The paper reviews progress and future prospects of two kinds of planar waveguide devices; they are (a) silica and silicon photonics multi/demultiplexers for communications and signal processing applications, and (b) a novel waveguide spectrometer based on Fourier transform spectroscopy for sensing applications.
I. INTRODUCTION
Silicon photonics is widely regarded as a promising technology to meet the requirements of rapid bandwidth growth and energyefficient onchip communication while reducing cost per bit. In all potential application areas it is widely recognized that use of wavelength division multiplexing (WDM) techniques will be critical in achieving the required high levels of data transmission. Si photonics devices will have to deal with several tens of different wavelengths of light in the nextgeneration multicore CMOS chips.
There are mainly four kinds of devices capable of multi/demultiplexing tens of WDM signals; they are ring resonators,latticeform filters, arrayed waveguide gratings (AWG) and planar Echelle gratings. The former two are cascaded devices relying on temporal multibeam interference effect and the latter two utilize spatial multibeam interference effect. In order to achieve good crosstalk characteristics in the temporal and spatial multibeam interference effects, uniformity of effective index
n_{c}
(=
β /k
), where
β
and
k
denote propagation constant and wave number, is critically important.Filter characteristics of four kinds of devices will be investigated and performance limitations of silicon photonics filters are discussed.
In the latter part of the paper, an integratedoptic spectrometer based on Fouriertransform spectroscopy will be described. A novel planar waveguide spectrometer consists of interleaved MachZehnder interferometer (MZI) array.Practical importance of Fouriertransform spectrometer is the ability to correct for interferometer defects caused by effective index fluctuations (phase errors) in data processing stage. Successful measurement results of the signal spectrum with 20GHz resolution by the spectrometer implemented in silicabased planar waveguide will be presented.
II. SILICON PHOTONICS WDM FILTERs
Flattop passband characteristics are required for filters in most of the WDM applications
[1

4]
. Crosstalk degradation in coupled ring resonators and latticeform filters are caused by both gap width error in directional couplers and optical path length error in the waveguides.
Effectiveindex fluctuation
δn_{c}
in silica Planar Lightwave Circuits (PLCs) have been measured to be about
δn_{c}
~1×10
^{?6}
by using Fourier transform spectroscopy
[5]
. Good crosstalk characteristics are obtained in silicabased AWGs as shown in
Fig. 1
. The relation between the effectiveindex fluctuationδnc and crosstalk (XT) has been investigated theoretically and experimentally
[6]
. Based on the investigations, the empirical expression for the relation between
δn_{c}
and XT has been obtained as
where
L_{ctr}
and λ denote array waveguide length in the central region and the wavelength of light signal, respectively.
L_{ctr}
of AWG in
Fig. 1
is
L_{ctr}
~ 15 mm. Substituting
Demultiplexing properties of 64 ch50 GHz spacingsilica AWG.
δn_{c}
~ 1×10
^{6}
,
L_{ctr}
~ 15 mm, and λ = 1.55 ㎛ into Eq.(1), we obtain XT ~ 40 dB. Although Eq. (1) gives good agreement with the experimental results, the author believes that it should be proved analytically. Crosstalk of the planar Echelle gratings is obtained based on the similar investigations as
where
n_{s}
and
δζ
denote the effective index in the slab region and the facet position fluctuation in the reflection mirrors. It is known from Eq. (2) that
δζ
should be about 5 nm in order to obtain 40 dB crosstalk in silica Echelle grating (
n_{s}
~ 1.5). Such a small
δζ
would be possible in the laboratory experiments
[7]
. However, the mask resolution for the commercial PLC products is normally about 25 nm~ 50 nm. This is the reason why commercial planar Echelle gratings could not achieve sufficient crosstalk value to be used in the current WDM systems.
Effectiveindex fluctuation
δn_{c}
in Siwire waveguides has been evaluated from the measurements on the variation of resonant wavelength in the cascaded ring resonators
[8]
. Peaktopeak resonance wavelength variation is 2
δλ
~ 2.4 nm. Then,
δn_{c}
is obtained as
δn_{c}=n_{c}δλ/λ_{0}~2×10^{3}
, where
n_{c}
= 2.519 and
λ_{0}
= 1.55 ㎛. Effectiveindex fluctuationδnc in Siwire waveguides can also be calculated by the vectorial finite element method
[3]
.
Fig. 2
(a) shows
n_{c}
of Siwire waveguide with thickness 2t = 0.22 ㎛ (blue) and its dependence on the core width 2a (red).
dn_{c}
/
d
(2
a
)at the typical core width 2a = 0.5 ㎛ is 1.3 ㎛
^{1}
= 1.3×10
^{3}
nm
^{1}
.
Fig. 2
(b) shows nc of Siwire waveguide with width 2a =0.5 ㎛ (blue) and its dependence on the core thickness 2t(red).
dn_{c}
/
d
(2
t
) at the typical core thickness 2t = 0.22 ㎛ is 3.4 ㎛
^{1}
= 3.4×10
^{3}
nm
^{1}
.
Core sidewall roughness of Siwire waveguide is measured to be about
σ_{width}
~ 2 nm
[9]
. Top silicon thickness uniformity of 6inch SOI (silicon on insulator) wafer is measured to be about +/ 2 nm
[10]
. However, the photonic device occupies just ~1 mm square or less.
(a) Effective index nc of Siwire waveguide with 0.22 μmthickness (blue) and its dependence on the core width 2a (red).(b). Effective index nc of Siwire waveguide with 0.5 μmwidth (blue) and its dependence on the core width 2t (red).
Thickness variation in 6inch SOI wafer.
Then, the thickness fluctuation would be less than
σ_{thickness}
~ 1 nm as shown in the central region of
Fig. 3
[6]
.Effectiveindex fluctuation
δn_{c}
in Siwire waveguide is then estimated to be
δn_{c}
=[
dn_{c}
/
d
(2
a
)]×
σ_{width}
~2.6×10
^{3}
,or
δn_{c}
=[
dn_{c}
/
d
(2
t
)]×σthickness ~3.4×10
^{3}
, respectively. Both of the theoretical estimations for the effectiveindex fluctuation
δn_{c}
agree well with the measured value. Effective index fluctuation
δn_{c}
against core width variation can be reduced by enlarging core width in the straight regions. For example,
dn_{c}
/
d
(2
a
) becomes to 0.35 ㎛
^{1}
=3.5×10
^{4}
nm
^{1}
at 2a = 0.8 ㎛
[11]
as shown in
Fig. 2
(a).
Sirib waveguide structure allows us to obtain much smaller
δn_{c}
as shown in
Fig. 4
, where core width W, core height H, and etch depth h are W = 0.5 ㎛, H = 0.3 ㎛,and h = 0.15 ㎛, respectively.
dn_{c}
/
dW
at W = 0.5 ㎛ is 6.4×10
^{4}
nm
^{1}
. However, the minimum bending radius becomes much larger compared to Siwire waveguides and makes the device size larger. Therefore, Siwire waveguide is still very attractive in making compact photonic devices.
Effectiveindex fluctuations of the order of
δn_{c}
=3×10
^{4}
~ 2×10
^{3}
determine the crosstalk values of the current Siwire AWGs to be about 20 dB
[11

13]
.
Echelle grating has been believed to be advantageous over AWG because only the facet position error causes crosstalk degradation. But, this is not true in Si Echelle grating since the effectiveindex fluctuation
δn_{s}
in the slab waveguide is substantially large as shown in
Fig. 5
.
dn_{s}
/
d
(2
t
) at the typical core thickness 2t = 0.22 ㎛ is 3.3×10
^{3}
nm
1
. Then, Eq. (2) for Si Echelle grating should be rewritten as
Effective index nc of Sirib waveguide (blue) and itsdependence on the core width W (red).
Effective index ns of Si slab waveguide (blue) and itsdependence on the core width 2t (red).
where
L_{ctr}
denotes the total path length in the central region of the slab. Eq. (3) explains why large channel count(30 ch3.2 nm spacing) Echelle grating has about 15 dB crosstalk, though small channel count (4 ch20 nm spacing)one had about 30 dB crosstalk
[14
,
15]
. The total path length
L_{ctr}
in the large channel count Echelle grating is almost 5 times longer than that of small channel count one.Therefore, the second term in Eq. (3) becomes dominant in the large channel count Echelle grating.
In order to achieve good crosstalk characteristics (< 20 dB) in both Siwire AWG and Echelle grating, (a) improvement in core width and thickness uniformity and/or(b) size reduction to make
L_{ctr}
small are strongly required.
Cascaded ring resonators and latticeform filters are also attractive candidates for filter applications in Si photonics.
Fig. 6
shows coupled resonator optical waveguide (CROW)
[1]
. Kappa’s are amplitude coupling coefficients in the directional couplers. Ring perimeter L = 27.7 ㎛ for the ring diameter of 4.4 ㎛. Free spectral range (FSR)between the adjacent resonance order is about 2,600 GHz,which allows us to make 13 ch200 GHz(1.6 nm) spacing WDM filter. FSR is inversely proportional to L.Therefore, ring resonator using other type of waveguide(such as silica PLC with bend radius of 5 mm) cannot obtain sufficiently wide FSR.
Fig. 7
(a) shows a filter response without effective index fluctuation (dotted lines)and with index fluctuation
δn_{c}
= 5×10
^{4}
only in the third ring (solid lines). It is shown that
δn_{c}
less than 10
^{3}
degrades crosstalk characteristics drastically.
Fig. 7
(b) is a filter response when κ
_{0}
is deviated from its ideal value 0.47 to 0.42. This amount of κ
_{0}
deviation can be caused by about +/ 13 nm gap width variation in the directional coupler.
Fig. 8
shows schematic configuration of threestage latticeform filter
[2]
. c
_{1}
to c
_{4}
are power coupling coefficients in the directional couplers. Channel spacing between the two
Coupled resonator optical waveguide (CROW).
(a) Filter response without effective index fluctuation(dotted lines) and δnc = 5x104 only in the third ring (solid lines).(b). Filter response when κ_{0} is deviated from 0.47 to 0.42.
Threestage latticeform filter.
output ports is given by
where
ΔL, N_{c}
and c are path length difference, group index (
N_{c}=n_{c}λdn_{c}/dλ
) of the waveguide and light velocity. In the typical Siwire waveguide,
ΔL
= 93 ㎛ gives the channel spacing
S_{ch}
= 400 GHz.
Fig. 9
shows a filter response without effective index fluctuation (dotted lines) and with random index fluctuation '
δn_{c}
' <5×10
^{4}
(solid lines). It is shown that
δn_{c}
less than 10
^{3}
degrades crosstalk characteristics drastically. It is also shown by other numerical simulation that when c
_{2}
is deviated from
Filter response without effective index fluctuation(dotted lines) and random index fluctuation 'δn_{c}' < 5x10^{4}(solid lines).
its ideal value 24.8% to 17.8%, crosstalk becomes about20 dB. This amount of c2 deviation can be caused by about +/ 20 nm gap width variation in the directional coupler. Experimentally, crosstalk level of about 10 dB has been obtained in Siwire latticeform filters
[16]
.
III. PLANAR FT SPECTROMETER
Spatial heterodyne spectroscopy (SHS) is an interferometric Fouriertransform technique based on a modified Michelson interferometer with no moving parts and relying on analysis of stationary interference patterns
[17]
. In the bulkoptic SHS, the mirrors of the Michelson interferometer are replaced by diffraction gratings to offer scanning capability for two wavefronts. The SHS concept has been generalized into a waveguide MachZehnder interferometer (MZI) array based on cosine fast Fourier transform (FFT)
[18]
. The path length difference in each asymmetrical MZI increases by
ΔL
, similar to AWG
[3]
. For any input wavelength, the entire output of a MZI array creates spatially oscillatory patterns, where the oscillation period is wavelength dependent due to the dispersive nature of the asymmetrical MZI.Each input wavelength has a unique fringe representation,which is the basis of the Fouriertransform relation between the input spectra and the output interferogram. Employing multiple input waveguides in the waveguide SHS is an important advantage over the existing AWGtype spectrometer,since it greatly increases the light capturing capability in proportion to the number of MZIs by using, for example,photonic lantern technology
[19]
. A photonic lantern is a device that efficiently converts light from a multimode fiber tip for light capturing to singlemode fibers connected to MZI input waveguides. The practical importance of the Fouriertransform spectrometer is the ability to correct for interferometer defects (phase errors) in data processing stage. The first waveguide SHS have been fabricated in silicononinsulator rib waveguides using stacks of multiple MZIs
[20]
. However, a measurement result on the spectrum has not been reported so far to our knowledge.
We reported a novel planar waveguide SHS configuration with an interleaved MZI array
[21]
. The interleaved configuration allows us to put 2~3 times more MZIs than the simple stacking layout when we compare two layout methods for the same spectrometer parameters. We made an array of 32 MZIs in silicabased PLC. The path length difference increment was
ΔL
= 162 ㎛, which resulted in 20 GHz resolution at the 1.55 ㎛ region. Phase errors in the asymmetrical MZIs were measured by the thermooptic phase scanning method
[22]
. The spectrum of the light source was successfully retrieved by correcting the MZI output data with the phase error values.
Figure 10
shows the configuration of the novel waveguide SHS with the interleaved MZI array. The total number of MZIs is N = 32. The waveguide core size is 4.5㎛× 4.5 ㎛ with 1.5% refractiveindex difference.The minimum bend radius is 2 mm. White boxes indicate 3 dB couplers consisting of either directional couplers or multimode interference couplers. The input and output waveguide separations at the chip ends are 15 and 50 ㎛,respectively. Waveguide arms in the MZI are intentionally inclined to both sides so that the waveguides intersect by more than 45º with each other. It is known that the excess loss of the waveguide crossing can be reduced as low as~ 0.02 dB/intersection when crossing angle is larger than 45º
[23]
. Dummy crossing waveguides are placed to make the total number of waveguide crossing equal for all MZIs. The chip size, including input and output fanout regions, is 43mm× 25 mm . We measured both crossport and throughport outputs
p ^{(k )}
and
q^{(k)}
in the
k
th (k = 0~ N1) MZI so that the spatial nonuniformity of the input light distribution can be corrected. The output power of each port was measured by shifting the singlemode fiber in the current preliminary experiments. Fibertofiber loss of MZIs are measured to be 4.2 ~ 5.4 dB.
The operational principle of a SHS spectrometer based on the MZI array has been elaborated in
[18]
. For a signal
s ( f
) passing through the
k
th MZI, a normalized crossport output is given by assuming negligible waveguide loss as
Planar waveguide SHS configuration with interleavedMZI array.
where
β
is a propagation constant, FSR is a free spectral range determined by
ΔL
, and
S
= ∫
_{f0}
^{f0+ FSR}
s
(
f
)
df
.
f_{0}
is denoted as the Littrow frequency at which phase delays in different MZIs become integer multiples of
2π
(
β
(
f
_{0}
)
ΔL
= 2
mπ
). Since MZI response repeats periodically with FSR, one needs to block the unnecessary spectral range by a bandpass filter. Based on the discrete cosine Fourier transform, the input spectrum
s
(
f_{n}
) (
f_{n}
=
f
_{0}
+
n ∙ FSR
/□, where □=2
N
=64) can be calculated from the measured output power
P
(
k
) as
In the above equation,
A
is a constant and
P
(
k
) for
n
=
N
~ □ ?1 is assumed to be
P
(□ ?
k
). Although FSR was sampled with N points in
[18]
, we sample it with 2N points in order to correctly represent the MZI outputs. Because MZI responses for the signal in the upper half of FSR,
s
(
f_{n}
) (
n
=
N
~□ ?1), have identical spatial fringe representation to those of the signal in the lower half, only the lower half of the signal spectrum can be measured. Resolution of the spectrometer is given by
δ f=c
/(
□n_{c}ΔL
)=
20 GHz.
Phase errors caused by effectiveindex fluctuations in the MZI array deteriorate the accuracy in the retrieved signal by Eq. (6).Phase error
δφ_{k}
in the
k
th MZI is expressed as
δφ_{k}
= (
2π/λ_{0}
)
δn_{c}
(
k
)
L_{k}
,where
δn_{c}(k)
and
L_{k}
denote effectiveindex fluctuation and MZI arm length, as shown in
Fig. 11
(a). A heater with length
l
was placed from outside of the chip on either one of the MZI arms to measure
δφ_{k}
. The throughport transmittance
q
^{(k)}
under the thermooptic effect is given by
Here,
H
is a heater power applied to the phase shifter,
α
is a coefficient of thermooptic refractiveindex change per unit heater power and
λ_{0}=c/ f_{0}
.
Figure 11
(b) shows an example of the thermooptic phase scanning measurement.The first extinction point indicated by
H_{0}
corresponds to the point at which the phase error is compensated for. The power between two adjacent extinction points
H_{T}
corresponds to an optical path length change with λ0. δφk is then given by
δφ_{k}=2π ∙H_{0}/H_{T}
. Effectiveindex fluctuation is obtained as
δn_{c}
(
k
) =(
δφ_{k}
/
L_{k}
)
λ_{0}
/
2π
. Measured
(a) MachZehnder interferometer in the kth stage and(b) throughport response versus heater power.
Measured effectiveindex fluctuation in the MZIarray.
δn_{c}
(
k
) in the MZI array is shown in
Fig. 12
.
A major advantage of the waveguide SHS based on Fouriertransform spectroscopy is that the interferometer defects due to effectiveindex fluctuations can be corrected in data processing stage. On the contrary, physical refractiveindex correction has been required for AWGs after the phase error measurement
[24]
. A known signal spectrum was coupled into the waveguide SHS. The normalized crossport output power distribution
P
(
k
) and the retrieved signal spectrum
s
(
λ_{n}
)(
λ_{n}
=
c/ f_{n}
) by the cosine FFT are shown in
Figs. 13
and
14
, respectively. The Littrow wavelength
λ_{0}
was determined by measuring the normalized crossport output at the second MZI
P
(
k
=1).
P
(1) rapidly oscillates with respect to the wavelength change. But, it reaches to stationary and the maximum value at
λ
_{max}
=
λ_{0}
[1+
δφ_{1}
/(2
πm
)]~
λ_{0}
.
λ_{0}
was measured to be 1550.1 nm. Solid curve in
Fig. 14
is the original signal spectrum measured by a bulk spectrometer. The Hanning
Measured crossport output power distribution inthe MZI array.
Retrieved signal spectrum by cosine Fourier transform.
window was multiplied to
P
(
k
) so as to reduce oscillatory features in the retrieved spectrum. The FSR in terms of wavelength is given by
λ_{FSR} = λ_{0} /m
= 10.24 nm. Signals in the range of λ = 1539.9 ~ 1545.04 nm are not shown in
Fig. 14
since they are mirrored replica of the spectrum in λ = 1545.2 ~ 1550.1 nm. Deviation of the measured spectrum from the original one is mainly due to the phase error
δφ'_{k}s
since they cannot be directly included in the cosine FFT analysis. The horizontal axis in
Fig. 13
is understood to be the optical path length difference divided by ncΔL. Then, the measured MZI output should be located at
k+δn_{c}Lk /ncΔL
instead of the ideal position,
k
. The correction can be done by using the measured data and the Lagrange interpolation to replace the unevenly spaced interferogram points by the evenly spaced ones
[25]
. Fouriertransform algorithms can then be applied to the evenly spaced interferogram points. For a large number of data points, as in bulkoptic Fouriertransform spectroscopy,a FFTbased procedure is a prerequisite. However,for a small number of N, the discretized form of Eq. (1), including phase errors,
Signal spectrum corrected by taking account of themeasured phase errors.
can be solved by
N×N
simultaneous equations. A signal spectrum corrected with the above procedure is shown in
Fig. 15
. The main part of the spectrum is accurately retrieved. Some oscillatory features in the peripheral spectral regions may be caused by the imperfection of the 3 dB couplers and differential attenuation in longer asymmetrical MZIs. Correction of these imperfections will be reported in the future.
IV. SUMMARY
Four kinds of silicon photonics WDM filters have been investigated in detail. It is made clear that (a) improvement in core width and thickness uniformity and (b) size reduction to make the device size small are strongly required in order to achieve good crosstalk characteristics(< 20 dB).
We have demonstrated a novel planar waveguide spectrometer implemented in silica PLC. The signal spectrum was successfully retrieved by correcting the MZI output data with the phase error values. Miniature spectrometers will be important for daily health care and environmental sensing applications since they are compact in size and potentially very low cost (disposable).
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2004
Fast Fourier transform for discontinuous function
IEEE Trans. on Antennas and Propagation
52
461 
465
DOI : 10.1109/TAP.2004.823965