## Engineering the spectral reflectance of microring resonators with integrated reflective elements |

Optics Express, Vol. 18, Issue 16, pp. 16813-16825 (2010)

http://dx.doi.org/10.1364/OE.18.016813

Acrobat PDF (2535 KB)

### Abstract

We present analysis and design of microring resonators integrated with reflective elements to obtain custom wavelength-selective devices. We introduce a graphical method that transforms the complicated design problem of the integrated structure into a simple task of designing a reflective element possessing an appropriate reflection profile. Configurations for obtaining a comb mirror, a single peak mirror, an ultranarrow band transmission filter, and a sharp transition mirror are presented as examples.

© 2010 Optical Society of America

## 1. Introduction

1. J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. **16**, 1331–1333 (2004). [CrossRef]

2. I. Chremmos and N. Uzunoglu, “Reflective properties of double-ring resonator system coupled to a waveguide,” IEEE Photon. Technol. Lett. **17**, 2110–2112 (2005). [CrossRef]

3. G. T. Paloczi, J. Scheuer, and A. Yariv, “Compact microring-based wavelength-selective inline optical reflector,” IEEE Photon. Technol. Lett. **17**, 390–392 (2005). [CrossRef]

4. J. Scheuer, G. T. Paloczi, and A. Yariv, “All optically tunable wavelength-selective reflector consisting of coupled polymeric microring resonators,” Appl. Phys. Lett. **87**, 251102 (2005). [CrossRef]

5. O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” J. Lightwave Technol. **23**, 3931–3946 (2005). [CrossRef]

6. Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” J. Lightwave Technol. **24**, 1865–1874 (2006). [CrossRef]

7. V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. **25**, 3142–3150 (2007). [CrossRef]

8. C. Vázquez and O. Schwelb, “Tunable, narrow-band, grating-assisted microring reflectors,” Opt. Commun. **281**, 4910–4916 (2008). [CrossRef]

9. H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express **17**, 10731–10737 (2009). [CrossRef] [PubMed]

11. Y. M. Kang, A Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. **41**, pp. 689–697 (2009). [CrossRef]

5. O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” J. Lightwave Technol. **23**, 3931–3946 (2005). [CrossRef]

12. B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. **23**, 1570–1572 (1998). [CrossRef]

13. O. Schwelb and I. Frigyes, “All-optically tunable filters built with discontinuity-assisted ring resonators,” J. Lightwave Technol. **19**, 380–386 (2001). [CrossRef]

14. T. Wang, Z. Zhang, F. Liu, Y. Tong, J. Wang, Y. Tian, M. Qiu, and Y. Su, “Modeling of quasi-grating sidewall corrugation in SOI microring add-drop filters,” Opt. Commun. **282**, 3464–3467 (2009). [CrossRef]

## 2. Analysis

*L*=

_{t}*L*+

*L*, where

_{s}*L*and

*L*correspond to the length of the ring and the reflective element respectively, as depicted in Fig. 1. All fields in this paper are assumed to be normalized in power. For simplicity, the coupling and transmission coefficients

_{s}*κ, τ*of the bus coupler and the round trip field attenuation in the ring

*α*are assumed to be frequency independent in this paper. One can easily extend the following analysis to obtain a more accurate model which involves spectrally varying coefficients, e.g. to account for refractive index and waveguide dispersions. Here, we will only consider a passive case,

*i.e.*, 0 <

*α*≤ 1. The effect of incorporating gain in a similar structure is studied in [15

15. D. Alexandropoulos, J. Scheuer, and N. A. Vainos, “Spectral properties of active racetrack semiconductor structures with intracavity reflections,” IEEE J. Selected Top. Quantum Electron. **15**, 1420–1426 (2009). [CrossRef]

16. Y. M. Kang, “Semi-analytic simulations of microring resonators with scattering elements,” M.S. thesis, University of Illinois, Urbana, IL (2010), http://hdl.handle.net/2142/15975.

**S**

^{†}

**S**=

**I**and the reciprocity condition

*S*

_{12}=

*S*

_{21}. We use

*e*time convention throughout this paper. Here,

^{−iωT}*r*and

*t*are the magnitude of the reflection and transmission coefficients of the integrated reflective element, respectively, such that

*r*

^{2}+

*t*

^{2}= 1, and

*ϕ, ψ*are phase terms.

11. Y. M. Kang, A Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. **41**, pp. 689–697 (2009). [CrossRef]

17. R. Grover, “Indium phosphide based optical micro-ring resonators,” Ph.D. thesis, University of Maryland, College Park, MD (2003), http://hdl.handle.net/1903/261.

*a*

^{+}

_{1}= 1,

*b*

^{−}

_{1}= 0, and lossless coupling condition

*κ*

^{2}+

*τ*

^{2}= 1 are assumed. Note that

*β*is the modal propagation constant in the ring waveguide. We define

*L*is chosen to satisfy

*θ*

_{0}+

*ϕ*

_{0}= 2

*mπ*for some integer

*m*(resonance at the design wavelength), and thus

*a*

^{−}

_{1}(

*θ*+

*ϕ*) =

*a*

^{−}

_{1}(Θ) and

*b*

^{+}

_{1}(

*θ*+

*ϕ*) =

*b*

^{+}

_{1}(Θ) hold.

*a*

^{−}

_{1}| and |

*b*

^{+}

_{1}| are independent of relative position of the integrated element in the ring, provided that the element is not directly coupled to the bus waveguide. In fact, only the phase of the reflection coefficient ∠

*a*

^{−}

_{1}is affected by the relative position of the reflective element. The transmission phase ∠

*b*

^{+}

_{1}is not affected.

### 2.1. Maximum Reflection Condition

*α*of the microring and the transmission coefficient

*τ*of the bus coupler are given parameters of the microring. In Eqs. (3) and (4), the variables we can engineer are

*r*(Θ) and

*t*(Θ). Note that we may neglect

*ψ*because it does not affect the output power. For a lossless reflective element, we have

*r*domain. We find the condition for obtaining maximum reflection that can be realized from the integrated microring for given

*α*and

*τ*by solving ∇

_{Θ,r}|

*a*

^{−}

_{1}(Θ,

*r*)|

^{2}=

**0**, which yields the reflective element’s critical reflection coefficient profile

*α*and

*τ*, this maximum reflectance |

*a*

^{−}

_{1c}|

^{2}exists and is the same for continuous points in the Θ-

*r*plane. At resonance Θ = 2

*mπ*, Eq. (8) reduces to

*α*

^{2}≈ 1 and

*κ*

^{2}≪ 1, Eq. (10) reduces to

12. B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. **23**, 1570–1572 (1998). [CrossRef]

*a*

^{−}

_{1}|

^{2}is proportional to the field buildup intensity of the — mode in the ring. A large value of |

*a*

^{−}

_{1}|

^{2}is evidence that the mode is in resonance in the structure. Therefore, the branching off of the peak reflection condition

*r*(Θ) in Fig. 2 for

_{c}*r*(Θ) >

_{c}*r*(0) corresponds to the resonance-splitting [18

_{c}18. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting in high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. **20**, 1835–1837 (1995). [CrossRef] [PubMed]

19. B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. **22**, 4–6 (1997). [CrossRef] [PubMed]

20. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B **17**, 1051–1057 (2000). [CrossRef]

21. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. **27**, 1669–1671 (2002). [CrossRef]

22. Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express **16**, 4621–4630 (2008). [CrossRef] [PubMed]

*α*,

*r*, and

*τ*are known.

*A*can be quite large for low loss devices and thus can be used for high sensitivity sensor applications [12

12. B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. **23**, 1570–1572 (1998). [CrossRef]

23. J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. **4**, 46–49 (2010). [CrossRef]

### 2.2. Graphical Solutions

*a*

^{−}

_{1}(Θ,

*r*)|

^{2}for different values of

*τ*

^{2}and

*α*

^{2}on the Θ-

*r*plane. As α or τ decreases, we observe that the full width half maximum (FWHM) of each individual peak increases.

*r*(0) and the resultant reflectance from the ring |

_{c}*a*

^{−}

_{1c}|

^{2}on the

*τ*

^{2}-

*α*

^{2}plane. For example, if

*τ*

^{2}= 0.9 and

*α*

^{2}= 1, we obtain

*r*(0) = 0.053 and |

_{c}*a*

^{−}

_{1c}|

^{2}= 1 from Fig. 3, which agrees with the values from Fig. 2(a). Note that

*r*(0) increases as

_{c}*α*or

*τ*decreases, and |

*a*

^{−}

_{1c}|

^{2}decreases as

*α*decreases or

*τ*increases. Thus, increasing

*α*increases the amplification factor

*A*whereas increasing

*τ*can either increase or decrease

*A*.

## 3. Design Examples

*r*(Θ) of the reflective element using the graphical solutions presented in the previous section. Throughout the analysis, we consider an integrated microring resonator with the parameters

*L*=100

_{t}*λ*

_{e,0}and

*τ*

^{2}=0.9, where

*n*is the effective index of the waveguide.

_{e}### 3.1. Comb of Reflection Peaks

*a*

^{−}

_{1}|

^{2}contour plot, we can construct a comb reflector with a spectrally flat

*r*(Θ). Figure 4(a) shows this simple case. The dashed line represents the desired reflection profile of the reflective element

*r*(Θ) overlaid on the contour plot, and its value is constant at

*r*(0) = 0.053 for

_{c}*α*

^{2}= 1. From the figure, one can easily anticipate a periodic reflection spectrum from the microring with peaks at Θ = 2

*mπ*. One of the physical candidates for the reflective element to achieve such a flat reflection profile is a low reflectivity Fabry-Pérot (FP) element. We refer to this type of integrated microring as an FP-MRR. For a low reflectivity FP element, the phase response is approximately a linear function of

*β*with the slope equal to its length

*d*; by choosing

*L*≫

*d*, we can approximate the reflection as a constant value. More detailed analysis to engineer the parameters is presented below.

*R*=

_{int}*r*

^{2}

_{int}is the reflection power from each interface. At the design wavelength, Eq. (12) can be expressed as:

*α*

^{2}= 1, one can choose the appropriate index contrast to get

*R*= 6.93×10

_{int}^{−4}such that we match the minimum critical reflection coefficient

*r*=

*r*(0).

_{c}*ϕ*(

*β*) ≈

*βd*for

*R*≪ 1, which yields

_{int}*d*≪

*L*. Therefore, we can effectively model the reflection profile of the FP element as a constant

*r*(Θ) ≈

*r*(0) near the design wavelength. Note that because the phase response in the ring is approximately linear, we choose

_{c}*L*to be an integer number of

_{t}*λ*

_{e,0}, which yields

*θ*

_{0}+

*ϕ*

_{0}≈ 200

*π*in this example.

*α*

^{2}= 1, 0.99, and 0.95. For each value of

*α*

^{2}, the FP reflection is set to

*r*=

*r*(0) = 0.053, 0.058, and 0.078 respectively. Note that the peak reflection of each FP-MRR corresponds to |

_{c}*a*

^{−}

_{1c}|

^{2}=1, 0.83, and 0.45, respectively. Thus, the ring resonator amplifies the reflectance by

*A*= 360, 250, and 74, respectively. For lossy cases, a decrease in

*τ*results in increases in the critical reflection coefficient

*r*(0) and the peak reflectance |

_{c}*a*

^{−}

_{1c}|

^{2}. However, the increase in

*r*(0) requires a higher value of

_{c}*R*from Eq. (13), which may be difficult to achieve from a simple index-contrast FP element. Furthermore, a higher value of

_{int}*R*causes deviation from the linear phase approximation of the FP element.

_{int}^{−4})λ

_{0}, (2.6 × 10

^{−4})

*λ*

_{0}, and (3.2 × 10

^{−4})

*λ*

_{0}for

*α*

^{2}= 1, 0.99, and 0.95, respectively at the design wavelength. In comparison, the FWHM values of buildup field intensity of the identical microrings with no internal reflection,

*i.e., r*(Θ)=0, are calculated to be (1.7 × 10

^{−4})

*λ*

_{0}, (1.8 × 10

^{−4})

*λ*

_{0}, and (2.5 × 10

^{−4})

*λ*

_{0}for the same set of

*α*

^{2}values.

25. V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. **29**, 1824–1834 (1993). [CrossRef]

11. Y. M. Kang, A Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. **41**, pp. 689–697 (2009). [CrossRef]

*α*

^{2}and

*τ*

^{2}, allowing an additional degree of freedom in engineering the peak shape. Additional advantages over the SGDBR include its more compact dimensions, simpler architecture, and reduced sensitivity to wafer scale variations due to its reuse of the same FP reflector.

### 3.2. Single Peak Reflector

*r*(Θ) of the reflective element at the ring resonant wavelengths other than the design wavelength. In other words, we are looking for a reflective element whose reflection profile satisfies

*N*-period Bragg grating as a reflective element. We first note that the total length of the grating is

_{g}= (

*β*–

*β*

_{0})

*L*is the detuned phase shift in the grating. We also note that the transmission phase shift of the low-reflectivity grating is roughly a linear function

_{g}*ϕ*(

*β*) ≈

*βL*, from which we obtain Θ ≈ (

_{g}*β*–

*β*

_{0})

*L*.

_{t}*p*is fixed for a given geometry of the structure. We re-write Eq. (16) as

*p*Θ) = 0 for all Θ = 2

*mπ*,

*m*≠ 0, so 2

*mpπ*should be an integer multiple of

*π*. Therefore, from Eq. (18) the only possible choices for

*p*are

*p*= 1. The corresponding grating lengths are

*R*and satisfy

_{int}*i.e., r*= 0 at Θ =

*mπ*for all nonzero integers

*m*. Figure 6(b) depicts the resultant reflectance spectra of the two DBR-MRRs for

*α*

^{2}= 1. It should be noted, however, that for the full DBR-MRR, the grating at the coupling region may cause some reflection and scattering, which is not considered in this paper.

*mπ*,

*m*≠ 0. However, the overall microring reflection will approach zero if the grating reflection goes to absolute zero, thus suppressing reflection at adjacent ring resonances. As a result, we observe only a single peak at the design wavelength as desired.

^{−4})

*λ*

_{0}for both the half DBR-MRR and the full DBR-MRR at the design wavelength for the lossless case. Compared to a continuous DBR, the DBR-MRR possesses several advantages such as a more compact structure, suppression of side mode ripples, the ability to engineer the FWHM from the microring parameters, and reduced sensitivity to wafer scale variations. Although there have been several studies on a cavity consisting of a ring resonator and Bragg grating [8

8. C. Vázquez and O. Schwelb, “Tunable, narrow-band, grating-assisted microring reflectors,” Opt. Commun. **281**, 4910–4916 (2008). [CrossRef]

14. T. Wang, Z. Zhang, F. Liu, Y. Tong, J. Wang, Y. Tian, M. Qiu, and Y. Su, “Modeling of quasi-grating sidewall corrugation in SOI microring add-drop filters,” Opt. Commun. **282**, 3464–3467 (2009). [CrossRef]

26. D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express **15**, 3156–3168 (2007). [CrossRef] [PubMed]

### 3.3. Ultranarrow Transmission Filter

*ϕ*(

*β*) ≈

*βL*no longer holds.

_{s}*N*-period DBRs on the left and the right half of the ring and gaps of length

*d*and

*L*. We assume that

*d*is an integer multiple of the grating period Λ. To make the analysis simpler, we re-define the DBR structure to be symmetric; that is, we exclude the last half-period portion at the bottom, as shown in Fig. 7. The length of the new DBR is then

*S*

_{11}=

*S*

_{22}on Eq. (2) and obtain the grating’s scattering matrix

*r*and

_{g}*t*are the magnitude of reflection and transmission coefficients of the grating, and

_{g}*ϕ*corresponds to the phase of the reflection coefficient. The + or − sign is taken when the last index of the DBR (orange) is high or low, respectively. Note that with the symmetric DBR definition, the length of the ring portion

_{g}*L̄*=

*L*+ Λ as shown in Fig. 7. We define

*θ*=

*βL̄*.

*d*+ 2

*L̄*as [24]

_{g}*r*

^{2}

*+*

_{g}*t*

^{2}

*= 1. From Eq. (23), we obtain*

_{g}*ϕ*= ∠

*S*

_{12}. The reflection power from the DBR-etalon is given by [24]

*R*=

_{g}*r*

^{2}

_{g}. Using the trigonometric identity

*θ*–

*θ*

_{0})+(

*ϕ*–

*ϕ*

_{0}) because the grating’s phase response

*ϕ*is not linear. One may employ a numerical simulation such as the transfer matrix method (TMM) to obtain the reflection profile

_{g}*r*(Θ) of the DBR-etalon as a function of the total detuned phase. In the appendix, we derive a closed form approximation of

*r*(Θ) for small Θ using the effective mirror model, which is insightful for designing the performance parameters, such as the FWHM.

*r*

^{2}

_{g}= 0.99,

*d*=

*L*= 0, and

*N*= 100 using the linear approximation method presented in the appendix. Figure 9 shows the transmission response of the device using TMM. The FWHM of the isolated DBR etalon

*δ*Θ

_{DBR-etalon}≈ 0.34

*π*is reduced to

*δ*Θ

_{DBR-E-MRR}≈ 0.016

*π*by integrating the DBR etalon into a microring. To find the microring response as a function of

*λ*, we substitute Θ(

*β*) = [(

*d*+ 2

*L*)Γ + 2

_{e}*L*+

_{e}*L*+ Λ)](

*β*–

*β*

_{0}) from the appendix, and we note

*L*is long or the reflection

_{e}*R*is large, and this yields a sharp response as a function of

_{g}*β*or

*λ*. For example,

*δ*Θ = 0.016

*π*corresponds to

*R*→ 1. The value of

_{g}*R*= 0.99 was chosen considering typical maximum reflectance values of planar DBRs.

_{g}*d*= 0, we get

*r*= 0 from Eq. (24) if

*ϕ*=

_{g}*mπ*for any integer

*m*. This corresponds to Θ = (

*β*–

*β*

_{0})Λ + 2

*mπ*because

*ϕ*(

_{g}*β*

_{0}) = 0. That is, for |(

*β*–

*β*

_{0})Λ| ≪

*π, i.e.*,

*λ*

_{0}.

### 3.4. Sharp Transition Mirror

*L*to

*L*′ =

*L*+ Δ

*L*, we obtain

*θ*′ =

*θ*+(

*β*–

*β*

_{0})Δ

*L*, which in turn shifts Θ′ = Θ + (

*β*–

*β*

_{0})Δ

*L*; that is, increasing

*L*shifts

*r*(Θ) horizontally to the right and increases the slope

*r*

^{2}

_{g}= 0.5, and Δ

*L*= 0.011

*λ*

_{e,0}. These values were chosen so that the etalon’s reflection coefficient curve (dashed) is approximately tangent to the critical reflection curve rc. This produces a spectrally wider high reflectance band. Adjustments to the parameters can be made to reduce the ripple at the expense of a narrower high reflectance band. Note that the null of the etalon’s reflection profile corresponds to the new “design” wavelength, which is at a different location than Θ = 0. By shifting the DBR-etalon reflection profile, we have engineered a sharp transition mirror. In the lossless case, the reflectance goes from 100% to 0% in

*δλ*=(7.4 × 10

^{−5})

*λ*

_{0}. A sharper transition can be made by increasing |

*r*|

_{g}^{2}and decreasing Δ

*L*at the expense of a narrower high reflectance bandwidth, more ripple, and more difficult fabrication tolerances.

## 4. Conclusion

- for fixed values of
*α*and*τ*, the maximum achievable reflectance is the same along a continuous curve in the Θ-*r*plane - in the lossless case, 100% reflectance can be obtained with weak reflective elements
- the FP-MRR can generate a periodic reflectance spectrum with peaks at the resonance wavelengths of the ring
- the DBR-MRR with the grating occupying either half or all of the ring suppresses reflection at adjacent resonance wavelengths of the ring and thereby produces a single peak profile
- the DBR-E-MRR reduces the FWHM of the DBR etalon and can be designed to function as either an ultranarrow filter or a sharp transition mirror.

*τ*. These integrated microring devices are potential candidates for a diverse assortment of compact optical components in planar photonic integrated circuits.

## Appendix

*r*(Θ) for the DBR etalon can be calculated numerically using TMM, but here we derive a closed form approximation so that we can quickly vary the design and understand the effect of each design parameter. In the analysis, we will restrict ourselves to the sharp phase transition region |Θ| ≪ 1. To estimate

*r*and phase

_{g}*ϕ*near the design wavelength can be effectively modeled as [24]

_{g}*r*is assumed to be constant near its design wavelength.

_{g}*ϕ*(

*β*) ≈ [(

*d*+ 2

*L*)Γ + 2

_{e}*L*](

_{e}*β*–

*β*

_{0})+

*ϕ*

_{0}. We can re-write

*θ*=(

*β*–

*β*

_{0})

*L̄*+

*β*

_{0}

*L̄*=(

*β*–

*β*

_{0})(

*L*+Λ)+

*θ*

_{0}. From these results and Eq. (27), we relate

*ϕ*–

*ϕ*to Θ as

_{g}## Acknowledgments

## References and links

1. | J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. |

2. | I. Chremmos and N. Uzunoglu, “Reflective properties of double-ring resonator system coupled to a waveguide,” IEEE Photon. Technol. Lett. |

3. | G. T. Paloczi, J. Scheuer, and A. Yariv, “Compact microring-based wavelength-selective inline optical reflector,” IEEE Photon. Technol. Lett. |

4. | J. Scheuer, G. T. Paloczi, and A. Yariv, “All optically tunable wavelength-selective reflector consisting of coupled polymeric microring resonators,” Appl. Phys. Lett. |

5. | O. Schwelb, “Band-limited optical mirrors based on ring resonators: analysis and design,” J. Lightwave Technol. |

6. | Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” J. Lightwave Technol. |

7. | V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. |

8. | C. Vázquez and O. Schwelb, “Tunable, narrow-band, grating-assisted microring reflectors,” Opt. Commun. |

9. | H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express |

10. | Y. M. Kang and L. L. Goddard, “Semi-analytic modeling of microring resonators with distributed Bragg reflectors,” in |

11. | Y. M. Kang, A Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. |

12. | B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. |

13. | O. Schwelb and I. Frigyes, “All-optically tunable filters built with discontinuity-assisted ring resonators,” J. Lightwave Technol. |

14. | T. Wang, Z. Zhang, F. Liu, Y. Tong, J. Wang, Y. Tian, M. Qiu, and Y. Su, “Modeling of quasi-grating sidewall corrugation in SOI microring add-drop filters,” Opt. Commun. |

15. | D. Alexandropoulos, J. Scheuer, and N. A. Vainos, “Spectral properties of active racetrack semiconductor structures with intracavity reflections,” IEEE J. Selected Top. Quantum Electron. |

16. | Y. M. Kang, “Semi-analytic simulations of microring resonators with scattering elements,” M.S. thesis, University of Illinois, Urbana, IL (2010), http://hdl.handle.net/2142/15975. |

17. | R. Grover, “Indium phosphide based optical micro-ring resonators,” Ph.D. thesis, University of Maryland, College Park, MD (2003), http://hdl.handle.net/1903/261. |

18. | D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting in high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. |

19. | B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. |

20. | M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B |

21. | T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. |

22. | Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express |

23. | J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photon. |

24. | L. A. Coldren and S. W. Corzine, |

25. | V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. |

26. | D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(230.1480) Optical devices : Bragg reflectors

(230.4040) Optical devices : Mirrors

(280.4788) Remote sensing and sensors : Optical sensing and sensors

(130.7408) Integrated optics : Wavelength filtering devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: June 23, 2010

Revised Manuscript: July 19, 2010

Manuscript Accepted: July 20, 2010

Published: July 23, 2010

**Citation**

Young Mo Kang, Amir Arbabi, and Lynford L. Goddard, "Engineering the spectral reflectance of microring resonators with integrated reflective elements," Opt. Express **18**, 16813-16825 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16813

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### References

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- R. Grover, “Indium phosphide based optical micro-ring resonators,” Ph.D. thesis, University of Maryland, College Park, MD (2003), http://hdl.handle.net/1903/261.
- D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting in high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995). [CrossRef] [PubMed]
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- D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express 15, 3156–3168 (2007). [CrossRef] [PubMed]

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