BSTJ 50: 1. January 1971: A Method for Measurement of the Duration of Picosecond Pulses by Beat Frequency Detection of Laser Output. (Hubbard, W.M.)

6.8 MB·English

HE BELL SYSTEM
TECHNICAL JOURNAL

som Seer?

A Method for Measurement of the
Duration of Picosecond Pulses by
Beat Frequency Detection of
Laser Output

Ry W. M. HUBBARD

{This paper deen woo out foe mouring the duration of mone
looked pierce! ler pee. 1 sinclar othe uo hoton Bsreacnce
tnd Setond Iacrvnte Govmaton toda in at mosoures wa the pulse
thiaton tiecty Int vther a eatatveation function oft sip, Tt
has the enutoge ita cen be ad for eer lupo repeiie Bhd
sinats,

{Two retlunls for sete-nining the curation of picosteand ulsce
awve een mnie, ‘Phe easier meta, whick stihgee eeeone bar.
‘none geneatins (SHU) ib Roniaesserytal, wae ayportd independ
‘rly almost snultascously by ML Males, W. Ku'ser and J.
(Giordnnine! I. A. Avmstrang end LLP. Webex? "Te second masthed,
‘whieh wills che twosphotex Enavectence {TPF} in eatain eye, 48
fet reporte! ly J. A. Giodcine* end his co-workers. Measurements
ff puae rats Iel rm eer elas hve been verte by mime
2

tous authors, Estensive nferenes to these papers ate neue a
roview arieis hy AT. TeVarin, WH. Glen, de, MJ. Benga and

ME, Meck
[Neituer of howe methoie meceytss pulse ducaion cirecty. Both,
in facl, moire the aninwoeelaten fieion (9) of he intensity

Te), ates

ee = [r+ 9

A. encefl meacuremont ef thy east ewe betwen >| sue peal
St the pute snd (ie) between guise is nseesary in onder to cee
Ite mbelase 02 aot te meunned valves reeeant the duration ot
pure AD pulee {Vhs yas etfs i fre TPH hy BP, Websrt
nd independeatly yd. Tl Rlantes, M.A. Dagan 18. Giow'tnne
find SL Shigivo, 1 the eumlesas cao ism te varsee, vale foe
pare AA pur, Tome sonecning ta slg wavetarm can be Ioiah'y
{nfered fern a koe nly of Ge)

The beat “respite stents (BED) ould peepee i his pa
pet mesanies 4 ve chatty, yay

Wyse = Rid 4B

[PL ou. nen

tn iia the ellen ni of Uae pia! seal 1/7 in the pie ree
tion ro nnd kT ie ta frequency of che aarmerie abeeen foe gnats
4. oo ser frm the Tact that Ifthe eaveect “enatrart ratio" i wo
‘observed, she reall ie ambigaone

i the proper “contrast ratio” ie cbssrred, then £( i eal {.., thom
8 no sagle madwacicn ofthe signal andl fa eases of practical iteret
he puke sdnvation iz caer composed with the oevied 2. ‘Tus, fr
femal by aj" 1 over the rion aon (Deval lntes Signin
tothe Hategesl and

neon erty = [hE meee bat

hw fe) is essentially tho autozorrlution funetion of eff) when
‘hare no angle mcalation. Te is therefore es good w mensure af pulse
lution se lathe antacorrlaton furetion 7
onuasiorrnesy oF ReneusoN PULSE a

‘dae cetain eonitions Mane i reson to belive tat the pubes re
vhimpe” Pi they have the form
ei) ~ But) exp ied + a8]
‘whore fie nal, slonly varying europe funtion, The messaged
nity Hs) sean intersting and stinciso behavior i Oi cae
‘This is conser in Seetivn TL Lt sal be possible in rome eases eo

Colorane by the BED method how saa, i ny “ebiep™ i pesent
Netther TPP nor SHG is oxpcole of pmviing this itormation

“The output 6(f) of laser it pesein fasetion which wn be written
in He fer

wo EAwiverwire

vgs ta ~ 1 et gti’ a the enter Fines ofthe spectrum
Ind hte amp def the wl nei he epectrum. I he phases
se rela by

wane ey

ie any eonsant, the snl £( i soqueneo of piles with no
WING modulation and the pulbe ezvalene Is che minum poeib.c
tteeaion for the set [4,!, Bush signa ie called “mode loeed”. 1
Guston (2) ie nue eatsiod, angle wvbolation (acd) a wider pulse)
Caen, Ta goer, if py isu ase of redon mambers “nisl” Gut
Povlnio) sal is obtial. Tho paw duretion of the signal &C) i

Uereforedensdant on 4.

“Coneidor the civ shown it Fig 2, The ln output o(0 is dvided
nto pal parte Ly the ta hybaid sire (beam wplittes) and the vo
Dens an rogmibine ia the saane rr after oa pall has afered
Petar mative to the other Heat trnstorning lenses ma Be requis!
aogier to amuresignment of faa pose frats of the ko interering
bouune, Mineor fis mute ates >that te delay in one arm of
fhe dice sn br vavid uver a aage worreponcing to one pio 0" thr
Ifecratgot, Rietor If is moter ova plas eok»acoute modulator
to that its position ean be vaio! prodisaly over advance uf a for
‘eign: for reasons wie wil bw expatineé bei The witpat of tbe
Tybee therfore
=

fey et 8}

So Atos (tus tatty} + os lw Hak 4 os) @

1 the sgaal is now applied ta a pmaluek domodulator (photedetecton),
me obtains a ot
vo

Teta + 06 — 2

EE ow ter or

owe bone theuh]

where
a
ana terms fa Bok hase
If hie Siena ie sow pus

yn gnome bes tne sill af amour r/2
i aawagh a avin Aizen which i Fe

Te ehonld be nota ion sive 8! — O forall, Vf ia independent
of 9.) and independont

= Ewe = om ew 1 wel ©

Oe eu readily understand cae netlh by vetoing chet the Felt
emu io general ost ftom che bts belveer. al passe pairs of
Tires separated by an nrieuk so. Le particular V(t} zesuts fom
wets” etrven one spect Hire ard itell. Siew on bens bebwoe
aisezent Hines continue in Vit], ne relative ohises hebeen ines
Fatenee ke real

‘tho een ea, square Law detovton of Pl) gives

+

‘We observ that te envoy dryvalence ig contained inthe ea thee
tran, LF one of the enzo i Ui interiercaster is rented Lavi
‘Sv eptical wavelengty tvs enntsibaton of taeee carn i capalled ul
{ance over ase opten! wavrenyth their average volun 'a 200). This
{2 cecomelshed by nmuntigg ous of tae Tire on € piszocovin
Fnedtoor wud ibratng i, be eeu igen ter pasting Urn
sla bespaaa ites) is gen by

Gai = DL BPR cas bat! —

fi
~ ee {fm
© sawn ering seeUNoN. CRRA, SUS AL

Wr panes to mea ein! for EO exrorte re. Cnet
the nunlelorknd eo 9, = nob ule impire 2” — 0S ~ 0. 'Thi gives
BGleg, oe BEEBE +e EB opted om

1 hin eumation anda the orale & tie paper fs snoranept (8)
fm Bat ata he niles. The od oeked ove mgursents one

{xtcemein thetenee tiie the sortest sore pn estent
Spith a puriielar set aulisaces [Ayh. The Peandors ee",

Gaevle exis uneoomy eset! on, a, rears bm
Shuoste gerne the exporter ale a Khe sgea. power fe conszant
Ii diye. aa experttiey ta na! Ey) fe this one ran bw obits. by
Deering thst Ue expert in vale of oe [Bq — Bal lima the Ia

so rior Tee ow Be} ia give By

© Goralle, mi

on we Maral

1 there

‘om. cen am
Equatins 1% 4 104 meine nF

‘Wer fr coy oro u genau 8
con mica es ee

ity ot

Ase fi

3 RUE AYBERAG TRONSICNL OCR, FAURE “OMY

‘¥oom equetion (15) we ean draw sn interesting comparison bo-
‘meen the BED method and the TPF and SHG methods. Tei clear
from equation (14) that RytO) i the power aretrim of the intensity
std Uherefore the wotoearmlation furetion of the Fatensity Se simply

pen (tl

‘Therefore the quantities measured by all chee methods depend only
on the quantities P(r). Tae reals ef the BFD methed dapend ox
‘he valves ow a single and fl je eeelle for TPP and BHO ca.
‘ne-valus for = ard all k, Foon: ecuatione (12) end (14), have

ro =| E acw(iege)

while fom eoustion (1

ae

10 | Seonlens)|

Bode
ne,
ret
‘Comparing equation (13) with (1) shows that
80D — Re LBC) exp (ha.
1 ithe (cope sgn fron ce eee With We en
ried.

That i,
Feeney

‘Yor the medelocked eace, the pulsse ere very short compared with
‘the repetition rate 1/1” Thus fora last the fost fe k= 1,2, 09+ 80
‘au pre Cekt)/T 1 for those values of for which #() ie salon
Gliferoct from aero. ‘This gives (sino from equation (18) 7) ie even
svhon the Bere al re

1

Fann = A) =

[ease val

Wve the fret term in equttien (15) ie jus saisod eosine with pera
{2/%, bot ie eum of the asd and third tormasis the equare of be
antceorreletinn fetion af AU}. This eam provicie & gael meaaare
Gf the putz duracin whe the signl is moe lock.

Sinee this raenciqu, like TPF and SHG, tmseses some ani
Semen emgerenS FMS ®

if the signal ie not rence lodked, 5 ie importants tae able to distin,
‘mich mods-ockel Inhevior don: roncne-leest behavior. ln o-dee
fo da this, consider Us quantice

oan -4

rl: Mele eae,

BE randow pus ee

Pork ia 6 Ti
nm 3 Em
See
|Z)
con ee epi Tent

Bun) 4 Bo) 6-38
the sigue not sted nee

tis itive to consider ow enw (0) iti oom BQ) fe
vusious eur "Ta thie end we consider haw epeial tuations, nama,
b pare FD rgaal, «model ul yrtial mode ‘ooking, snd. a “chiped™
Dale. Consider net the wnusoidlly modal pure YM sgzal

fest + nth

18) 608 as | ei.
"This use especial nee mst C1) th
A, = Sally t= all

‘The msg exprsesion for Coie ia tefore
10 say say evening macnn JoLasat, sasusay Li

‘This son be reduecd, hy mone of & wel-known Lengel ‘unction
itomily tw

oan ~ lao cin

Note whet Uy(0) = 4 waeeece Uuf0) = 0, — 4,9, Alo, the
laggest value thot Gu(e) & — 1,2, => eam assuma is more than 9 dD)
below Gy(0) fr the PM eg

‘Tho simplest model for purtat modcLockng is to let the obese, of
‘the oth spectral lino ofthe Ice be uniforay distributed on te interval
Cody = ex, en) Bobb w Moule Caso eleutin aud au wale
Saluteion were wade, The wilytan clas iy ever Bee
‘Theresia of both oeulations are precentog ia Fig 3

Consiter equation (8). Th order uo detarnine the expestaion value
(ensamblearesegs) (UG) wemnust compte che valu a or (0s ~ dl
‘Tree ene aie (for > O}

Che Tem =

fos =H
Gwe The = wok

(ooa = 208 Bank — Bhar dd =

(Cuno 111: All ubserpts ciated
Gone Be ob das

yee

(ous it, =
Then

9 YX wtel ox ("3% = 4 ws — we

Be —

r)eu

+ 2 EAR ow (Pe

)+ 4 corer]
ai cun be mvt Ue fo

Ba = Go

FCF WEE, ccm | Een nor]