Microring Resonator Channel Dropping Filters

Microring Resonator Channel 

Dropping Filters 

Integrated Optics 

Nick Miller

Attributes of microring resonators for channel dropping 

• Microring and microdisk structures can potentially be used as efficient add-drop filters in an 

integrated optics device for wavelength division multiplexing (WDM). They are particularly 

attractive because of their small size may allow high density integration on a chip. 

• Ideally in an WDM communications system, only a single channel is “dropped” from the 

signal bus leaving the other channels unaffected. This can be accomplished with a microring 

filter if the ring is small enough that it resonates at only a single frequency within the WDM 

communication window. This is analogous to placing a short etalon in a laser cavity in order to 

transmit only a single wavelength in the lasing bandwidth. 

• If the microring resonator is constructed from an electrically controllable refractive index, 

then the add-drop filter can potentially be dynamically tuned or used for very fast modulation 

and/or switching. 

• Multiple microrings can be cascaded (or coupled) to achieve high order filter characteristics.

Microring resonator filter evanescently 

side coupled to signal bus 

The incident wave is s i , the transmitted 

wave is s t , the dropped wave is s d , and 

the added wave is s f . 

Wavelength response of the microring 

resonator filter at the drop port 

Coupled mode theory (dashed) vs. FDTD simulation (solid). 

Resonance peak occurs at 1.335um 

and the FSR is approximately 0.05um. 

B.E. Little, S.T. Chu, H. A. Haus, J. Foresi, and J. –P. Laine, “Microring Resonator Channel 

Dropping Filters,” IEEE Journal of Lightwave Technology, 16 (6) pp.998-1005 (1997).

Determining the modes of the microring resonator cavity 

Solving the wave equation in a cylindrical index 

structure can be complicated. Often a conformal 

transformation is applied to the cylindrical index 

structure making it straight but with an 

exponential index distribution. [See Kraus for a 

explanation of the conformal transformation]. 

Look at the transformed index distribution. The 

index for radial values less than the inner ring 

radius is always less than the core index. 

Therefore the ring provides TIR at the inner 

boundary and energy leaks inward. The wave 

equation solution is an eponentially decaying 

function like that of a typical slab waveguide. 

However, the index for radial values greater than 

the outer ring radius grows exponentially until it 

becomes greater than the core index. This 

means we have good guidance but longer have 

TIR. The wave equation solution for these radial 

values is a Hankel function with a complex 

propagation constant. These are leaky modes. 

M. Heiblum and J.H. Harris, “Analysis of curved optical waveguides by conformal 

transformation,” IEEE Journal of Quantum Electronics, 11 (2) pp.75-83 (1975).

Normalized fundamental TE mode profiles (top) and 

snapshots of the propagating E-fields (bottom) 

Bent waveguide 

Straight waveguide 

γ/k0 = 1.293 - j7.521x10-6 β/k0 = 1.314 

Contrast the bent and straight waveguides: 1. The guided mode in the straight waveguide is centered on 

the core while in the bent waveguide the mode favors the outer radial boundary. The effective index of 

the straight waveguide is real, while the effective index of the bent waveguide complex and hence leaky. 

K.R. Hiremath, R. Stoffer, M. Hammer, “Modeling of circular integrated optical microresonators by 2-D 

frequency domain coupled mode theory,” Optical Communications 257 pp.277-297 (2006).

Input signal 

Snapshots of the TE mode propagating E-fields 

as computed by coupled mode theory 

Off-resonance wavelength At resonance wavelength 

These snapshots show the small energy in the ring cavity off resonance contrasted with the energy built 

up in the cavity at resonance. (Note the energy in the cavity is considerably greater than that of the 

input straight waveguide). At resonance energy also couples (i.e. is dropped) into the lower left guide. 



Microring vs. microdisk resonators 

• A disk structure, like a ring, can support multiple azimuthal resonant 

modes. However, the disk will additionally support multiple radial modes. 

These radial modes are concentrated about the circumference of the disk 

and are also known as whispering gallery modes (WGM). 

D.R. Rowland and J.D. Love, “Evanescent wave coupling of whispering gallery 

modes of a dielectric cylinder,” IEE Proceedings-J 140 (3) pp.177-188 (1993).

Examples of microdisk resonators 

Layer description of an SOI 

microdisk resonator filter 

SEM picture of a symmetric add-drop 

filter before the overlaying box is grown. 

A. Morand, Y. Zhang, B. Martin, K. Phan-Huy, D. Amans, and P. Benech, “Ultra-compact microdisk 

resonator filters on SOI substrate,” Optics Express, 14 (26) pp.12814-12821 (2006).

• A ring structure can be designed to support only a single resonant 

modes within a particular communications bandwidth. If a disk of equal 

outer radius is substituted for the ring, it will most probably support multiple 

radial modes within the communications bandwidth. However, it can be 

shown (next slide) that these multiple modes are not normally a problem. 

TE 0, TE 1, TE 2, and TE 3 whispering gallery modes. (R = 5μm) 

Radial mode profile (top), Snapshot of propagating E-field (bottom) 



• Despite a disk structure having multiple radial modes, the disk may be 

appropriate for a resonator filter because only the desired fundamental mode 

is efficiently excited due to the poor overlap with higher radial-order modes. 

Snapshot of propagating E-field in the microdisk filter at the minor 

TE 1 resonance (left) and at the major TE 0 ,resonance (right) 

Observe a significant transmitted E-field at the minor resonance while the 

transmitted E-field is almost fully rejected at the major resonance. 



Tuning a microring resonator filter 

The frequency response of a microring resonator filter is determined by the 

microring’s diameter and core index (relative to the clad index) 

If the microring resonator is constructed from an electrically controllable refractive 

index, then the add-drop filter can potentially be dynamically tuned or used for very 

fast modulation and/or switching. 

If one requires static channel dropping of a few wavelengths from an optical signal 

bus, multiple microring resonators (one for each desired drop channel) can be used.

1x3 add-drop filter 

The microdisk filter add-drops specific frequencies based on the microdisk diameter. Below is 

an SEM picture of a 1X3 add-drop filter composed of three microdisks, each of slightly different 

diameter. The plot at the lower right is the frequency response of this 1x3 filter. Note the FSR of 

a single filter is approximately 5nm and that the separation between ports is approximately 2nm. 

P. Koonath, T. Indukuri, and Bahram Jalali, “Add-drop filters utilizing vertically coupled microdisk resonators in 

silicon,” Applied Physics Letters, 86 091102 (2005).

Method for adjusting coupling into a microdisk resonator 

The coupling of a straight waveguide to a microdisk resonator can be adjusted by varying the 

distance between the straight waveguide and the microdisk resonator (in this case by a MEMs 

actuator). 

M.M. Lee, M.C. Wu, “Tunable coupling regimes of silicon microdisk resonators 

using MEMS actuators,” Optics Express, 14 (11) pp.4703-4712 (2006).





Transmission spectra for under, over, and critically coupled resonators 

Without bias, the waveguide remains straight and the 

coupling coefficient with the WGM modes of the microdisk 

is negligible. The resonator is under-coupled (a). 

Increasing applied voltage bends the waveguide towards 

the microdisk thereby increasing the coupling coefficient. 

The coupling coefficient gradually increases until it equals 

the round-trip resonator loss, causing the transmission to 

drop precipitously at the resonant wavelength. The 

resonator is now critically-coupled (b). 

Further increases of the applied voltage results in a still 

greater coupling coefficient causing the transmission 

intensity of increase. The resonator is over-coupled (c). 



Transmission curve for microdisk-coupled 

waveguide at its resonant wavelength 



Multiple microrings used to achieve high order filter characteristics 

Because microring resonators are so compact, multiple rings can be combined to construct higher 

order filters to meet various frequency response requirements. 

Multiple microring resonators 

(b) Cascaded resonators 

(c) Coupled resonators 

Spectra of filters composed of one, 

two, and three coupled microrings 

B.E. Little, S.T. Chu, H. A. Haus, J. Foresi, and J. –P. Laine, “Microring Resonator Channel 

Dropping Filters,” IEEE Journal of Lightwave Technology, 16 (6) pp.998-1005 (1997).

Microring outer diameter [μm] 

9 

8 

7 

6 

5 

4 

3 

2 

1 

Microdisk fabrication limitations 

High Q WGM microdisk resonators require a 

Large indices make the microdisk sensitive to 

large index differential for efficient guiding and 

surface roughness and cylindricity which are limited 

are therefore often constructed from III-V or 

by the low tolerance lithography processes. 

silicon semiconductor materials. SEM micrograph of a R=2.5mm Si microdisk 

R 

min 

= 

8 

⎡ 

⎢⎣ 

0 

1 

n 2 2 

core 

nclad 

( ) − ) − ( ) ⎤ 

n 1 arccos 

clad 

ncore 

⎥⎦ 

M. Heiblum and J.H. Harris, “Analysis of curved optical 

waveguides by conformal transformation,” IEEE Journal 

of Quantum Electronics, 11 (2) pp.75-83 (1975). 

Rmin equation is plotted below to demonstrate the 

small microdisks require a high index contrast. 

Minimum diameter waveguide microring for λ = 1.0 μm 

0 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 

Microring-to-cladding index difference [Δn] 

λ 

(a) Sideview showing SiO2 undercut and pedestal. 

(b) Top view of disk. (c) Top-edge zoom-in showing 

roughness. (d) Plot of radius variation vs. arc length 

M. Borselli, K. Srinivasan, P.E. Barclay, and O. 

Painter, “Rayleigh scattering, mode coupling, and 

optical loss in silicon microdisks,” Applied Physics 

Letters, 85 (17) pp.3693-3695 (2004).

Microdisk fabrication limitations 

Another major fabrication hurdle to using microdisks in resonator filters is ensuring 

reproducibility of the microdisk-to-waveguide coupling. 

To address the problem of coupling reproducibility, vertically coupled devices have been 

constructed where the coupling region is defined mainly by layer thickness (which can be 

precisely controlled by methods such as epitaxial crystal growth) as opposed to lithography. 

SEM picture of a microdisk resonator on the top 

silicon layer with linear bus waveguides underneath 

P. Koonath, T. Indukuri, and Bahram Jalali, “Add-drop filters utilizing vertically coupled microdisk 

resonators in silicon,” Applied Physics Letters, 86 091102 (2005).

Modeling microring resonator channel dropping filters 

I attempted to duplicate the results of the paper, 

B.E. Little, S.T. Chu, H. A. Haus, J. Foresi, and J. –P. Laine, “Microring Resonator Channel Dropping 

Filters,” IEEE Journal of Lightwave Technology, 16 (6) pp.998-1005 (1997). 

The authors used coupled mode theory to predict the operation of the microring resonator filter 

and verified it using FDTD analysis. I repeated the FDTD simulation using the FDTD simulation 

tool from Lights. The microring resonator structure used in the FDTD simulation is as follows: 

•Ring and bus indices, n g = 3.0 surrounded by air, index n air = 1.0. 

•The ring and bus waveguide widths are both 0.2 μm. 

•The ring has an outer radius of 1.8 μm and the separation 

between the ring and the bus is 0.2 μm. 

•The FDTD analysis meshes the microring resonator add-drop 

filter shown at the right. The square mesh contains 540 by 540 

elements, each 10nm on a side. Using the 1-D waveguide mode 

solver, the fundamental mode E-field is placed near the bottom of 

the bus waveguide at the right.

Results for the microring resonator channel dropping filter 

I ran many FDTD simulations, but present only three results. 

1. The microring resonator was operated using the at-resonance wavelength of 

1.335μm. The FDTD simulation confirms that this structure does provide a 

channel dropping function at this wavelength. 

2. The same microring resonator was operated using the off-resonance 

wavelength of 1.315μm. The FDTD simulation shows that the structure does 

not resonate at this wavelength and therefore not drop a channel. 

3. A microdisk resonator was modeled (using the same outer radius as the 

microring resonator) and operated at a wavelength of 1.335μm. This simulation 

confirmed that the whispering gallery modes (WGMs) of microdisk resonator 

allow the microdisk to function similarly to the microring resonator.

Numerical FDTD simulation of the microring 

structure at resonance. 

This .mpeg shows the field 

profile based on the FDTD file 

“Nicksp12” on Lights. 

The FDTD simulation becomes 

unstable after approximately 

100um propagation time, as is 

visible in the movie. 

If the FDTD simulation ran 

longer, we would expect to see 

a much greater energy build up 

in the ring cavity, and close to 

100% drop channel efficiency.

Microring resonator drop filter at resonance 

This plot shows the power along 

the lower edge based on the 

FDTD file “Nicksp12” on Lights. 

Because the FDTD simulation 

becomes unstable after 

approximately 100μm, energy at 

the drop channel (shown by the 

small bump on the left) is not 

nearly 100% as expected.

Numerical FDTD simulation of the microring 

structure off resonance. 




Again, the FDTD simulation 


approximately 100μm time. 

If the FDTD simulation ran 

longer, we would expect to see 

little build up of energy in the 

ring cavity and continued poor 

drop channel efficiency.

Microring resonator drop filter off resonance 




Because we are off resonance, 

no drop energy is visible at the 

drop channel at the lower left.

Microdisk resonator structure used in a 

numerical FDTD simulation 

• Ring and bus indices, n g = 3.0 surrounded by air, index 

n air = 1.0. 

• The bus waveguide width is 0.2 μm. 

• The disk has an outer radius of 1.8 μm and the 

separation between the disk and the bus is 0.2 μm. 

• The FDTD analysis meshes the microdisk resonator adddrop 

filter shown at the right. The square mesh contains 

540 by 540 elements, each 10nm on a side. Using the 1- 

D waveguide mode solver, the fundamental mode E-field 

is placed near the bottom of the right hand bus waveguide.

Numerical FDTD simulation of the microdisk 

structure at resonance. 




Again, the FDTD simulation 


approximately 100um time. If 

the FDTD simulation ran longer, 

we would expect to see a much 

greater energy build up in the 

disk cavity, and much higher 

drop channel efficiency. Also 

note the multiple (perhaps two) 

radial modes visible inside the 

disk cavity.

Microdisk resonator drop filter near resonance 




Because the FDTD simulation 


approximately 100um, energy at 

the drop channel (shown by the 

small bump on the left) is quite 

small. However, it is also 

smaller than the microring case 

probably because we are 

operating slightly off the 

resonance peak.

REFERENCES 

[1] B.E. Little, S.T. Chu, H. A. Haus, J. Foresi, and J. –P. Laine, “Microring Resonator Channel Dropping 

Filters,” IEEE Journal of Lightwave Technology, 16 (6) pp.998-1005 (1997). 

[2] K.R. Hiremath, R. Stoffer, M. Hammer, “Modeling of circular integrated optical microresonators by 2-D 

frequency domain coupled mode theory,” Optical Communications 257 pp.277-297 (2006). 

[3] D.R. Rowland and J.D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric 

cylinder,” IEE Proceedings-J 140 (3) pp.177-188 (1993). 

[4] P. Koonath, T. Indukuri, and Bahram Jalali, “Add-drop filters utilizing vertically coupled microdisk 

resonators in silicon,” Applied Physics Letters, 86 091102 (2005). 

[5] K.H. Vahala, “Optical Microcavities,” Nature 424 pp.839-846 (2003). 

[6] M. Heiblum and J.H. Harris, “Analysis of curved optical waveguides by conformal transformation,” 

IEEE Journal of Quantum Electronics, 11 (2) pp.75-83 (1975). 

[7] M.M. Lee, M.C. Wu, “Tunable coupling regimes of silicon microdisk resonators using MEMS 

actuators,” Optics Express, 14 (11) pp.4703-4712 (2006). 

[8] A. Morand, K. Phan-Huy, Y. Desieres, and P. Benech, “Analytical study of the microdisk’s resonant 

modes coupling with a waveguide based on the perturbation theory,” IEEE Journal of 

Lightwave Technology, 22 (3) pp.827-832 (2004). 

[9] A. Morand, Y. Zhang, B. Martin, K. Phan-Huy, D. Amans, and P. Benech, “Ultra-compact microdisk 

resonator filters on SOI substrate,” Optics Express, 14 (26) pp.12814-12821 (2006). 

[10] M. Borselli, K. Srinivasan, P.E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and 

optical loss in silicon microdisks,” Applied Physics Letters, 85 (17) pp.3693-3695 (2004). 

[11] Kraus, J.D., Electromagnetics, McGraw-Hill, New York, 1953.

Microring Resonator Channel Dropping Filters

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