Oct 20, 2006 - use a calibrated broadband photodetector. Experiment shows that the proposed method is as accurate as the swept frequency method using a.
INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 39 (2006) 4578–4581
doi:10.1088/0022-3727/39/21/012
Estimation of frequency response of directly modulated lasers from optical spectra Ning Hua Zhu, Tao Zhang, Ya Li Zhang, Gui Zhi Xu, Ji Min Wen, Heng Pei Huang, Yu Liu and Liang Xie State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People’s Republic of China
Received 16 June 2006, in final form 11 September 2006 Published 20 October 2006 Online at stacks.iop.org/JPhysD/39/4578 Abstract A simple method for estimating the frequency responses of directly modulated lasers from optical spectra is presented. The frequencymodulation index and intensity-modulation index of a distributed feedback laser can be obtained through the optical spectrum analyses. The main advantage is that the measurement setup is very simple. Only a microwave source and an optical spectrum analyser are needed and there is no need to use a calibrated broadband photodetector. Experiment shows that the proposed method is as accurate as the swept frequency method using a network analyzer and is applicable to a wide range of modulation powers.
derived. A comparison between the results obtained using our method and the swept frequency method [1] has been made.
1. Introduction Directly modulated semiconductor lasers are essential for highspeed optical transmission and signal processing systems. Quick measurements of the characteristic parameters, such as the frequency response and the chirp, are required in the fabrication and optimization of the devices. In the past two decades, many methods for measuring the frequency responses of optoelectronic devices have been proposed. The most widely used methods are the swept frequency method [1], the pulse spectrum analysis method [2], the interferometric frequency-modulation (FM) sideband method [3] and the optical heterodyne detection method [4]. The method based on the optical spectrum analysis has been established for the measurement of the chirp parameter and frequency responses of various modulators [5–12]. Compared with the conventional method using a vector network analyzer (VNA), this method is attractive since there is no need to use broadband photodetector. This method has been used for characterizing the chirp parameter of semiconductor lasers [13–15]. Until now, this method has not been applied to measure the frequency responses of directly modulated lasers. This paper represents a simple method for estimating the frequency response of directly modulated lasers from the optical spectra measured using an optical spectrum analyzer. The relations between the FM and intensity-modulation (IM) index and optical carrier and sideband powers have been 0022-3727/06/214578+04$30.00
© 2006 IOP Publishing Ltd
2. Theoretical background For a single longitudinal mode semiconductor laser under the modulation of a small sinusoidal current, the electric field can be expressed as [3, 8] E(t) = E0 1 + m cos(ωm t)ei[ω0 t+β sin(ωm t+θ)] , (1) where m is the effective amplitude modulation index, β is the effective frequency-modulation (FM) index, ω0 is the optical frequency, ωm is the current modulation frequency and θ is the phase shift between the amplitude and frequency modulation. Assuming m 1, the amplitude E can be converted into the following Fourier–Bessel transformation [3, 8]: +∞ E(t) = E0 ei[ω0 t+p(ωm t+θ)]
p=−∞
m (2) [Jp−1 (β)e−iθ + Jp+1 (β)eiθ ] . 4 Here Jn (β) is the nth Bessel function of the first kind. From (2) the pth order sideband power of the modulated output light can be written as p 2 Hp = I0 Jp (β) 1 − m sin θ . (3) β × Jp (β) +
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Estimation of frequency response of directly modulated lasers
Accordingly, the first-sideband strengths relative to the carrier are m H+1 /H0 = J12 (β) 1 − sin θ /J02 (β), (4) β m 2 (5) H−1 /H0 = J1 (β) 1 + sin θ /J02 (β). β From these equations, we have J12 (β)/J02 (β) = (H+1 + H−1 )/(2 × H0 ).
(6)
Besides, in case that the FM-modulation index β 1 [7], (7)
It has been shown that this formula is a good approximation when β < 0.6, which makes the calculation very simple. Once the optical carrier power H0 and the sideband powers H+1 and H−1 are measured, β can be determined from (6). In addition, m can be expressed as [16] 2β(ωm ) m(ωm ) = , ωg 2 α 1+ ωm
(8)
where α is the chirp parameter (also denoted as the linewidth enhancement factor) and ωg is the characteristic angular frequency. Normally, α is constant at relatively low modulation levels. Typically, for a 1.55 µm InGaAsP distributed feedback (DFB) laser, α = 2–3 and fg = ωg /2π = 2.1 GHz [16]. The IM-modulation index m can be obtained from (8). The frequency response of the laser can, therefore, be obtained from the optical carrier and sideband powers measured at different modulation frequencies. According to [17], ωg is given by ωg = κP /τph .
(9)
Here κ is the gain compression coefficient, P is the optical output power per facet and τph is the lifetime. And the laser gain g0 is given by g0 = a(J − Jth )(1 − κP ).
(10)
Here J is the current density, Jth is the threshold current density and a is a constant. Then the P –I curve of the DFB laser can be expressed as P =
I − Ith . b + κ(I − Ith )
(11)
Here Ith is the threshold current and b is a constant. The optical spectra of a directly modulated DFB laser can be measured using an optical spectrum analyzer. From the spectra the peak powers of the carrier and ±1 sideband modes can be obtained. It should be noted that the spectra of the optical sidebands will be broadened when the modulation frequency increases. The spectral width (often denoted as laser chirp) of the directly modulated laser is given by [17] ν0 = 2 (β + 1) fm .
(12)
In this case, the optical carrier and sideband powers can be calculated collecting all optical powers within the 3 or 6 dB linewidth of the actual spectra.
Figure 1. Optical spectra of a DFB laser modulated at different frequencies.
OPtical Power(mW/Facet)
J12 (β)/J02 (β) ≈ 0.25β 2 .
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3. Experiment and discussion In the experiment a 1.55 µm DFB laser fabricated in our laboratory was used. The laser threshold current is 16.6 mA and the optical output power was about 3.5 mW/facet at 25 mA. A network analyzer (Agilent 8720D) was used as the microwave source, and the modulation electrical power was −5 dBm. Because the modulation power is much lower than the optical output power, the small signal approximation is valid. The spectra of the DFB laser modulated at different frequencies were measured by an optical spectrum analyzer (Advantest Q8384) and shown in figure 1. As shown in figure 2, the P –I curve of the DFB laser is measured and simulated using (11). It should be noted that the output power is the laser power before coupling, while the output power after coupling is about 30% of it. Then κ and Ith is characterized (note that κP is not related with the coupling index). For this DFB laser κ = 0.018 16 mW and Ith = 16.56 mA. The laser output power is about 3.5 mW/facet at 25 mA. Assuming that τph = 5 ps, the corresponding fg is 2.02 GHz. From the measured spectra, the FM-modulation index β of the laser can be calculated using (6) and is shown in figure 3(a), where the solid rectangles show the FM-modulation index β calculated from the peak powers of the carrier and ±1 sideband modes, and the open circles show the β calculated using the total powers within the full width half maximum (FWHM) 4579
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of the carrier and sideband modes. Due to the resolution limitation of the optical spectrum analyzer, the FWHM width cannot be read out from measured spectra when the modulation frequency is less than 3 GHz, and the corresponding data cannot be obtained. Normally, the microwave output power of the network analyzer will change with the increase in the microwave frequency. It can be measured using an electrical spectrum analyzer (Advantest R3132). In order to remove the effects of the variation of the driver output with microwave frequency, the measured data are used to normalize the IM-modulation index calculated from (8). Figure 3(b) shows the estimated frequency responses of the laser. According to (8), α has no relationship with the normalized frequency response. The normalized frequency response is the relative frequency response assuming that the response at DC is 0 dB. Therefore, there is no need to measure the parameter α. In order to check the accuracy of our method, the laser was also measured using the swept frequency method [1]. Before measurement, the photo-detector was calibrated using an improved optical heterodyne method [18]. The measured data are also given in figure 3(b) for comparison. It can be clearly seen that a good agreement between our method and the swept frequency method is obtained. From figure 3 and (8) one can see that the FM-modulation index β > 1 at low frequencies (1–4 GHz), while the IMmodulation index m is relatively low (m 1). It implies that equation (7) is not valid in this case. However, (6) and (8) can be used to estimate β and m. When the modulation frequency is near the resonance frequency of the laser, the IM-modulation index became so large that the small-signal approximation is no longer satisfied. Therefore, the responses estimated from the optical spectra are not accurate and do not agree with the results from the VNA method. At higher
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Figure 3. (a) FM-modulation index and (b) frequency responses of the DFB laser, where the solid rectangle and open circle show the data calculated from the peak powers and total powers within FWHM of the carrier and sideband modes, respectively. The solid line shows the results obtained using the swept frequency method.
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Figure 4. (a) Output powers of the main peak ( ), +1 sideband mode (•) and −1 sideband mode (◦) of the laser under different modulation powers. (b) FM-modulation index of the laser under different modulation powers.
modulation frequencies (fm > 6 GHz), equation (8) tends to a linear relationship between β and m, and the proportionality factor is α/2. From figure 3 one can also see that the results calculated from the peak powers and total powers are similar. The reason might be that the spectrum broadening cannot be observed due to the limitation of the resolution bandwidth of the optical spectrum analyzer. On the other hand, the carrier and sideband modes may have similar line shapes and broadening when the modulation frequency varies. From (6) it can be seen that the influence of the spectrum broadening are cancelled. Therefore, the frequency response estimation method from the peak powers is easy to carry out and accurate enough for some applications when only a quick test is required. The peak optical powers of the sidebands under various modulation power levels are measured and given in figure 4(a), where the modulation frequency is fixed to be 10 GHz. Figure 4(b) shows the corresponding FM-modulation index. It is obvious that the calculated FM-modulation index is linearly proportional to the modulation power, when the modulation power is less than 5 dBm. From figure 4 and (12) one can see that the laser chirp will linearly increase with the modulation power at a certain modulation frequency when the modulation power is below 5 dBm. This implies that our method is suitable for wider modulation power ranges.
4. Conclusion A simple method for estimating the frequency response of directly modulated lasers from the optical spectrum measured using an optical spectrum analyzer is established based on the method for the FM response measurement proposed by Bjerkan et al [8] which can be used to measure the frequency responses of the directly modulated lasers. And
Estimation of frequency response of directly modulated lasers
the formulation of this method is much simpler than that of Bjerkan’s method. Compared with the interferometric FM sideband method proposed by Hemery et al [3], the optical spectrum analysis method demands less resources. This technique is very attractive because the measurement frequency range depends only on the microwave source and there is no need to use a calibrated broadband photodetector. This method can also be used to measure the chirp of the laser. Experiment shows that our method is as accurate as the swept frequency method using a network analyzer and is applicable to a wide range of modulation powers. Although our analysis is based on a single longitudinalmode laser, the theory could also be applied in multimode lasers when mode separation is larger than the modulation frequency. Normally, the mode separation of a FP laser is over 100 GHz. Therefore, the proposed method can be used to analyze FP lasers.
[6] [7] [8]
[9]
[10]
[11]
Acknowledgments The work is supported in part by the National Natural Science Foundation of China (60510173, 60536010 and 60506006) and the National Basic Research Program of China (2006CB604902).
[12] [13] [14]
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