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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 7043–7051
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Performance influence of carrier absorption to the Mach-Zehnder-interference based silicon optical switches

Haifeng Zhou, Yong Zhao, Wanjun Wang, Jianyi Yang, Minghua Wang, and Xiaoqing Jiang  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 7043-7051 (2009)
http://dx.doi.org/10.1364/OE.17.007043


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Abstract

The free carrier absorption effect in silicon modulation is a detrimental behavior that can influence the crosstalk of interference-based optical switches. Based on the experimental analysis of a 2×2 p-i-n silicon switch, we give a conservative estimate of the crosstalk ability of Mach-Zehnder optical switches. Experimental result shows that, while using a 1475μm-long phase shifter, the loss penalty almost reaches 1.45dB/π, which deteriorates the most ideal crosstalk to just 30dB. The possible solutions to overcome this limitation are also discussed at the cost of the other device performance.

© 2009 Optical Society of America

1. Introduction

Ever since the emergence of integrated optics, photonic devices are continuously pursuing even “smaller, swifter, smarter, simpler and saving more energy and cost” (5S) implementations. In recent years, optics on silicon platform opens the door to resolve the current micro-electronics bottlenecks [1

1. G.T. Reed, “The optical age of silicon,” Nature 427, 595–596 (2004). [CrossRef] [PubMed]

]. However, it still remains a challenge to externally modulate light effectively with high performances [2

2. M. Lipson, “Overcoming the limitations of microelectronics using Si nanophotonics: solving the coupling, modulating and switching challenges,” Nanotechnology 15, S622–S627 (2004). [CrossRef]

]. Due to the promise of high-speed modulation, free carrier dispersion (FCD) effect has gained widespread application in optical modulation. Meanwhile, Mach-Zehnder interference (MZI) structure is inherently considered as the mainstream way to implement modulators [3

3. G. T. Reed, “Silicon optical modulators,” Mater. Today , 40–50 (2005). [CrossRef]

, 7–13

7. G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon Mach-Zehnder waveguide interferometers based on the plama dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991). [CrossRef]

], switches and filters. Its advantages in bandwidth and fabrication are irreplaceable by the resonant structures such as ring, disk, Bragg grating, even photonic crystal. Hence, it is a natural thing to combine the FCD with the MZI structure to implement broad-bandwidth silicon modulators or switches.

In the beginning, because of the relatively weak refractive index change (<10-3) and the carrier’s lifetime in this effect [4

4. R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon.” J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

], most work was devoted to enhance the modulation efficiency and improve the modulation speed. However, the influence of the coexisting free carrier absorption (FCA) was scarcely studied in a MZ-based device. As shown in Table.1, the extinction ratios (ER) are no more than 22dB even in the fabricated modulators even under the condition of wavelength scanning [11

11. A. Liu, L. Liu, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007). [CrossRef] [PubMed]

], mainly due to the voltage-controlled loss penalty to the phase modulation. Without this negative effect, the low-speed thermo-optical silicon switches can readily achieve a high switching crosstalk of 25dB beyond [5

5. T. Goh, M. Yasu, K. Hattori, A. Himeno, M. Okuno, and Y. Ohmori, “Low-loss and high-extinction-ratio silica-based strictly nonblocking 16×16 thermo-optical matrix switch,” IEEE Photon. Technol. Lett. 10, 810–812 (1998). [CrossRef]

, 6

6. T. Chu, S. Ishida, and Y. Arakawa, “Compact 1×N thermo-optic switches based on silicon photonic wire waveguides,” Opt. Express. 13, 10109–10114 (2005). [CrossRef] [PubMed]

].

Table.1. Extinction ratios of the reported MZ modulators

table-icon
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The 1×2 or 2×2 optical switches are extremely crucial to construct a switching array with large port count [5

5. T. Goh, M. Yasu, K. Hattori, A. Himeno, M. Okuno, and Y. Ohmori, “Low-loss and high-extinction-ratio silica-based strictly nonblocking 16×16 thermo-optical matrix switch,” IEEE Photon. Technol. Lett. 10, 810–812 (1998). [CrossRef]

]. As for a silicon MZ modulator, one can achieve infinite ER at the expense of the excess loss in theory, as long as the OFF state is assumed to be totally off. However, it is not the case for a 2×2 MZ switch, or with even larger port counts, whose crosstalk (CT) is quite limited by the FCA. Clearly, we should take good care of the every switching state simultaneously. This paper focuses on the influence of FCA to an MZI-based optical switch supported by theory and our recent experimental results.

2. Theoretical prediction

2.1 Deterioration of power imbalance to the switching performance

The output intensity of an MZI device is determined by the loss and phase information of the beam from each path. It is well know that the power imbalance deteriorates the completeness of interference. Specifically, for the case of two-beam interference in a modulator, the most ideal (namely possible) extinction ratio (ER) can be expressed by

ER=20log10[(1+r)/(1r)](dB)
(1)

where r is the power imbalance factor closely before the interference occurs. According to this expression, Figure 1 schematically shows the relation between ER and r, which presents an intuitive estimation of the ER under the condition of unbalanced interference. It indicates that, in order to obtain a modulator with ER beyond 30 dB, r should be within the scope of [0.9, 1.1]. If the power imbalance problem is serious, typically with r<0.65, the most ideal crosstalk can never exceed 20dB. While adding a coupler to compose an 2×2 optical switch, both the two states should be taken good care of to achieve high performance. If the added coupler is ideally assumed to be lossless and free from the phase distortion, the switching crosstalk (CT) is identical to the ER, and can be calculated by Eq.(1) as well.

Fig. 1. Possible extinction ratio (ER) under the condition of unbalanced interference of two beams

2.2 Free carrier absorption (FCA) effect in silicon

It is necessary to examine quantitatively the free carrier absorption effect in silicon. The Kramers-Kronig analysis of optical absorption spectrum enables R. Soref et.al to investigate the FCD effects in silicon, which is formulated by the expressions below at a wavelength (λ) of 1.55μm [4

4. R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon.” J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

]

Δn=Δne+Δnh=8.8×1022ΔN8.5×1018(ΔP)0.8
(2)
Δα(/cm)=Δαe+Δαh=8.5×1018ΔN+6.0×1018ΔP
(3)

where ΔN and ΔP are the concentration change of electron and hole in cm-3, respectively. Δn and Δα are the refractive index and absorption coefficient variations. The subscripts “e” or “h” means the contribution is from electron or hole, respectively.

Fig. 2. (a) Comparison of the modulation efficiency of electrons and holes in FCD effect; and (b) loss penalty l dB/π for unit π phase shift under different injected concentrations @ 1.31μm and 1.55μm

The required length of a π-phase shifter can be estimated by L π=λ/(2∣Δn∣). By using Eqs.(2–3) and the expression

l(dB/π)=10×log10[exp(Δα(/cm)×Lπ(μm))]
(4)

Figure 2(b) shows the loss penalties l (dB/π) for a phase shift of π at specific concentration changes with and without ΔN. By taking both the electron and hole into account, the typical values of l (dB/π) with the carrier densities varying from 1015cm-3 to 1017-18.5cm-3 are within the range from 0.7dB to 1.5dB. Even in the case only hole effect exists, the l (dB/π) value reaches 0.83dB (i.e. r=0.8265) with ΔP =5×1017cm-3 [3

3. G. T. Reed, “Silicon optical modulators,” Mater. Today , 40–50 (2005). [CrossRef]

].

2.3 Phase shifter with FCA effect installed into an MZI-based switch

Fig. 3. Theoretical framework of an MZI-based switch and the parameters for optical field

In Fig. 3, the phase shifters using the FCA effect are installed into an MZI-based switch device now. For the sake of description, the superscripts “in”, “md” and “out” mean the input, middle (positions after modulated) and output positions; “a”, “ψ” and “φ” are the amplitudes, phase variables and phase modulation magnitudes; the subscripts “A” and “B” mean the upper and lower paths, respectively. T MMI is the transfer matrix of a 2×2 MMI coupler.

As listed in Table 2, there are four typical schemes to realize 2×2 optical switching. The letter “ t ” is the loss penalty in a π-phase shifter and equals to 10- l;(dB/π)×π/10; “MPI” stands for maximum power imbalance before interference on different states, i.e. max(a A md/a B md); “MMM” stands for maximum modulation magnitude on individual phase shifter. The possible CT of all the schemes can be obtained by replacing the variable r in Eq.(1) with MPI.

For the Case 1 in Table 2, where two interferometric arms are initially in phase (ψ A in-ψ B in=0) or out of phase (ψ A in-ψ B in=π) with equal intensities (a A in/a B in=1), the MPI equals to t and the CT can just reach 26.5dB for ΔP=5×1017cm-3 and 21.5dB for ΔP=ΔN=5×1017cm-3at best. There is an approach to reduce the loss penalty by pre-biasing the initial power ratio (a A in/a B in) of the two arms to be t -1/2 or t 1/2 (Case 2). This way makes the power imbalance factors a A md/a B md on one state to be t 1/2 and another 1:t 1/2, respectively. The loss penalty is distributed to both the two states, which makes an optical switch with the CT of 32.5dB for ΔP=5×1017cm-3 and 27.5dB for ΔP=ΔN =5×1017cm-3. As indicated in the Case 3, pre-biasing a constant phase shifter π/2 (ψ A in-ψ B in=π/2) is also an option to achieve the same CT as the Case 2, which is adopted in our experiment to reduce the maximum modulation magnitude (MMM) to π/2. Phase is also easier than initial power ratio to be biased by considering the practical realization. Study shows that these two biasing methods may achieve the best CT one can obtain. Since the MPI still takes the value of t 1/2, the pull-push mechanism in the Case 4 cannot further improve the crosstalk any more. It just reduces the MMM to a quarter of that in the case 1.

Table 2. Comparison to the four typical operation styles of MZ modulation

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Obviously, a higher injected concentration produces larger carrier concentration change, and thus reduced the device length. But, in the meanwhile, the loss penalty l dB/π increases dramatically, which further reduces the device CT seriously, as shown in Fig. 2(b). Hence, there is a tradeoff in carrier injection concentration between the length of phase shifter and the desired CT. In order to give an intuitive guideline for device optimization, the required lengths of π-phase shifter L π and the possible CT are simultaneously calculated to observe the tradeoff in Fig. 4 by varying the initial and final carrier densities.

Fig. 4. The contour of the switching CT limits and the necessary length order of a π/2 phase shifter, correspondent to the cases 2–4 in Table. 2

3. Experimental demonstration and analysis

A 2×2 MZI switch fabricated by CMOS-compatible technique is taken as an example here. As shown in Fig. 5, this device consists of an MZI structure by cascading two 2×2 MMI coupler, and uses the conventional p-i-n structure. The wafer was (100) orientation with p-doping (14Ω.cm<ρ<22Ωcm). Figure 5 also presents the rib waveguide cross section, with 1μm SiO2 buried layer. The testing uses a single-wavelength light source at 1550nm. The transmission curves from each output port were measured by lensed fiber-to-fiber coupling at different injected currents. It should be noted that the positive and negative current means the cathode A works and cathode B works, respectively.

Fig. 5. Schematic views of the fabricated 2×2 MZ switch, the right of which is SEM photograph of the waveguide cross section

One can fit the transmission characteristic curves with the formula of the free carrier dispersion and the derived matrix multiplication expression below

[aAoutexp(iψAout)aBoutexp(iψBout)]=12[1jj1][αAexp(iφA)00αBexp(iφB)][aAinexp(iψAin)aBinexp(iψBin)]
(5)

In our device, L arm=1475μm; CINP is about 2.1×1016cm-3/mA; the value of Γ is estimated to be 0.34. The effective carrier injection density ΔN eff=ΔP eff is about 4.6×1017cm-3 for 7π-phase shift, which is defined by Δn -1 (λ/2/L arm), where Δn -1 is the inverse function of Eq.(2). In Fig. 6, we plot the induced phase changes and the power losses during the fitting process. The loss penalty l dB/π is about 1.45dB/π on account of both the hole and electron effects. This loss value increases dramatically by increasing the injected current.

Fig. 6. The estimated phase change and loss penalty against the injected current in the 2×2 switch

To plot the fitting curves of the transmission spectrum, the pre-biased initial power ratio and the constant phase difference are intentionally guessed to align the experimental figure. In the device, a A in/a B in=1.012 with an shortened 3-dB MMI splitter; ψ A in-ψ B in=π/3.2 due to the fabrication error; (a A in a B in)1/2=-3.6dB resulted from the excess loss. The transmission curves and the fitted ones are presented in Fig. 7. Because the initial state is not symmetrical as expected, the transmission spectrums are different for the cases the cathode A works (CT>19.5dB) and the cathode B works (CT<17.1dB). The envelope through the transmission valleys shows the modulation loss deteriorates the CT of the optical switch seriously. The power imbalance factors at the four “ON” and “OFF” states are 0.65, 0.93, 0.81(MPI) and 0.53, respectively. Even if this switch is symmetrical at initial state (i.e. a A in/a B in=1, Δ A in=Δ32in) and the shallow valley of the transmission spectrum can be fine detected, the most ideal crosstalk one can obtain is no more than 30dB.

Fig. 7. The measured transmission spectrum and the fitting curves by considering the FCD effect

4. Discussions

Unlike the speed and modulation efficiency, the loss penalty cannot be eliminated by simply scaling down the device dimension to improve the efficiency in theory. Both the real and imaginary parts of the complex dielectric permittivity vary by increasing the injected density. Hence, it makes no sense to the loss penalty for unit phase change.

As Fig. 2(b), the loss penalty decreases with the decreased injection concentration, but not significantly. This point is indicated by our device in above section. What is worse, low-density injection makes the device length increasing exponentially (typically possible CT equals to 29.6dB and Lπ=4000μm while the effective carrier injection density ΔP=ΔN=5×1031cm-3) and then unsuitable for large-scale integration.

One can use specific structures (e.g. ring-coupled MZI structure) to reduce the necessary phase shift and further favor the two switching states in power balance to improve the CT. But these methods are not only complex but also at the cost of the operation bandwidth. Another approach is to dynamically serve the pre-biased splitting ratio, which should maintain the imbalance factor as close to unity as possible for each switching states. The co-working of the extra electrodes greatly leads to the complexity of the device structure and controlling system. Definitely, hybrid integrated waveguide system may successfully relieve this problem but it is beyond the scope of this paper.

The best approach may be to balance the FCA through adjusting the waveguide structure free from the bandwidth issue. For example, a desired structure may work like this: on one hand, the carrier absorption is increased by carrier injecting, on the other hand, the carrier-induced refractive index reduction can abnormally enhance the optical confinement and decrease the waveguide loss. If the carrier absorption can be compensated by the decreased waveguide loss, the power imbalance resulted from the modulation is removed. The implementation details are still left as an open issue.

5. Conclusions

The influence of the loss penalty in a carrier-injected MZI silicon photonic switch was addressed from the basic theory and the practical device fabrication. The CT limits induced by the carrier absorption were given for the conventional design of silicon MZI devices. If a compact and high-crosstalk optical switch is necessary, one should tune the splitter of the first stage dynamically to favor both the two switching states. The paper is intended to provide a roadmap for researchers to design a high-CT, high-speed and wavelength-insensitive silicon optical switch by carrier dispersion effect.

Acknowledgments

This work is supported by the Natural Basic Research Program of China (No. 2007CB613405), and the Natural Science Foundation of China (No. 60777015).

References and links

1.

G.T. Reed, “The optical age of silicon,” Nature 427, 595–596 (2004). [CrossRef] [PubMed]

2.

M. Lipson, “Overcoming the limitations of microelectronics using Si nanophotonics: solving the coupling, modulating and switching challenges,” Nanotechnology 15, S622–S627 (2004). [CrossRef]

3.

G. T. Reed, “Silicon optical modulators,” Mater. Today , 40–50 (2005). [CrossRef]

4.

R. A. Soref and B. R. Bennett, “Electro-optical effects in silicon.” J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

5.

T. Goh, M. Yasu, K. Hattori, A. Himeno, M. Okuno, and Y. Ohmori, “Low-loss and high-extinction-ratio silica-based strictly nonblocking 16×16 thermo-optical matrix switch,” IEEE Photon. Technol. Lett. 10, 810–812 (1998). [CrossRef]

6.

T. Chu, S. Ishida, and Y. Arakawa, “Compact 1×N thermo-optic switches based on silicon photonic wire waveguides,” Opt. Express. 13, 10109–10114 (2005). [CrossRef] [PubMed]

7.

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon Mach-Zehnder waveguide interferometers based on the plama dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991). [CrossRef]

8.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A highspeed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature , 427, 615–618 (2004). [CrossRef] [PubMed]

9.

Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and Ray T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105(1–3) (2005). [CrossRef]

10.

L. Liao, D. S. Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3134 (2005). [CrossRef] [PubMed]

11.

A. Liu, L. Liu, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007). [CrossRef] [PubMed]

12.

W. M. J. Green et al, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17106–17113 (2007). [CrossRef] [PubMed]

13.

D. M. Morini, L. Vivien, J. M. Fedeli, E. Cassan, P. Lyan, and S. Laval, “Low loss and high speed optical modulator based on a lateral carrier depletion structure,” Opt. Express 16, 334–339 (2008). [CrossRef]

14.

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon Mach-Zehnder waveguide interferometers based on the plasma dispersion effect,” Appl. Phys. Lett. 59, 771–773 (1991). [CrossRef]

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(130.3120) Integrated optics : Integrated optics devices

ToC Category:
Integrated Optics

History
Original Manuscript: March 6, 2009
Revised Manuscript: April 2, 2009
Manuscript Accepted: April 2, 2009
Published: April 13, 2009

Citation
Haifeng Zhou, Yong Zhao, Wanjun Wang, Jianyi Yang, Minghua Wang, and Xiaoqing Jiang, "Performance influence of carrier absorption to the Mach-Zehnder-interference based silicon optical switches," Opt. Express 17, 7043-7051 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7043


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References

  1. G. T. Reed, "The optical age of silicon," Nature 427, 595-596 (2004). [CrossRef] [PubMed]
  2. M. Lipson, "Overcoming the limitations of microelectronics using Si nanophotonics: solving the coupling, modulating and switching challenges," Nanotechnology 15, S622-S627 (2004). [CrossRef]
  3. G. T. Reed, "Silicon optical modulators," Mater. Today, 40-50 (2005). [CrossRef]
  4. R. A. Soref and B. R. Bennett, "Electro-optical effects in silicon." J. Quantum. Electron. QE-23,123-129 (1987). [CrossRef]
  5. T. Goh, M. Yasu, K. Hattori, A. Himeno, M. Okuno, and Y. Ohmori, "Low-loss and high-extinction-ratio silica-based strictly nonblocking 16×16 thermo-optical matrix switch," IEEE Photon. Technol. Lett. 10, 810-812 (1998). [CrossRef]
  6. T. Chu, S. Ishida, and Y. Arakawa, "Compact 1×N thermo-optic switches based on silicon photonic wire waveguides," Opt. Express. 13, 10109-10114 (2005). [CrossRef] [PubMed]
  7. G. V. Treyz, P. G. May, and J. M. Halbout, "Silicon Mach-Zehnder waveguide interferometers based on the plama dispersion effect," Appl. Phys. Lett. 59, 771-773 (1991). [CrossRef]
  8. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, "A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor," Nature 427,615-618 (2004). [CrossRef] [PubMed]
  9. Y. Q. Jiang, W. Jiang, L. L. Gu, X. N. Chen, and Ray T.  Chen, "80-micron interaction length silicon photonic crystal waveguide modulator," Appl. Phys. Lett. 87, 221105(1-3) (2005). [CrossRef]
  10. L. Liao, D. S. Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, "High speed silicon Mach-Zehnder modulator," Opt. Express 13, 3129-3134 (2005). [CrossRef] [PubMed]
  11. A. Liu, L. Liu, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, "High-speed optical modulation based on carrier depletion in a silicon waveguide," Opt. Express 15, 660-668 (2007). [CrossRef] [PubMed]
  12. W. M. J. Green et al, "Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator," Opt. Express 15, 17106-17113 (2007). [CrossRef] [PubMed]
  13. D. M. Morini, L. Vivien, J. M. Fedeli, E. Cassan, P. Lyan, and S. Laval, "Low loss and high speed optical modulator based on a lateral carrier depletion structure," Opt. Express 16, 334-339 (2008). [CrossRef]
  14. G. V. Treyz, P. G. May, and J. M. Halbout, "Silicon Mach-Zehnder waveguide interferometers based on the plasma dispersion effect," Appl. Phys. Lett. 59, 771-773 (1991). [CrossRef]

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