analysis of spurious rf signal caused by retardation in optical two-tone signal generator utilizing...

7/24/2019 Analysis of spurious RF signal caused by retardation in optical two-tone signal generator utilizing polarisation mani…

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registance terminating the modulation electrode of MZM.Here, the optical fibers are short and occupied bandwidthof the OTT signal is not so wide (e.g.: for f 0=10 GHz,wavelength separation of 4 f 0 corresponds to 0.32nm), sowe neglect their dispersion. Assuming that the phasemodulation at either arm of the MZM is #" cos2$ f 0t , we

obtain the lightwave EO after it passes through the polar-izer as follows:

(1)

where the first and second rows represent P and S polari-zation, respectively. Note that the sinusoidally modulat-ed P-polarized component is converted from the S-polarized component by a polarization-rotation element." is the rotation angle for projecting the polarization, and# is the polarization angle of the incident linearly polar-ized lightwave. J m(#" ) are the mth-order Bessel functionsof the first kind, with an argument #" . Hereafter, #" isassumed to be less than 2.405; J m(#" ) ( 0n ! ) is positive.In addition, $ 0 is the optical frequency of the incidentlightwave, and c is speed of lightwave in vacuum; forsimplicity, hereafter exp[ j2$$ 0(t-nez/c)] is omitted. ne iseffective refractive index of either mode in PMF from port3 of OC. Polarization-mode dispersion in the PMF be-tween PC and port 1 of OC is omitted (this effect appearsas shortening of effective length of the PMF between port3 of OC and the quarter-wave plate (QWP), owing to po-larization rotation). And % is the retardation originatingfrom the PMF, and from QWP to compensate for theirstatic retardation. As an initial condition, QWP angle isadjusted so as to compensate the retardation of the PMF;i.e. % = 0. For % = 0 and infinite ! POL , the carrier lightwavedisappears perfectly in the output lightwave when thefollowing condition is satisfied [11]:

!sin! sin" +cos! cos" J 0 (!! ) = 0. (2)

Since MZM does not generate odd-order sidebands, themain components in the transmitted lightwave are ± 2nd-order sidebands when eq.(2) is satisfied; beating of them,obtained from the photodiode with sufficient frequency

bandwidth, is desired frequency-quadlpled RF signal. Itcan be also explained using a schematic of optical ampli-tude spectrum for each polarization [11]. By substitutingEq. (2) into Eq. (1), for a slight deviation of % from zero, EO is derived to be

(3)

where ASB denotes a series of optical sidebands:

(4)

Although the first and second terms of Eq. (3) indicate thecarrier amplitude, their origins are different; the formerdepending on % , originates in retardation, whereas thelatter is due to the imperfection of the polarizer. From Eq.(3), the optical power of the carrier lightwave, P0 , is de-rived as follows:

(5)

The beat RF signal i0 , which is generated by direct detec-tion of EO , is approximately derived as

(6)

where some terms contributing to the DC component of i0 are omitted in Eq. (6). Because ASB shows a discrete spec-trum with a frequency spacing of f 0 , i0 is also a series witha fundamental frequency of f 0. Hereafter, the nf 0 frequen-

Fig. 1. Analysis model of OTT signal generator for RF frequencyquadrupling. Double and single lines denote optical paths and RFlines, respectively. # : polarization controller; OC: Optical circulator;PBS: polarizing beam splitter; MZM: Mach-Zehnder optical modula-

tor with an extinction ratio of ! !"!; PRE: 90° polarization rotation ele-ment; & /4, & /2: wave plates; ! POL: polarizer with an extinction ratio of! POL; PD: photodiode.

( )0 e2OP

O

OS POL

1 0 cos sin

sin cos0 1

j t n z c E e

E

!" # #

# # $

% & '& ' & '

= = ( )( ) ( )( ) %* +* + * + E

( ) ( )0 e 0 e{2 2 } {2 (2 1) }2 12

MZM

( )cos ( 1) ( )

,

sin

j nf t n z c j n f t n z cn nn

n

j

J J e j e

e

! !

"

# $ #

%

$

&' ( + (

+

=(&

) *+ ,-. /( - +0 1

2. /0 13 4. /

(5 6

7

O

2POL

tan tan

cos cos 1 tantan

cos

SB

SB

j A

A

! " #

" # # "

" $

% +& '( )

= * +( )% +

, -( ). /0 1

E

0

POL

0cos cos ( )

1 sin0

cos

j J ! " # " #

" $

% &' (% & ) *

= +) * ) *'+ , ) *+ , POL

cos

1cos ,sinSB

A

!

" !

#

$ %& '

+ & '(& ') *

0 e

0 e

0 e

{2 2 ( / )}

2

1

{2 ( 2 ) ( / )}

2

{2 (2 1) ( / )}

2 1

MZM

( 1) ( )

( )

( 1)

( ) .

j nf t n z cn

SB n

n

j n f t n z c

n

n j n f t n z c

n

n

A J e

J e

j J e

!

!

!

"

"

" #

$% &

=

& &&

$+ &

+

=&$

'= & ()

*+ ( +

' *&+ (, -, -) +

.

.

22 2 2 2

0 02

POL

1 sincos cos ( ).

cos P J

! " # ! #

# $

% &= + '( )

( )* +

[ ]

[ ]

2 2 2

0 0 0

0

2

POL

2 ( ) (cos cos ) Im

2 ( )Re

cos

SB

SB

i J A

J A

! " ! #

!

$ !

% = & '

'+

E

2 2 2

2

POL

11 cos cos ,

cos SB

A ! " # !

$ %+ +& '

( )



cy component of the first term depends on % , and the oth-ers are denoted as #' % (n) and I 0(n), respectively; i.e.,

(7)

The residual optical carrier described in the first andthe second term of eq. (3) induces spurious RF signals, via

beating with optical sidebands described in the thirdterms of eq. (3). For the second-order RF signal, both ( 0n and ( % n are equal to 8$ f 0nez/c and originate from the groupdelay of the OTT signal. Then I 0(n=2) and #I 0% (n=2) arederived as follows:

(8)

(9)

Then the increase in the second-order spurious RF sig-nal power #P2 due to the increase in #I % (n=2) is

(10)

in units of decibels. Under this analysis model, the odd-order spurious RF signals become zero owing to thephase relation between each pair of optical sidebands.Even if the spurious signal may appear owing to slightdeviation of bias voltage and/or chirp in the MZM [12],this power would be weaker than the even-order RF spu-rious signals.

3 RESULTS AND DISCUSSIONS

Using the above derivation, we estimated fluctuationof the spurious RF power in the experimentally obtainedconversion signal. Fig. 2 shows optical spectra of thegenerated OTT signal to be converted into an RF signal,one of which showing CSR of 25.7dB is previously re-ported [13]. Here # , #" , and f 0 are 17°, 2.2, and 10 GHz,respectively. Power and wavelength of incident carrierwas 6.23 dBm and 1549.96 nm, respectively. Althoughspectra were acquired every few minutes under the samesettings, the carrier component gradually increased. Be-cause the intensities of the other sidebands remain con-stant, the increase was not due to drift in the bias voltage

applied to the MZM. Fig. 3 shows the CSR dependence ofthe second-order spurious (frequency: 20 GHz) RF power.In the calculation, ! POL and ! MZM were set to 28.2 and 26.5dB, respectively, on the basis of measurement results.The calculation result using the above equation shows

good agreement with the results evaluated experimental-

ly. This indicates that the 6-dB degradation of the CSRresults in 1.7-dB increase in #P2. By the derivation, thespur signal power at a 22.5-dB CSR is evaluated to be!11.3 dB against the desired fourth-order (40 GHz) RFsignal. The retardation expected from the carrier intensi-ty is also plotted in Fig. 3, which indicates that the CSRwould be degraded by the 0.2-rad retardation drift in thePMF.

5 CONCLUSION

In summary, we performed model analysis of an OTT

signal generator in which undesired carrier is suppressedusing a polarizer, in order to evaluate degree of spuriousRF signal obtained from the OTT signal. The polarizationchange due to a 0.2-rad retardation in the PMF causes a 6-dB increase in the residual carrier in the generated OTT

( )

( )

0 0 0 0

0

0

( ) cos 2 ( )

( ) sin 2 ( ) .

n

n

n

i I n nf t

I n nf t ! !

" #

" #

$

=

%= +&

'+( +

)

*

{2

12 2 2

1MZM

2 1 2 1

MZM

( )4 ( ) ( )

1( ) ( ) ,

n n

n

n n

J J J

J J

! ! !

"

! ! "

#

+

=

$ +

% &' $ & &(

)

*+ & & +

,

-

0 20 2 2

POL POL

4 ( ) ( ) 1( 2) 1

cos cos

J J I n

! !

" ! " !

# $% %= & ' + +( )

* +

0 2( 2) 4 ( ) ( ) . I n J J ! " " ! # = $ # #

( )( )2

2 10 010log 1 ( ) / ( ) P i n i n!

" = + "

Fig. 2. Optical spectra of lightwave to be converted into RF

signal. Zero of horizontal and vertical axis corresponds to the

wavelength of 1549.96 nm, and optical power of incident light-wave, respectively.

Fig. 3. Second-order spurious RF power (left vertical axis)

obtained from experiment (open circles) and analytical calcula-

tion (dashed lines) versus suppression ratio of optical carrier

against desired ±second-order sidebands. Left vertical axis is

normalized by the value at a 22.5-dB suppression ratio. Solid

line indicates expected retardation (right vertical axis).



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signal, which induces a 1.7-dB increase in the second-order spurious signal.

ACKNOWLEDGMENT

The authors would like to thank Mr. K. Higuma ofSumitomo Osaka Cement Co. Ltd. and Dr. T. Sakamo-

to of National Institute of Information and communi-cations Technology (NICT) for supplying equipments,and to thank Prof. G. W. Lu of Tokai University forfruitful discussions. This work was in part supported by Ministry of Internal affairs and Communications, Japan (SCOPE, 142103013), Gunma university founda-tion for science and technology, Japan and JSPS(15K06050).

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Akito Chiba received the B.E. degree in electric and precision engi-neering, and the M.E. and Ph.D. degreesin the field of electronicsand information engineering from Hokkaido University, Sapporo,Japan,in 2000, 2002, and 2005, respectively. From 2005–2010, hewas with New-Generation Network Research Center, National Insti-tute of Information and CommunicationsTechnology (NICT), Koganei,

Tokyo, Japan, where he was engaged in lithium niobate electroopticdevices and their applications to optical communication. From 2010–2011, he joined the Faculty of Engineering, Shizuoka University,Hamamatsu, Shizuoka, Japan, for CREST Project supported byJapan Science and Technology Agency, where he was involved inthe development of cathodoluminescent thin film for electron-beam-assisted high-resolution optical imaging. Since 2011, he has been anAssistant professor in the Division of Electronics and Informatics,Faculty of Science and Technology, Gunma University, Kiryu, Gun-ma, Japan. His current research interests include the field of appliedoptics and fiber optics utilizing modulation for optical communicationand measurement. Dr. Chiba is a member of the Optical Society,IEEE Photonics Society, the Japan Society of Applied Physics, Opti-cal society of Japan, and the Institute of Electronics, Information, andCommunication Engineering of Japan.

analysis of spurious rf signal caused by retardation in optical two-tone signal generator utilizing...

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