1d photonic waveguide

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 9, SEPTEMBER 2007 2435

One-Dimensional PhotonicCrystal Rib Waveguides

Jeremy Goeckeritz, Student Member, IEEE, and Steve Blair, Member, IEEE

AbstractWe analyze an optical waveguide that consists of a1-D photonic crystal (PC) embedded in a large cross-sectional ribwaveguide. The PC provides control over the dispersion prop-erties of the waveguide, while the rib geometry provides a lowloss and versatile mechanism for confining light. The structure isanalyzed using the 3-D finite-difference time-domain method. Thesimulation results indicate that extremely low-loss waveguiding ispossible over a defect band. Moreover, the PC has a complete 1-Dphotonic band gap with a gapmidgap ratio (/mid) of 0.913,which is one of the largest ratios ever reported for a PC.

Index TermsFinite-difference time domain (FDTD), in-tegrated optics, optical losses, optical waveguides, photonic

crystals (PCs).

I. INTRODUCTION

PHOTONIC CRYSTALS (PCs) have been widely recog-

nized as a potential technology for creating densely inte-

grated optical circuits [1], [2]. One type of PC that has been

studied intensively is the PC-slab line-defect waveguide. These

waveguides use refractive index guiding in the vertical direction

and a line of defects within a 2-D PC lattice to confine light

in the lateral direction (for example, see [3, Fig. 1]). This

type of PC has the advantages of being compatible with other

planar optical devices and is relatively simple to fabricate. One-dimensional photonic wire PCs have also received attention

for the same reasons. This type of PC is implemented by

inserting holes or deep gratings into a channel waveguide [4],

[5]. These structures have shown promise as filters, modulators,

and switches [6][8]. However, propagation loss in both types

of PCs has been a critical limiting factor to the realization of

practical devices.

Early on, researchers realized that PCs with a large ver-

tical refractive index contrast could support a Bloch mode

and, thereby, mitigate some out-of-plane scattering losses.

Bogaerts et al. [9] showed that a vertical dielectic contrast

(n2core n2cladding) of approximately 11 is needed to support

such a mode. When using a high index-guiding material (e.g.,silicon or gallium arsenide), an air cladding is required to obtain

the necessary contrast. In fact, the PC-slab waveguides with

the lowest propagation losses found in literature are routinely

constructed from membranes suspended in air [3], [10], [11].

These structures, however, are incompatible with integrated

optics and electrooptics. This is particularly evident considering

Manuscript received January 16, 2007; revised May 4, 2007.The authors are with the Electrical and Computer Engineering Department,

University of Utah, Salt Lake City, UT 84112 USA.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/JLT.2007.902740

that most high-density electronics are composed of multiple

layers. Thin suspended structures can also exhibit birefringence

due to mechanical stress from electrodes, heaters, or bond pads

placed near or on top of the membrane.

In this paper, we analyze a waveguide that consists of a 1-D

PC embedded in a large cross-sectional rib waveguide. This

hybrid structure combines the dispersion properties of a PC

and the versatility of a rib waveguide. We show that, using

3-D finite-difference time-domain (FDTD) simulations, these

properties are attainable without the need to undercut the PC rib

waveguide (PCRW). Furthermore, low-loss waveguiding over anarrow wavelength band is possible using defects in the PC.

This creates a suitable condition for implementing filters or

slow-light waveguides based on the PCRW structure.

Periodic structures have been placed in rib waveguides pre-

viously [12][14]. However, these rib waveguides had either

shallow-etched gratings or the gratings were not wide enough

to cover the entire area of the optical mode within the rib

waveguide. Furthermore, they were not analyzed in terms of

their photonic band-gap properties. Here, we analyze, for the

first time, a large cross-sectional PCRW composed of deep

gratings and show how the waveguide geometry can be used

to minimize out-of-plane scattering loss.

II. PC RIB WAVEGUIDES

Experimental research has shown that a rib waveguide

with a relatively large cross section can be monomode even

for a large refractive index difference between the core and

cladding [15]. Fig. 1(a) shows the cross section of a typical

rib waveguide. The single-mode condition is described by the

following inequalities [16]:

w

H 0.3 +

h/H1 h

H

(1)

0.5 h

H 1 (2)

where w is the waveguide width, H is the total waveguideheight, and h is the slab height. This type of waveguide isreferred to as a shallow-etched rib waveguide because of

constraint (2). When both conditions are satisfied, higher order

modes in the waveguide radiate into the lateral regions, leaving

only one mode bound under the rib [16].

A PCRW is created by inserting deep gratings in the rib and

the surrounding slab. The gratings are quarter-wavelength gaps

with a period of a. The waveguiding sections between eachof the gaps are a quarter wavelength divided by the effective

0733-8724/$25.00 2007 IEEE


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2436 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 9, SEPTEMBER 2007

Fig. 1. (a) Cross section of a rib waveguide showing the rib widthw, the slabheight h, and the total height H. (b) Illustration of a PCRW with period a. The

top cladding is not shown for clarity.

index of the unpatterned rib waveguide. In the lateral direction,

the gratings extend beyond the rib so the entire waveguide

mode is impacted by the refractive index modulation. In the

vertical direction, the gratings cut through the entire waveguide

and the top and bottom claddings. The PCRW is illustrated

in Fig. 1(b). We classify this structure as a 1-D PC due to the

strong in-plane refractive index modulation and the associated

photonic band gap.

III. SIMULATION PARAMETERS

The PCRW is numerically analyzed using the 3-D FDTDmethod [17]. The simulations have a spatial resolution of

approximately a/10 in the x-direction, a/18 in the y-direction,and at least a/20 in the z-direction. The time step is approx-imately 17 as and the simulations are run for 219 time stepsto ensure a fine spectral resolution. The simulation boundary

conditions are perfectly matched layers [18], except along

the yz plane at x = 0, where the rib waveguide is symmet-ric. Here, a symmetry boundary condition is used to reduce

the simulation time and memory requirements. The launched

source is a Gaussian pulse with a transverse profile matching

the fundamental mode of the unpatterned rib waveguide. Two

monitors, one at the beginning of the waveguide and the otherat the end, are used to capture the reflected (R) and transmitted(T) powers, respectively. The loss (L) is calculated usingthe formula L = 1 (T+ R). The spectral response of thestructure is obtained by taking the fast Fourier transform of the

fields at the monitors.

Throughout this paper, the rib width to total height ratio

(w/H) is 0.83 and the slab height to total height (h/H)is 0.66. The total height H is 3.15 m unless specificallystated otherwise. This height is selected to create a mode size

(FWHM) of 2.5 m in the vertical direction to match the spotsize of a commercially available lensed optical fiber. These

ratios satisfy the single-mode conditions, which were verified

using the beam-propagation method [17]. In addition, in allsimulations, the gratings extend to the edge of the simulation

Fig. 2. Transmission and reflection spectra for a membrane PCRW having alattice period of approximately 380 nm. (a) Optical response for TE excitation.The gapmidgap ratio is 0.906. (b) Optical response for TM excitation. Thegapmidgap ratio is 0.840.

domains (i.e., to the boundary edge in the x-direction). In a ribwaveguide, the mode extends beyond the center of the rib into

the lateral regions. The gratings were chosen to extend to the

edge of the simulation domain to cover the entire mode.

IV. SIMULATION RESULTS

We first simulate a PCRW with a core index of 3.45, having

claddings and gratings comprised of air (nair = 1). The grat-ings extend through the waveguide. This structure corresponds

to a silicon- or gallium-arsenide-suspended membrane. The

spectral response for six periods and TE polarization (electricfield in the x-direction) is shown in Fig. 2(a). The dashed lineis the transmission, and the solid line is the reflection. In these

simulations, six periods are used to minimize the computation

time yet still provide the spectral properties of the structure.

An extremely wide photonic band gap is clearly visible, cen-

tered on 1550 nm. The zeroth-order band gap has a gapmidgap

ratio (/mid) of 0.906. The first-order band gap can alsobe seen in the figure, centered at 380 nm. Fig. 2(b) shows the

spectral response for the TM polarization. The gapmidgap

ratio is 0.840. The spectra for both polarizations are nearly

identical, indicating that the PCRW possesses a complete 1-D

band gap, as expected. In Fig. 3(a), the spectral response for

TE-polarized light incident on a PCRW with a core index of3.45, a cladding of 1.45, and air gratings is shown. The gratings


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GOECKERITZ AND BLAIR: 1-D PHOTONIC-CRYSTAL RIB WAVEGUIDES 2437

Fig. 3. Transmission and reflection spectra for a PCRW having a cladding of1.45 and air gratings. (a) Optical response for TE excitation. The gapmidgapratio is 0.913. (b) Optical response for TM exciatation. The gapmidgap ratiois 0.842.

extend entirely through the waveguide and both claddings. The

zeroth-order band gap has a gapmidgap ratio of 0.913, the

largest one, according to our knowledge, ever observed at these

wavelengths [19], [20]. Fig. 3(b) shows the same simulation

with TM-polarized light. In this case, the gapmidgap ratio is

0.843. The PCRW with a cladding of 1.45 has slightly larger

gapmidgap ratios than the membrane case due to a larger

effective index and, subsequently, a larger in-plane refractive

index modulation.

The properties of the PCRW can be analyzed by exploring

the details of how a rib waveguide confines light. Higher order

modes in a rib waveguide disperse laterally into the side regionswhere they quickly attenuate. This occurs when the effective

indexes of the higher order rib modes are lower than the

effective index of the fundamental mode of the slab region.

This confinement method results in a fundamental mode under

the rib with a very large effective index, nearly the same as the

index of the guiding material. This is evident by the nearly iden-

tical gapmidgap ratios of the PCRWs with cladding indexes of

1 and 1.45. Furthermore, as a result of the rib waveguides large

effective index, the PCRW has a very large in-plane refractive

index modulation. For example, the fundamental mode of the

unpatterned-membrane rib waveguide has an effective index of

3.43, which leads to an in-plane index modulation (neff nair)

of 2.43. This, in turn, generates an extremely wide photonicband gap.

Fig. 4. PCRW-defect-cavity simulations with three trenches on each side ofthe cavity. The core index is 3.45, and the cladding and gratings have an indexof 1.45. (a) Transmission and reflection for a PCRW with a height of 3.15 m.The calculated loss is 0.15. (b) Loss as a function of total waveguide height Hfor the defect PCRW.

A. Loss Calculations

To calculate the loss of the PCRW, one period is removed

from the lattice to create a resonant cavity. The cavity is

surrounded by three periods on each side. This creates a central

pass band or impurity band within the band gap, as shown in

Fig. 4(a). The PCRW, in this case, has a core index of 3.45and claddings and gratings of 1.45. In these simulations, the

gratings are filled with the same material as the claddings.

This simplifies the fabrication by eliminating the need to etch

through the top and bottom claddings when creating the grat-

ings. The loss of the waveguide is calculated at the center of the

pass band using the equation L = 1 (T+ R). From Fig. 4(a),the calculated loss of this PCRW is 0.15. This is due to the lack

of a guiding mechanism in the gratings, which results in out-of-

plane scattering [21].

Next, we investigate the effect of the total waveguide height

Hon loss. Once again, the PCRW has a core index of 3.45 andcladdings and gratings of 1.45. Several PCRWs are simulated,

each with different total heights and constant w/H and h/Hratios. The results are shown in Fig. 4(b). The plot shows that


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2438 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 9, SEPTEMBER 2007

Fig. 5. Transmission and reflection spectra for (a) the PCRW with its periodmultiplied by 1.55 to shift the first-order band gap to the 1550-nm wavelengthand (b) the same PCRW with a defect cavity. In both plots, the PCRW has aheight Hof 6 m, and the period a is approximately 593 nm.

the loss can be made arbitrarily small by using an increasingly

larger waveguide height. The decrease in loss is most likely due

to the larger mode size. The thicker waveguides have larger

modes, which experience less diffraction; consequently, less

light is being scattered out of the gratings.

Fabricating a PCRW with a large height would be very chal-

lenging. For example, a rib waveguide with an effective index

of 3.43 would have gratings separated by only 113-nm-wide

waveguide segments (1550/[4

neff], where 1550 is the workingwavelength in nanometers). Note that the quarter-wavelength-wide waveguide segments between gratings are smaller than

the quarter-wavelength gratings and are, therefore, the limiting

factor to fabrication. For a total waveguide height H of 6 m,an aspect ratio of 52.6 would be required.

This problem can be avoided, however, by using one of

the higher order band gaps. For example, by increasing the

period a of the PCRW (i.e., increasing the distance between thegratings), the first-order band gap can be shifted to the desired

wavelength. The spectral properties for a PCRW, with a core

index of 3.45, cladding and grating index of 1.45, a waveguide

height H of 6 m, and a period multiplied by 1.55, are shown

in Fig. 5(a). The waveguiding segments between gratings arenow 328 nm wide and the gratings are 267 nm wide. The first-

order band gap can be seen at 1.5 m. Also visible is thezeroth- and second-order band gaps centered at 3.1 and 1 m,respectively.

To calculate the loss for this structure, the PCRW was simu-

lated again with a defect cavity. The cavity has three periods on

each side. Fig. 5(b) shows the spectral properties. Although the

gapmidgap ratio is only 0.33, it is still comparable to that ofa 2-D PC [19]. The loss, however, is extremely low. The trans-

mission at 1500 nm is 0.99 and the reflection is less than 0.01.

To fabricate this modified PCRW, an aspect ratio of 22.5

is needed, which is attainable with various etching techniques

[22], [23]. This structure does not have increased loss because

the width of the gratings is not changed. Instead, the width of

the waveguiding section between gratings is increased, which

does not impact the scattering loss.

V. SUMMARY AND CONCLUSION

In this paper, we introduced a new type of 1-D PC waveguide.

Simulations of the PCRW showed an extremely wide photonic

band gap and potential low-loss waveguiding. It was also shown

that the loss could be controlled by increasing the waveguide

height. This property is possible due to the ability to scale the

rib waveguide. By increasing the total waveguide height, light

within the gratings is unable to scatter out of the PCRW. In

addition, the low losses are achievable without suspending the

waveguide in air.

These properties make the PCRW suitable for applica-

tions requiring strong optical confinement. For example, the

waveguide is appealing for constructing high-quality factor

resonant cavities. Furthermore, a series of cavities spaced ap-

propriately could be used to create a slow-light waveguide (i.e.,coupled-cavity waveguide) for optical time-delay elements [3].

The rib-waveguide geometry is also ideal for constructing ac-

tive optical devices. The rib geometry seems to be the geometry

of choice for creating silicon modulators, switches, wavelength

converters, and lasers [24][27]. A coupled-cavity PCRW, as a

part of these devices, could enhance the salient benchmarks of

each of these structures. In addition, due to the scalability of the

rib waveguide, the PCRW can be directly coupled to a single-

mode optical fiber. This eliminates the need to construct feed

waveguides and tapers for accessing the PCRW.

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Jeremy Goeckeritz (S01) received the B.S. andM.E. degrees in electrical engineering from the Uni-versity of Utah, Salt Lake City, in 2002 and 2004,respectively, where he is currently working towardthe Ph.D. degree in electrical engineering.

His research interests include photonic-crystal de-vices, integrated photonics, and microfluidics.

Steve Blair (S91M92) received the B.S. and M.S.degrees from RoseHulman Institute of Technology,

Terre Haute, IN, in 1991 and 1993, respectively, andthe Ph.D. degree from the University of Colorado,Boulder, in 1998.

Since 1998, he has been an Assistant Profes-sor with the Electrical and Computer EngineeringDepartment, University of Utah, Salt Lake City.His research interests include slow-light nonlinearoptics, plasmonics, photonic microsystems, and mi-croarray technology.

1d photonic waveguide

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