Ssn 320, B. B. Godfrey, Diffraction-free Microwave Propagation, Nov 89, Air Force Weapons Laboratory

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Sensor and Simulation Notes Note 320 7 November Diffraction-Free 1989 Microwave Propagation Brenclan B. Godfrey Weapons Kirtland Laboratory (AFSC) AFB, New Mexico 87117 Abstract The properties modes limited realizable are of three reviewed. practical antennas. value mathematically It or is shown exhibits diffraction-free that the each usual of microwave these diffraction modes r:ite prop:lg:l[it)ll either (or is t)t physic:tlly . I. Introduction Conventional beam in expands a Rayleigh optics predicts theory cross-sectional area Here, z is the propagation range. that a well (Lr/z) 2 as col!; mateci after microw:l\e propagating beyond distance, (1) Lr = A/~ is the Rayleigh wavelength. As launched high from a times at the antenna years i. to not finite aperture The on upper bound suggestion limit. by the energy that proves but T. allow a T. Although are the the is the barn (~ requires this radiation = 0.1 Iluxes Air model. m) Achievi]l: range. a fc\\ breukd{ni 11 microwave Wu’s times. known wave microwave energy transport In fact, neither his calculations nor his experiment ---? obtain an at better support w:iic ivi[ll on upper This antenna. indefinitely concept not carrying with Iinli[td oic r propagation do Section fields Il:ive prop:lg:ltion missile” duration, literature renliztible to from missiles three dit’frac[ion-free diffraction-free “electromagnetic rise or the>c the scientific principal cmnot tr-ansverse th:lt physically distances preclude in t!le p:l>[ revie~vs find research not the without correct beam electromagnetic fast in Huygen’s large during p:iper we are at subnanosecond well This published authors not studies propag:~tion mathematically density does exceedingly that to appearing employs Section distances. requiring km of wave schemes antennas. they tens Unfortunately, and risetime sense, Ray!eigh propagation. various III. ~ a 3 km experimenttil free-space the microwave Section profiles by diffraction limited and microwave according and results. following bound without show Basically, derived many theoretical substantiated value. fields at has antenna propagation are area, a 3 GHz antenna diffraction-free e., antenna the limiting factor in some applications. exciting practical the several diffraction-free usual densities purport potentially in power becomes spreading, either radius at the example, 10 m greater However, six is a numerical microwave hundred A range, IV is difl’r;lct little treats J. this the in energy Bessel-fllnctit)n than an:~lyztd (Ilc and Durnin’s radi:ll diffraction ,. 8 >, f,, ,; 1 I~~ J . m The conclusion. W. Ziolkowski central in for in that does great launching these waves literature V. not over wave to of While diffract, J. a most lead us; Brittingham focused-wave its energy concluding references in is finite transport text no are R. has :1 contained antennas better bibliography the and mode ent=rgy Moreover, to The N. of distances. patterns. known modes” Section extend conventional relevant “focused-wave treated packet that proposed for are wave wings intriguing than lists by first al] tiuthor and date of publication. This The paper scalar solutions free-space throughout can be the the vector antenna size. scalar fields, field if Scalar with thought fields electromagnetic Additionally, of deals of can pattern characteristic waves also as be Hertz a are of [A. good wavelengths than vector potentials, derived itself is rather scalar from which Sezginer, 1985]. approximation are short compared in their own in terms interest fields. to that to right, the e. :., as acoustic waves in water. II. Estimates Fields principle generated [Ziolkowski, by an 1989a], of Microwave antenna an can Diffraction be expressed approximation to the (2) is evaluated and located scalar of Huyge II’s wave equu(io[l at positions Green’s theorem. R2 = (X - X’)2 + (y - y’)2 + The wave function (x’,y’,z’) on the antenna Then, f in the (Z - Z’)2 right side of surface and at retarded Let the antema near the z-axis be and oriented far from time t - R/c. along the Eq. the antenna, z-axis the field ctin be near z’ = approximated as (3) (). From this follows an upper bound on the magnitude -. If(x,y,z,t) I ~ is evident It z ‘2) & or faster at an finite (4) that must The fdl off is impossible does to rule field as distances infinity bound, distances. f large to upper (4) ~.. sufficiently Eq. over I % Eq. propagation being -$ from Diffraction-free (4), g I of& pattern z- * (and from [Wu, out the a as antenna. 1985 b]. I ioweve r, diffraction-free from power propagation focusing antenna cun increase with z over a limited range, for instance. The field at Rayleigh the range antenna can also to be a be obtained plane from f wave, Eq. = (3). Specify foexp[i(kz - ~t)] the with o/c = k. Then, in the far field region f(x,y,z,t) = f. uA/27rcz With the (5) substitution = u becomes A/~, as desired. Alternative, 211c/A, the more rigorous derivations III. The Electromagnetic About frequency ‘? z -- 6 fi~r Zb-t Wu from the the his T. T. antenna wave easily variation implies microwave pulse times, and by with a t~-% the simple arguments a finite rate at exceeding the frequency one-half w:lve of A -4- leading high at to destroys Rayleigh in < t This ~. w-%-’ integrand O the Eq. (4) the slow range, :IS < 1. can be result is frequency head (3) Eq. :Ls v:lries Diffr:iction of ~vi[ll energy :tml)litl]de missile.” choice the in 19S9]; variation temporal wa~’e p:ickets decay [Shen, (4). Thus, at The appropriate Eq. wA/2Tc exist. transient o “electromagnetic 1987]. distribution that large z-l [Lee, the distances as the the showed 1985a]. length length Missile Concept for [Wu, packet slow Wu W-%-’ pulse arbitrarily reconciled early ago dependence 9 and dubbed made five years scule is f:lil. of sin:ular [it Truncating spati:~] defined the fall-off in terms M ● of the cutoff frequency [Wu, 1989 b], — The essence by a simple of example, the electromagnetic missile considered in the domain. a current pulse I(t) produces f(o,(),z,t) = I(t where now step ● R2 function = AZ =R -z. steadily, Az does not diffract, the packet for more tail the of a2/2z. Thus, general [Lee, whereupon wave Shen, a fast radius parabolic about 4 ft. the width at 49 ft. was antenna driven by z out radius is shows very a way propagation to a front that ~ less than be the pulse energy axis, occur the width similar the a decreasing rota] A losses of of the from Qualitatively, AZ becomes to distance. distance wave width For 1%%]. square the the such a [Shen, picture has only pulse in been in the rise time, eats into the head as well. is analysis rising consistent with electromagnetic and energy found to be an experiment pulse measured transmitted at distances decreased about wtis very 50 psec, [Shen, launched of up nearly also to as from 1988] in a f[. 2 Beyond 49 ft. -1 The pulse z . in approximate :lgreement predictions. though the energy instead of the z ‘2 electromagnetic missiles of long over do not would decay of an decay antenna seem be only length results for a 10 m radius at km. Moreover, producing electromagnetic in ordinary practical For distances. 100 m radius 0.1 %), f in 1989]. Even energy = although with until antenna with theoretical antenna large and valid packet simple very does the 6 for inversely 1987; which Z-l tail pulses, diffraction This to. R the illustrated (6) ~ being (analagous decreases derived a2, Expanding = A disk well I(t - R/c) - + pulse is the on-axis field, Z/C) Z2 time concept instance, 16 psec antenna such at long -5- at is of diffracting transmitting a wave packet 1000 km. requires phasing order pulses, large launched The the amounts from same 10 km or for a 1 m radius a pulse an accuracy of 16 psec or better. for missile u pulse antenn:l antenna (o n. * IV. The Bessel-Function Profile Beam Concept One exact solution to the scalar wave equation is f = fO JO(~r) exp[i(kz - ~t)] k2 with u 22= /c zero. The 2.4/K surrounded T/&. Although (~r)-%, each central peak. radial + ~2. pattern Jo of by is Eq. the (7) ring Bessel consists concentric the ring (7) of rings about the same of central peak by amount of corresponding to order of rtidius approximately with decrease solutions Nonaxisymmetric a spaced amplitudes contains function radius energy Eq. as as (7) the :lIso exist but are of less interest. J. 1987a] to Durnin can (7) naaO/1.2~ Durnin also to this This Durnin’s waves antenna, Eq. Rayleigh range to profile in terms is, (l). Doing by obtain of and These = J profile provided waves 2mc/ti of before packets propagate is a distance is the :10 .. :lnd (o 1; wavelength. half-radius profile >> :1~ the beginning simil:lr tca/x Here, waves Bessel-function a so factor course, the Eq. is seen however, instead, should, Of beam wave [Durnin, found 011 diffr:lct. beams have remtirkably properties. comparison frequency. bounded antennas face. na02/J that comput:ltionaliy significantly. Gaussian only that finite antenna peak, concluded good diffraction used central generated he from diffracting propagate basis the demonstrated 1987b] [Durnin, across the of have generated before radius them be rings many i. e., coworkers experimentally and Eq. and (l), to be diffraction-free efficient in terms of antenna be shows of the a to that waves these for require ratio little range the compared 2/~a waves The misleading. a specified less being more per area. -6- Rayleigh less antenn:l 2/nKa. than invested than size the The the length range prop:uyte energy efficient energy diffraction of of the th:ln the :lnd pl:lne wat’e wa\cs Bessel-function pl:lne but is wwe much beum less It has been by a finite-sized pointed antenna, out the Bessel-function profile can be viewed as a line focus [DeBeer, beam, as produced 1987]. V. The Focused-Wave Mode Concept Research Brittingham’s on diffraction-free discovery of the focused-wave f = fO exp[-ks]/[zO s = r2/[z0 It propagates at from peak zo/k%, complex is its However, can yield Q in central and a Nonaxisymmetric Eq. the positive at length difficulty: waves (8) z = in The g direction ct. Z real corresponding has a serious as with ordinary a finite energy The is width in is Eq. taken (8) PJIIs off in of the centr:il That f I approximately part to and 20. as also the are physical known al] is wave. [Bela nger, shortcoming, plane waves, wave infinite a superposition packet [Ziolkowski, energy of 1985]. [WU, 1984]. focused-wave One modes such solution 1989a] constant focused-wave ~ mode + i(z - ct)][ks + b] sets is the largely Another energy difficulty components [Heyman, negative component lurge. (The validity with cut in Eq. of (9) this off. radius at also sets It R. in modes both W. can be claim which the the tail maximum of the propag:l[ion z = b/2k. focused-wave flowing 1987a]. (9) spherical distance for which there is no dispersion, directions 1983] (8) peak the f = f. exp[-ks]/[zo with by 1985]. is [Ziolkowski, The mode, [Brittingham, triggered + i(z - et)] speed not 1984; Sezginer, was + i(z - et)] - i(z + et) directions is propagation the is -7- to the they and argues, exponentially unclear that positive Ziolkowski made is are negative however, small author.) acaus:ll, that by choosing [n any axi:ll the k/1~ cast, 3 the causality launched is issue subsidiary from a realizable Ziolkowski numerically used. an antenna radius the central pulse Rayleigh range calculations of was a zfj = a = the focused-wave m, found the mode k Eq. also = can (2) to Z. that is 0.1 103 the m, psec. essentially all less With thun radius only the b distance antenna distance and of the in his linearly energy in the examples was in the pulse wings. focused-wave performed as well used had an effective the Rayleigh cm before range showing did Ziolkowski less mode [Ziolkowski, area was of evidence well, but propagation 1989c]. In 36 and cm2, The 180 cm. is preparing experiments 1.5 this case the Z. was about focused-wave cm with mode radius a was shorter in water rect:tngu]ar 0.2 wave not I{enct, roughly I ()() from tl~c launched necessarily Rayleigh range were untenn:t cm. propagated A Gaussian of diffraction. its experiments optimol. in order to put his models to a more incisive test. VI. Acknowledgments The and H. author Zucker and J. O’Laughlin is indebted for 9 be from m-l, propagation be Increasing generation 1.6710-4 to diffraction-free Note mode diffraction-free five. the m, corresponding from of focused-wave 1.6710-5 scale 0.5 factor 1989a]. Acoustic antenna investigated time increased [Ziolkowski, numerical The by whether antenna. Parameters disk antennas. = 101O were to to C. Baum, informative provided background discussions. material. -8- A. Biggs, W. H. Baker Brandt, R. Ziolkowski, suggested this study, 7) /1j .’Jh i’; ,?, u 9 VII. Bibliography P. A. Belanger, “Packetlike Opt. SOC.Am. & P. 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