ThB1
10.30–10.45
80-GHz Intrinsic 3-dB Bandwidth of Directly Modulated
Semiconductor Lasers under Optical Injection Locking
Erwin K. Lau, Xiaoxue Zhao, Connie Chang-Hasnain, Ming C. Wu
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA
Tel: +1-510-643-0808. Fax: +1-510-643-6637. Email: elau@eecs.berkeley.edu
Abstract: We identify key parameters that control the low-frequency damping commonly
observed in optical injection-locked lasers. We demonstrate, experimentally and theoretically, that
by biasing the slave laser at higher current, the impact of this damping can be eliminated. A
record-high 80-GHz intrinsic 3-dB frequency is achieved.
Introduction
Directly modulated semiconductor lasers are compact and low-cost, making attractive sources for optical
communication systems. Despite much research, however, the maximum 3-dB bandwidth, f3dB, is limited to 30-40
GHz by relaxation oscillation, damping, and nonlinear gain compression [1,2]. Optical injection locking has been
shown to dramatically increase the resonance frequency of directly modulated lasers. Resonance frequencies as high
as 72 GHz have been observed [3,4]. However, their bandwidth can be significantly lower than the resonance. In
this paper, we identify the key parameter that results in low bandwidth. We experimentally demonstrate an intrinsic
3-dB frequency of 80 GHz in injection-locked vertical cavity surface-emitting lasers (VCSELs). We also derive an
analytical expression for the maximum 3-dB frequency of optical injection-locked lasers, showing bandwidths
greater than 150 GHz are achievable.
Theory
The resonance frequency of injection-locked lasers can be greatly enhanced by increasing the injection ratio, R,
and detuning frequency, Δf [5]. While the resonance frequency can be greatly enhanced, the bandwidth of the
directly-modulated injection-locked laser has suffered due to a first-order pole ωP in the transfer function
1
1
2
H (ω ) ≈
,
(1)
2
2
1 + (ω ω P ) 1 − (ω ω ) 2 + γω ω 2 2
R
R
where ωR is the resonance frequency and γ is the damping frequency (the zero is high frequency and is neglected).
Thus, despite having greatly enhanced resonance frequencies, the bandwidth of previous experiments have been
limited by ωP, which has not been well-understood. Recently, we have developed physical insight to the nature of
this pole, giving concrete design rules in order to maximize its frequency [5]. The approximate value of ωP is
⎛
α ⎞⎟
(2)
gS ,
ω P ≈ γ N + ⎜1 +
⎜ τ pω R ⎟ 0
⎝
⎠
where γN is the carrier recombination rate, α is the linewidth enhancement parameter, τP is the photon lifetime, g is
the linear gain rate, and S0 is the photon number. The pole frequency is proportional to the carrier recombination
rate, enhanced by stimulated emission, gS0. Thus, the most straight-forward way to improve the frequency of the
pole is to increase the slave laser current bias, which increases the photon number.
[
] (
20
100
0
fP [GHz]
Frequency
[GHz]
RF Response [dB]
f
P
10
9Ith
-10
5Ith
-20
-30
1.3Ith
-40
-50
0
)
80
3dB
f
3dB,FR
60
40
20
0
1 2
20
40
60
80
100
Modulation Frequency [GHz]
(a)
f
4
6
8
Bias Current, I/I
I/Ith
th
(b)
10
Fig. 1. (a) Experimental VCSEL (dotted) and theoretical (solid) frequency responses of optical injection-locked VCSEL at different DC bias
currents. 3-dB frequencies of 1.4 and 80 GHz for the experimental curves, respectively, are shown in circles. (b) Extracted first-order pole
frequencies (fP), with corresponding 3-dB frequencies (f3dB). Experimental free-running 3-dB frequencies (f3dB,FR) also marked.
978-1-4244-1783-4/08/$25.00©2008 IEEE
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Experiment
In order to demonstrate this bandwidth enhancement, we directly modulated a 1.55-µm vertical-cavity surfaceemitting laser (VCSEL). We changed the bias current to the slave while maintaining a constant injection ratio (~1213 dB) and resonance frequency (68 GHz). Fig. 1(a) shows the experimental VCSEL frequency response curves
(dotted) for 1.3× and 5×Ith, plotted after de-embedding the RC parasitic pole, which we found to be 16 GHz. The RC
pole was determined to be consistent by a fit over a wide range of resonance frequencies. The free-running output
powers were -11 and -0.86 dBm, respectively. We observed an increase in the intrinsic 3-dB frequency from 1.5
GHz to 80 GHz. Theoretical curves (solid), based on a small-signal analysis of the rate equations [5], match well to
the experimental curves. An additional theoretical frequency response curve at 9×Ith is given, showing the clear
trend of bandwidth enhancement with increasing slave laser bias current. With a bias of ≥ 5×Ith, the 3-dB bandwidth
extends beyond the resonance frequency, and we can achieve an intrinsic 3-dB bandwidth of 80 GHz. The extracted
experimental pole frequencies are shown in Fig. 1(b). The figure shows that a pole enhancement of only ~22 GHz
(by biasing to 5×Ith) is needed to achieve the 80-GHz 3-dB bandwidth. With a higher power master laser, we expect
to push the bandwidth to higher frequencies. The electrical parasitics may be overcome with superior packaging
and/or laser design.
Maximum 3-dB Bandwidth
In order to determine the maximum possible bandwidth enhancement of an injection locked laser, we analyze the
bandwidth of the transfer function shown in (1). This function is complicated to analyze with respect to injection
locking bias conditions, but a few key observations can be made. First, the first-order pole fp decreases as resonance
frequency increases. Therefore, it is important to balance the enhanced resonance frequency with obtaining a large
fp. However, increasing slave laser bias and injection ratio increases both the maximum resonance frequency and the
first-order pole. So, it is important to increase both bias and master laser power.
The maximum bandwidth would occur when damping equals zero. To obtain an estimate of the maximum
bandwidth, we calculate the bandwidth at this simple case via Eq. (1). This results in a closed-form solution for both
the resonance frequency and bandwidth:
f R = f P 2 (3 3 − 5) ≈ 3.068 f P
and
f3db , max = f P
[4 (3
3 − 5)
]
2/3
+ 3 + 2 3 ≈ 3.7321 f P .
(3)
If we increase the damping so that γ = fP, this results in a response peak that does not exceed the DC response level.
In this 3-dB ripple case, the bandwidth is only 10% smaller than the value given in (3), resulting in a maximum
bandwidth of 3.35×fP.
Experimentally, it is simple to modify both the resonance frequency and damping of the injection-locked laser by
adjusting the injection power and the frequency detuning. Bandwidth enhancement should not be limited by the
maximum resonance frequency, as we expect fR > 200 GHz to be achievable. Realistically, the first-order pole, fP,
will ultimately determine the maximum obtainable 3-dB bandwidth. When the resonance frequency is increased to
> 100 GHz, the first-order pole frequency ωP approximates to ω P ≈ gS 0 = ω R2 0 γ P , where ωR0 is the resonance
frequency of the free-running laser, defined as ω R2 0 = γ P gS 0 . If we assume a maximum fR0 ≈ 50 GHz and a typical
photon lifetime of 3 ps, then ωP ≈ ωR0. In other words, the first-order pole can be roughly as large as the maximum
3-dB bandwidth of the free-running laser. Therefore, the maximum obtainable 3-dB bandwidth of the injectionlocked laser will be at least 3.35 times the 3-dB bandwidth of the free-running laser. Hence, if a laser can achieve a
free-running 3-dB bandwidth of 50 GHz, then we project the maximum injection-locked bandwidth to be > 168
GHz. This factor of 3.35× bandwidth enhancement is a marked improvement over the current limits of directly
modulated semiconductor lasers.
Conclusion
In summary, by increasing the slave bias current, the carrier decay rate can be increased, thus enhancing the firstorder pole, fP. We have demonstrated intrinsic 3-dB bandwidths of 80 GHz in directly modulated VCSELs;
bandwidths approaching 200 GHz are fundamentally possible. We have also shown injection locking can achieve a
greater than three-fold enhancement of bandwidth over conventional direct modulated lasers.
References
[1]
[2]
[3]
[4]
[5]
S. Weisser, E. C. Larkins, K. Czotscher, W. Benz, et al., IEEE Photon. Technol. Lett., vol. 8, pp. 608-10, 1996.
R. S. Tucker, J. Lightwave Technol., vol. 3, pp. 1180-1192, 1985.
E. K. Lau, H.-K. Sung, and M. C. Wu, in Proc. Opt. Fiber Commun. Conf., Anaheim, CA, 2006, p. OThG2.
L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, et al., IEEE Photon. Technol. Lett., vol. 18, pp. 367-369, Jan. 2006.
E. K. Lau, H. K. Sung, and M. C. Wu, IEEE J. Quantum Electron., vol. 44, pp. 90-99, Jan. 2008.
172
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