Slow-light in a vertical-cavity semiconductor optical amplifier

Slow-light in a vertical-cavity semiconductor optical amplifier

Nicolas Laurand, Stephane Calvez and Martin D. Dawson Institute of Photonics , SUPA, University of Strathclyde, 106 Rottenrow, Glasgow G4 0NW, United Kingdom

[email protected]

Anthony E. Kelly Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8LT, UK

Abstract: This paper discusses the effect of slow-light in Vertical-Cavity Semiconductor Optical Amplifiers. A Fabry-Perot model is used to predict the group delay (GD) and GD-bandwidth performance of a VCSOA operated in reflection in the linear regime. It is shown that the GD depends on all cavity parameters while the GDxGD-bandwidth product only depends on the gain. Experimental demonstration with a 1300nm GaInNAs VCSOA is used to validate the model and demonstrate tunable GDs between 25 and 100 ps by varying the VCSOA gain. Experimental distortion of the signals induced by nonlinear effects is also presented.

©2006 Optical Society of America

OCIS codes: (999.9999) Slow-Light; (250.7260) Vertical cavity surface emitting lasers; (250.5980) Semiconductor optical amplifiers; (230.5590) Quantum-well devices.

References and links

1. R. W. Boyd and D. J. Gauthier, "Slow" and "Fast" Light," in Progress in Optics, 43, E. E. Wolf, ed., (Amsterdam: Elsevier, 2002), pp. 497-530.

2. I. Frigyes and A. J. Seeds, "Optically generated true-time delay in phased-array antennas," IEEE Trans. Microwave Theory Tech. 43, 2378-2386 (1995).

3. G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).

4. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, "Slow-light optical buffers: Capabilities and fundamental limitations," J. Lightwave Technol. 23, 4046-4066, (2005).

5. P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. L. Wang, S. W. Chang, and S. L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).

6. S. W. Chang and S. L. Chuang, "Slow light based on population oscillation in quantum dots with inhomogeneous broadening," Phys. Rev. B 72, art. 235330 (2005).

7. 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, 65-69 (2005).

8. H. R. Chang, D. D. Smith, K. A. Fuller, J. O. Dimmock, D. A. Gregory, and D. O. Frazier, "Slow and fast light in coupled microresonators," in Advanced Optical and Quantum Memories and Computing II, H. J. Coufal, Z. U. Hasan, and A. E. Craig,eds., Proc SPIE 5735, 40-51 (2005).

9. A. B. Matsko, D. V. Strekalov, and L. Maleki, "On the dynamic range of optical delay lines based on coherent atomic media," Opt. Express 13, 2210-2223 (2005).

10. S. Minin, M. R. Fisher, and S. L. Chuang, "Current-controlled group delay using a semiconductor Fabry-Perot amplifier," Appl. Phys. Lett. 84, 3238-3240 (2004).

11. M. R. Fisher, S. Minin, and S. L. Chuang, "Tunable optical group delay in an active waveguide semiconductor resonator," IEEE J. Sel. Top. Quantum Electron. 11, 197-203, 2005.

12. A. Stapleton, S. Farrell, H. Akhavan, R. Shafiiha, Z. Peng, S.-J. Choi, J. O’Brian and P. D. Dapkus, "Optical phase characterization of active semiconductor microdisk resonators in transmission," Appl. Phys. Lett. 88, art. 031106 (2006).

13. X. X. Zhao, P. Palinginis, B. Pesala, C. J. Chang-Hasnain, and P. Hemmer, "Tunable ultraslow light in vertical-cavity surface-emitting laser amplifier," Opt. Express 13, 7899-7904 (2005).

14. N. Laurand, S. Calvez, M. D. Dawson, A. C. Bryce, T. Jouhti, J. Konttinen, and M. Pessa, "Performance comparison of GaInNAs vertical-cavity semiconductor optical amplifiers," IEEE J. Quantum Electron. 41, 642-649 (2005).

#71393 - $15.00 USD Received 25 May 2006; revised 16 June 2006; accepted 19 June 2006

(C) 2006 OSA 24 July 2006 / Vol. 14, No. 15 / OPTICS EXPRESS 6858

1. Introduction

Dynamic control of the light propagation velocity opens up interesting opportunities both for fundamental studies of light-matter interaction [1] and the realization of variable optical delay lines. The latter devices have generated much attention because of their potential applications as antenna beam formers in radio frequency photonics [2] and as optical buffers for future optical networks [3-4]. Exploiting the compactness and amenability to integration of semiconductors, slow-light and fast-light regimes, referring to a signal positive and negative group delay (GD) have been reported using material [5-6] or spatial [7-8] dispersion effects. To overcome the buffering limitations of lossy slow-light components [9], the research effort has been focused on the demonstration of tunable delays in lossless or amplifying regimes mainly with in-plane devices such as semiconductor optical amplifiers (SOAs) [10], waveguide or microdisk resonators [11-12]. It is only very recently that experiments were conducted on vertical-cavity surface-emitting lasers (VCSELs) [13] bringing to the field all the advantages of the vertical geometry including easy coupling with optical fibers, inherent polarization insensitivity, wavelength tunability, on-wafer testing and suitability for the production of two dimensional arrays. In that study, the GD was measured to reach up to 40 ps in the amplification regime and up to 100 ps above lasing threshold in a regime attributed to injection locking.

Here, we report detailed theoretical and experimental investigations of slow-light effects in a vertical-cavity semiconductor optical amplifier (VCSOA) operated in reflection mode. In section 2, we present a simple model to analyze the effect of the device cavity parameters on the GD and on the GD-bandwidth in the linear regime i.e. for low input powers. Sections 3 and 4 are dedicated to the experimental assessment of tunable GDs in a 1.3-μm GaInNAs VCSOA operated in the linear and nonlinear regime respectively.

2. Theory

In this section, we present the theoretical analysis of the slow-light behavior of a VCSOA operated in reflection in the linear regime i.e. when power-induced carrier and/or refractive index changes are negligible. Using a Fabry-Perot analysis and taking into account that there is generally a mismatch between the cavity mode and the incident signal spot size, it can be shown that the gain and phase on reflection of a VCSOA are given by:

( )( )

222

222

2

0

sin41

sin4

)()1()(

ϕ

ϕ

ϕλ

sbfsbf

sbfsbf

ki

ksbfsbfMf

gRRDgRR

gRRDgRDR

egRRgRRCRG

+−

+−=

−+−= ∑∞

= (1)

ϕϕ

λφcos)()1(

sin)(tan)(

2 ⋅+⋅⋅−⋅+⋅

⋅−⋅⋅=

DRgRgDRR

DRgRArc

fsbsbf

fsb (2)

In Eq. (1) and Eq. (2) φ=(4πLC)/λ is the phase accumulated by the wave after one round-trip in the cavity, Rf and Rb are, respectively, the front and back DBR intensity reflectivity, gs is the single-pass gain, Lc is the optical length of the cavity including the field penetration depths in the mirrors and CM is the coupling factor between incident wave and the cavity mode. Equation (2) is calculated by taking the argument of Eq. (1) and we have used D=CM-CMRf+Rf. The following analytical expression for the GD can be derived from Eq. (2):



ϕϕ

ϕπλ

λλφλ

22222222

2222

2

cos4cos)()1(2)(

cos)()1()(2

2

)()(

sbffssbbfsbffsbf

sfsbbffsbC

DgRRRDgDgRRRgDRRRDgRR

gRDgDRRRRDgR

c

L

cd

dGD

++⋅⋅+⋅−++⋅+

⋅⋅−⋅+⋅−−⋅⋅

=⋅⋅

⋅−=(3)

An alternative representation of slow-light effects consists in using the slow-down factor, S, defined [10] as the ratio of the GD by the intra-cavity round-trip time (S(λ)=GD(λ)c/LC) instead of GD. Their similitude means that we will essentially concentrate on the analysis of the GD. Moreover, for their application as optical buffers, it is important to ascertain that the variable delay lines have a GD-bandwidth sufficient to avoid distortion of the modulated signals to be stored. A useful parameter to evaluate this capability is the product of the GD by the GD-bandwidth, which we refer to here as the GDxGDB product. Using the same approach as above, it can be shown that the GDxGDB product for a transmission-VCSOA is roughly constant and equal to 1/π. However, for a reflection-VCSOA, this parameter is not constant and was evaluated numerically in this paper as no sufficiently simple expression was found. This difference in behaviour between the two modes of operation is the direct consequence of the importance of the first reflection on the control of the device phase in the reflection mode. The remaining of this section focuses on the analysis of Eq. (3) and of the GDxGDB product. From Eq. (3), it can be seen that the GD depends on the cavity parameters and on the gain of the active region. The GD spectrum has a bell-shape, with maximum delay being achieved at the VCSOA resonant wavelength [see Fig. 3(b)]. It also suggests that the GD (and consequently the slow-down factor) can be varied by changing the gain (see Fig. 1) and/or tuning the VCSOA resonance.

Fig. 1. Top: VCSOA GD as a function of the device gain for different cavity parameters with corresponding threshold curves. Bottom: GDxGD-bandwidth product as a function of device gain.

Figure 1 represents the theoretical GD on the resonance (φ=2kπ with k being an integer) in

reflection (top) and the GDxGDB product (bottom) as a function of the VCSOA device gain G in dB (and for G≥0 dB). The calculations were done for a component with a back mirror reflectivity Rb=99.4%, an optical cavity length of 6-λ (λ=1290nm) and a top-reflectivity Rf of 99.3%, 98.7% and 98%. We also present the case of a VCSOA with an optical cavity length of 2-λ and Rf=98.8%. The coupling coefficient was chosen constant at CM~0.5, following an

0 5 10 15 20 250.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65 0 5 10 15 20 250

20

40

60

80

100

120

GD

xGD

-ban

dwid

th p

rodu

ct

VCSOA reflection gain [dB]

Rf=98.7%/Lc=2λc

Rf=98%/Lc=6λc

Rf=98.7%/Lc=6λc

93% Threshold Lc=2λc

GD

[ps]

93% Threshold Lc=6λcRf=99.3%/Lc=6λ

c



evaluation that our VCSOA would operate with a 4.8μm diameter gain aperture in the amplication regime. We can see in Fig. 1 that all curves have the same pattern: the GD increases with the gain but the evolution is not linear. The maximum achievable delay depends on how close to threshold the VCSOA can be operated under stable conditions. We consider this point is reached for 93% of threshold. This maximum delay value is found by the point at which the GD lines cross the corresponding threshold curves designated by (93% Threshold Lc=6-λ) and (93% Threshold Lc=2-λ). The threshold curves were computed by calculating the pump power necessary to reach threshold in our structures with the use of rate-equations [14]. gs was then calculated for a pump power of 93% of the threshold for each reflectivity value, and the VCSOA maximum delay was obtained by the use of (3). Higher cavity reflectivity yields higher GD at all reachable gains. At G=0 dB i.e. gs= [ ] ( )[ ]fbf RDRR +⋅+1 , the GD for the 6-λ structure with Rf=99.3%, 98.7% and 98% is

60 ps, 35 ps and 20 ps respectively while the maximum delay is 85 ps, 80 ps and 75 ps. For similar reflectivity, a shorter cavity of 2-λ yields lower delays at 10 ps for G=0 dB and 25 ps at threshold.

The analysis of the bottom part of Fig. 1 suggests that the GDxGDB product decreases nonlinearly with increasing device gain, but is independent of all the other cavity parameters (reflectivities, length). Therefore, for a given gain, there is a trade-off between GD and GD bandwidth. The choice of the cavity parameters depends on the application. If one is mainly interested in high delay values at low amplification, higher reflectivities and a longer cavity length are preferable, as long as the bandwidth can accommodate the modulated signal. If one needs to operate at higher gain for similar delays, lower reflectivities should be chosen. It is also interesting to note that, for all gains, the GDxGDB product of a reflection-VCSOA is higher than for a transmission-VCSOA.

3. Tunable delay in the linear regime

In this section, we present tunable delay characterization results of a 1290-nm GaInNAs VCSOA having a total cavity length of 6-λ, Rb=99.5% and Rf~98.8%. A full description of this device can be found in [14]. The GD was measured using the modulation phase-shift method [see Fig. 2(a)]. The VCSOA was optically-pumped by a source at 980-nm [14]. The signal was provided by a tunable laser source, which was fed into a 10Gb/s intensity modulator. The modulator was driven by a sinusoidal signal at 1 GHz provided by a RF function generator. Its output was sent through port 1 of an optical circulator. The signal from port 2 of the circulator and the pump wavelength were combined inside the injection fiber with a pump-coupler. The injection fiber was butt-coupled to the surface of the VCSOA where the mode field diameters of the pump and of the signal were 7 μm and 8 μm respectively. The reflected amplified signal was obtained on port 3 of the circulator and passed through a 50/50 coupler. One arm of the coupler was fed to an optical spectrum analyzer, which allowed us to monitor both the signal and the VCSOA spectra. The other arm of the coupler was sent to an Agilent Infinium DCA-J Oscilloscope with a 55GHz Optical Channel via a 1300-nm SOA. The signal power arriving at the SOA was under -14 dBm for all VCSOA gains, well below the SOA saturation input power. The oscilloscope was triggered with the 1-GHz signal from the RF source.

For the linear regime study, the signal power at the VCSOA input was fixed at -24dBm in order to prevent any carrier saturation effects that may result in distortion and hence affect the GD of the signal. The appearance of non-linear effects at higher input powers is discussed in section 4.



0 500 1000 1500 2000

Time base [ps]

Osc

illos

cop

e si

gn

al

Reference

G=2dB

G=6dB

G=10dB

G=13d

G=16dBGD~100ps

(a) (b)

Fig. 2. (a) VCSOA GD measurement set-up; (b) Examples of normalized RF signal delay measurements in linear regime at different VCSOA gain.

The reference was taken for an input wavelength well outside the VCSOA resonance,

because then the signal is directly reflected from the VCSOA top mirror. This choice of reference is consistent with previous reports [13] and with the telecommunication industry standard approach where the delays are measured with respect to the case where the device under test is absent, i.e. when the signal does not propagate through the device. It is also compatible with the definitions of the GD and the slow-down factor as described in [10], where the reference is taken for a fully absorptive (gs=0) device. In our case, in this situation, the only contribution is the top mirror reflection and GD is predicted to be nil (Eq. 3). This was ascertained by measuring a GD~0ps for on-resonance excitation of an unpumped device.

We then measured the GD for an on-resonance injected signal at different G. Examples of the delay measurements by recording the phase shift of the normalized RF signal at different gain G are shown in Fig. 2(b). Results for positive device gains are represented in Fig. 3(a). Starting at GD~0ps for an unpumped device, by increasing G from 0 to 17 dB, the GD varies from 25 ps to 100 ps, which is equivalent to changing the slow-down factor S [10] from 1400 to 4000. The theoretical curve in Fig. 3(a) was calculated for CM=0.5 using (3). A good agreement with the experimental data is found for G between 0 and 13 dB. For high gain (G>15dB) the prediction underestimates the actual delay: for G~17dB, the measured delay is ~100 ps, while the predicted value for CM=0.5 is 75 ps. A better fit is obtained by using CM~0.38, which corresponds to higher mismatch between the incoming signal and the cavity mode that we attribute to spatial hole burning effects.

The GD bandwidth for different G was recorded by tuning the input signal wavelength. The gain and delay spectra for G=17dB are shown in Fig 3(b). We also recorded the GD bandwidth for G=8dB and G=4dB. We found a GD bandwidth at half maximum of 3.8 GHz for G=17dB, 13.3 GHz for G=8dB and 19 GHz for G=4dB. The corresponding GDxGDB products are 0.38, 0.55 and 0.6 respectively. These observations are consistent with the predictions of decreasing GDxGDB product with increasing gain made in section 2.

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25Chip Gain [dB]

Del

ay [

ps]

DataTheoretical curve

Laser threshold

0

20

40

60

80

100

1290 1290.2 1290.4 1290.6 1290.8 1291Wavelength [nm]

Del

ay [p

s]

0

5

10

15

20

Gai

n [dB

]

VCSOA delay

Delay theory

VCSOA Gain

Gain theory

(a) (b)

Fig. 3. (a) Group delay as a function of the VCSOA gain in dB; (b) Gain and delay spectra for G=17dB and GD=100 ps.



4. Non linear effects

At higher input powers, carrier saturation effects induce distortion of the signal through self-phase modulation. The saturation of the quantum wells not only decreases the available gain but also changes the index of refraction and consequently the VCSOA resonant wavelength. We recorded the VCSOA output signal for different input powers and witnessed signal distortion. Figure 4(a) shows such a measurement for a given VCSOA resonance-input signal detuning (around 0), an input power (Pin) varying from -24dBm to -11dBm and a small-signal gain Gsm~16dB. The distortion and the GD increase with Pin.

We also measured the output signal for varying input wavelengths at different Pin and Gsm~13dB. An illustration of the observations is provided in Fig. 4(b) for Pin=-11dBm. The wavelength range over which one can see these non-linear effects and their amplitudes are dependent on Pin and its magnitude compared to the saturation input power.

The appearance of such distorsion prevents the definition of a single GD value and can be considered as a limiting factor for this optical buffer embodiment.

Fig. 4. (a) VCSOA output signal for different Pin. (b) VCSOA output signal for signal-VCSOA resonance detuning of -40, 0 and 40 pm for Pin=-11dBm and a small-signal gain Gsm~13dB.

5. Conclusion

We have studied, theoretically and experimentally, tunable slow-light using a reflection-VCSOA operated in the linear amplification regime. We have shown that the GD depends on the gain and cavity parameters while the GDxGD bandwidth product is only a function of the gain. Therefore, for a fixed amplification, there is a trade-off between delay and bandwidth. For operation at low gain, the best choice is to use a high-reflectivity and relatively long cavity. The highest delay is then obtained as long as the GD bandwidth is sufficient not to distort the signal. If operation at high-gain is desired, a lower reflectivity is necessary. A lower reflectivity yields to a wider bandwidth for a given gain but also allows operation at high amplification, whereas the gain is limited to low values for high reflectivities.

Tunable GDs between 25 ps and 100 ps and a GDxGD bandwidth product between 0.35 and 0.6 with no noticeable distortion for a 1-GHz sinusoidal modulated signal injected at the VCSOA resonance were experimentally demonstrated. Given the GD bandwidth measured, we believe that the same device can delay 2.5-GHz signals with similar GD values. Further increase in GD should be possible by cavity optimization and/or cascading VCSOAs.

Finally, non-linear effects have been recorded for input powers above -24dBm. Self-phase modulation of the signal resulted in distortion and prevents the definition of a single GD value. The amount of distortion was seen to depend on the input power and on the separation between the signal wavelength and the VCSOA resonance.

Acknowledgment

The authors would like to thank Agilent for the loan of the fast oscilloscope and Professor Sibbett’s group of the University of St Andrews, for initial loan of equipment.

0 500 1000 1500 2000Time scale [ps]

Po

wer

[a.

u.]

Increasing Pin

(a)

0 500 1000 1500 2000Time scale [ps]

Po

wer

[a.

u.]

Reference signal

detuning=-40pm detuning=40pm

detuning=0nm

(b)



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Slow-light in a vertical-cavity semiconductor optical amplifier