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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26184–26199
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Traveling wave electrode design of electro-optically modulated coupled-cavity surface-emitting lasers

Mateusz Zujewski, Hugo Thienpont, and Krassimir Panajotov  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 26184-26199 (2012)
http://dx.doi.org/10.1364/OE.20.026184


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Abstract

We present a novel design of an electro-optically modulated coupled-cavity vertical-cavity surface-emitting laser (CC-VCSEL) with traveling wave electrodes of the modulator cavity, which allows to overcome the RC time constant of a traditional lumped electrode structures. The CC-VCSEL optical design is based on longitudinal mode switching which has recently experimentally demonstrated a record modulation speed. We carry out segmented transmission line electrical design of the modulator cavity in order to compensate for the low impedance of the modulator section and to match the 50 Ω electrical network. We have optimized two types of highly efficient modulator structures reaching −3 dB electrical cut-off frequency of fcut-off = 330 GHz with maximum reflection of −22 dB in the range from fLF = 100 MHz to fcut-off and 77 – 89% modulation efficiency.

© 2012 OSA

1. Introduction

The CC-VCSEL design offers the possibility of independent bias of the two cavities (mesas). Due to the cavity coupling, the CC-VCSEL possesses two longitudinal modes and can emit light either on the long, on the short or on both wavelength modes simultaneously [10

10. P. Michler, M. Hilpert, and G. Reiner, “Dynamics of dual-wavelength emission from a coupled semiconductor microcavity laser,” Appl. Phys. Lett. 70, 2073–2075 (1997). [CrossRef]

, 12

12. J. Carlin, R. Stanley, P. Pellandini, U. Oesterle, and M. Ilegems, “The dual wavelength Bi-vertical cavity surface-emitting laser,” Appl. Phys. Lett. 75, 908–910 (1999). [CrossRef]

14

14. V. Badilita, J. F. Carlin, M. Illegems, M. Brunner, G. Vershaffelt, and K. Panajotov, “Control of polarization switching in vertical coupled-cavities surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 365–367 (2004). [CrossRef]

]. Chen et al. proposed a ”push-pull” modulation scheme in which a current is injected out of phase in the two active cavities, keeping the total photon density unchanged while varying the longitudinal mode distribution [21

21. C. Chen, K. L. Johnson, M. Hibbs-Brenner, and K. D. Choquette, “Push-Pull Modulation of a Composite-Resonator Vertical-Cavity Laser,” IEEE J. Quantum Electron. 46, 438–446 (2010). [CrossRef]

]. Another way of increasing the bandwidth of a CC-VCSEL is to use one cavity as a light source and the second one as a modulator via electro-optic (EO) effect [15

15. J. Hudgings, R. Stone, S. Lim, K. Lau, and C. Chang-Hasnain, “Comparative study of the analog performance of a vertical-cavity surface-emitting laser under gain and cavity loss modulation,” Appl. Phys. Lett. 77, 2092–2094 (2000). [CrossRef]

20

20. M. Yakimov, J. van Eisden, V. Tokranov, M. Varanasi, S. R. Oktyabrsky, E. M. Mohammed, and I. A. Young, “Concept of feedback-free high-frequency loss modulation in detuned duo-cavity vertical cavity surface-emitting laser,” J. Vac. Sci. Technol., B 28 (2010). [CrossRef]

, 22

22. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

]. As the vertical design makes possible a monolithic growth of a modulator cavity coupled to the VCSEL active cavity, a significant reduction of coupling losses, complexity and cost is expected. An electro-absorption (EA) modulated CC-VCSEL has been presented in [18

18. J. Van Eisden, M. Yakimov, V. Tokranov, M. Varanasi, E. M. Mohammed, I. A. Young, and S. Oktyabrsky, “Modulation properties of VCSEL with intracavity modulator,” Proc. of SPIE 6484, A4840 (2007).

]: the active cavity is not directly perturbed however, the overall photon density changes when modulating the absorption in the passive cavity thus limiting the modulation bandwidth to the RO frequency. A way of overcoming the impact of absorption change has been suggested in [20

20. M. Yakimov, J. van Eisden, V. Tokranov, M. Varanasi, S. R. Oktyabrsky, E. M. Mohammed, and I. A. Young, “Concept of feedback-free high-frequency loss modulation in detuned duo-cavity vertical cavity surface-emitting laser,” J. Vac. Sci. Technol., B 28 (2010). [CrossRef]

]: a careful choice of the detuning between the two cavities can set the resonance wavelength at a point where the reflection from the passive to the active cavity for two different values of absorption is the same, eliminating the feedback to the active VCSEL cavity. Alternatively, an electro-refractive (ER) modulation can be used. Recently, an ER modulated CC-VCSEL has demonstrated a 35 GHz optical bandwidth, limited by the photodetector speed, and 60 GHz electrical bandwidth [19

19. V. A. Shchukin, N. N. Ledentsov, J. A. Lott, H. Quast, F. Hopfer, L. Y. Karachinsky, M. Kuntz, P. Moser, A. Mutig, A. Strittmatter, V. P. Kalosha, and D. Bimberg, “Ultrahigh-speed electrooptically-modulated VCSELs: modeling and experimental results,” Proc. of SPIE 6889, H8890 (2008).

]. We have recently discussed the possibility of polarization and wavelength switching induced by ER effect [22

22. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

]. An electro-optic resonance modulation (ERM) has been experimentally demonstrated in [23

23. T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express 20(5), 5099–5107 (2012). [CrossRef] [PubMed]

]: an electro-refractive effect wavelength switching [22

22. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

] between longitudinal modes of ≈ 1 nm separation has lead to output power modulation up to a record frequency of 52 GHz [23

23. T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express 20(5), 5099–5107 (2012). [CrossRef] [PubMed]

].

It appears that for all of the EO modulated (EOM) CC-VCSEL designs the electrical-parasitics set the limit to the modulation bandwidth. Recently, we have optimized a CC-VCSEl with lumped electrodes achieving a 100 GHz electrical bandwidth [24

24. M. Zujewski, H. Thienpont, and K. Panajotov, “Electrical Design of High-Speed Electro-Optically Modulated Coupled-Cavity VCSELs,” J. Lightwave Technol. 29(19), 2992–2998 (2011). [CrossRef]

,25

25. M. Zujewski, H. Thienpont, and K. Panajotov, “Electro-optically modulated coupled-cavity VCSELs: electrical design optimization for high-speed operation,” Proc. of SPIE 8432, 84320C (2012). [CrossRef]

]. We have shown that the only way to further increase the modulation speed is to reduce the lateral size of the device in order to decrease the time constant of the equivalent electrical circuit. However, the smaller the device, the harder to manufacture, which makes the lumped electrode design impractical. Much higher electrical bandwidth can be achieved by traveling-wave (TW) electrode design in which the RC time constant is not a limitation [26

26. D.M. Pozar, Microwave Engineering, 2nd ed. (New York: Wiley, 1998)

, 27

27. R.E. Collin, Foundations for Microwave Engineering (IEEE Press, 2001) [CrossRef]

]. Moreover, the cost and complexity can be further reduced by integrating the source and the modulator. Recently, such an integrated TW-EAM based on segmented TW electrode design [28

28. R. Lewen, S. Irmscher, U. Westergren, L. Thylen, and U. Eriksson, “Segmented transmission-line electroabsorption modulators,” J. Lightwave Technol. 22(1), 172–179 (2004). [CrossRef]

] has been monolithically integrated with a distributed feedback laser achieving a 100 GHz modulation bandwidth [29

29. M. Chacinski, U. Westergren, B. Stoltz, L. Thylen, R. Schatz, and S. Hammerfeldt, “Monolithically Integrated 100 GHz DFB-TWEAM,” J. Lightwave Technol. 27(16), 3410–3415 (2009). [CrossRef]

]. For TW modulators three main phenomena set the bandwidth limit: microwave reflections, propagation losses and velocity mismatch between traveling light wave and modulation microwave. Ideally, TW EOM would be only limited by the last two ones [30

30. R. Lewen, S. Irmscher, and U. Eriksson, “Microwave CAD circuit Modeling of a traveling-wave electroabsorption modulator,” IEEE Trans. Microw. Theory Tech. 51(4, Part 1), 1117–1128 (2003). [CrossRef]

]. Furthermore, using segmented TW electrode design, the return losses can be significantly reduced [28

28. R. Lewen, S. Irmscher, U. Westergren, L. Thylen, and U. Eriksson, “Segmented transmission-line electroabsorption modulators,” J. Lightwave Technol. 22(1), 172–179 (2004). [CrossRef]

, 31

31. M. Chacinski, U. Westergren, B. Stoltz, and L. Thylen, “Monolithically Integrated DFB-EA for 100 Gb/s Ethernet,” IEEE Electron Dev. Lett. 29(12), 1312–1314 (2008). [CrossRef]

]. This is done by compensating the lower than 50 Ω characteristic impedances of the modulator sections by the much higher characteristic impedance of the passive sections. Additionally, if the the load resistance is properly matched, these structures tend to have flat response and very low reflections over wide frequency range. Taking advantage of all these TW-EAM-DFB achievements, we will present in this paper a TW electrode design for EOM CC-VCSEL that is capable of reaching much higher electrical cut-off frequency than a similar structure with lumped electrodes. In our new TW electrode CC-VCSEL the modulation speed will be only limited by the time of extracting the carriers from the intrinsic region of modulator.

The paper is organized as follows: in section 2 we describe the TW EOM CC-VCSEL structure together with its optical and electrical design. In section 3 we present the simulation results, discuss the influence of the design parameters on the device performance and propose an optimized TW EOM CC-VCSEL theoretically capable of ≈ 330 GHz electrical modulation speed. Section 4 concludes the work.

2. Traveling wave electrooptically modulated coupled-cavity VCSEL (TW EOM CC-VCSEL): structure

2.1. CC-VCSEL optical design

The npn bottom-emitting CC-VCSEL structure is presented in Fig. 1(a). The DBRs are designed for 980 nm wavelength and consist of Al0.2Ga0.8As / Al0.9Ga0.1As quarter-wavelength layers with: 31, 28 and 25 pairs in the top, middle and bottom section, respectively. Heavily doped (p = 20 × 1018) 3λ/4 Al0.2Ga0.8As + λ/4 Al0.9Ga0.1As, P current-spreading layers divide the middle DBR into two parts. The 15 pairs of the middle DBR above this contact layer together with the whole top DBR are low (p = 5 × 1017 cm−3) doped. The doping levels of the remaining 13 pairs of the middle DBR under the P layers and of the bottom DBR are typical for common VCSELs: 0.85 and 1.6 × 1018 cm−3 (depending on the distance from the contact layers). The intrinsic region resistivity is assumed to be 4 × 109 Ωcm [32]. The EOM section consists of k periods of 3 strongly coupled GaAs quantum wells (QWs) (k× 3SCQWs) with Al0.2Ga0.8As barriers and Al0.2Ga0.8As spacers (k = 1, 2, 3 depending on the cavity length). In our simulations we consider 3 different lengths of the EOM cavity: ha = 1λ, 1.5λ and 2λ. The bottom active cavity is 1λ thick and contains three 8 nm GaAs QWs with 4 nm Al0.2Ga0.8As barriers and Al0.2Ga0.8As spacers and AlOx current confinement layer.

Fig. 1 Scheme of a bottom emitting electrooptically modulated coupled-cavity VCSEL (EOM CC-VCSEL) (a) and 3D schematic view of three section traveling wave electrode EOM CC-VCSEL (b). The top (bottom) cavity is independently driven by voltage (current) source.

We base the optical design of the CC-VCSEL on the structure presented by Germann et al. [23

23. T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express 20(5), 5099–5107 (2012). [CrossRef] [PubMed]

]: the detuning between the two cavities is chosen such that the splitting between the two longitudinal modes is Δλ ≈1nm. Our procedure of finding the resonant wavelengths and threshold gains of CC-VCSEL is based on the one dimensional transfer matrix method [22

22. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

]. This procedure provides the resonant wavelengths and threshold gains of the whole coupled cavity structure. In Fig. 2 we present the reflectivity spectrum (a) and the optical power and refractive index distributions along the structure (b) for the case of 1.5λ modulator cavity. The optical power distributions for the short (λS) and the long (λL) wavelength modes are quite similar; therefore only the one for the λS mode is shown. The experimental data of [23

23. T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express 20(5), 5099–5107 (2012). [CrossRef] [PubMed]

] have demonstrated an electro-optic induced switching between 2 longitudinal modes resulting in a resonance wavelength shift [22

22. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

] of ≈ 0.5 nm. Assuming a quadratic (QEO) and linear (LEO) electro optic effect in the QWs of our modulator, we are able, by careful detuning of the two cavities, to achieve similar wavelength switching. We mention, that we hereby focus on the electrical speed optimization of the CC-VCSEL only and do not consider the optimization of the QWs for large EO response (we take the same values of the linear rLEO and quadratic sQEO electro-optic coefficients as in [33

33. A. Bhatnagar, D. W. E. Allsopp, X. Chen, M. P. Earnshaw, and W. Batty, “Eletrorefraction Associated with WannierStark Localization in Strongly Coupled Three-Quantum-Well Structures,” IEEE J. Quantum Electron. 36, 702–707 (2000). [CrossRef]

, 34

34. M. P. Earnshaw and D. W. E. Allsopp, “Electrooptic Effects in GaAsAlGaAs Narrow Coupled Quantum Wells,” IEEE J. Quantum Electron. 37, 897–904 (2001). [CrossRef]

], i.e. rLEO = 1.7 × 10−12 m/V and sQEO = 4 × 10−18 m2/V2). Figure 3 presents the threshold gains (a) and the resonance wavelengths (b) of the two longitudinal modes as a function of the modulating electrical field. At a modulating electrical field of EEOMS>L4.8×106(V/m), a switching between the short λS and the long λL mode is observed. Moreover, by a small change of the cavity detuning, we can shift EEOMS>L towards higher or lower modulation voltages. As an example, for a 1.5 λ modulator cavity length EEOMS>L corresponds to a negative potential drop of −4.2 V between the modulator electrodes. In such a way, the CC-VCSEL structure is theoretically able to achieve wavelength shift of ≈ 0.5 nm with a small voltage swing around this bias point.

Fig. 2 EOM CC-VCSEL: (a) Reflectivity spectrum and (b) refractive index (navy line) and short wavelength (λS) optical power distribution along the CC-VCSEL.
Fig. 3 CC-VCSEL resonance wavelengths λL (red line) and λS (blue line) (a) and threshold gains (b) for the resonant two longitudinal modes as a function of modulating electrical field EEOM.

2.2. Equivalent circuit of EO modulated cavity

In Fig. 1(b), a 3D scheme of segmented TW EOM CC-VCSEL is presented. The structure consists of bottom emitting CC-VCSEL with a bottom VCSEL mesa connected to a current source and a top modulator mesa with traveling wave electrodes. The modulator section is surrounded by two passive sections: the left side passive section is connected to a load resistance, whereas the right-side section - to a voltage source. In Fig. 4 and Fig. 5 we present the 3D schemes of the modulator and the passive sections (a) together with their electrical equivalent circuits (b) and the parameters that describe their dimensions. For the modulator (Fig. 4(a)) hn, ha and hp are the lengths of the top DBR, the top modulator cavity and the 15 pairs of the middle DBR, respectively. Summed up they give the top mesa height: HA = hn + ha + hp. Wg is the ground electrode slot and Wa - the top mesa width. The remaining parameters are common for the modulator and the passive sections: We - is the micro stripe width and tc and tg - the micro stripe and the ground electrode thicknesses. We assume that the metal electrodes are elliptically shaped as in [30

30. R. Lewen, S. Irmscher, and U. Eriksson, “Microwave CAD circuit Modeling of a traveling-wave electroabsorption modulator,” IEEE Trans. Microw. Theory Tech. 51(4, Part 1), 1117–1128 (2003). [CrossRef]

].

Fig. 4 3D scheme (a) and electrical equivalent circuit (b) of the active (modulating) section of the modulator cavity of the TW EOM CC-VCSEL.
Fig. 5 3D scheme (a) and electrical equivalent circuit (b) of the passive section of the modulator cavity of the TW EOM CC-VCSEL.

The equivalent circuits and the calculation of their parameters are based on the work of Lewen et al. [30

30. R. Lewen, S. Irmscher, and U. Eriksson, “Microwave CAD circuit Modeling of a traveling-wave electroabsorption modulator,” IEEE Trans. Microw. Theory Tech. 51(4, Part 1), 1117–1128 (2003). [CrossRef]

]. For the modulator part (Fig. 4(b)), a high frequency equivalent circuit model is used to describe the serial impedance Zm. Here: L1 is the electrode inductance and L2 represents the inductive coupling between the substrate and the ground electrode. The losses are described by 3 resistances: RCG - ground metal loss, RSC - corresponding to the induced current in the substrate and RC - the loss dissipation in the conductor strip. The series resistance Rs of the top and part of the middle DBR layers Rs = Rs-top + Rs-middle is calculated by the models described in [35

35. C. Chang, L. Chrostowski, and C. Chang-Hasnain, “Parasitics and design considerations on oxide-implant VC-SELs,” IEEE Photon. Technol. Lett. 13, 1274–1276 (2001). [CrossRef]

, 36

36. W. Nakwaski, M. Osinski, and J. Cheng, “Spreading resistance in proton-implanted vertical-cavity surface-emitting diode lasers,” Appl. Phys. Lett. 61, 3101–3103 (1992). [CrossRef]

]. The parallel admittance Ym is composed of the intrinsic region capacitance Cint, the resistance Ra and the strip capacitance Cext outside of the top mesa. The influence of the mesa walls has been included into Cint and Cext following [30

30. R. Lewen, S. Irmscher, and U. Eriksson, “Microwave CAD circuit Modeling of a traveling-wave electroabsorption modulator,” IEEE Trans. Microw. Theory Tech. 51(4, Part 1), 1117–1128 (2003). [CrossRef]

]. According to the equivalent circuit, Zm and Ym are expressed as:
Zm=jωL1RSC+RCG(RSC+jωL2)ω2L2(L1L2)RSC+RCG+jω(L1L2)+RC
(1)
and
Ym=jωCintRa+1Rs(jωCintRa+1)+Ra+jωCext.
(2)

Fig. 6 Schemes of the two types of TW EOM structures (top) and simplified equivalent circuit of the whole segmented TW-EO modulator (bottom).

2.3. Transmission line modeling

We implement the transfer matrix method [26

26. D.M. Pozar, Microwave Engineering, 2nd ed. (New York: Wiley, 1998)

, 27

27. R.E. Collin, Foundations for Microwave Engineering (IEEE Press, 2001) [CrossRef]

, 38

38. S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers UniversityPiscataway, NJ, 2008)

] in order to calculate the electrical frequency response of the segmented TW electrode EOM. In this method, each section n is described by two values: its characteristic impedance Z0,n=Zn/Yn and its complex propagation constant γn=ZnYn, where Zn is the section series impedance and Yn - the parallel admittance. The propagation of the modulating microwave signal in the section n with length dn is obtained from:
[VninInin]=mn[VnoutInout],
(5)
where the transfer matrix mn is given by:
mn=[cos(γndn)jZ0,nsin(γndn)j1Z0,nsin(γndn)cos(γndn)].
(6)
The voltage VS and the current IS at the voltage source interface (see Fig. 6) are obtained by multiplying the matrices of all N sections in the structure, i.e.:
[VSIS]=[M11M12M21M22][VLIL],M=n=1Nmn.
(7)
Here VL and IL are the voltage and the current at the interface of the load resistance ZL: VL = ZLIL. Having obtained the matrix M of the whole structure, we can express its equivalent characteristic impedance Z0,eq = VS/IS as:
Z0,eq=ZLM11+M12ZLM21+M22,
(8)
Now, the voltage source parameters VS and IS can be expressed as:
VS=VZ0,eqZS+Z0,eq,IS=VZS+Z0,eq,
(9)
where ZS is the voltage source impedance. Having applied these boundary conditions we are able to express the voltage and the current at each interface i between the different sections comprising the TW-EOM:
[ViIi]=n=Nimn1[VSIS],mn1=[cos(γndn)jZ0,nsin(γndn)j1Z0,nsin(γndn)cos(γndn)].
(10)
The forward and the backward propagating voltages in the ith section are calculated as:
Vi+=12(Vi+Z0,iIi),Vi=12(ViZ0,iIi)
(11)
Due to the fact that light emission of the CC-VCSEL with TW electrode configuration occurs perpendicular to the modulation microwave, we do not consider velocity mismatch between this wave and the light wave as a limiting factor of high speed operation. The −3 dB cut-off frequency fcut-off will therefore depend on the propagation losses, the microwave reflections and the saturation velocity of the carriers being swept out from the modulator cavity. Considering the propagation losses, we define the cut-off frequency fcut-off as:
VEOM(fcutoff)=VEOM(fLF)12,
(12)
where the low frequency (LF) is taken equal to fLF = 100 MHz. In order to calculate the sweep out time we use for the carrier saturation velocity a value of vsat = 0.72 × 105 (m/s) [39,40]. The microwave reflection ΓS is defined as the ratio of the backward VS to the forward VS+ voltage at the voltage source interface (see Fig. 6):
ΓS=20log10VS(f)VS+(f).
(13)
We also introduce a new parameter: the voltage modulation efficiency ηM defined as the ratio of the voltage amplitude VEOM at the middle of modulator section to the voltage amplitude of an ideal structure with 50 Ω characteristic impedances of all sections, 50 Ω load resistance and no propagation losses. Due to the fact that ηM decreases with frequency, we take its value at fcut-off:
ηM=VEOM(fcutoff)Videal×100%
(14)
We mention that during optimization we always ascertain that the maximum reflection max(ΓS) given by Eq. (13) is lower than −20 dB in the range from fLF to fcut-off.

3. Simulation results

3.1. TW EOM CC-VCSEL

Fig. 7 Characteristic impedances of the passive and active modulator sections (a) and equivalent characteristic impedances of type A and B structures (b) as a function of frequency of modulation.

In Table 1 and Table 2 we present the modulator and the passive section parameters used to calculate the characteristic impedances and the propagation constants. Gold contacts with conductivity of 4.4643×107 Ω−1 m−1 are used [41].

Table 1. Modulator section parameters

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Table 2. Passive section parameters

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The higher passive sections of type B structure than the ones of type A structure result in smaller strip capacitance but in larger polyimide losses. This causes a significant increase of the characteristic impedance (see Fig. 7(a)).

Table 3. Modulator circuit parameters

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Table 4. Passive circuit parameters (types A, B)

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In the Fig. 8 we present a comparison of the cut-off frequency fcut-off (a) and (b), the maximum reflection max(ΓS) in the range of modulation frequencies fLF < f < fcut-off (c), (d) and ηM (e), (f) for the 2 types of OEM structures. The color scale maps show these 3 parameters as a function of the length dp3 of the passive section p3 and of the load resistance ZL. The lengths of the passive segments are fixed to dp1 = 25 μm and dp2 = 11 μm and the one of the modulator segment - to dm = 12 μm. The EOM cavity is 1.5 λ long. The desirable regions of high cut-off frequency and modulation voltage efficiency are the ones in red color in Fig. 8(a), (b), (e) and (f), whereas the ones of minimal reflection are in blue color in Fig. 8(c) and (d). The cut-off frequency of both structures is limited for a large parameter range in Fig. 8(a), (b) by the carrier sweep-out time which for the presented case of 1.5 λ EOM cavity, gives a value of fcut-off ≈ 330 GHz. Comparing the reflection maps in Fig. 8(c) and (d) we see that the optimum load resistance ZL is close to the equivalent characteristic impedance Z0,eq of about 60 (80) Ω of the whole type A (B) structure (see Fig. 7(b)). For ZL values lower than Z0,eq the voltage efficiency ηM is almost constant, except for short dp3 sections. In that case, also fcut-off reaches its maximum value limited by the sweep out time. If the load resistance is larger than Z0,eq, ηM will rise, but on the price of higher reflection ΓS and lower cut-off frequency fcut-off.

Fig. 8 Color maps presenting the cut-off frequency fcut-off (a), (b), the maximum reflectivity max(ΓS) in the range of fLF to fcut-off (c), (d) and the modulation efficiency ηM (e), (f) for A and B types of TWE-EOM structures (left and right column, respectively) as a function of p3 segment length and load resistance ZL.

In Fig. 9 the response R = 20log10(VEOM(f)/VEOM(LF)) of type A (a) and type B (b) TWE-EOM is presented as a function of modulation frequency. In both types of structures the response is very flat over a wide frequency range. It is worth mentioning, that the reflection - even for values of ZL quite different from the optimal value of Z0,eq - is higher than −20 dB at low modulation frequencies only.

Fig. 9 Frequency response R and microwave reflection ΓS for type A (a) and type B (b) structure. The p3 section length is fixed to dp3 = 250 μm.

In Fig. 10 we present the distribution of the voltage along the type B TW EOM for two frequencies of operation: fLF (a) and fcut-off (b).

Fig. 10 Distribution of the voltage amplitude along type B TW OEM for fLF = 100 MHz (a) and fcut-off = 330 GHz (b).

3.2. Design parameters analysis

Fig. 11 Cut-off frequency fcut-off as a function of the length (a) dp1 of the passive section p1 and (c) dm of the modulator section m. (b) and (d) show the reflection ΓS for the 4 points (A, B, C, D) that are marked in (a) and (c), respectively.

An increase of the electrode stripe width We would influence most of the electrical equivalent circuit parameters of the passive and the modulator sections by lowering their characteristic impedances. This in turn, would lead to smaller load resistance needed for the high speed -low reflection optimization. In Fig. 12 the cut-off frequency fcut-off and the maximal reflection max(ΓS) are shown as a function of load resistance ZL for the type A (a), and type B (b) structures and for 3 different values of the electrode stripe width We. For best performance, the dip of ΓS should be aligned with the maximum of fcut-off (marked with vertical short blue lines). Both structures show the same tendency: the minimum value of the reflection shifts towards smaller load resistance ZL slower than the maximum fcut-off ’border’. This means that for wider electrode strips, one needs to consider the tradeoff between the cut-off frequency and reflection in the TWE-OEM design. In our device, we use segmented transmission line mainly to compensate for the low characteristic impedance of the modulator section by the higher impedance of the passive sections. A change in the electrode strip width influences all types of segments, but a change of the ground slot influences only the modulator section. The wider Wg the faster raises the characteristic impedance Zm with frequency.

Fig. 12 Cut-off frequency fcut-off and the maximum reflection ΓS as a function of load resistance ZL for type A (a), and type B (b) structure and for 3 different values of electrode stripe width We = 12, 16 and 20 μm.

In Fig. 13(left) the cut-off frequency fcut-off and the maximum reflection ΓS are shown as a function of the load resistance ZL for the type A and B structures and for 3 different values of the electrode strip width Wg. The reflectivity ΓS is shown as a function of the modulation frequency on the right side figures for both structure types and for fixed load resistance of ZL = 55 Ω (type A) and ZL = 85 Ω (type B). Reduction of Wg shifts the maximum fcut-off towards smaller ZL. Although, the dip in the max(ΓS(ZL)) dependence stays at the same place when changing the ground slot width, the reflection rises for both structure types. Nevertheless, it does not exceed the maximum value occurring at fLF for the type A structure, which is not the case for the type B structure. In summary, only the type A structure can be optimized for high speed - low reflectivity operation for the smallest Wg = 12 μm equal to We and to the top mesa width: reaching the maximum possible fcut-off and not exceeding −20 dB ΓS reflections. Similar behavior can be observed when changing the top mesa width Wa, but on a much smaller scale.

Fig. 13 (left) Cut-off frequency fcut-off and maximum reflection max(ΓS) as a function of load resistance ZL for type A and type B TW electrode structures and for 3 different values of the ground slot width Wg = 12, 18 and 26; (right) Reflection ΓS as a function of modulation frequency for type A and type B structures and for the 3 values of Wg.

In general, we have observed that type A structure can be optimized for much lower than −20 dB reflection (except for frequencies close to fLF) while being speed - limited by the carrier extraction time even in the case of 1 λ long modulator cavity. However, the modulation efficiency ηM is lower than for the case of type B structure (usually by 10–15 %). Optimized structers of both types with 1.5 λ long EOMcavity are theoretically able to reach fcut-off limited by the carrier saturation velocity; for type A: max(ΓS) = −21.5 dB and ηM = 77 % with ZL = 55 Ω, whereas for type B: max(ΓS) = −22 dB and ηM = 89 % with ZL = 85 Ω.

4. Conclusion

We have proposed an electrooptically modulated coupled-cavity VCSEL with traveling wave electrodes configuration of the modulator cavity in order to overcome the electric parasitics limit on the modulation bandwidth. The optical design has been based on electro-optic effect induced longitudinal mode switching for which recently published experimental data demonstrated a record speed of 52 GHz [23

23. T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express 20(5), 5099–5107 (2012). [CrossRef] [PubMed]

]. We carry out segmented transmission line design in order to compensate for the low impedance of the modulator section and match the 50 Ω electrical network. We have optimized two types of structures and have reached maximum cutoff modulation frequencies limited only by the carrier sweep-out time saturation velocity and having lower than −20 dB reflections to the voltage source and high modulation efficiency of ηM = 77 – 89%. These optimized structures for a modulator cavity length of 1.5 λ are theoretically able to reach ≈ 330 GHz modulation speed.

Acknowledgment

The authors acknowledge the financial support of FWO-Vlaanderen project G.0657.09N and of OZR-VUB.

References and links

1.

B. Lannoo, G. Das, J. Nelis, B. Charbonnier, A. Pizzinat, M. Popov, A. Gavler, C. P. Larsen, D. Chiaroni, T. Koonen, E. Tangdiongga, H. van den Boom, H. Wessing, M. Giltrelli, B. Ortega, I. Artundo, G. Puerto, G. Treffner, J. Faller, E. Hugues Salas, G. Tartarini, P. Faccin, R. Gaudino, E. Ortego, M. Rizzetti, W. Grabowski, and E. Grard, “Grant Agreement No. 212 352, ALPHA Architectures for fLexible Photonic Home and Access networks,” White paper 2011, ”[ONLINE]” (2012). http://www.ict-alpha.eu/upload/institutter/com/alpha/white%20paper%20d1.3p_v01d.pdf

2.

N. Savage, “Linking with light [high-speed optical interconnects],” IEEE Spectros . 39, 32–36 (2002). [CrossRef]

3.

E. Mohammed, A. Alduino, T. Thomas, H. Braunisch, D. Lu, J. Heck, A. Liu, I. Young, B. Barnett, G. Vandentop, and R. Mooney, “Optical interconnect system integration for Ultra-Short-Reach applications,” Intel Technol. J 8(2), 115–127 (2004).

4.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C.-K. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: Terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12, 1032–1044 (2006). [CrossRef]

5.

Y. C. Chang, C. S. Wang, and L. A. Coldren, “High-efficiency, high-speed vcsels with 35Gbit/s error-free operation,” Electron. Lett. 43(19), 1022–1024 (2007). [CrossRef]

6.

A. N. Al-Omari, I. K. Al-Kofahi, and K. L. Lear, “Fabrication, performance and parasitic parameter extraction of 850 nm high-speed vertical-cavity lasers,” Semicond. Sci. Technol. 24 (2009). [CrossRef]

7.

P. Westbergh, J. S. Gustavsson, B. Kogel, A. Haglund, A. Larsson, A. Mutig, A. Nadtochiy, D. Bimberg, and A. Joel, “40 Gbit/s error-free operation of oxide-confined 850 nm VCSEL,” Electron. Lett. 46(14), 1014–1015 (2010). [CrossRef]

8.

P. Moser, P. Wolf, J.A. Lott, G. Larisch, A. Payusov, A. Mutig, W. Unrau, N.N. Ledentsov, W. Hofmann, and D. Bimberg, “High-speed VCSELs for energy efficient computer interconnects,” Proc. of SPIE 8432, 843202 (2012). [CrossRef]

9.

R. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Coupled semiconductor microcavities,” Appl. Phys. Lett. 65(16), 2093–2095 (1994). [CrossRef]

10.

P. Michler, M. Hilpert, and G. Reiner, “Dynamics of dual-wavelength emission from a coupled semiconductor microcavity laser,” Appl. Phys. Lett. 70, 2073–2075 (1997). [CrossRef]

11.

A. Fischer, K. Choquette, W. Chow, H. Hou, and K. Geib, “Coupled resonator vertical-cavity laser diode,” Appl. Phys. Lett. 75, 3020–3022 (1999). [CrossRef]

12.

J. Carlin, R. Stanley, P. Pellandini, U. Oesterle, and M. Ilegems, “The dual wavelength Bi-vertical cavity surface-emitting laser,” Appl. Phys. Lett. 75, 908–910 (1999). [CrossRef]

13.

M. Brunner, K. Gulden, R. Hovel, M. Moser, J. Carlin, R. Stanley, and M. Ilegems, “Continuous-wave dual-wavelength lasing in a two-section vertical-cavity laser,” IEEE Photon. Technol. Lett. 12, 1316–1318 (2000). [CrossRef]

14.

V. Badilita, J. F. Carlin, M. Illegems, M. Brunner, G. Vershaffelt, and K. Panajotov, “Control of polarization switching in vertical coupled-cavities surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 365–367 (2004). [CrossRef]

15.

J. Hudgings, R. Stone, S. Lim, K. Lau, and C. Chang-Hasnain, “Comparative study of the analog performance of a vertical-cavity surface-emitting laser under gain and cavity loss modulation,” Appl. Phys. Lett. 77, 2092–2094 (2000). [CrossRef]

16.

D. M. Grasso, D. K. Serkland, G. M. Peake, K. M. Geib, and K. D. Choquette, “Direct modulation characteristics of composite resonator vertical-cavity lasers,” IEEE J. Quantum Electron. 42, 1248–1254 (2006). [CrossRef]

17.

A. Paraskevopoulos, H. J. Hensel, W. D. Molzow, H. Klein, N. Grote, N. N. Ledentsov, V. A. Shchukin, C. Moeller, A. R. Kovsh, D. A. Livshits, I. L. Krestnikov, S. S. Mikhrin, P. Matthijsse, and G. Kuyt, “Ultra-high-bandwidth (> 35 GHz) electrooptically-modulated VCSEL,” in Optical Fiber Communication Conference, 2006 , 2699–2701 (2006).

18.

J. Van Eisden, M. Yakimov, V. Tokranov, M. Varanasi, E. M. Mohammed, I. A. Young, and S. Oktyabrsky, “Modulation properties of VCSEL with intracavity modulator,” Proc. of SPIE 6484, A4840 (2007).

19.

V. A. Shchukin, N. N. Ledentsov, J. A. Lott, H. Quast, F. Hopfer, L. Y. Karachinsky, M. Kuntz, P. Moser, A. Mutig, A. Strittmatter, V. P. Kalosha, and D. Bimberg, “Ultrahigh-speed electrooptically-modulated VCSELs: modeling and experimental results,” Proc. of SPIE 6889, H8890 (2008).

20.

M. Yakimov, J. van Eisden, V. Tokranov, M. Varanasi, S. R. Oktyabrsky, E. M. Mohammed, and I. A. Young, “Concept of feedback-free high-frequency loss modulation in detuned duo-cavity vertical cavity surface-emitting laser,” J. Vac. Sci. Technol., B 28 (2010). [CrossRef]

21.

C. Chen, K. L. Johnson, M. Hibbs-Brenner, and K. D. Choquette, “Push-Pull Modulation of a Composite-Resonator Vertical-Cavity Laser,” IEEE J. Quantum Electron. 46, 438–446 (2010). [CrossRef]

22.

K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express 18, 27525–27533 (2010). [CrossRef]

23.

T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express 20(5), 5099–5107 (2012). [CrossRef] [PubMed]

24.

M. Zujewski, H. Thienpont, and K. Panajotov, “Electrical Design of High-Speed Electro-Optically Modulated Coupled-Cavity VCSELs,” J. Lightwave Technol. 29(19), 2992–2998 (2011). [CrossRef]

25.

M. Zujewski, H. Thienpont, and K. Panajotov, “Electro-optically modulated coupled-cavity VCSELs: electrical design optimization for high-speed operation,” Proc. of SPIE 8432, 84320C (2012). [CrossRef]

26.

D.M. Pozar, Microwave Engineering, 2nd ed. (New York: Wiley, 1998)

27.

R.E. Collin, Foundations for Microwave Engineering (IEEE Press, 2001) [CrossRef]

28.

R. Lewen, S. Irmscher, U. Westergren, L. Thylen, and U. Eriksson, “Segmented transmission-line electroabsorption modulators,” J. Lightwave Technol. 22(1), 172–179 (2004). [CrossRef]

29.

M. Chacinski, U. Westergren, B. Stoltz, L. Thylen, R. Schatz, and S. Hammerfeldt, “Monolithically Integrated 100 GHz DFB-TWEAM,” J. Lightwave Technol. 27(16), 3410–3415 (2009). [CrossRef]

30.

R. Lewen, S. Irmscher, and U. Eriksson, “Microwave CAD circuit Modeling of a traveling-wave electroabsorption modulator,” IEEE Trans. Microw. Theory Tech. 51(4, Part 1), 1117–1128 (2003). [CrossRef]

31.

M. Chacinski, U. Westergren, B. Stoltz, and L. Thylen, “Monolithically Integrated DFB-EA for 100 Gb/s Ethernet,” IEEE Electron Dev. Lett. 29(12), 1312–1314 (2008). [CrossRef]

32.

“[ONLINE]” (2012). http://www.ioffe.ru/SVA/NSM/Semicond/AlGaAs/bandstr.html

33.

A. Bhatnagar, D. W. E. Allsopp, X. Chen, M. P. Earnshaw, and W. Batty, “Eletrorefraction Associated with WannierStark Localization in Strongly Coupled Three-Quantum-Well Structures,” IEEE J. Quantum Electron. 36, 702–707 (2000). [CrossRef]

34.

M. P. Earnshaw and D. W. E. Allsopp, “Electrooptic Effects in GaAsAlGaAs Narrow Coupled Quantum Wells,” IEEE J. Quantum Electron. 37, 897–904 (2001). [CrossRef]

35.

C. Chang, L. Chrostowski, and C. Chang-Hasnain, “Parasitics and design considerations on oxide-implant VC-SELs,” IEEE Photon. Technol. Lett. 13, 1274–1276 (2001). [CrossRef]

36.

W. Nakwaski, M. Osinski, and J. Cheng, “Spreading resistance in proton-implanted vertical-cavity surface-emitting diode lasers,” Appl. Phys. Lett. 61, 3101–3103 (1992). [CrossRef]

37.

A. Al-Omari and K. Lear, “Dielectric characteristics of spin-coated dielectric films using on-wafer parallel-plate capacitors at microwave frequencies,” IEEE Trans. Dielectr. Electr. Insul. 12, 1151–1161 (2005). [CrossRef]

38.

S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers UniversityPiscataway, NJ, 2008)

39.

“[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/quay/node39.html#fig-40

40.

“[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/brech/ch_5_4.htm

41.

“[ONLINE]” (2012). http://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html

OCIS Codes
(230.2090) Optical devices : Electro-optical devices
(260.6580) Physical optics : Stark effect
(250.4110) Optoelectronics : Modulators
(140.7260) Lasers and laser optics : Vertical cavity surface emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 20, 2012
Revised Manuscript: September 24, 2012
Manuscript Accepted: October 1, 2012
Published: November 5, 2012

Citation
Mateusz Zujewski, Hugo Thienpont, and Krassimir Panajotov, "Traveling wave electrode design of electro-optically modulated coupled-cavity surface-emitting lasers," Opt. Express 20, 26184-26199 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26184


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References

  1. B. Lannoo, G. Das, J. Nelis, B. Charbonnier, A. Pizzinat, M. Popov, A. Gavler, C. P. Larsen, D. Chiaroni, T. Koonen, E. Tangdiongga, H. van den Boom, H. Wessing, M. Giltrelli, B. Ortega, I. Artundo, G. Puerto, G. Treffner, J. Faller, E. Hugues Salas, G. Tartarini, P. Faccin, R. Gaudino, E. Ortego, M. Rizzetti, W. Grabowski, and E. Grard, “Grant Agreement No. 212 352, ALPHA Architectures for fLexible Photonic Home and Access networks,” White paper 2011, ”[ONLINE]” (2012). http://www.ict-alpha.eu/upload/institutter/com/alpha/white%20paper%20d1.3p_v01d.pdf
  2. N. Savage, “Linking with light [high-speed optical interconnects],” IEEE Spectros. 39, 32–36 (2002). [CrossRef]
  3. E. Mohammed, A. Alduino, T. Thomas, H. Braunisch, D. Lu, J. Heck, A. Liu, I. Young, B. Barnett, G. Vandentop, and R. Mooney, “Optical interconnect system integration for Ultra-Short-Reach applications,” Intel Technol. J8(2), 115–127 (2004).
  4. L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C.-K. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: Terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron.12, 1032–1044 (2006). [CrossRef]
  5. Y. C. Chang, C. S. Wang, and L. A. Coldren, “High-efficiency, high-speed vcsels with 35Gbit/s error-free operation,” Electron. Lett.43(19), 1022–1024 (2007). [CrossRef]
  6. A. N. Al-Omari, I. K. Al-Kofahi, and K. L. Lear, “Fabrication, performance and parasitic parameter extraction of 850 nm high-speed vertical-cavity lasers,” Semicond. Sci. Technol.24 (2009). [CrossRef]
  7. P. Westbergh, J. S. Gustavsson, B. Kogel, A. Haglund, A. Larsson, A. Mutig, A. Nadtochiy, D. Bimberg, and A. Joel, “40 Gbit/s error-free operation of oxide-confined 850 nm VCSEL,” Electron. Lett.46(14), 1014–1015 (2010). [CrossRef]
  8. P. Moser, P. Wolf, J.A. Lott, G. Larisch, A. Payusov, A. Mutig, W. Unrau, N.N. Ledentsov, W. Hofmann, and D. Bimberg, “High-speed VCSELs for energy efficient computer interconnects,” Proc. of SPIE8432, 843202 (2012). [CrossRef]
  9. R. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Coupled semiconductor microcavities,” Appl. Phys. Lett.65(16), 2093–2095 (1994). [CrossRef]
  10. P. Michler, M. Hilpert, and G. Reiner, “Dynamics of dual-wavelength emission from a coupled semiconductor microcavity laser,” Appl. Phys. Lett.70, 2073–2075 (1997). [CrossRef]
  11. A. Fischer, K. Choquette, W. Chow, H. Hou, and K. Geib, “Coupled resonator vertical-cavity laser diode,” Appl. Phys. Lett.75, 3020–3022 (1999). [CrossRef]
  12. J. Carlin, R. Stanley, P. Pellandini, U. Oesterle, and M. Ilegems, “The dual wavelength Bi-vertical cavity surface-emitting laser,” Appl. Phys. Lett.75, 908–910 (1999). [CrossRef]
  13. M. Brunner, K. Gulden, R. Hovel, M. Moser, J. Carlin, R. Stanley, and M. Ilegems, “Continuous-wave dual-wavelength lasing in a two-section vertical-cavity laser,” IEEE Photon. Technol. Lett.12, 1316–1318 (2000). [CrossRef]
  14. V. Badilita, J. F. Carlin, M. Illegems, M. Brunner, G. Vershaffelt, and K. Panajotov, “Control of polarization switching in vertical coupled-cavities surface-emitting lasers,” IEEE Photon. Technol. Lett.16, 365–367 (2004). [CrossRef]
  15. J. Hudgings, R. Stone, S. Lim, K. Lau, and C. Chang-Hasnain, “Comparative study of the analog performance of a vertical-cavity surface-emitting laser under gain and cavity loss modulation,” Appl. Phys. Lett.77, 2092–2094 (2000). [CrossRef]
  16. D. M. Grasso, D. K. Serkland, G. M. Peake, K. M. Geib, and K. D. Choquette, “Direct modulation characteristics of composite resonator vertical-cavity lasers,” IEEE J. Quantum Electron.42, 1248–1254 (2006). [CrossRef]
  17. A. Paraskevopoulos, H. J. Hensel, W. D. Molzow, H. Klein, N. Grote, N. N. Ledentsov, V. A. Shchukin, C. Moeller, A. R. Kovsh, D. A. Livshits, I. L. Krestnikov, S. S. Mikhrin, P. Matthijsse, and G. Kuyt, “Ultra-high-bandwidth (> 35 GHz) electrooptically-modulated VCSEL,” in Optical Fiber Communication Conference, 2006, 2699–2701 (2006).
  18. J. Van Eisden, M. Yakimov, V. Tokranov, M. Varanasi, E. M. Mohammed, I. A. Young, and S. Oktyabrsky, “Modulation properties of VCSEL with intracavity modulator,” Proc. of SPIE6484, A4840 (2007).
  19. V. A. Shchukin, N. N. Ledentsov, J. A. Lott, H. Quast, F. Hopfer, L. Y. Karachinsky, M. Kuntz, P. Moser, A. Mutig, A. Strittmatter, V. P. Kalosha, and D. Bimberg, “Ultrahigh-speed electrooptically-modulated VCSELs: modeling and experimental results,” Proc. of SPIE6889, H8890 (2008).
  20. M. Yakimov, J. van Eisden, V. Tokranov, M. Varanasi, S. R. Oktyabrsky, E. M. Mohammed, and I. A. Young, “Concept of feedback-free high-frequency loss modulation in detuned duo-cavity vertical cavity surface-emitting laser,” J. Vac. Sci. Technol., B28 (2010). [CrossRef]
  21. C. Chen, K. L. Johnson, M. Hibbs-Brenner, and K. D. Choquette, “Push-Pull Modulation of a Composite-Resonator Vertical-Cavity Laser,” IEEE J. Quantum Electron.46, 438–446 (2010). [CrossRef]
  22. K. Panajotov, M. Zujewski, and H. Thienpont, “Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching,” Opt. Express18, 27525–27533 (2010). [CrossRef]
  23. T. D. Germann, W. Hofmann, A. M. Nadtochiy, J.-H. Schulze, A. Mutig, A. Strittmatter, and D. Bimberg, “Electro-optical resonance modulation of vertical-cavity surface-emitting lasers,” Opt. Express20(5), 5099–5107 (2012). [CrossRef] [PubMed]
  24. M. Zujewski, H. Thienpont, and K. Panajotov, “Electrical Design of High-Speed Electro-Optically Modulated Coupled-Cavity VCSELs,” J. Lightwave Technol.29(19), 2992–2998 (2011). [CrossRef]
  25. M. Zujewski, H. Thienpont, and K. Panajotov, “Electro-optically modulated coupled-cavity VCSELs: electrical design optimization for high-speed operation,” Proc. of SPIE8432, 84320C (2012). [CrossRef]
  26. D.M. Pozar, Microwave Engineering, 2nd ed. (New York: Wiley, 1998)
  27. R.E. Collin, Foundations for Microwave Engineering (IEEE Press, 2001) [CrossRef]
  28. R. Lewen, S. Irmscher, U. Westergren, L. Thylen, and U. Eriksson, “Segmented transmission-line electroabsorption modulators,” J. Lightwave Technol.22(1), 172–179 (2004). [CrossRef]
  29. M. Chacinski, U. Westergren, B. Stoltz, L. Thylen, R. Schatz, and S. Hammerfeldt, “Monolithically Integrated 100 GHz DFB-TWEAM,” J. Lightwave Technol.27(16), 3410–3415 (2009). [CrossRef]
  30. R. Lewen, S. Irmscher, and U. Eriksson, “Microwave CAD circuit Modeling of a traveling-wave electroabsorption modulator,” IEEE Trans. Microw. Theory Tech.51(4, Part 1), 1117–1128 (2003). [CrossRef]
  31. M. Chacinski, U. Westergren, B. Stoltz, and L. Thylen, “Monolithically Integrated DFB-EA for 100 Gb/s Ethernet,” IEEE Electron Dev. Lett.29(12), 1312–1314 (2008). [CrossRef]
  32. “[ONLINE]” (2012). http://www.ioffe.ru/SVA/NSM/Semicond/AlGaAs/bandstr.html
  33. A. Bhatnagar, D. W. E. Allsopp, X. Chen, M. P. Earnshaw, and W. Batty, “Eletrorefraction Associated with WannierStark Localization in Strongly Coupled Three-Quantum-Well Structures,” IEEE J. Quantum Electron.36, 702–707 (2000). [CrossRef]
  34. M. P. Earnshaw and D. W. E. Allsopp, “Electrooptic Effects in GaAsAlGaAs Narrow Coupled Quantum Wells,” IEEE J. Quantum Electron.37, 897–904 (2001). [CrossRef]
  35. C. Chang, L. Chrostowski, and C. Chang-Hasnain, “Parasitics and design considerations on oxide-implant VC-SELs,” IEEE Photon. Technol. Lett.13, 1274–1276 (2001). [CrossRef]
  36. W. Nakwaski, M. Osinski, and J. Cheng, “Spreading resistance in proton-implanted vertical-cavity surface-emitting diode lasers,” Appl. Phys. Lett.61, 3101–3103 (1992). [CrossRef]
  37. A. Al-Omari and K. Lear, “Dielectric characteristics of spin-coated dielectric films using on-wafer parallel-plate capacitors at microwave frequencies,” IEEE Trans. Dielectr. Electr. Insul.12, 1151–1161 (2005). [CrossRef]
  38. S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers UniversityPiscataway, NJ, 2008)
  39. “[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/quay/node39.html#fig-40
  40. “[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/brech/ch_5_4.htm
  41. “[ONLINE]” (2012). http://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html

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