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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12318–12325
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Large optical spectral range dispersion engineered silicon-based photonic crystal waveguide modulator

Amir Hosseini, Xiaochuan Xu, Harish Subbaraman, Che-Yun Lin, Somayeh Rahimi, and Ray T. Chen  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 12318-12325 (2012)
http://dx.doi.org/10.1364/OE.20.012318


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Abstract

We present a dispersion engineered slow light silicon-based photonic crystal waveguide PIN modulator. Low-dispersion slow light transmission over 18nm bandwidth under the silica light line with a group index of 26.5 is experimentally confirmed. We investigate the variations of the modulator figure of merit, Vπ × L, as a function of the optical carrier wavelength over the bandwidth of the fundamental photonic crystal waveguide defect mode. A large signal operation with a record low maximum Vπ × L of 0.0464 V⋅mm over the low-dispersion optical spectral range is demonstrated. We also report the device operation at 2GHz.

© 2012 OSA

1. Introduction

Slow light in photonic crystal waveguides (PCWs) has been extensively studied for potential on-chip applications such as optical delay lines and enhanced non-linearity due to increased light-matter interaction [1

1. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

-3

3. R. Iliew, C. Etrich, T. Pertsch, and F. Lederer, “Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals,” Phys. Rev. B 77(11), 115124 (2008). [CrossRef]

]. Ultra-compact on-chip photonic devices can be realized by exploiting the enhanced light-matter interaction provided by the slow light operation [4

4. Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005). [CrossRef]

]. However, the narrow optical bandwidth of non-engineered PCW slabs due to their highly dispersive group velocity in the slow light regime restricts their applications [5

5. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001). [CrossRef] [PubMed]

]. For example, a PCW Mach-Zehnder modulator operating with RF bandwidth as high as 10 Gb⋅s−1 was recently reported, with an optical wavelength range of only 0.7 nm [6

6. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

-7

7. H. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “Photonic Crystal Silicon Optical Modulators: Carrier-Injection and Depletion at 10 Gb/s,” IEEE J. Quantum Electron. 48(2), 210–220 (2012). [CrossRef]

]. Also, an electro-optic polymer refilled double heterostructure slotted PCW was shown to enable optical modulation over 0.7 nm optical wavelength range [8

8. J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, and J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009). [CrossRef]

]. Therefore, in order to cover about 20 nm optical bandwidth in a typical integrated dense wavelength-division multiplexing (DWDM) system, several different designs will be necessary. In order to avoid having different PCW modulators for operation at each optical wavelength, a PCW modulator that can achieve slow light operation over a large bandwidth is required. A low-voltage and high speed optical modulator based on band-engineered slotted PCWs refilled with an electro-optic polymer was theoretically investigated in [9

9. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

]. High-yield and repeatable low-dispersion slow-light devices can be achieved by fabrication-friendly dispersion engineering of PCWs with only a single hole size [10

10. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

-12

12. S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

]. A band-engineered thermo-optic modulator with 10 nm optical wavelength range was demonstrated in [13

13. L. O'Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2(3), 404–414 (2010). [CrossRef]

]. Additionally, insertion of a group-index-taper coupler between the conventional strip waveguides and the low group velocity PCWs is necessary in order to efficiently couple light into and out of the device [14

14. A. Mekis and J. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19(6), 861–865 (2001). [CrossRef]

]. It was recently shown that due to the existence of the evanescent modes at the boundary between two photonic crystals with different group indices [15

15. C. Martijn de Sterke, K. B. Dossou, T. P. White, L. C. Botten, and R. C. McPhedran, “Efficient coupling into slow light photonic crystal waveguide without transition region: role of evanescent modes,” Opt. Express 17(20), 17338–17343 (2009). [CrossRef] [PubMed]

], short (8-16 periods) step-couplers can be used for efficient coupling between single mode silicon strip waveguides and low-dispersion slow light PCWs [16

16. A. Hosseini, X. Xu, D. N. Kwong, H. Subbaraman, W. Jiang, and R. T. Chen, “On the role of evanescent modes and group index tapering in slow light photonic crystal waveguide coupling efficiency,” Appl. Phys. Lett. 98(3), 031107 (2011). [CrossRef]

].

In this paper, we report a Mach Zehnder Interferometer (MZI) modulator based on a low-dispersion slow-light PCW with step couplers with the lowest Vπ × L reported for a PCW based modulator to the best of our knowledge. We also investigate the variation of Vπ × L as a function of the optical carrier wavelength, and experimentally confirm a low and nearly constant Vπ × L over the low-dispersion slow light transmission region. Modulation operation up to 2 GHz is also experimentally confirmed using lumped electrodes.

2. Design and simulation

A schematic of the band engineered PCW is shown in Fig. 1(a)
Fig. 1 (a) A schematic of band engineered PCW and PCW coupler. (b) Band structures of the designed band-engineered PCW and step PCW coupler. Silica light line (n = 1.45) is shown by a dashed green light. (c) Variations of the group index and (d) group velocity dispersion (GVD) over the bandwidth of intersect. (b), (c) and (d) are simulation results using 3D Rsoft Bandsolve. The low-dispersion slow-light wavelength range is highlighted in (b), (c) and (d).
. The lattice constant is a = 392 nm. The thickness of the silicon layer and the buried oxide layers are 250 nm and 3 µm, respectively. Refractive indices of the top cladding, core layer, and the bottom cladding materials are nair = 1, nSi = 3.47, nSiO2 = 1.45, respectively. Dispersion engineering is done by shifting the 3 innermost rows parallel to the defect line [12

12. S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

] with the parameters s1, s2, and s3, as depicted in Fig. 1(a). Figure 2(b)
Fig. 2 Schematic of (a) PIN diode embedded PCW modulator arm, and (b) cross section showing doping concentrations and structural dimensions
shows the simulated band diagram for the dispersion engineered PCW with dW = 0, s1 = 0, s2 = −0.05a, s3 = 0.25a, and r = 0.27a, where dW is the change in the width of the defect line with respect to a W1 PCW, and r is the hole radius. Variations of the group index (ng) and group velocity dispersion (GVD) as functions of the wavelength are shown in Figs. 2(c) and 2(d), respectively. Group index ng = 26.7 ± 10% over a bandwidth of 18 nm (1539 nm~1557 nm), corresponding to delay–normalized bandwidth product of ng(∆ω/ω) = 0.31, is achieved.

In order to efficiently couple light into and out of the PCW from the input and output strip silicon waveguides, 8-period long PCW step couplers (dW = 0.15a, s1 = 0, s2 = 0, s3 = 0, and r = 0.27a) are designed to interface the input and output strip waveguide to the slow light PCW [12

12. S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

]. The band diagram of the PCW coupler is depicted in Fig. 1(b) that shows an overlap between the low-dispersion slow-light bandwidth of the engineered PCW and the low-dispersion fast-light bandwidth of the PCW coupler. Although the usable part of the band of the step coupler lies slightly above the silica light line, both numerical and experimental results show that the silica bottom cladding causes negligible radiation loss for a small number of periods (~<20) [16

16. A. Hosseini, X. Xu, D. N. Kwong, H. Subbaraman, W. Jiang, and R. T. Chen, “On the role of evanescent modes and group index tapering in slow light photonic crystal waveguide coupling efficiency,” Appl. Phys. Lett. 98(3), 031107 (2011). [CrossRef]

- 19

19. C. Y. Lin, A. X. Wang, W. C. Lai, J. L. Covey, S. Chakravarty, and R. T. Chen, “Coupling loss minimization of slow light slotted photonic crystal waveguides using mode matching with continuous group index perturbation,” Opt. Lett. 37(2), 232–234 (2012). [CrossRef]

].

In order to design a MZI modulator, one notices that utilizing the perturbation theory, the required length (L) of the MZI to achieve a π phase shift is given as [2

2. M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19(9), 2052–2059 (2002). [CrossRef]

]
Lλ012σ(nδn)1ng
(2)
where, λ0 is the free space wavelength, σ is the fraction of the total optical mode energy that propagates inside the region where the refractive index (n) is perturbed by an amount of δn. ng = c/vg is the group index, where c and vg are the speed of light and optical mode group velocity, respectively. Due to the high group index (c/vg > 25) offered by our design, the length of the electrodes along the PCW can be short. We choose a length of 80 µm, in order to achieve π phase shift with low power operation, i.e. low δn change. In order to achieve the required refractive index perturbation, plasma dispersion effect in a PIN structure is utilized. A schematic of the structure in the active arm is shown in Fig. 2(a), and the doping profile is shown in Fig. 2(b).

3. Fabrication

A symmetric MZI is designed by placing two 98 µm long PCWs (including 6.3 µm couplers) at the two arms. 1x2 Multimode Mode Interference couplers (MMIs) are used for beam splitting/combining, as shown in Fig. 3(a)
Fig. 3 A schematic of photonic crystal MZI modulator; scanning electronic microscope images of the active arm of the modulator and the photonic crystal waveguide coupler are shown as insets.
. One of the PCWs is doped to from a PIN, as shown in Fig. 3(b). The length of the electrodes is slightly less than that of the slow light PCWs to avoid break-down due to the generation of dense currents along the edges of PCWs, as discussed in [23

23. L. Gu, Micro-and Nano-Periodic-Structure-Based Devices for Laser Beam Control 99–100 (ProQuest, 2007).

].

The modulator is fabricated on a Uni-bond silicon-on-insulator wafer with a 250 nm top silicon layer and 3 µm buried oxide layer. Photonic crystal waveguides, photonic crystal couplers and strip waveguides are patterned in one step using a JEOL JBX-6000FS electron-beam lithography system followed by reactive ion etching. The windows for P+ and N+ implantation were opened by photolithography. Ion implantations of Boron at 30 KeV (surface concentration of 3.00 × 1014/cm2) and phosphorus at 50 KeV (surface concentration of 1.72 × 1014/cm2) were performed to obtain an average doping concentration of about 5 × 1019 cm−3. Thermal rapid annealing for 1 min at 950 °C in a flowing nitrogen environment was performed afterwards to anneal the lattice defects and activate the implanted ions.

Electrode contact windows were then opened by photolithography and the native oxide inside the windows was removed. Aluminum electrodes were made by electron-beam evaporation and a subsequent lift off process. Finally, an ohmic contact was formed by post metallization annealing at a temperature of 400 °C for 30 mins [20

20. L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of pin-diode-based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008). [CrossRef]

]. SEM images of the fabricated PCW on one arm of the fabricated modulator device are also shown in Fig. 3.

4. Device characterization

The group index of a single PCW is determined through on-chip Fourier transform spectral interferometer, as previously reported [12

12. S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

]. Figure 4(a)
Fig. 4 (a) Output spectrum of PCW device (red curve) and the calculated group index based on FT method (blue curve). The PCW transmission curve is also provided as a reference; (b) static characteristic of the PIN diode;
shows the measured group index as a function of wavelength. Our results indicate a low-dispersion (with less than ± 10% fluctuations in group index) transmission over 18 nm bandwidth (1539 nm~1557 nm) with an average group index of 26.5. Figure 4(a) also shows the transmission characteristics of a single photonic crystal waveguide (including PCW couplers) obtained by coupling a Transverse Electric (TE)-polarized light from a broadband amplified spontaneous emission (ASE) source covering 1520~1620 nm into the Fourier transform spectral interferometer [12

12. S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

]. The transmission data is normalized to the output spectrum of a single mode waveguide. The insertion loss of a single PCW (excluding fiber-waveguide coupling losses and propagation loss inside silicon waveguides) is determined to be 3.8 ± 1.1 dB over the low dispersion bandwidth (1539 nm~1557 nm) [12

12. S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

].

The total insertion loss (fiber-to-fiber) is 19.8dB, which includes 7dB Fiber-to-strip waveguide coupling loss per facet, 3dB insertion loss for each MMI, and 3.8dB insertion loss for the PCW. From data mentioned above, one can see that the loss mainly comes from the fiber-to-waveguide coupling.

Before performing the modulation tests, we first performed static tests on the fabricated modulator devices. The static characteristic of the PIN diode obtained using Agilent B1500a semiconductor parameter analyzer is shown in Fig. 4(b). The forward linear resistance is ~200 Ohm.

Measurements of the figure of merit Vπ × L and data transmission, described below, are carried out by coupling light from a TE-polarized tunable laser (Santec MLS-2000) into the device through butt coupling and tuning to λ = 1550.48 nm. The modulated output is detected with a gain switchable photodetector (Thorlab PDA10CS) and displayed on the oscilloscope (Agilent 86100A). The voltage Vπ required to produce a carrier injection-induced π phase shift is measured by applying a 100 kHz triangular electrical drive signal, as shown in Fig. 5(a)
Fig. 5 (a) triangular electrical drive signal with a Vpp of 1.12 V and Voffset of 1.25 V (top). The over modulated optical signal indication a Vπ of 0.58 V (bottom); (b) Variations of Vπ versus the optical carrier wavelength; (c) the optical signal of 2 GHz operation at λ = 1550.48 nm. The low-dispersion slow-light wavelength range is highlighted in (b).
, to a MZI modulator with 80 μm long active arm under a forward bias Vbias = 1.25 V. The drive amplitude is increased until the slope of the modulated optical signal changed sign at the peaks/troughs of the drive waveform, as illustrated in Fig. 5(a) [6

6. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

]. A complete half-period of optical modulation is observed for a peak-to-peak applied voltage of Vπ = 0.58 V, leading to a figure of merit of Vπ × L = 0.0464 V⋅mm, which is less than one third of the lowest Vπ × L for a PCW modulator reported so far [6

6. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

].

Next, by tuning the optical carrier wavelength over the C band (1520 nm-1560 nm), we obtained variations of Vπ versus optical wavelength as shown in Fig. 5(b). Due to Fabry-Perot oscillations caused by the input and output facets and also back reflections at the MMI's and PCW's interfaces with the strip waveguides, the output optical power fluctuates with wavelength over the low-dispersion bandwidth. At wavelengths that correspond to the peaks of the Fabry-Perot oscillations, the output optical power is high and we are able to observe clear over-modulations [see Fig. 5(b)]. From the over-modulated signal, we were able to deduce the Vπ value.

According to Eq. (2), at a constant L, since δn is linearly proportional to Vπ, one can show
VπBλ0ng
(3)
where, B is a constant. The trend in Vπ variations closely follow those of the group index as depicted in Fig. 4(a). Interestingly, the group index slightly increases at shorter wavelengths over the low-dispersion slow light bandwidth (λ≥1539nm); one notices that the Vπ slightly decreases at shorter wavelengths over the low-dispersion slow light bandwidth consistent with Eq. (2) (λ≥1539nm).

The rectangular electrical signal for GHz operation is generated through Agilent 8133A 3 GHz pulse generator. The Vbias is 1.25 V and the Vpp is 1.50 V. The output optical signal is amplified by erbium-doped fiber amplifier and converted to electrical signal by a 22 GHz photodetector (DSC30S). The waveform is captured by Agilent 86100A as shown in Fig. 5(c). We were able to achieve 2 GHz operating speed using 80 μm long lumped electrodes. Due to excess noise generated by our EDFA, we were unable to accurately determine the extinction ratio of our modulator device.

5. Conclusion

In conclusion, an ultra low-power, large bandwidth photonic-crystal-waveguide-based silicon Mach Zehnder modulator was proposed and demonstrated. The modulator arms consisted of our designed band-engineered slow light photonic crystal waveguide, which demonstrated a large group index of 26.5 over an 18 nm bandwidth. By embedding the photonic crystal waveguide in a PIN diode structure, modulation operation with a record-low Vπ × L of 0.0464 V.mm via carrier injection into an 80 µm long active section was experimentally demonstrated. The modulator Vπ × L remains nearly constant over the low-dispersion slow-light bandwidth. Using the same structure, a maximum modulator operation up to 2GHz was also obtained. Further improvement in devices performance is expected by optimizing the electrical and optical design of the MZI structure.

Acknowledgments

This research was supported by AFOSR Small Business Technology Transfer (STTR) under Grant No. FA9550-11-C-0014 (Program Manager - Dr. Gernot Pomrenke).

References and links

1.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

2.

M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19(9), 2052–2059 (2002). [CrossRef]

3.

R. Iliew, C. Etrich, T. Pertsch, and F. Lederer, “Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals,” Phys. Rev. B 77(11), 115124 (2008). [CrossRef]

4.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005). [CrossRef]

5.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001). [CrossRef] [PubMed]

6.

H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

7.

H. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “Photonic Crystal Silicon Optical Modulators: Carrier-Injection and Depletion at 10 Gb/s,” IEEE J. Quantum Electron. 48(2), 210–220 (2012). [CrossRef]

8.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, and J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009). [CrossRef]

9.

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

10.

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

11.

S. Schulz, L. O’Faolain, D. Beggs, T. White, A. Melloni, and T. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010). [CrossRef]

12.

S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, and R. T. Chen, “Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor,” Opt. Express 19(22), 21832–21841 (2011). [CrossRef] [PubMed]

13.

L. O'Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2(3), 404–414 (2010). [CrossRef]

14.

A. Mekis and J. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19(6), 861–865 (2001). [CrossRef]

15.

C. Martijn de Sterke, K. B. Dossou, T. P. White, L. C. Botten, and R. C. McPhedran, “Efficient coupling into slow light photonic crystal waveguide without transition region: role of evanescent modes,” Opt. Express 17(20), 17338–17343 (2009). [CrossRef] [PubMed]

16.

A. Hosseini, X. Xu, D. N. Kwong, H. Subbaraman, W. Jiang, and R. T. Chen, “On the role of evanescent modes and group index tapering in slow light photonic crystal waveguide coupling efficiency,” Appl. Phys. Lett. 98(3), 031107 (2011). [CrossRef]

17.

C. H. Cox III, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006). [CrossRef]

18.

G. Li, C. Sun, S. Pappert, W. Chen, and P. Yu, “Ultrahigh-speed traveling-wave electroabsorption modulator-design and analysis,” IEEE Trans. Microw. Theory Tech. 47(7), 1177–1183 (1999). [CrossRef]

19.

C. Y. Lin, A. X. Wang, W. C. Lai, J. L. Covey, S. Chakravarty, and R. T. Chen, “Coupling loss minimization of slow light slotted photonic crystal waveguides using mode matching with continuous group index perturbation,” Opt. Lett. 37(2), 232–234 (2012). [CrossRef]

20.

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of pin-diode-based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008). [CrossRef]

21.

Y. Tang and B. Wang, “Study of active width-reduced line-defect photonic crystal waveguides for high speed applications,” Proc. SPIE 7135, 71350R, 71350R-8 (2008). [CrossRef]

22.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18(26), 27627–27638 (2010). [CrossRef] [PubMed]

23.

L. Gu, Micro-and Nano-Periodic-Structure-Based Devices for Laser Beam Control 99–100 (ProQuest, 2007).

OCIS Codes
(200.4650) Optics in computing : Optical interconnects
(250.5300) Optoelectronics : Photonic integrated circuits
(250.7360) Optoelectronics : Waveguide modulators
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Photonic Crystals

History
Original Manuscript: March 14, 2012
Revised Manuscript: May 11, 2012
Manuscript Accepted: May 11, 2012
Published: May 16, 2012

Citation
Amir Hosseini, Xiaochuan Xu, Harish Subbaraman, Che-Yun Lin, Somayeh Rahimi, and Ray T. Chen, "Large optical spectral range dispersion engineered silicon-based photonic crystal waveguide modulator," Opt. Express 20, 12318-12325 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12318


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References

  1. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005). [CrossRef] [PubMed]
  2. M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B19(9), 2052–2059 (2002). [CrossRef]
  3. R. Iliew, C. Etrich, T. Pertsch, and F. Lederer, “Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals,” Phys. Rev. B77(11), 115124 (2008). [CrossRef]
  4. Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett.87(22), 221105 (2005). [CrossRef]
  5. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett.87(25), 253902 (2001). [CrossRef] [PubMed]
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