Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Analysis of optical-signal processing using an arrayed-waveguide grating

Hirokazu Takenouchi, Hiroyuki Tsuda, and Takashi Kurokawa

Open Access Open Access

Abstract

We analyzed optical-signal processing based on time-space conversion in an arrayed-waveguide grating (AWG). General expressions for the electric fields needed to design frequency filters were obtained. We took into account the effects of the waveguides and clearly distinguished the temporal frequency axis from the spatial axis at the focal plane, at which frequency filters were placed. Using the analytical results, we identified the factors limiting the input-pulse width and clarified the windowing effect and the effect ofphase fluctuation in the arrayed waveguide.

©2000 Optical Society of America

Full Article  |  PDF Article
More Like This
Analysis and design of arrayed waveguide gratings with MMI couplers

P. Muñoz, D. Pastor, and J. Capmany
Opt. Express 9(7) 328-338 (2001)

Phase errors and statistical analysis of silicon-nitride arrayed waveguide gratings

Qi Han, Daniel Robin, Antoine Gervais, Michaël Ménard, and Wei Shi
Opt. Express 30(24) 42784-42800 (2022)

Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system

Zhenxing Wang, Konstantin S. Kravtsov, Yue-Kai Huang, and Paul R. Prucnal
Opt. Express 19(5) 4501-4512 (2011)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)
Figure 1.
Figure 1. Schematic diagrams of time-space-conversion optical-signal processing using (a) DGs and (b) AWGs.

Download Full Size | PDF

Figure 2.
Figure 2. Model and axes used for analysis. Spatial frequency axes were used instead of spatial axes at the interface between the I/O waveguide and the first slab waveguide and at the focal plane.

Download Full Size | PDF

Figure 3.
Figure 3. Spectral filtering using narrow-stripe mirror: (a) profile of narrow stripe mirror, (b) electric field near ξ=0, (c) temporal frequency spectrum reflected by narrow stripe mirror, (d) temporal output waveform. The shape of the output waveform reflects crosstalk at the focal plane.

Download Full Size | PDF

Figure 4.
Figure 4. Figure of merit (flatness of envelope of temporal waveform) and loss versus shape of distribution function (a/Nd). Envelope of temporal waveform became flatter as a/Nd became larger, but the loss became larger. There is thus a trade-off relation between loss and the figure of merit. The a/Nd of the previously reported AWG was 0.57.

Download Full Size | PDF

Figure 5.
Figure 5. Number-of-waveguides dependence on coefficient of determination (R 2) calculated from output pulse shape for m=72. A phase error of 0.8×10-2 rad/mm is a typical standard deviation in a silica-based waveguide with a relative refractive index difference of 0.75%.

Download Full Size | PDF

Tables (1)

Tables Icon

Table 1 Parameters used in AWG simulation

View Table

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

f ( t ) = u ( t ) exp ( i 2 π ν 0 t ) ,
F ( ν ) = U ( ν − ν 0 ) ≡ U ν .
F 0 , ν ( x 0 ) = U ν · e ( x 0 ) = U ν w IO π · exp ( − x 0 2 w IO 2 ) .
β ( x 1 ) = w IO π i α exp { − ( π w IO ) 2 ( x 1 α ) 2 } ,
α = c L f n s ν 0 ,
f 1 , ν ( x 1 ) = U ν · [ { β ( x 1 ) · rect ( x 1 Nd ) } * δ S ( x 1 ) ] * exp ( − π x 1 2 w AW 2 ) ,
δ S ( x ) ≡ ∑ p = − N ⁄ 2 N ⁄ 2 − 1 δ ( x 1 − pd ) ,
rect ( x ) = { 1 ( ∣ x ∣ < 1 ⁄ 2 ) 0 ( otherwize ) ,
θ ( x , ν ) = 2 π m ν ν 0 d x · δ S ( x ) .
f 2 , ν ( x 2 ) = exp { i θ ( x 2 , ν ) } · f 1 , ν ( x 2 )
= U ν · [ { β ( x 2 ) · rect ( x 2 Nd ) · exp ( i 2 π m ν ν 0 d x 2 ) } * δ S ( x 2 ) ]
* exp ( − π x 2 2 w AW 2 ) .
F 3 , ν ( ξ ) = π w AW 2 i α U ν { B ( ξ ) * sinc ( Nd ξ ) * δ ( ξ − m ν ν 0 d ) } Δ Sum ( ξ ) exp ( − π 2 w AW 2 ξ 2 ) ,
ξ ≡ ν 0 n s c L f x 3 = x 3 α ,
Δ S ( ξ ) = ∑ p = − N ⁄ 2 N ⁄ 2 − 1 exp ( − i 2 π pd ξ )
B ( ξ ) = α 3 ⁄ 2 i π w IO exp { − ( α ξ ) 2 w IO 2 } .
ξ = m ν ν 0 d
γ = ν x 3 = ν 0 2 n s d mc L f = ν 0 d m α .
ν FSR = ν 0 m .
Δ ν = ν 0 Nm .
Δ ν = ν 0 d m Δ ξ ≡ ν 0 N eff · m ,
G 3 , ν ( ξ ) = π w AW 2 i α · U ν · H ( ξ ) · { B ( ξ ) * sinc ( Nd ξ ) * δ ( ξ − m ν ν 0 d ) }
× Δ S ( ξ ) · exp ( − π 2 w AW 2 ξ 2 ) ,
g 2 , ν ( x 2 ) = U ν · { h ( x 2 ) * ( β ( x 2 ) · rect ( x 2 Nd ) · exp ( i 2 π m ν ν 0 d x 2 ) ) * δ S ( x 2 ) }
* exp ( − π x 2 2 w 2 )
g 1 , ν ( x 1 ) = U ν · [ { h ( x 1 ) * ( β ( x 1 ) . rect ( x 1 Nd ) · exp ( i 2 π m ν ν 0 d x 1 ) ) * δ S ( x 1 ) }
× exp ( − i 2 π m ν ν 0 d x 1 ) ] * exp ( − π x 1 2 w 2 ) .
G 0 , ν ( ξ ) = π w AW 2 i α · U ν · { H ( ξ + m ν ν 0 d ) · ( B ( ξ ) * sinc ( Nd ξ ) ) · Δ S ( ξ + m ν ν 0 d ) }
× exp ( − π 2 w AW 2 ξ 2 ) .
V ν = ∫ e ( α ξ ) · G 0 , ν ( ξ ) d ξ
= π w AW 2 i α · U ν ∫ e ( α ξ ) · H ( ξ + m ν ν 0 d ) · ( B ( ξ ) * sinc ( Nd ξ ) ) · Δ S ( ξ + m ν ν 0 d )
× exp ( − π 2 w AW 2 ξ 2 ) d ξ .
Δ t = 1 ν FSR = m ν 0 .
T 0 = 1 Δ ν = Nm ν 0 .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use