated with the two energy band based gain model, the required carrier density N is given. Then, combining with carrier rate equation Eq. (9), the threshold current I_th will be solved numerically. With the simulation parameters given in Table 1., a threshold current of 21.884mA is obtained for

1.55 μ m

peak lasing. In fact, this current is slightly lower than the real threshold as the noises will consume the carriers, hence the calculated threshold current is just the integral operation current.

Under the calculated threshold current, the memory unit is stimulated by the spontaneous emission, and iterated until the carrier density is stable. Figure 2 shows the lasing mode spectra on threshold. At this time, and the roundtrip net gain is calculated to be 0.9998, slightly lower than 1.

Fig. 2 Lasing modes spectra at threshold of the memory unit. The integral operation wavelength is at

λ_{0} = 1.55 μ m

Figure 3 shows the light step function response performances in the memory unit of a 25ps FWHM Gaussian optical pulse is injected into the memory unit under different peak power

P_{p e a k}

. We can see that for

P_{p e a k} = 0.01 m W

low power light pulse injection case, a light field of only 0.05mW is excited in the ring resonator as shown in Fig. 3(d), and little carriers are consumed, the roundtrip net gain is decreased from 0.9998 to 0.9983 as shown in Fig. 3(a). Hence, the gain matching condition is not seriously impacted, and the light step function in the memory unit approaches to the ideal step function response is shown in Fig. 3(d). However, as the injection power increases, more carriers are consumed. For

P_{p e a k} = 0.1 m W

light pulse injection case, a higher light field of 0.5mW is excited in the ring resonator after the input pulse is injected at time of 200ps as shown in Fig. 3(e), more carriers are consumed, and the gain matching condition is deteriorated from 0.9998 to 0.9909 at time of 600ps as shown in Fig. 3(b), leading to the step function performance deviates from the ideal performance is shown in Fig. 3(e). After 600ps, as light in the memory unit decreases, little carriers are consumed, then carriers and roundtrip net gain are recovered by the injected current. For

P_{p e a k} = 1 m W

light pulse injection, higher light field of about 4.8mW is built in the memory unit, carriers are consumed faster, leading to faster drop from 0.9998 to 0.962 of the roundtrip net gain and faster deterioration of the gain matching condition as shown in Fig. 3(c), hence light decreases faster than

P_{p e a k} = 0.1 m W

case as shown in Fig. 3(f). After 300ps, carriers begin to recover by the injected current.

Fig. 3 A 25ps FWHM Gaussian optical pulse is injected into the novel memory unit. (a), (b), (c) Roundtrip net gain dynamics for input peak power of 0.01mW, 0.1mW and 1mW respectively. (d), (e), (f) Step function response performances of the memory unit for input peak power of 0.01mW, 0.1mW and 1mW respectively. The dashed lines are ideal step function response, and solid lines are simulated results.

3.2. Memory operation of the optical memory unit

For read operation of the memory unit, a reversely biased voltage pulse should be loaded on the lower EAM of the EAM-MZI switch. Figure 4 shows the memory operation for a 25ps FWHM Gaussian light pulse under different peak power

P_{p e a k}

. Taking

P_{p e a k} = 0.01 m W

for example, as the input pulse shown in Fig. 4(b) is injected into the optical memory unit at time of 100ps, a light step function is responded in the memory unit as shown in Fig. 4(c), and there is no light output from the memory unit as shown in Fig. 4(c) until we need to read out the information (assumed to be at time of 1100ps for 1000ps storage time). At time of 1100ps a reversely biased voltage pulse with peak voltage of 4V is loaded on the lower EAM of the EAM-MZI switch as shown in Fig. 4(a). After that, there will be a light pulse with peak power of about

P_{o u t}^{p e a k} = 1.5 μ W

read out from the output port as shown in Fig. 4(d), and the light in the memory unit is erased as shown in Fig. 4(c). As analyzed before, for different peak power

P_{p e a k}

of the input light pulse, there will be different step functions respond in the memory unit as shown in Fig. 4(c), (g) and (k), hence read out pulses with different peak power

P_{o u t}^{p e a k}

will be obtained as shown in Fig. 4(d), (h) and (l).

Fig. 4 Memory operation of a 25ps FWHM Gaussian light pulse with different peak power P_peak .

Figure 5 shows the different peak power

P_{o u t}^{p e a k}

of the read out pulse versus input peak power

P_{p e a k}

. We can see that initially when the input peak light power is weak, the output peak power increases as the input peak power increases to about 0.15mW. This is for the reason that when the input light is weak, a near ideal step function is obtained in the memory unit, and as the input power increases, more light will be stored in the memory unit, hence the read out peak power increases. However, when an input light pulse higher than 0.15mW peak power is injected into the memory unit, as the

P_{p e a k}

increases, the carriers will be consumed faster, leading to the gain matching condition be destroyed faster, and the step function be more deteriorated. Hence the light stored in the memory unit begins to decrease, and the read out peak power decreases. The curve of the read out peak power versus input peak power is not smooth, which is caused by the noises.

Fig. 5 Output peak power

P_{o u t}^{p e a k}

versus input peak power

P_{p e a k}

From the step response performances of the memory unit shown in Fig. 3(d), (e) and (f), we can see that as time increases, the light stored in the memory unit gradually decreases depend on the input peak power

P_{p e a k}

, hence the read out power will also decrease. Figure 6(a) shows the normalized read out power at different time for different input peak power

P_{p e a k}

. We can see that the normalized read out power decreases as time increases, and as

P_{p e a k}

increases, the normalized read out power decreases faster, for the reason that higher

P_{p e a k}

leads to faster gain matching condition deterioration. To characterize the ability of storage time of the memory unit, we define the effective storage time as the time when the normalized read out power decreases to 0.5. Figure 6(b) shows the effective storage time versus different input peak power

P_{p e a k}

. We can see that the effective storage time decreases as

P_{p e a k}

increases. When

P_{p e a k}

is about 0.01mW, the effective storage time can be as long as 2500ps. Hence, the proposed memory unit can work better for lower power light pulse storage. Though such 2500ps storage time is shorter than the previously reported the longest storage time of 17μs in on-chip photonic memory unit [8], our proposed device can work on room temperature compare to ultra-low temperature required in [8]. What’s more, such 2500ps storage time is much longer than the currently reported the longest delay time of 500ps of the on-chip optical delay lines [32

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]

] for high speed data stream, and it can be further improved by improving the integral performances. From the previous analysis, we can see that the lower light field power is built in the memory unit, the less carriers will be consumed, and the less the gain matching condition will be disturbed, then the better step function and storage performances of the device will be gotten. This gives us a tenet to design device and select the work condition to ensure the gain matching condition is not seriously affected. A smaller device size means a smaller sampling time, leading to higher light power built in the ring resonator. On the other hand, for a given size of the device, higher input peak power or wider pulse width also result in higher light power built in the ring resonator. To obtain better work performances, these parameters should be considered and optimized in practice. Additionally, to obtain better step function and further improve the storage performances, other gain material may be explored. Recently, an optical integrator based on silicon ring resonator utilizing Raman gain for satisfying gain matching condition has been analyzed [33

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Raman based silicon photonic integrator,” to be presented at the 8th Pacific Rim Conference on Lasers and Electro-Optics (CLEO®/Pacific Rim 2009), Shanghai, China, 30 August - 3 September, 2009.

], and it performs excellent step function characteristics. We believe that it is promising to obtain the optical integrator based memory unit with much longer storage time.

Fig. 6 (a) The normalized read out power at different read time of read operation for different P_peak . (b) The effective storage time versus different input peak power P_peak .

The energy consumption per bit can be evaluated by the energy consumption by bias current for gain matching condition and the voltage pulse loaded on the EAM for read/write operation. With the biasing threshold current of 21.8mA and the typical electric potential between the anode and cathode of about 1.0 Volt, the energy consumption for gain matching condition is about 1.09pJ/bit for data of 20Gbit/s with 25ps pulse width. The energy consumption per bit of the EAM can be calculated by

E_{E A M} = (1 / 2) C_{c a p} V_{p p}^{2}

[34

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008). [CrossRef]

] with

C_{c a p}

and

V_{p p}

as the capacitance of the EAM and peak-to-peak driving voltage for read/write operation respectively. With a capacitance

C_{c a p}

as low as 0.1pF [24] and

V_{p p}

of 4V in our simulation, the energy consumption per bit of the EAM is approximately 0.8pJ/bit. Hence, the total energy consumption per bit is expected to as low as 1.89 pJ/bit. Such energy consumption per bit is comparable with the slow light buffer with an energy consumption per bit of 2~3 pJ/bit for around 1000 bits buffering [19]. What’s more, such energy consumption per bit can be further reduced by reducing the threshold current, working with higher bit rate with narrower pulse width, and designing the more effective EAM with lower capacitance [34] and peak-to-peak driving voltage.

3.3. Influences of the coupling coefficient of the EAM-MZI switch

The previous analyses are based on the ideal assumption that the coupling coefficient of the EAM-MZI

κ_{0} = \sqrt{0.5}

to totally avoid leakage light output before read operation. However, in practice, there will be technique error leading

κ_{0}

to deviate from

\sqrt{0.5}

, and further impacting the memory performances. Figure 7 shows the influences on the memory operation and threshold current by coupling coefficient

κ_{0}

. We can see that for

κ_{0} = \sqrt{0.5}

, we get an ideal elimination of the leakage light as shown in Fig. 7(a) and the lowest threshold current as shown in Fig. 7(b). However, as previously analysis in section 2.1, as coupling coefficient

κ_{0}

deviates from

\sqrt{0.5}

, there will be more leakage light output before read operation as shown in Fig. 7(a), and results in higher bias current as shown in Fig. 7(b). However, the ER still keep higher than 10dB in a coupling coefficient range of

\sqrt{0.48} \sim \sqrt{0.52}

. Hence, to ensure good performances of our proposed memory unit, a power coupling coefficient tolerance

Δ κ_{0}^{2}

of the EAM-MZI of about 0.04 is expected.

Fig. 7 (a) Normalized read out power for different coupling coefficient

κ_{0}

. (b) Threshold current versus different power coupling coefficient

κ_{0}^{2}

4. Conclusion

We have proposed and analyzed a novel loadable and erasable memory unit based on active microring resonator associated with EAM-MZI switch for read control on III-V material system. Based on the two energy band gain model, light propagation equation in the active ring waveguide, and transfer function of the EAM-MZI switch, the integral performances and memory operations are simulated and analyzed in detail for different input power of the injected light pulse. Simulations show that this memory unit can work well for low power high speed light pulse. If this novel memory unit is cascaded connected and densely integrated, it has the potential for high speed low light power large scale data stream storage.

Acknowledgement

This research was sponsored by the National Natural Science Foundation of China (Grant No. 60577007), the National Basic Research Program of China (Grant No. 2006CB302805), and the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-04-0715).

References and links

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2.	J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22(5), 1062–1074 (2005). [CrossRef]
3.	Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]
4.	Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007). [CrossRef]
5.	A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004). [CrossRef]
6.	Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006). [CrossRef]
7.	S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007). [CrossRef]
8.	S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999). [CrossRef] [PubMed]
9.	Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008). [CrossRef]
10.	M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. 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]
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27.	J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed]
28.	E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007). [CrossRef] [PubMed]
29.	I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef]
30.	G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007). [CrossRef]
31.	Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000). [CrossRef]
32.	F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
33.	Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Raman based silicon photonic integrator,” to be presented at the 8th Pacific Rim Conference on Lasers and Electro-Optics (CLEO®/Pacific Rim 2009), Shanghai, China, 30 August - 3 September, 2009.
34.	J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008). [CrossRef]

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(200.4490) Optics in computing : Optical buffers
(200.4560) Optics in computing : Optical data processing
(210.4680) Optical data storage : Optical memories
(230.5590) Optical devices : Quantum-well, -wire and -dot devices

ToC Category:
Optics in Computing

History
Original Manuscript: May 6, 2009
Revised Manuscript: June 18, 2009
Manuscript Accepted: June 18, 2009
Published: July 13, 2009

Citation
Yunhong Ding, Xiaobei Zhang, Xinliang Zhang, and Dexiu Huang, "Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit," Opt. Express 17, 12835-12848 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12835

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References

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002). [CrossRef]
J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22(5), 1062–1074 (2005). [CrossRef]
Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]
Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007). [CrossRef]
A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004). [CrossRef]
Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006). [CrossRef]
S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007). [CrossRef]
S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999). [CrossRef] [PubMed]
Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008). [CrossRef]
M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. 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]
N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995). [CrossRef]
N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006). [CrossRef] [PubMed]
N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007). [CrossRef] [PubMed]
J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008). [CrossRef]
M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett. 33(12), 1348–1350 (2008). [CrossRef] [PubMed]
Y. P. R. Slavík, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic Temporal Integrator,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), CPDB3 http://www.opticsinfobase.org/abstract.cfm?URI=URI=CLEO-2008-CPDB2003 .
N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006). [CrossRef]
Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008). [CrossRef]
R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008). [CrossRef]
K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef]
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]
S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005). [CrossRef]
L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005). [CrossRef]
H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001). [CrossRef]
W. D. Sacher and J. K. S. Poon, “Dynamics of microring resonator modulators,” Opt. Express 16(20), 15741–15753 (2008). [CrossRef] [PubMed]
M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001). [CrossRef]
J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006). [CrossRef] [PubMed]
E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007). [CrossRef] [PubMed]
I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef]
G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007). [CrossRef]
Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000). [CrossRef]
F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Raman based silicon photonic integrator,” to be presented at the 8th Pacific Rim Conference on Lasers and Electro-Optics (CLEO®/Pacific Rim 2009), Shanghai, China, 30 August - 3 September, 2009.
J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008). [CrossRef]

Azaña, J.
Beals, M.
Bernardis, S.
Bian, J.
Bichler, M.
Binh, L. N.
Binsma, H.
Boucher, Y.
Boyd, R. W.
Cheng, J.
Chi, N.
Connelly, M. J.
Danckaert, J.
De Vries, T.
Den Besten, J. H.
Ding, Y. H.
Donati, S.
Dong, P.
Dorren, H. J.
Fu, S. N.
Giuliani, G.
Gong, Y. D.
Hamann, H. F.
Hanlim, L.
Heebner, J. E.
Hill, M. T. D.
Ho, S. T.
Hou, L. P.
Huang, D. X.
Jaeho, H.
Jaehoon, L.
Jichai, J.
Kapsalis, A.
Kawakami, Y.
Kawanishi, H.
Khoe, G. D.
Khurgin, J. B.
Kim, S. S.
Kimerling, L. C.
Kotthaus, J. P.
Laybourn, P. J. R.
Leijtens, X. J.
Li, Y. J.
Lim, M. S.
Lipson, M.
Liu, A. M.
Liu, J.
McNab, S. J.
Michel, J.
Miglierina, R.
Mikroulis, S.
Mineo, N.
Murai, H.
Muriel, M. A.
Ngo, N. Q.
Ning, G.
O’Boyle, M.
Oei, Y. S.
Oh, T. W.
Park, J.
Park, S.
Pomerene, A.
Poon, J. K. S.
Preciado, M. A.
Quoc Ngo, N.
Riding, J. L.
Sacher, W. D.
Scire, A.
Sekaric, L.
Sharaiha, A.
Shibuya, Y.
Shum, P.
Smalbrugge, B.
Smit, M. K.
Sorel, M.
Stamataki, I.
Sun, R.
Syvridis, D.
Tucker, R. S.
Verschaffelt, G.
Vlasov, Y.
Vlasov, Y. A.
Wada, H.
Wang, L. F.
Wang, L. W.
Wang, W.
Wang, Z. R.
Wegscheider, W.
Wixforth, A.
Wu, C. Q.
Xia, F. N.
Xu, Q. F.
Yamada, K.
Yamauchi, Y.
Yonggyoo, K.
Yu, S. Y.
Yuan, G. H.
Zhang, X. B.
Zhang, X. L.
Zhou, E. B.
Zhou, F.
Zhu, H. L.
Zimmermann, S.

Appl. Opt.

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006). [CrossRef] [PubMed]

Electron. Lett.

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004). [CrossRef]

IEEE J. Lightwave Technol.

Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006). [CrossRef]
R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008). [CrossRef]
N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006). [CrossRef]

IEEE J. Quantum Electron.

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001). [CrossRef]
I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006). [CrossRef]
Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000). [CrossRef]
K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef]
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]
S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007). [CrossRef]

IEEE Photon. Technol. Lett.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005). [CrossRef]
H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001). [CrossRef]
Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008). [CrossRef]

J. Mod. Opt.

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002). [CrossRef]

J. Opt. Soc. Am. B

J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22(5), 1062–1074 (2005). [CrossRef]

Nat. Photonics

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008). [CrossRef]

Nat. Phys.

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007). [CrossRef]

Nature

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]
M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. 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]

Opt. Commun.

N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995). [CrossRef]
S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007). [CrossRef]
Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008). [CrossRef]

Opt. Express

Opt. Lett.

Science

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999). [CrossRef] [PubMed]

Other

Y. P. R. Slavík, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic Temporal Integrator,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), CPDB3 http://www.opticsinfobase.org/abstract.cfm?URI=URI=CLEO-2008-CPDB2003 .
Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Raman based silicon photonic integrator,” to be presented at the 8th Pacific Rim Conference on Lasers and Electro-Optics (CLEO®/Pacific Rim 2009), Shanghai, China, 30 August - 3 September, 2009.

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