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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 15 — Jul. 23, 2007
  • pp: 9147–9151
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Supermode Si/III-V hybrid lasers, optical amplifiers and modulators: A proposal and analysis

Amnon Yariv and Xiankai Sun  »View Author Affiliations

Optics Express, Vol. 15, Issue 15, pp. 9147-9151 (2007)

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We describe a hybrid laser structure which consists of an amplifying III-V waveguide proximity-coupled to a passive Si waveguide. By operating near the synchronism point (where the phase velocities of the individual waveguides are equal), we can cause the optical power to be confined to any of the two waveguides. This is accomplished by control of waveguides’ geometry. In the portion of the supermode resonator where amplification takes place, the mode is confined nearly completely to III-V guide thus realizing a near maximal gain. Near the output facet, the mode power is confined to the Si waveguide thus optimizing the output coupling. This is to be contrasted with approaches which depend on evanescent field penetration into the III-V medium to obtain gain.

© 2007 Optical Society of America

1. Introduction

2. Supermode Si/III-V hybrid laser

3. Supermode theory and supermode control in Si/III-V hybrid laser

The ability to spatially confine the optical power to any one of the two waveguides follows directly from the theory of Supermodes. According to this theory [3

3. A. Yariv, in Optical Electronics in Modern Communications (Oxford Univ. Press, New York, 1997), pp. 526–531.

], the modes of a system consisting of two coupled waveguides can be obtained by a diagonalization of the more conventional coupled-mode equations used to describe them.

Fig. 1. A schematic representation of the two supermodes E o and E e for three values of the mismatch parameter δ.

We refer to Fig. 1 which shows two waveguides 1 and 2 coupled, by proximity, to each other. The transverse (x, y) dependency of the supermode consists of a linear combination of the modes of the separate (uncoupled) waveguides which combination travels with a single phase velocity. It can be written as:


For a given mode of the individual waveguides there exist two modes of the coupled system, which we designate by the subscripts o and e. Each of these supermodes is determined by the ratio (a/b) and by a propagation constant β. These are given by [3]:




and κ is given by an overlap integral involving u 1 and u 2, and the index perturbation function.

Of particular interest are the three limiting values: (1) δ<0 while |δ|≫|κ|, (2) δ=0, (3) δ>0 and δ≫|κ|. The corresponding modes are respectively:

(1) δ<0 (β12), |δ|≫|κ|


where ε=κ2δ1.

(2) δ=0 (β12)


(3) δ>0 (β12), δ≫|κ|


where ε=κ2δ1.

Fig. 2. A schematic representation of the laser structure with one tapered adiabatic transition. See Fig. 3(a) for definition of the directions x, y, z with relation to waveguide geometry.

Fig. 3. (a). A cross-section of the Si (bottom) – AlGaInAs (top) structure. The top III-V waveguide mesa width=3.34 µm. Si waveguide height H=0.80 µm. (b), (c) and (d) are the optical field profiles (color coded) for the cases δ>0 (W=0.84 µm), δ=0 (W=0.99 µm), and δ<0 (W=1.20 µm), respectively. The fraction of the energy in each waveguide is given at the bottom of each colorgram.

4. Simulation results and discussion

To demonstrate the importance of supermode control, we have calculated the confinement factors, for the even mode, in the quantum well region, ΓQW, and in the Si guide, ΓSi, for different Si guide widths. In the evanescent coupling scheme, as mentioned before, there exists a tradeoff between ΓQW and ΓSi. With a fixed Si guide width of 1.10 µm, ΓQW=0.067 and ΓSi=0.757. In our supermode coupling scheme, if we vary the Si guide width near the output facet from at main body 0.75 µm to at the output facet 1.35 µm, we will have at main body ΓQW=0.268, and at the output facet ΓSi=0.892. Thus we can increase the ΓQW, hence the exponential gain constant of the laser mode, from 0.067 to 0.268, i.e. a factor of 4×. We also increase the output coupling by, a less impressive, 18%.

5. Conclusion

We propose a supermode hybrid Si/III-V laser design. This approach gets away from the reliance on evanescent tails. Its theoretical foundation is the theory of coupled waveguides, and more specifically, the concept of supermodes – the modes of a system of two or more coupled waveguides. The supermode resonator based on this system can be designed such that the optical energy is confined to either the Si or to the III-V waveguide as desired. This is achieved, most easily, by tailoring the width of one of the waveguides. We can thus use each of the two component waveguides optimally: The III-V guide for gain, the Si waveguide for chip transport and output coupling. This methodology can be extended straightforwardly to hybrid laser amplifiers and to phase or amplitude modulators and thus form the basis of a new hybrid optoelectronic circuitry.


The authors acknowledge valuable assistance from Dr. Joyce Poon and Mr. Lin Zhu.

References and links


O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004). [CrossRef] [PubMed]


A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14, 9203–9210 (2006). [CrossRef] [PubMed]


A. Yariv, in Optical Electronics in Modern Communications (Oxford Univ. Press, New York, 1997), pp. 526–531.


E. Kapon, J. Katz, and A. Yariv, “Supermode Analysis of Phase-Locked Arrays of Semiconductor-Lasers,” Opt. Lett. 9, 125–127 (1984). [CrossRef] [PubMed]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(140.5960) Lasers and laser optics : Semiconductor lasers
(250.3140) Optoelectronics : Integrated optoelectronic circuits

ToC Category:
Integrated Optics

Original Manuscript: May 11, 2007
Revised Manuscript: July 6, 2007
Manuscript Accepted: July 7, 2007
Published: July 11, 2007

Amnon Yariv and Xiankai Sun, "Supermode Si/III-V hybrid lasers, optical amplifiers and modulators: A proposal and analysis," Opt. Express 15, 9147-9151 (2007)

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