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736 CHINESE OPTICS LETTERS / Vol. 6, No. 10 / October 10, 2008

Slow and fast light in quantum-well and quantum-dot

semiconductor optical amplifiers

Invited Paper

Piotr Konrad Kondratko, Akira Matsudaira, Shu-Wei Chang, and Shun Lien Chuang

Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA

Received June 16, 2008

Slow and fast light in quantum-well (QW) and quantum-dot (QD) semiconductor optical amplifiers (SOAs)

using nonlinear quantum optical effects are presented. We demonstrate electrical and optical controls of

fast light using the coherent p opulation oscillation (CPO) and four wave mixing (FWM) in the gain regime

of QW SOAs. We then consider the dependence on the wavelength and modal gain of the pump in Q W

SOAs. To enhance the tunable photonic delay of a single QW SOA, we explore a serial cascade of multiple

amplifiers. A model for the number of QW SOAs in series with variable optical attenuation is developed

and matched to the experimental data. We demonstrate the scaling law and the b andwidth control by

using the serial cascade of multiple QW SOAs. Experimentally, we achieve a phase change of 160

◦

and

a scaling factor of four at 1 GHz using the cascade of four QW SOAs. Finally, we investigate CPO and

FWM slow and fast light of QD SOAs. The experiment shows that the bandwidth of the time delay as a

function of the modulation frequency changes in the absorption and gain regimes due to the carrier-lifetime

variation. The tunable phase shift in QD SOA is compared between the ground- and first excited-state

transitions with different modal gains.

OCIS codes: 230.4320, 270.1670, 250.5980.

doi: 10.3788/COL20080610.0736.

1. Introduction

A compact, electrically a nd optically tunable optical

buffer which o perates at room temperatur e is one of the

essential elements in the future optical communication

system. An all optical buffer eliminates the need for

electrical-to-optical and optical-to-electrical conversions

of the transmitted signal. It can provide data s torage to

buffer optical signals during the traffic jam of informa-

tion flow. These requirements stimulate the investigation

of the slow and fast light. Since most of the slow- and

fast-light phenomena are based on the dispersion and

phase tuning from materials or des igned spatial struc-

tures, they can also be applied to other areas such as

dispersion compensation (pulse shaping) and the o ptical

control of microwave a ntenna arrays.

There are several approaches to implement slow a nd

fast light. The conventional one is to switch the sig-

nal pulse into a fib e r loop

[1]

. This scheme can provide

high bandwidth and multi-bit delay but requires phys-

ical switching of the signal into the fiber loop. Since

the length of the fiber is fixed, the time delay is fixed.

Thus, only discrete rather than continuous tuning is pos-

sible by using different lengths of fiber s. The second

type is based on the exotic quantum or nonlinear optical

interactions between light and matter such as e le c tro-

magnetically induced transparency (EIT) and coherent

population oscillation (CPO)

[2−4]

. A large slowdown

factor is the most spectacular feature of this approach.

However, some examples in this category require ex-

treme operation conditions such as low temperature or

bulky experimental setup. Also, the bandwidth is lim-

ited by the co rresponding dynamics of the system, and in

many cases is too narrow to be used in real applications.

The third type is to utilize the filter effect from the

designed spa tial structure such as ring resonators

[5]

photonic-crystal waveguides

[6]

. This approach can pro-

vide the necessary tunability and bandwidth engineering.

However, the shortcoming from dispersion still requires

improvement.

For c ompact integration with active optoelectronic de-

vices, it is desirable to implement optical buffers on

semiconductors, which can als o provide electrical and

optical control of slow and fast light. The basic working

principle of slow or fast light is to manipulate the group

velocity of the wave packet by the engineering of linear

dispersion or nonlinear propagation. An example for the

first category which is commonly used in semiconduc-

tors is CPO, and an instance of the second type is the

four wave mixing (FWM), which is usually a ccompanied

with the presence of CPO. Compared with other control

schemes, semiconductor slow-light devices can offer not

only optica l

[7,8]

but also electrical control based on the

forward current injection or reverse voltage bias

[9−16]

This featur e makes the semiconductor unique among

other slow- a nd fa st-light schemes.

In this letter, we first discuss the fas t light based on

CPO and FWM in quantum wells (QWs). The exper-

iments of electrical and optical control of the fast-lig ht

system are then presented with new data. Wavelength

and modal gain dependences of the pump laser are ob-

served and modeled. We show that our theoretical re-

sults agree very well with experiments. Furthermore,

we demonstrate the scaling law by using casc aded QW

semiconductor optical amplifiers (SOAs) operating above

transparency. Finally, slow and fast light in quantum-dot

(QD) SOAs are investigated using absorption and gain

by changing the bias current.

2. Slow and fast light via CPO and FWM

Coherent population osc illation is the bea ting of the

carrier density induced by an intense pump and pro be

signal. Usually, the pump is a continuous-wave (CW)

1671-7694/2008/100736-07

 2008 Chinese Optics Letters

October 10, 2008 / Vol. 6, No. 10 / CHINESE OPTICS LETTERS 737

laser beam with a frequency close to the transition en-

ergies of the upper and lower states. In semiconductor

nanostructures, such states can be the first conduction

and heavy-hole (HH) valence subbands in QWs, or the

ground conduction and valence states of QDs. The in-

tense pump light saturates the abso rption or gain of the

material, depending on whether the device is biased in

the absorption or gain re gime. Suppose that the sig-

nal with a frequency detuning from the pump frequency

is incident into the material. If the detuning is much

larger than the inverse of the population lifetime, the

induced population beating cannot follow the high-speed

modulation and will have a small oscillation magnitude.

In this case, the signal simply experiences the saturated

gain and absorption. On the other hand, if the frequency

detuning is small, the magnitude of the induced beating

can be significant, and par t of the sig nal energy can be

converted into the population beating without being dis-

sipated or amplified by the medium. Corres po ndingly,

there will be an absorption or ga in dips centered at the

pump frequency on the absorption/gain spectrum. From

the Kramers Kronig relation, a positive-slop e (negative-

slope) variation of the refractive-index spectra will ac-

company this absorption (gain) dip. The corresponding

group velocity is inversely pr oportional to the group

index n

, which is related to this slope:

n + ω

∂n

∂ω

, (1)

where c is the vacuum speed of the light, n is the real

part of the refractive index. In the absorption regime,

the induced slope ∂n/∂ω is pos itive (a larger group index

), and thus slow light is obtained. In co ntrast, the neg-

ative slope in the gain regime (a smaller n

) leads to fast

light. The above picture des crib e s the linear respons e

exp erienced by the signal. In addition, the induced pop-

ulation beating can also generate a conjugate signal via

the nonlinear FWM. The effect of FWM is important in

the gain regime and cannot be discarded.

For CPO and FWM based on s e miconductor mater i-

als, there are two main effects which can influence the

slow and fast light when the electrica l curre nt injection

or reverse voltage bias is applied to the semiconductor

nanostructure. One is the change of the electronic-state

occupation, which affects the background gain or absorp-

tion. The other is the bias-dependent carrier dynamics,

which changes the linear and nonlinear susceptibilities ex-

perienced by the signal. The former determines whether

the signal experiences slowdown or speedup w hile both

factors play a significa nt role on the amount of time de-

lay, pulse broadening, and distortion.

Let us take a QD SOA as an example. Slow light is

present in the reverse-bias regime and the small forward-

bias r e gime before the zero modal gain is reached. Fur-

thermore, the recombination lifetimes (carrier dynamics)

in the forward and reverse bias regimes are different

because in the reverse-bias regime, the carriers can be

swept out of QDs by the applied electric field and thus

lead to a shorter lifetime

[11,13]

. The shorter lifetime re-

sults in a broader bandwidth for the signal, but also less

amount of time delay. O n the other hand, the lifetime

is pretty constant in the forward-bias regime before the

transparency is reached, mainly due to a constant radia-

tive lifetime. This indicates that different mechanisms

corresponding to distinct carrier dy namics may be in-

volved in the slow-light phenomena.

The even higher current injection into QDs above the

transparency level brings the slow-light regime into the

fast-light regime

[15]

as a result of the gain dip rather than

absorption dip. However, in the gain regime, in addition

to CPO, FWM also becomes important because both of

the signal and generated conjugate can be amplified and

converted to each other in the SOA. In general, for a

sinusoidally-modulated signal, the phase shift, which is

related to the amount of time advance in the fast-light

regime, is influenced by CPO and FWM simultaneously,

and their effects cannot be separated. In the gain regime,

other nonradiative recombination mechanisms also come

into play, which le ad to a shorter carrier lifetime

[15]

. The

faster carrier dynamics will again influence the a mount

of advance in the fast-light regime.

The slow and fast light in other systems such as QW or

bulk SOAs follow similar mechanis ms , but their different

carrier dynamics can show distinct characteristics of slow

and fast light. One of the key factors is the linewidth en-

hancement factor

[17]

. The linewidth enhancement factor

can lead to skewed lineshape of the gain dip, a nd as a

result, both slow and fast light can be obser ved based on

CPO in the gain regime

[18]

. Note that the effect of the

linewidth enhancement factor is not always present in the

exp eriment. For example, in the phase-shift experiment

of the sinusoida lly -modulated signal, the phase advance

of the modulated signal does not reflect the effect of the

linewidth enhancement factor

[19]

3. Slow and fast light experiment

Figure 1 shows the experimental setup used in the mea-

surements of CPO a nd FWM slow and fast light in the

SOA. A strong pump beam from the distributed-feedback

(DFB) laser diode is modulated by an external modulator

with a continuously variable radio frequency (RF) signa l

from a network analyzer. A modulated signal is coupled

into the SOA by fiber lense s. The magnitude and the

phase differences of RF modulated signal are measured

by the network analy z e r at different current injections

into the SOA. An erbium-doped fiber amplifier (Amp)

is inserted to preamplify the modulated input signal so

that the signal in the a bsorption regime ca n be mea-

sured. The gain of this Amp is kept constant thro ughout

the exper iment. The experiment is performed at room

Fig. 1. Experimental setup used in measuring single modu-

lated slow and fast light. VOA: variable optical attenuator;

PD: photodetector; PC: polarization controller; ISO: isolator.

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