U.S. patent application number 15/466405 was filed with the patent office on 2017-10-12 for phase error compensating apparatus.
This patent application is currently assigned to Electronics and Telecommunications Research Instit ute. The applicant listed for this patent is Electronics and Telecommunications Research Institute. Invention is credited to Hwan Seok CHUNG, Sae Kyoung KANG, Heuk PARK.
Application Number | 20170293076 15/466405 |
Document ID | / |
Family ID | 59998041 |
Filed Date | 2017-10-12 |
United States Patent
Application |
20170293076 |
Kind Code |
A1 |
PARK; Heuk ; et al. |
October 12, 2017 |
PHASE ERROR COMPENSATING APPARATUS
Abstract
Provided is a phase error compensating apparatus. The phase
error compensating apparatus may include a waveguide array disposed
between a first free propagation region and a second free
propagation region and configured to allow a light signal passed
through the first free propagation region to move toward the second
free propagation region, in which a length of each of the
waveguides included in the waveguide array may be adjusted to
compensate for a phase error of light signals passed through the
waveguides.
Inventors: |
PARK; Heuk; (Daejeon,
KR) ; KANG; Sae Kyoung; (Daejeon, KR) ; CHUNG;
Hwan Seok; (Daejeon, KR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Electronics and Telecommunications Research Institute |
Daejeon |
|
KR |
|
|
Assignee: |
Electronics and Telecommunications
Research Instit ute
Daejeon
KR
|
Family ID: |
59998041 |
Appl. No.: |
15/466405 |
Filed: |
March 22, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G02B 6/12011 20130101;
H04J 14/02 20130101 |
International
Class: |
G02B 6/12 20060101
G02B006/12; G02B 27/00 20060101 G02B027/00 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 8, 2016 |
KR |
10-2016-0043580 |
Claims
1. A phase error compensating apparatus, comprising: an input
waveguide corresponding to an input port to which a light signal is
to be input; an output waveguide corresponding to an output port
from which a light signal is to be output; a first free propagation
region in which the light signal input through the input waveguide
is to be propagated; a second free propagation region in which a
light signal is to be propagated toward the output waveguide; and a
waveguide array comprising waveguides, disposed between the first
free propagation region and the second free propagation region, and
configured to allow a light signal passed through the first free
propagation region to move toward the second free propagation
region, wherein lengths of the waveguides are adjusted to
compensate for a phase error of light signals passed through the
waveguides, and wherein a length of a waveguide among the
waveguides is adjusted based on a phase error of a light signal
passed through the waveguide, a center wavelength of a light signal
passed through the waveguide array, and an effective refractive
index of the waveguide.
2. The apparatus of claim 1, wherein the waveguide array comprises
a straight portion in which the waveguides are formed to be
straight and a circular arc-shaped portion in which the waveguides
are formed to be in a circular arc shape.
3. The apparatus of claim 2, wherein a length of the straight
portion is adjusted based on a central angle of the circular
arc-shaped portion.
4. The apparatus of claim 2, wherein a radius of the circular
arc-shaped portion is adjusted based on a central angle of the
circular arc-shaped portion and a length of the straight
portion.
5. (canceled)
6. The apparatus of claim 1, wherein a length of each of the
waveguides is adjusted based on a phase of a waveguide
corresponding to a light signal having a greatest phase error among
the light signals passed through the waveguides.
7. A phase error compensating apparatus, comprising: an input
waveguide corresponding to an input port to which a light signal is
to be input; an output waveguide corresponding to an output port
from which a light signal is to be output; a first free propagation
region in which a light signal input through the input waveguide is
to be propagated; a second free propagation region in which a light
signal is to be propagated toward the output waveguide; and a
waveguide array comprising waveguides, disposed between the first
free propagation region and the second free propagation region, and
configured to allow the light signal passed through the first free
propagation region to move toward the second free propagation
region, wherein lengths of the waveguides are adjusted to
compensate for a phase error of light signals passed through the
waveguides, and wherein a length of each of the waveguides is
adjusted based on a phase of a waveguide corresponding to a light
signal having a greatest phase error among the light signals passed
through the waveguides.
Description
CROSS-REFERENCE TO RELATED APPLICATION(S)
[0001] This application claims the priority benefit of Korean
Patent Application No. 10-2016-0043580 filed on Apr. 8, 2016, in
the Korean Intellectual Property Office, the disclosure of which is
incorporated herein by reference for all purposes.
BACKGROUND
1. Field
[0002] One or more example embodiments relate to an optical
communication device, and more particularly, to an arrayed
waveguide grating (AWG).
2. Description of Related Art
[0003] In optical communications, wavelength-division multiplexing
(WDM) is a transmission method that may allocate a plurality of
signals to different wavelength bands, and simultaneously transmit
the signals through a single optical fiber. An arrayed waveguide
grating (AWG) may be necessary for the WDM, and include an arrayed
waveguides (also referred to as a waveguide array herein) including
a plurality of waveguides having different lengths each. The AWG
may distribute a light signal to each of the waveguides based on
each wavelength, and may multiplex or demultiplex the light signal
using a difference among light paths based on the different lengths
of the waveguides.
[0004] A loss and a crosstalk may occur due to a phase error while
a plurality of light signals is passing through the waveguides. The
phase error of the light signals passing through the AWG may occur
due to, for example, a distortion of a radiation pattern at an
input port of the AWG, a distortion occurring in a boundary between
the waveguide array and a free propagation region, and a distortion
occurring due to an interference among the waveguides included in
the waveguide array. To correct such a phase error, a method of
eliminating the aforementioned causes while maintaining a
difference in length among the waveguides is used.
SUMMARY
[0005] An aspect provides a phase error compensating apparatus that
may compensate for a phase error despite a cause of the phase error
not being eliminated.
[0006] According to an aspect, there is provided a phase error
compensating apparatus including an input waveguide corresponding
to an input port to which a light signal is to be input, an output
waveguide corresponding to an output port from which a light signal
is to be output, a first free propagation region in which the light
signal input through the input waveguide is to be propagated, a
second free propagation region in which a light signal is to be
propagated toward the output waveguide, and a waveguide array
disposed between the first free propagation region and the second
free propagation region, and configured to allow the light signal
passed through the first free propagation region to move toward the
second free propagation region. A length of each of the waveguides
included in the waveguide array may be adjusted to compensate for a
phase error of light signals passed through the waveguides.
[0007] The waveguide array may include a straight portion in which
the waveguides included in the waveguide array are formed to be
straight and a circular arc-shaped portion in which the waveguides
included in the waveguide array are formed to be in a circular arc
shape.
[0008] A length of the straight portion may be adjusted based on a
central angle of the circular arc-shaped portion.
[0009] A radius of the circular arc-shaped portion may be adjusted
based on the central angle of the circular arc-shaped portion and
the length of the straight portion.
[0010] A length of a waveguide included in the waveguide array may
be adjusted based on a phase error of a light signal passed through
the waveguide, a center wavelength of the light signal of the AWG,
and an effective refractive index of the waveguide.
[0011] A length of each of the waveguides included in the waveguide
array may be adjusted based on a phase of a waveguide corresponding
to a light signal having a greatest phase error among the light
signals passed through the waveguides.
[0012] According to example embodiments, a phase error may be
compensated for despite a cause of the phase error not being
eliminated.
[0013] Additional aspects of example embodiments will be set forth
in part in the description which follows and, in part, will be
apparent from the description, or may be learned by practice of the
disclosure.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] These and/or other aspects, features, and advantages of the
present disclosure will become apparent and more readily
appreciated from the following description of example embodiments,
taken in conjunction with the accompanying drawings of which:
[0015] FIG. 1 is a diagram illustrating a structure of a phase
error compensating apparatus according to an example
embodiment;
[0016] FIG. 2 is a conceptual diagram illustrating a phase error
compensating apparatus according to an example embodiment;
[0017] FIGS. 3A and 3B are diagrams illustrating a phase error
prior to adjustment of a length of each waveguide included in a
waveguide array of a phase error compensating apparatus according
to an example embodiment;
[0018] FIGS. 4A and 4B are diagrams illustrating a length of each
waveguide included in a waveguide array subsequent to compensation
for a phase error illustrated in FIGS. 3A and 3B according to an
example embodiment;
[0019] FIGS. 5A and 5B are diagrams illustrating a configuration of
a phase error compensating apparatus according to an example
embodiment; and
[0020] FIGS. 6A and 6B are diagrams illustrating spectrums of light
signals output from, respectively, an existing arrayed waveguide
grating (AWG) and a phase error compensating apparatus according to
an example embodiment.
DETAILED DESCRIPTION
[0021] Hereinafter, some example embodiments will be described in
detail with reference to the accompanying drawings. Regarding the
reference numerals assigned to the elements in the drawings, it
should be noted that the same elements will be designated by the
same reference numerals, wherever possible, even though they are
shown in different drawings. Also, in the description of
embodiments, detailed description of well-known related structures
or functions will be omitted when it is deemed that such
description will cause ambiguous interpretation of the present
disclosure.
[0022] Various alterations and modifications may be made to the
examples. Here, the examples are not construed as limited to the
disclosure and should be understood to include all changes,
equivalents, and replacements within the idea and the technical
scope of the disclosure.
[0023] Terms such as first, second, A, B, (a), (b), and the like
may be used herein to describe components. Each of these
terminologies is not used to define an essence, order or sequence
of a corresponding component but used merely to distinguish the
corresponding component from other component(s). For example, a
first component may be referred to a second component, and
similarly the second component may also be referred to as the first
component.
[0024] It should be noted that if it is described in the
specification that one component is "connected," "coupled," or
"joined" to another component, a third component may be
"connected," "coupled," and "joined" between the first and second
components, although the first component may be directly connected,
coupled or joined to the second component. In addition, it should
be noted that if it is described in the specification that one
component is "directly connected" or "directly joined" to another
component, a third component may not be present therebetween.
Likewise, expressions, for example, "between" and "immediately
between" and "adjacent to" and "immediately adjacent to" may also
be construed as described in the foregoing.
[0025] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting. As
used herein, the singular forms "a," "an," and "the," are intended
to include the plural forms as well, unless the context clearly
indicates otherwise. It will be further understood that the terms
"comprises," "comprising," "includes," and/or "including," when
used herein, specify the presence of stated features, integers,
steps, operations, elements, and/or components, but do not preclude
the presence or addition of one or more other features, integers,
steps, operations, elements, components, and/or groups thereof.
[0026] Unless otherwise defined, all terms, including technical and
scientific terms, used herein have the same meaning as commonly
understood by one of ordinary skill in the art to which this
disclosure pertains. Terms, such as those defined in commonly used
dictionaries, are to be interpreted as having a meaning that is
consistent with their meaning in the context of the relevant art,
and are not to be interpreted in an idealized or overly formal
sense unless expressly so defined herein.
[0027] Hereinafter, examples are described in detail with reference
to the accompanying drawings. Like reference numerals in the
drawings denote like elements, and a known function or
configuration will be omitted herein.
[0028] FIG. 1 is a diagram illustrating a structure of a phase
error compensating apparatus according to an example embodiment.
Referring to FIG. 1, the phase error compensating apparatus
includes an input waveguide 110, a first free propagation region
120, a waveguide array 130, a second free propagation region 140,
and an output waveguide 150. The input waveguide 110 may correspond
to an input port to which a light signal is to be input. The output
waveguide 150 may correspond to an output port from which a light
signal is to be output.
[0029] The waveguide array 130, which indicates arrayed waveguides,
may include a plurality of waveguides. The waveguides may have
different lengths. The waveguides may be arranged to be a circular
arc of a fan shape, having a same center. Here, when a distance
from a waveguide to a center increases, a length of the waveguide
may gradually increase.
[0030] For example, as illustrated in FIG. 1, a waveguide 131 may
have a shortest length among the waveguides included in the
waveguide array 130 because the waveguide 131 is located closest to
the center of the fan shape. Similarly, a waveguide 132 may have a
longest length among the waveguides included in the waveguide array
130 because the waveguide 132 is located on an outermost side of
the waveguide array 130. Thus, respective lengths of the waveguides
may be different from one another.
[0031] The waveguides included in the waveguide array 130, the
input waveguide 110, and the output waveguide 150 may be an element
configured to transmit a light signal using total internal
reflection of light. Here, a waveguide may include a polymer,
glass, lithium niobate (LiNbO.sub.3) or lithium tantalate
(LiTaO.sub.3), and silicon (Si).
[0032] The phase error compensating apparatus includes the first
free propagation region 120 in which a light signal to be input
through the input waveguide 110 is to be propagated, and the second
free propagation region 140 in which the light signal passed
through the waveguide array 130 is propagated toward the output
waveguide 150. That is, the light signal input through the input
waveguide 110 may be freely propagated in the first free
propagation region 120, and the light signal passed through the
waveguide array 130 may be freely propagated in the second free
propagation region 140.
[0033] A form of a boundary between the first free propagation
region 120 and the waveguide array 130 may be identical to a
circumference of a fan shape with a center being at a point at
which the input waveguide 110 meets the first free propagation
region 120. In such a case, respective light signals to be
transferred to the waveguides included in the waveguide array 130
may generally have the same phase. In addition, a form of a
boundary between the second free propagation region 140 and the
waveguide array 130 may be identical to a circumference of a fan
shape with a center being the output waveguide 150. In such a case,
a phase difference among the light signals passed through the
waveguides included in the waveguide array 130 may be maintained in
the second free propagation region 140.
[0034] Although each of the input waveguide 110 and the output
waveguide 150 is illustrated as a single waveguide in FIG. 1, the
input waveguide 110 or the output waveguide 150 of the phase error
compensating apparatus may include a plurality of waveguides.
[0035] As described above, the lengths of the waveguides included
in the waveguide array 130 may different from one another. For
example, under the assumption that a plurality of output waveguides
is connected to different portions of the second free propagation
region 140, when the waveguides transmit light signals with
different wavelengths, the light signals may form images in
different portions of the second free propagation region 140 based
on the wavelengths. Thus, the light signals with the different
wavelengths may reach the output waveguides, respectively.
[0036] Thus, the phase error compensating apparatus may demultiplex
a light signal including the light signals with the different
wavelengths. The phase error compensating apparatus may multiplex
the light signals having the different wavelengths onto a single
light signal.
[0037] In principle, phases of the light signals output from the
waveguides included in the waveguide array 130 may need to have a
same designed value. However, the phases of the light signals may
be distorted during the light signals passing through the first
free propagation region 120 and the waveguide array 130, and thus a
phase error may occur. The phase error may indicate how a phase of
a light signal is distorted while the light signal is passing
through the first free propagation region 120 and the waveguide
array 130. Thus, a light signal reaching the output waveguide 150
may have a phase that is different from the designed value due to
the phase error. The phase error may be different among the
waveguides included in the waveguide array 130.
[0038] The phase error may occur due to various reasons. For
example, a radiation pattern may be distorted while a light signal
is being propagated in the first free propagation region 120, and
thus a phase error may occur. For another example, a phase error
may occur while a light signal propagated in the first free
propagation region 120 is passing through the boundary between the
first free propagation region 120 and the waveguide array 130. For
still another example, a phase error may occur due to interference
among the waveguides included in the waveguide array 130.
[0039] Such a phase error may result in a loss of a light signal to
be output to the output waveguide 150. When the output waveguide
150 of the phase error compensating apparatus includes a plurality
of waveguides, the phase error may result in interference among the
waveguides, and a crosstalk among light signals output from the
phase error compensating apparatus.
[0040] According to an example embodiment, a length of each of the
waveguides included in the waveguide array 130 of the phase error
compensating apparatus may be adjusted, and thus the phase error
may be compensated for. Thus, the phase error compensating
apparatus may compensate for the phase error even when the reasons
or causes of the phase error described in the foregoing are not
eliminated. The phase error compensating apparatus may reduce the
loss of the light signal to be output through the output waveguide
150, and also the crosstalk.
[0041] FIG. 2 is a conceptual diagram illustrating a phase error
compensating apparatus according to an example embodiment. The
phase error compensating apparatus will be described in more detail
with reference to FIG. 2.
[0042] Referring to FIG. 2, an input port 210 corresponds to the
input waveguide 110 of FIG. 1, a first free propagation region 220
corresponds to the first free propagation region 120 of FIG. 1, a
grating 230 corresponds to the waveguide array 130 of FIG. 1, a
second free propagation region 240 corresponds to the second free
propagation region 140 of FIG. 1, and an output port 250
corresponds to the output waveguide 150 of FIG. 1.
[0043] A light signal input through the input port 210 may be
propagated in the first free propagation region 220. A lens 221 of
FIG. 2 corresponds to the boundary between the first free
propagation region 120 and the waveguide array 130 of FIG. 1. As
described above, a form of the boundary may be identical to a
circumference of the light signal being propagated in the first
free propagation region 120, and thus phases of light signals
passed through the lens 221 may need to be identical to one
another.
[0044] A light signal passed through the grating 230 may proceed
toward the second free propagation region 240. Light signals
passing through the second free propagation region 240 may form an
image on the output port 250. A phase of a light signal is
illustrated in a form of a wavefront in FIG. 2. A phase of a light
signal may be distorted while the light signal is passing through
the first free propagation region 220 or the lens 221. A phase
error that may occur due to the distortion of the phase may distort
the image to be formed on the output port 250, which may result in
a loss of the light signal and a crosstalk among light signals
having different wavelengths.
[0045] According to an example embodiment, a length of each of a
plurality of waveguides included in a waveguide array of the phase
error compensating apparatus may be adjusted based on a phase
error. In FIG. 2, the adjusted length of each of the waveguides is
conceptually illustrated as a compensator 260. The compensator 260
may compensate for a phase based on a wavefront when a light signal
proceeds to the second free propagation region 240 from the output
port 250. Thus, a form of a wavefront of a phase of a light signal
passed through the compensator 260 may correspond to a form of the
wavefront of the light signal when the light signal proceeds to the
second free propagation region 240 from the output port 250. That
is, a phase error may be compensated for through the compensator
260 of the phase error compensating apparatus.
[0046] FIGS. 3A and 3B are diagrams illustrating a phase error
prior to adjustment of a length of each waveguide included in a
waveguide array of a phase error compensating apparatus according
to an example embodiment. Hereinafter, it is assumed that the
waveguide array of the phase error compensating apparatus includes
a total of six waveguides, and a difference in length among the
waveguides is consistent as .DELTA.L.
[0047] Referring to FIG. 3A, a z axis 310 located at a point at
which z is 0 (z=0) indicates an end portion of the waveguide array.
That is, the z axis 310 corresponds to a boundary between the
waveguide array and a second free propagation region. In addition,
under the assumption, when a length of a k-th waveguide is L(k) (or
L.sub.k as illustrated in FIG. 3), L(k+1)-L(k)=.DELTA.L.
[0048] As described above, six light signals passed through the six
waveguides, respectively, may have a phase error, and phases of the
six light signals may be different from one another on the z axis
310. A phase front 320 is a line that visualizes a phase difference
among the six light signals, and connects locations of the six
light signals on a waveguide in which the phases of the six light
signals are the same. As illustrated in FIG. 3A, a light signal
passed through a third waveguide has a greatest distance between
the phase front 320 and the z axis 310 among the six light signals,
and thus a phase error of the light signal may be the greatest
among the light signals. Similarly, a phase error of a light signal
passed through a first waveguide may be the smallest among the
light signals.
[0049] FIG. 3B is a graph 330 illustrating phase errors measured
from the z axis 310. ".DELTA..phi.(k)" (or ".DELTA..phi..sub.k" as
illustrated in FIG. 3B) indicates a phase error of a light signal
passed through a k-th waveguide. Referring to FIG. 3B,
".DELTA..phi.(1)" indicates a smallest value, and ".DELTA..phi.(3)"
indicates a greatest value. According to an example embodiment, a
length of the k-th waveguide of the phase error compensating
apparatus may be adjusted based on .DELTA..phi.(k).
[0050] FIGS. 4A and 4B are diagrams illustrating a length of each
waveguide included in a waveguide array subsequent to compensation
for the phase error illustrated in FIGS. 3A and 3B according to an
example embodiment. According to an example embodiment, a length of
a k-th waveguide of the phase error compensating apparatus may be
determined by adding, to L(k), a length c(k) to compensate for a
phase error. Thus, a final length L'(k) of the k-th waveguide of
the phase error compensating apparatus may be defined by Equation 1
below.
L'(k)=L(k)+c(k) [Equation 1]
[0051] When the c(k) of the phase error compensating apparatus is
adjusted, phases of respective light signals passed through
waveguides included in the waveguide array may correspond to a
designed value at an end portion of the waveguide array. Referring
to FIG. 4A, the phase error compensating apparatus may add the c(k)
to the L(k) to match a phase front 410 to the end portion of the
waveguide array. Thus, the phases of the light signals passed
through the waveguides may correspond to the designed value at the
end portion of the waveguide array. Thus, a loss of a light signal,
a crosstalk, and the like due to a phase error may be reduced.
[0052] According to an example embodiment, the c(k) may be
determined based on a phase of a waveguide corresponding to a light
signal having a greatest phase error among the light signals passed
through the waveguides included in the waveguide array. Referring
to FIG. 4A, the c(k) may be adjusted based on a phase of a third
waveguide having a greatest phase error. Thus, a length of a
waveguide to be added for compensating for the phase error may be
minimized.
[0053] FIG. 4B is a graph 420 illustrating the c(k) (C.sub.k as
illustrated in FIG. 4B). Referring to FIG. 4B, c(3) corresponding
to the third waveguide having the greatest phase error may be 0,
because the respective lengths of the waveguides included in the
waveguide array are adjusted based on a phase of a waveguide
corresponding to a light signal having a greatest phase error.
Similarly, c(1) corresponding to a first waveguide having a
smallest phase error may be a greatest value.
[0054] According to an example embodiment, the length c(k) for
compensating for a phase error of the phase error compensating
apparatus may be determined based on .DELTA..phi.(k). In detail,
the c(k) may be determined based on Equation 2 below.
c ( k ) = - ( .DELTA..PHI. ( k ) 2 .pi. + m k ) .lamda. n eff +
.alpha. [ Equation 2 ] ##EQU00001##
[0055] In Equation 2, ".alpha." denotes a real number, and may be
set to be consistent with respect to all the waveguides included in
the waveguide array. "n.sub.eff" denotes an effective refractive
index of the k-th waveguide, and ".lamda." denotes a wavelength of
the light signal passing through the k-th waveguide. In AWG, the
center wavelength may be used for ".lamda.". "m.sub.k" denotes an
integer that is arbitrarily selected.
[0056] Referring to Equations 1 and 2, the final length L'(k) of
the k-th waveguide of the phase error compensating apparatus may be
determined based on Equation 3 below.
L ' ( k ) = L ( k ) - ( .DELTA..PHI. ( k ) 2 .pi. + m k ) .lamda. n
eff + .alpha. [ Equation 3 ] ##EQU00002##
[0057] An arrayed waveguide grating (AWG) be embodied in various
forms. For example, the AWG may be provided as a box type, a flat
type, and a horseshoe type. Hereinafter, based on a horseshoe type
AWG, an example of adjusting a length of each waveguide included in
a waveguide array of a phase error compensating apparatus will be
described.
[0058] FIGS. 5A and 5B are diagrams illustrating a configuration of
a phase error compensating apparatus according to an example
embodiment. Referring to FIG. 5A, a point P 501 indicates a central
point of a circular arc C 502, which is a boundary between a first
free propagation region and a waveguide array. A light signal input
through an input waveguide may be propagated from the point P
501.
[0059] According to an example embodiment, a waveguide array of a
phase error compensating apparatus based on a horseshoe type AWG
may be divided into a straight portion in which a plurality of
waveguides included in the waveguide is straightly formed, and a
circular arc-shaped portion in which the waveguides are formed to
be a circular arc shape. Referring to FIG. 5A, a point S 503
indicates a boundary between a straight portion and a circular
arc-shaped portion of a k-th waveguide included in the waveguide
array. l.sub.k 504 indicates a length of a line connecting the
point P 501 and the point S 503, and a length of the straight
portion of the k-th waveguide may be a value obtained by
subtracting a radius of the circular arc C 502 from the l.sub.k
504.
[0060] As illustrated in FIG. 5A, .theta..sub.k 506 indicates an
angle formed between the line connecting the point P 501 and the
point S 503 and an z axis, and a line connecting the point P 501
and a point W 505 and the z axis, respectively. R.sub.k 507
indicates a radius of the circular arc-shaped potion of the k-th
waveguide. A central angle of a circular arc B 508 of the circular
arc-shaped portion of the k-th waveguide may be designed to be the
.theta..sub.k 506. A point Q indicates a central point of the line
connecting the point P 501 and the point W 505, and a line 509
connecting the point Q and a point U may be a symmetry axis of the
waveguide array. L.sub.g 510 indicates a length of a line
connecting the point P 501 and the point Q. The point W 505
indicates a point corresponding to the point P 501 in a second free
propagation region.
[0061] According to an example embodiment, the length of the
straight portion or the radius of the circular arc-shaped portion
of the k-th waveguide of the phase error compensating apparatus may
be adjusted, and thus a phase error may be compensated for. In
detail, the length of the straight portion or the radius of the
circular arc-shaped portion of the k-th waveguide may be adjusted
based on a central angle of the circular arc-shaped portion of the
k-th waveguide.
[0062] The phase error compensating apparatus may be symmetrical
based on the line 509 connecting the point Q and the point U. When
a length of a light path with respect to an entirety of the first
free propagation region, the waveguide array, and the second free
propagation region of a light signal passed through the k-th
waveguide is La(k), La(k) may be represented by Equation 4 using
the symmetry described above.
La ( k ) 2 = l k + R k .theta. k [ Equation 4 ] ##EQU00003##
[0063] Referring to FIG. 5B, a relationship represented by Equation
5 may be established between R.sub.k 507 and l.sub.k 504.
R k = [ L - l k cos .theta. k ] sin .theta. k [ Equation 5 ]
##EQU00004##
[0064] Equation 6 below may be obtained by substituting Equation 5
to Equation 4.
La ( k ) 2 = l k + [ L - l k cos .theta. k ] .theta. k sin .theta.
k = l k ( 1 - .theta. k cot .theta. k ) + L .theta. k sin .theta. k
[ Equation 6 ] ##EQU00005##
[0065] Referring to Equation 6, La(k) may be linearly proportional
to k 504. In addition, La(k) may be determined by the central angle
.theta..sub.k 506 of the circular arc-shaped portion of the k-th
waveguide. According to an example embodiment, a length of a
straight portion of each of the waveguides of the phase error
compensating apparatus may be adjusted, and thus a phase error may
be compensated for. In detail, when a variation in the length of
the straight portion of the k-th waveguide is .delta.(k) and a
final adjusted length of the straight portion of the k-th waveguide
for the compensation for a phase error is La'(k), a relationship
between .delta.(k) and La'(k) may be represented by Equation 7
below using the c(k).
La ' ( k ) 2 = La ( k ) + c ( k ) 2 = ( l k + .delta. k ) ( 1 -
.theta. k cot .theta. k ) + L .theta. k sin .theta. k [ Equation 7
] ##EQU00006##
[0066] A relationship between the c(k) and the .delta.(k) as
represented by Equation 8 below may be derived by eliminating the
La(k) from Equations 6 and 7.
.delta. ( k ) = c ( k ) 2 ( 1 - .theta. k cot .theta. k ) [
Equation 8 ] ##EQU00007##
[0067] Referring to Equation 8, the length of the straight portion
of the k-th waveguide of the phase error compensating apparatus may
be adjusted based on the c(k) and the .theta..sub.k 506 in Equation
2.
[0068] According to an example embodiment, a radius of a circular
arc-shaped portion of each waveguide included in the waveguide
array of the phase error compensating apparatus may be adjusted,
and thus a phase error may be compensated for. Here, it may be
assumed that the L.sub.g 510 and the .theta..sub.k 506 are the same
before and after the adjustment of lengths of the waveguides
included in the waveguide array to compensate for a phase error.
Under such an assumption, when a variation of a radius R.sub.k 507
of the circular arc-shaped portion of the k-th waveguide is c(k),
Equation 5 may be converted to Equation 9 below.
R k + ( k ) = [ L - ( l k + .delta. ( k ) ) cos .theta. k ] sin
.theta. k [ Equation 9 ] ##EQU00008##
[0069] From Equations 5 and 9, a relationship between the
.epsilon.(k) and the c(k) may be derived as represented by Equation
10 below.
( k ) = - .delta. ( k ) cot .theta. k = - c ( k ) 2 ( tan .theta. k
- .theta. k ) [ Equation 10 ] ##EQU00009##
[0070] Referring to Equation 10, the radius of the circular
arc-shaped portion of the k-th waveguide of the phase error
compensating apparatus may be adjusted based on the c(k) and the
.theta..sub.k 506 in Equation 2.
[0071] FIGS. 6A and 6B are diagrams illustrating spectrums of light
signals output from, respectively, an existing AWG and a phase
error compensating apparatus according to an example embodiment.
Referring to FIGS. 6A and 6B, the existing AWG and the phase error
compensating apparatus described herein may demultiplex a plurality
of light signals having different wavelengths being between 1540
nanometers (nm) and 1560 nm.
[0072] Referring to FIG. 6A, a crosstalk among a plurality of
demultiplexed light signals to be output from the existing AWG may
be greater than or equal to -18 decibels (dB). Referring to FIG.
6B, in comparison to the existing AWG, a crosstalk among a
plurality of light signals to be output from an AWG to which the
phase error compensating apparatus is applied may be less than or
equal to -20 dB, or less than or equal to -30 dB for some light
signals. That is, the phase error compensating apparatus may
compensate for a phase error of the light signals, and thus the
crosstalk in the phase error compensating apparatus may be improved
compared to the crosstalk in the existing AWG.
[0073] While this disclosure includes specific examples, it will be
apparent to one of ordinary skill in the art that various changes
in form and details may be made in these examples without departing
from the spirit and scope of the claims and their equivalents. The
examples described herein are to be considered in a descriptive
sense only, and not for purposes of limitation. Descriptions of
features or aspects in each example are to be considered as being
applicable to similar features or aspects in other examples.
Suitable results may be achieved if the described techniques are
performed in a different order, and/or if components in a described
system, architecture, device, or circuit are combined in a
different manner and/or replaced or supplemented by other
components or their equivalents.
[0074] Therefore, the scope of the disclosure is defined not by the
detailed description, but by the claims and their equivalents, and
all variations within the scope of the claims and their equivalents
are to be construed as being included in the disclosure.
* * * * *