Traveling wave electrode design of electro-optically modulated coupled-cavity surface-emitting lasers

doi:10.1364/OE.20.026184

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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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▸ Article Outline
– Abstract
1. Introduction
2. Traveling wave electrooptically modulated coupled-cavity VCSEL (TW EOM CC-VCSEL): structure
3. Simulation results
4. Conclusion
– References and links

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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 f_cut-off = 330 GHz with maximum reflection of −22 dB in the range from f_LF = 100 MHz to f_cut-off and 77 – 89% modulation efficiency.

1. Introduction

Constantly growing number of services like: high speed Internet, video streaming and conferencing, remote monitoring or ultra high definition video are the driving force for the next generation networks. Limitations of the copper or coax cable bandwidths are already being reached, and in the long term perspective of expected traffic evolution, only optical networks and interconnects can provide enough capacity and flexibility to satisfy the needs. In long distance communication links, light-based systems are indispensable however, in short distance and local area networks the cost issue of replacing old generation networks with new optical ones prevents their wide employment. It is therefore most important to develop not only high bandwidth and low-power, but also low-cost solutions [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

–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).

]. One of the best candidates for light sources in such systems are Vertical-Cavity Surface-Emitting Lasers (VCSELs). Their properties, like low power consumption, single longitudinal mode operation, circular beam emission, 2D array mass production and on wafer testing are the reason for many groups to explore high-speed VCSEL designs with directly or indirectly modulated devices [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]

–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]

]. Although directly modulated VCSELs recently presented by e. g. Moser et al. [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]

] have shown a record speed in error free transmission of ≈ 45 Gbit/s, the relaxation oscillation (RO) phenomenon which occurs during energy exchange between the carrier and photon reservoirs prevents further increase of modulation bandwidth. The concept of Coupled-Cavity VCSELs (CC-VCSELs) in which two vertical cavities are separated by a coupling mirror [9

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

] suggests several ways of overcoming the RO bandwidth limitation [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]

–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 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

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

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

]. 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

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

–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

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

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

]: 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

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

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

]: an electro-refractive effect wavelength switching [22

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

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

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]

]. 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

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

, 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

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

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

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

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

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 Al_0.2Ga_0.8As / Al_0.9Ga_0.1As quarter-wavelength layers with: 31, 28 and 25 pairs in the top, middle and bottom section, respectively. Heavily doped (p = 20 × 10¹⁸) 3λ/4 Al_0.2Ga_0.8As + λ/4 Al_0.9Ga_0.1As, 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

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

]. The EOM section consists of k periods of 3 strongly coupled GaAs quantum wells (QWs) (k× 3SCQWs) with Al_0.2Ga_0.8As barriers and Al_0.2Ga_0.8As spacers (k = 1, 2, 3 depending on the cavity length). In our simulations we consider 3 different lengths of the EOM cavity: h_a = 1λ, 1.5λ and 2λ. The bottom active cavity is 1λ thick and contains three 8 nm GaAs QWs with 4 nm Al_0.2Ga_0.8As barriers and Al_0.2Ga_0.8As spacers and AlO_x 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

]: 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

]. 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 (λ_S) and the long (λ_L) wavelength modes are quite similar; therefore only the one for the λ_S mode is shown. The experimental data of [23

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

] 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 r_LEO and quadratic s_QEO electro-optic coefficients as in [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]

], i.e. r_LEO = 1.7 × 10⁻¹² m/V and s_QEO = 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

E_{EOM}^{S - > L} \approx - 4.8 \times 10^{6} (V / m)

, a switching between the short λ_S and the long λ_L mode is observed. Moreover, by a small change of the cavity detuning, we can shift

E_{EOM}^{S - > L}

towards higher or lower modulation voltages. As an example, for a 1.5 λ modulator cavity length

E_{EOM}^{S - > 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 (λ_S) optical power distribution along the CC-VCSEL.

Fig. 3 CC-VCSEL resonance wavelengths λ_L (red line) and λ_S (blue line) (a) and threshold gains (b) for the resonant two longitudinal modes as a function of modulating electrical field E_EOM.

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)) h_n, h_a and h_p 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: H_A = h_n + h_a + h_p. W_g is the ground electrode slot and W_a - the top mesa width. The remaining parameters are common for the modulator and the passive sections: W_e - is the micro stripe width and t_c and t_g - the micro stripe and the ground electrode thicknesses. We assume that the metal electrodes are elliptically shaped as in [30

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

]. For the modulator part (Fig. 4(b)), a high frequency equivalent circuit model is used to describe the serial impedance Z_m. 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: R_CG - ground metal loss, R_SC - corresponding to the induced current in the substrate and R_C - the loss dissipation in the conductor strip. The series resistance R_s of the top and part of the middle DBR layers R_s = R_s-top + R_s-middle is calculated by the models described in [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]

]. The parallel admittance Y_m is composed of the intrinsic region capacitance C_int, the resistance R_a and the strip capacitance C_ext outside of the top mesa. The influence of the mesa walls has been included into C_int and C_ext following [30

]. According to the equivalent circuit, Z_m and Y_m are expressed as:

Z_{m} = \frac{j ω L_{1} R_{SC} + R_{CG} (R_{SC} + j ω L_{2}) - ω^{2} L_{2} (L_{1} - L_{2})}{R_{SC} + R_{CG} + j ω (L_{1} - L_{2})} + R_{C}

(1)

and

Y_{m} = \frac{j ω C_{int} R_{a} + 1}{R_{s} (j ω C_{int} R_{a} + 1) + R_{a}} + j ω C_{ext} .

(2)

In Fig. 5(b), the series impedance Z_p of a passive section is composed of the strip conductor inductance L_p and losses R_Cp. The equivalent admittance Y_p consists of the polyimide losses R_shunt and R_p [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]

, 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]

] and the micro strip capacitance C_p. R_shunt, the polyimide shunt resistance, is assumed to be of the order of R_shunt ∼ 10¹² Ω [6

]. The Z_p and Y_p are expressed as:

Z_{p} = j ω L_{p} + R_{Cp}

(3)

Y_{p} = \frac{j ω C_{p}}{j ω C_{p} R_{p} + 1} + \frac{1}{R_{shunt}}

(4)

We compare hereafter two different structures, called type A and type B and presented in Fig. 6. Sections p₁ and p₃ are the passive ones, placed next to the voltage source and the load resistance, respectively. Sandwiched between them are the passive sections p₂ and the active modulator section m. The lengths of the p₂ sections d_p₂ are equal to the difference between the bottom and the top mesa radii of the CC-VCSEL: r_b = d_p₂ + r_t. All sections of the type A device have the same height H_A equal to H_A = h_n + h_a + h_p - which is the top mesa height. For the type B structure the p₁ and p₃ section heights are equal to H_B, which is the sum of the top and bottom mesas: H_B = H_A + H_{bottom mesa}. In Fig. 6 we also present a simplified electrical equivalent circuit of the whole segmented transmission line structure implied for calculating the electrical cut-off frequency.

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

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

, 27

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

, 38

S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University Piscataway, 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

Z_{0, n} = \sqrt{Z_{n} / Y_{n}}

and its complex propagation constant

γ_{n} = \sqrt{Z_{n} Y n}

, where Z_n is the section series impedance and Y_n - the parallel admittance. The propagation of the modulating microwave signal in the section n with length d_n is obtained from:

[\begin{matrix} V_{n}^{in} \\ I_{n}^{in} \end{matrix}] = m_{n} [\begin{matrix} V_{n}^{out} \\ I_{n}^{out} \end{matrix}],

(5)

where the transfer matrix m_n is given by:

m_{n} = [\begin{matrix} cos (γ_{n} d_{n}) & j Z_{0, n} sin (γ_{n} d_{n}) \\ j \frac{1}{Z_{0, n}} sin (γ_{n} d_{n}) & cos (γ_{n} d_{n}) \end{matrix}] .

(6)

The voltage V_S and the current I_S at the voltage source interface (see Fig. 6) are obtained by multiplying the matrices of all N sections in the structure, i.e.:

[\begin{matrix} V_{S} \\ I_{S} \end{matrix}] = [\begin{matrix} M_{11} & M_{12} \\ M_{21} & M_{22} \end{matrix}] [\begin{matrix} V_{L} \\ I_{L} \end{matrix}], M = \prod_{n = 1}^{N} m_{n} .

(7)

Here V_L and I_L are the voltage and the current at the interface of the load resistance Z_L: V_L = Z_LI_L. Having obtained the matrix M of the whole structure, we can express its equivalent characteristic impedance Z_0,eq = V_S/I_S as:

Z_{0, eq} = \frac{Z_{L} M_{11} + M_{12}}{Z_{L} M_{21} + M_{22}},

(8)

Now, the voltage source parameters V_S and I_S can be expressed as:

V_{S} = \frac{V Z_{0, eq}}{Z_{S} + Z_{0, eq}}, I_{S} = \frac{V}{Z_{S} + Z_{0, eq}},

(9)

where Z_S 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:

[\begin{matrix} V_{i} \\ I_{i} \end{matrix}] = \prod_{n = N}^{i} m_{n}^{- 1} [\begin{matrix} V_{S} \\ I_{S} \end{matrix}], m_{n}^{- 1} = [\begin{matrix} cos (γ_{n} d_{n}) & - j Z_{0, n} sin (γ_{n} d_{n}) \\ - j \frac{1}{Z_{0, n}} sin (γ_{n} d_{n}) & cos (γ_{n} d_{n}) \end{matrix}] .

(10)

The forward and the backward propagating voltages in the i^th section are calculated as:

V_{i}^{+} = \frac{1}{2} (V_{i} + Z_{0, i} I_{i}), V_{i}^{-} = \frac{1}{2} (V_{i} - Z_{0, i} I_{i})

(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 f_cut-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 f_cut-off as:

V_{EOM} (f_{cut - off}) = V_{EOM} (f_{LF}) \frac{1}{\sqrt{2}},

(12)

where the low frequency (LF) is taken equal to f_LF = 100 MHz. In order to calculate the sweep out time we use for the carrier saturation velocity a value of v_sat = 0.72 × 10⁵ (m/s) [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

]. The microwave reflection Γ_S is defined as the ratio of the backward

V_{S}^{-}

to the forward

V_{S}^{+}

voltage at the voltage source interface (see Fig. 6):

Γ_{S} = 20 {log}_{10} \frac{V_{S}^{-} (f)}{V_{S}^{+} (f)} .

(13)

We also introduce a new parameter: the voltage modulation efficiency η_M defined as the ratio of the voltage amplitude V_EOM 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 η_M decreases with frequency, we take its value at f_cut-off:

η_{M} = \frac{V_{EOM} (f_{cut - off})}{V_{ideal}} \times 100 %

(14)

We mention that during optimization we always ascertain that the maximum reflection max(Γ_S) given by Eq. (13) is lower than −20 dB in the range from f_LF to f_cut-off.

3. Simulation results

3.1. TW EOM CC-VCSEL

For CC-VCSEL with traditional lumped electrodes, we have shown in our previous works [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

] that the pnp configuration performs better - not only because of the higher electrical cut-off frequency, but also because of the lower internal losses. However, for the TW electrode CC-VCSEL considered here the npn structure results in higher series resistance R_s of the DBRs in the modulator mesa, which leads to faster increase of its characteristic impedance with frequency (Fig. 7(a)). This makes the overall electrical performance of npn CC-VCSEL better as the modulator series resistance is typically much lower than the optimum 50 Ω. Furthermore, the threshold gain increase is not significant:

g_{th}^{npn} - g_{th}^{pnp} \approx 15 {cm}^{- 1}

(13 cm⁻¹) for λ_S (λ_L), mainly due to the low doping of the DBRs.

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

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

Table 1 Modulator section parameters

h_n	4.914	μm
h_a	0.523	μm
h_p	2.280	μm

W_e	12	μm
W_a	12	μm
W_g	26	μm

t_c	2.0	μm
t_g	0.3	μm

σ_p-sub	3.84 × 10³	Ω⁻¹ m⁻¹
P_layer-thick.	0.298	μm

Table 2 Passive section parameters

H_A	7.717	μm
H_B	14.800	μm

W_e	12	μm
W_g	0	μm

t_c	2.0	μm
t_g	0.3	μm

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)).

In Table 3 and 4 we list the calculated parameters for the equivalent electrical circuits of the modulator and the passive sections. We assume, as in our previous work [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]

], that the capacitances and polyimide losses are frequency dependent up to 40 GHz and for f > 40 GHz remain constant.

Table 3 Modulator circuit parameters

L₁	422	nH/m
L₂	240	nH/m

R_SC	35	MΩ/m
R_C	461	$Ω / (m \sqrt{GHz})$
R_CG	7	$Ω / (m \sqrt{GHz})$
R_s	86.4	Ωmm
R_a	174	GΩm

C_int (LF)	2284	pF/m
C_ext (LF)	68	pF/m

Table 4 Passive circuit parameters (types A, B)

L_p,A	309	nH/m
L_p,B	420	nH/m

R_C,A(LF)	213	$Ω / (m \sqrt{GHz})$
R_C,B(LF)	209	$Ω / (m \sqrt{GHz})$
R_p,A(LF)	6.1	kΩm
R_p,B(LF)	11.6	kΩm
R_shunt	1×10¹²	Ω/m

C_p,A(LF)	103	pF/m
C_p,B(LF)	73	pF/m

In the Fig. 8 we present a comparison of the cut-off frequency f_cut-off (a) and (b), the maximum reflection max(Γ_S) in the range of modulation frequencies f_LF < f < f_cut-off (c), (d) and η_M (e), (f) for the 2 types of OEM structures. The color scale maps show these 3 parameters as a function of the length d_p₃ of the passive section p₃ and of the load resistance Z_L. The lengths of the passive segments are fixed to d_p₁ = 25 μm and d_p₂ = 11 μm and the one of the modulator segment - to d_m = 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 f_cut-off ≈ 330 GHz. Comparing the reflection maps in Fig. 8(c) and (d) we see that the optimum load resistance Z_L is close to the equivalent characteristic impedance Z_0,eq of about 60 (80) Ω of the whole type A (B) structure (see Fig. 7(b)). For Z_L values lower than Z_0,eq the voltage efficiency η_M is almost constant, except for short d_p₃ sections. In that case, also f_cut-off reaches its maximum value limited by the sweep out time. If the load resistance is larger than Z_0,eq, η_M will rise, but on the price of higher reflection Γ_S and lower cut-off frequency f_cut-off.

Fig. 8 Color maps presenting the cut-off frequency f_cut-off (a), (b), the maximum reflectivity max(Γ_S) in the range of f_LF to f_cut-off (c), (d) and the modulation efficiency η_M (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 Z_L.

In Fig. 9 the response R = 20log₁₀(V_EOM(f)/V_EOM(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 Z_L quite different from the optimal value of Z_0,eq - is higher than −20 dB at low modulation frequencies only.

Fig. 9 Frequency response R and microwave reflection Γ_S for type A (a) and type B (b) structure. The p₃ section length is fixed to d_p₃ = 250 μm.

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

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

3.2. Design parameters analysis

In the previous section we have shown results for structures which main dimensions are listed in Table 1 and Table 2. In this section, we will discuss the impact on the TW OEM performance of any change of these parameters. One of the way to increase the electrical cut-off frequency of a lumped electrode CC-VCSEL is to decrease p − i − n junction capacitance [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]

]. This can be done by either reducing the lateral size of the whole device or by increasing the thickness of the intrinsic region [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]

]. However, longer modulator cavity means longer extraction time of carriers generated in the QWs. Furthermore, the potential difference between modulator electrodes has to be higher in case of thicker intrinsic layer to achieve the same electric field strength as in case of shorter cavity. Integrating CC-VCSEL into a TW structure allows reduction of EOM cavity length. Moreover, it becomes preferable to have it short, because carrier sweep out time becomes one of the most influential factors on modulation speed: e.g. 1 λ long EOM cavity would be limited to ≈ 500 GHz whereas 2 λ long EOM cavity - to ≈ 250 GHz. As a general rule, shorter EOM cavity is more fragile to small parameter change regarding the electrical as well as the optical design. On the other hand, if carefully tuned it is capable of extremely high modulation speeds.

In Fig. 11 the dependences of the cut-off frequency f_cut-off on the passive section p₁ length d_p1 (a) and on the modulator section m length d_m (c) are presented. Figures 11(b) and (d) show the reflection Γ_S for the 4 points (A, B, C, D) that are marked in Fig. 11(a) and (c), respectively. Because both d_m and d_p₁ are small, even if they are increased slightly (e.g. by 5, 10 μm) the modulation speed would decrease dramatically. On the other hand, an increase of d_p1 would result in lower reflections to the voltage source, except for frequencies close to f_LF, for which the reflection stays at the same level. Contrary to that behavior, an increase of modulator length d_m would also increase the reflection Γ_S. The same situation happens when the length d_p2 of the passive section p₂ is increased. Larger diameters of the bottom CC-VCSEL mesa would basically increase the total lengths of the passive sections before and after the modulator. For the case of the passive section next to the load resistance, this would not influence the device performance (see Fig. 8) however, for the case of the passive section before the modulator the losses would increase.

Fig. 11 Cut-off frequency f_cut-off as a function of the length (a) d_p₁ of the passive section p₁ and (c) d_m of the modulator section m. (b) and (d) show the reflection Γ_S for the 4 points (A, B, C, D) that are marked in (a) and (c), respectively.

An increase of the electrode stripe width W_e 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 f_cut-off and the maximal reflection max(Γ_S) are shown as a function of load resistance Z_L for the type A (a), and type B (b) structures and for 3 different values of the electrode stripe width W_e. For best performance, the dip of Γ_S should be aligned with the maximum of f_cut-off (marked with vertical short blue lines). Both structures show the same tendency: the minimum value of the reflection shifts towards smaller load resistance Z_L slower than the maximum f_cut-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 W_g the faster raises the characteristic impedance Z_m with frequency.

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

In Fig. 13(left) the cut-off frequency f_cut-off and the maximum reflection Γ_S are shown as a function of the load resistance Z_L for the type A and B structures and for 3 different values of the electrode strip width W_g. The reflectivity Γ_S is shown as a function of the modulation frequency on the right side figures for both structure types and for fixed load resistance of Z_L = 55 Ω (type A) and Z_L = 85 Ω (type B). Reduction of W_g shifts the maximum f_cut-off towards smaller Z_L. Although, the dip in the max(Γ_S(Z_L)) 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 f_LF 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 W_g = 12 μm equal to W_e and to the top mesa width: reaching the maximum possible f_cut-off and not exceeding −20 dB Γ_S reflections. Similar behavior can be observed when changing the top mesa width W_a, but on a much smaller scale.

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

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

]. 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 η_M = 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.

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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

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
N. Savage, “Linking with light [high-speed optical interconnects],” IEEE Spectros. 39, 32–36 (2002). [CrossRef]
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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]
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]
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]
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]
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]
R. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Coupled semiconductor microcavities,” Appl. Phys. Lett.65(16), 2093–2095 (1994). [CrossRef]
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]
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]
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]
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]
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]
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]
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]
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).
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).
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).
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]
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]
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]
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]
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]
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]
D.M. Pozar, Microwave Engineering, 2nd ed. (New York: Wiley, 1998)
R.E. Collin, Foundations for Microwave Engineering (IEEE Press, 2001) [CrossRef]
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]
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]
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]
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]
“[ONLINE]” (2012). http://www.ioffe.ru/SVA/NSM/Semicond/AlGaAs/bandstr.html
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]
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]
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]
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]
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]
S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers UniversityPiscataway, NJ, 2008)
“[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/quay/node39.html#fig-40
“[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/brech/ch_5_4.htm
“[ONLINE]” (2012). http://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html

Alduino, A.
Al-Kofahi, I. K.
Allsopp, D. W. E.
Al-Omari, A.
Al-Omari, A. N.
Badilita, V.
Baks, C. W.
Barnett, B.
Batty, W.
Bhatnagar, A.
Bimberg, D.
Bour, D. P.
Braunisch, H.
Brunner, M.
Budd, R. A.
Carlin, J.
Carlin, J. F.
Chacinski, M.
Chang, C.
Chang, Y. C.
Chang-Hasnain, C.
Chen, C.
Chen, X.
Cheng, J.
Chiniwalla, P.
Choquette, K.
Choquette, K. D.
Chow, W.
Chrostowski, L.
Coldren, L. A.
Collin, R.E.
Dangel, R.
Doany, F. E.
Dolfi, D. W.
Earnshaw, M. P.
Eriksson, U.
Fischer, A.
Geib, K.
Geib, K. M.
Germann, T. D.
Grasso, D. M.
Grote, N.
Guckenberger, D.
Gulden, K.
Gustavsson, J. S.
Haglund, A.
Hammerfeldt, S.
Heck, J.
Hegde, S.
Hensel, H. J.
Hibbs-Brenner, M.
Hilpert, M.
Hofmann, W.
Hopfer, F.
Horst, F.
Hou, H.
Houdre, R.
Hovel, R.
Hudgings, J.
Ilegems, M.
Illegems, M.
Irmscher, S.
Joel, A.
John, R. A.
Johnson, K. L.
Kalosha, V. P.
Karachinsky, L. Y.
Kash, J. A.
Klein, H.
Kogel, B.
Kovsh, A. R.
Krestnikov, I. L.
Kucharski, D.
Kuchta, D. M.
Kuntz, M.
Kuyt, G.
Kwark, Y. H.
Larisch, G.
Larsson, A.
Lau, K.
Lear, K.
Lear, K. L.
Ledentsov, N. N.
Ledentsov, N.N.
Lewen, R.
Libsch, F. R.
Lim, S.
Lin, C.-K.
Liu, A.
Livshits, D. A.
Lott, J. A.
Lott, J.A.
Lu, D.
Matthijsse, P.
Michler, P.
Mikhrin, S. S.
Moeller, C.
Mohammed, E.
Mohammed, E. M.
Molzow, W. D.
Mooney, R.
Moser, M.
Moser, P.
Mutig, A.
Nadtochiy, A.
Nadtochiy, A. M.
Nakwaski, W.
Nyikal, H.
Nystrom, M.
Oesterle, U.
Offrein, B. J.
Oktyabrsky, S.
Oktyabrsky, S. R.
Orfanidis, S.J.
Osinski, M.
Panajotov, K.
Paraskevopoulos, A.
Patel, C. S.
Payusov, A.
Peake, G. M.
Pellandini, P.
Pepeljugoski, P. K.
Pozar, D.M.
Quast, H.
Reiner, G.
Rosner, J.
Savage, N.
Schares, L.
Schatz, R.
Schaub, J. D.
Schow, C. L.
Schulze, J.-H.
Schuster, C.
Serkland, D. K.
Shan, L.
Shchukin, V. A.
Stanley, R.
Stoltz, B.
Stone, R.
Strittmatter, A.
Tan, M. R. T.
Tandon, A.
Thienpont, H.
Thomas, T.
Thylen, L.
Tokranov, V.
Trewhella, J. M.
Trott, G. R.
Tsang, C. K.
Unrau, W.
van Eisden, J.
Vandentop, G.
Varanasi, M.
Vershaffelt, G.
Wang, C. S.
Weisbuch, C.
Westbergh, P.
Westergren, U.
Wolf, P.
Yakimov, M.
Young, I.
Young, I. A.
Zujewski, M.

Appl. Phys. Lett.

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

Electron. Lett.

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]
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]

IEEE Electron Dev. Lett.

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]

IEEE J. Quantum Electron.

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]
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]
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]
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]

IEEE J. Sel. Top. Quantum Electron.

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]

IEEE Photon. Technol. Lett.

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]
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]
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]

IEEE Spectros

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

IEEE Trans. Dielectr. Electr. Insul.

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]

IEEE Trans. Microw. Theory Tech.

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]

Intel Technol. J

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).

J. Lightwave Technol.

J. Vac. Sci. Technol., B

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]

Opt. Express

Optical Fiber Communication Conference, 2006

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).

Proc. of SPIE

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).
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).
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]
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]

Semicond. Sci. Technol.

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]

Other

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
D.M. Pozar, Microwave Engineering, 2nd ed. (New York: Wiley, 1998)
R.E. Collin, Foundations for Microwave Engineering (IEEE Press, 2001) [CrossRef]
“[ONLINE]” (2012). http://www.ioffe.ru/SVA/NSM/Semicond/AlGaAs/bandstr.html
S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers UniversityPiscataway, NJ, 2008)
“[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/quay/node39.html#fig-40
“[ONLINE]” (2012). http://www.iue.tuwien.ac.at/phd/brech/ch_5_4.htm
“[ONLINE]” (2012). http://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html

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