Optical X wave communications

Transcription

1 15 March 1999 Optcs Communcatons Optcal X wave communcatons Jan-yu Lu 1, Shpng e Department of Boengneerng, The UnÕersty of Toledo, Toledo, O 4366, USA Receved 13 August 1998; revsed 4 January 1999; accepted 5 January 1999 Abstract Ths paper presents a new communcaton system usng optcal X waves whch, n theory, can propagate to an nfnte dstance wthout spreadng. In practce, when these waves are produced wth a fnte aperture and energy, they have a large depth of feld. A system model usng optcal X waves as carrers to transfer sgnals s establshed. The relatonshp between optcal X wave and the conventonal communcaton systems s studed. Smulaton demonstratng the performance of the optcal X wave communcaton systems s presented. q 1999 Elsever Scence B.V. All rghts reserved. PACS: Sz Keywords: Optcal X wave; Wreless communcatons 1. Introducton Recently, there s a great nterest n the study of X waves for medcal magng and other physcs related areas w1 11 x. Theoretcally, X waves can propagate to an nfnte dstance wthout changng ther shapes f they are prowx 2. In practce, duced wth an nfnte aperture and energy when these waves are produced wth a fnte aperture and energy, they have a large depth of feld w3, 4 x. Because of ths property, they can have applcatons n communcaton systems. Usng optcal X waves n communcatons has several advantages. Frst, t can ncrease the capacty of the communcatons because optcal X waves are spatally orthogonal whch allows a multple-rng to emt. Second, t s secure because the waves can only be detected by an optcal X wave array that has the same array response as that of transmsson. Thrd, t has a low probablty of ntercepton due to the precse pontng and trackng provded by the narrow transmttng beams wth lttle dffrac- 1 E-mal: jlu@eng.utoledo.edu ton. Fnally, t may have less nterference to other sources of communcatons and has less mult-path effects because optcal X waves propagate n a confned space and the transmtter and the recever have to be collmated wth each other. Applcatons of optcal X wave communcatons may span areas n commercal and mltary markets as well as scentfc research. As the need for personal communcaton servces expand, optcal X wave systems wll become ncreasngly mportant to mult-node commercal communcaton networks. In all these nstances, optcal X wave technology can make use of current rado frequency Ž RF. technologes by recevng RF or optcal X wave communcatons from the ground, transferrng the nformaton wth optcal X wave through space, and retransmttng va RF or optcal X wave carrers to a destnaton ground ste. The optcal X wave system can also be operated n parallel wth other assets, snce t s spatally confned and collmated. Optmzaton of current and future space and ground assets wll provde rapd global transfer of dgtal mages, voce and other data n future secure hgh-speed communcaton networks r99r$ - see front matter q 1999 Elsever Scence B.V. All rghts reserved. PII: S

2 188 J. Lu, S. eroptcs Communcatons X wave concept An n-dmensonal scalar wave equaton for source-free, wx lossless, and sotropcrhomogeneous meda s gven by 2 n 2 2 E 1 E ž Ý E x j c E t / js1 y Fs Ž. 1 where x Ž js1,2,...,n. j, represent rectangular coord- nates n an N-dmensonal space, t s tme, n s an nteger, c s a constant and represents the speed of the wave, and FsF Ž x, x,...,x ;t. 1 2 n s an n-dmensonal complex wave feld. Lettng ns3, x1sx, x2sy, x3sz, one obtans an mth-order non-rotatng X wave Žas opposed to the rotatng X waves gven by Eq. Ž 12. n Ref. wx. 2 F Ž r,t. scos m fyf BŽ k. J Ž krsnz. Xm m =e ykw a ycosz Ž zyc 1 t.x dk, Ž. 2 where m s an nteger, ms,1,2,..., Jm s an mth-order Bessel functon of the frst knd, rsž r,f, z. s a pont n y1 space, fstan Ž yrx. s the azmuthal angle, and f s the ntal azmuthal angle Ž polarzaton. of the beams at the plane zs, Bk s the transmttng or recevng transfer functon of a mcrowave antenna, an optcal devce, or an acoustc transducer, a s the constant that determnes the fall off speed of the hgh frequency compowx 2, and nent of the X waves, z s the Axcon angle c scrcosz s the phase velocty. Eq. Ž. 1 2 s also an exact soluton to Eq. Ž. 1. From Eq. Ž. 2, t can be seen that X waves have a constant phase velocty for all frequency components or have an nfnte depth of feld. In practce, the aperture of a wave source s always fnte. In ths case, X waves have a fnte but large depth of feld,.e., they can propagate to a large dstance wthout sgnfcant dstortons. 3. System mode The block dagram of the optcal X wave communcaton system wth a rng antenna s shown n Fg. 1, where the sgnal transmtted by the th rng transmtter s gven by w1,12x X I STŽ r,t. s 2 PT dž. t f Ž. t cos v tqf Ž. t sn v t, Ž. 3 where r X s the radus of the th rng of the transmtter, s1,2,..., N, PT s the power ampltude of the th transmtted sgnal, v s the angular carrer frequency, d Ž. t s the bnary data of the th nformaton, f I Ž. t and f Ž. t are n-phase and quadrature weghts of the format of the arbtrary sgnals Ž modulaton format., respectvely. Immedately after the transmttng lens Žrngs are placed at the focal plane of the lens., the sgnal s carred by an optcal X wave that s proportonal to the spatal Fourer transform of a rng wx 1, w x F Ž r,t. AF S Ž r X,t., Ž 4. X s T where F Ž r,t. X s a zeroth-order optcal X wave produced by the th rng. ŽFor smplcty, we consder only the zeroth-order X waves. gher-order X waves requre rngs modulated by cosmž fyf., where f s the ntal azmuthal angle, see Eq. Ž. 2, and s not rotary symmetrc.. Fs s the spatal Fourer transform. If the Axcon angle of the optcal X waves Žsee Eq. Ž 2.. s zero Žthe rng dameter s zero and the rng s shrunk to a pont source., the wave-feld after the lens s a plane wave and s not a Fg. 1. Model of the optcal X wave communcaton systems.

3 J. Lu, S. eroptcs Communcatons functon of r and the optcal X wave communcaton system becomes a conventonal system. If multple optcal X waves are produced smultaneously by multple rngs, a hybrd optcal X wave, F Ž r,t. X, that s a lnear superposton of all the ndvdual optcal X waves s produced. In ths case, data are naturally scrambled at the passage of the waves. The hybrd optcal X wave s gven by N F X r,t s Ý F X r,t. 5 s1 At the recever, a devce Ža lens n optcs and acoustc cases. s used to separate the optcal X waves and decomposes them back nto rngs Ž Fg. 1.. At the focal dstance after the lens of the recever, the receved sgnal at the th rng s proportonal to the nverse spatal Fourer transform of the optcal X wave produced wth the th transmttng rng S Ž r,t. AF F Ž r,t. qnž t. y1 X R s X w st Ž. t ) S Ž r X,tyt. qn Ž. t, Ž. 6 x T where F X Ž r,t. X s approxmately a delayed verson of F Ž r,t. X, ) s the convoluton wth respect to tme, T Ž. x t s the mpulse response of the optcal X wave communcaton system, whch s related to the aperture sze and the propagaton dstance of the optcal X wave ŽWth an nfnte aperture, F wt Ž.x x t '1. For smplcty, n the followng, we assume F wt x Ž.x t '1.. N Ž t. s the Fourer transform of the nose of the th channel, n Ž. t, that s assumed to be the whte Gaussan nose, and t s the delay tme. Followng the conventonal detecton method, the output of the th rng s gven by yrng t s SRŽ r,tyt. Rrng t dt, 7 y Ž. Ž. where r s the radus of the th rng and R Ž. rng t can be expressed as Ž. Ž. I Rrng tqt s 2 PR f t cosv t Ž. Ž. Ž. qf t sn v t. 8 Note that S r,t here s not a functon of r and y Ž. R rng t ncludes the transfer functon of the recever rng Žfor smplcty, we also assume that the transfer functons of recever rngs are equal to 1.. The above convoluton s expressed by y Ž. t sr Ž. t qr Ž. t, Ž. 9 rng XTXR ntxr x where RX X t s2 PTPR d tyt yt T R y Ž. f Ž tyt yt. cos v Ž tyt yt. = I qf tytyt sn v tytyt = f I tyt cos v tyt qf tyt sn v tyt dt. 1 After flterng, synchronous detecton and samplng, the convoluton of the desred sgnals from each rng s gven by 1 T I 2 2 X X 2 T R Ž. Ž. Ž. T R R T s P P d t f t q f t dt, Ž 11. where T s the sgnal cycle. The energy content of the receved sgnals s as follows, T I 2 Ž. I and f Ž. t dtsc T Ž 12. T 2 Ž. f Ž. t dtsc T Ž 13. for the n-phase and quadrature components, respectvely, and where CI and C are n-phase and quadrature constants, respectvely. The demodulated sgnals are gven by RX X T s" PT PR CTd n, 14 T R where Cs 1 Ž C qc. 2 I and dn s the bnary data of the nformaton. As n the conventonal analyss w12 x, the convoluton of the nose at each recever rng s wrtten as I n XŽ. R T R y R t s 2 P n tyt f t cosv t qf t snvt dt. 15 After flterng, synchronous detecton and samplng, the convoluton of the nose at each rng Ž channel. s gven by w12x R Ž T. sl ql, Ž 16. ntxr I where LI and L are n-phase and quadrature components of the convoluton of the nose, respectvely. Because the nose and the array response are uncorrelated, the effects of the nose component are very small. The nput to the decson devce s Lsyrng Ž T. s"adnqliql, Ž 17. where A s a constant.

4 19 J. Lu, S. eroptcs Communcatons If dnsq1 represents the logc symbol 1 and dnsy1 represents the logc symbol, the decson devce produces the symbol 1 f L) and the symbol f L-. An error occurs f L- when dnsq1orf L) when dnsy1. The probablty that Ls s zero. 4. Smulaton results Smulaton of optcal X wave communcatons s performed for a laser Ž optcal. communcaton system and s based on the optcal X wave theory w1,2,4,8 x. Zeroth-order optcal X waves Ž axally symmetrc. are assumed n the smulaton. A coaxal mult-rng laser gun s used as a wave source. The rngs of a laser gun are modulated ndvdually to form dfferent sgnal channels. Assumng there are two rngs Ž channels. and the outputs of the rngs are shrunk wth an optcal magng system to form two smaller rngs of rad of about 1 and 2 mm, respectvely, the transmttng system n Fg. 1 can be used to produce multple optcal X waves drectly and transfer sgnals through the space over a large dstance n parallel. The results of the smulaton are shown n Fg. 2. The condtons for the smulaton are gven n the fgure Žwave- length s assumed to be 1.55 mm Žcenter frequency of about Gz. and both the dameter and the focal length of the transmsson lens are 5 mm.. Wth these parameters, the depths of feld of the optcal X waves wx 2 are about 125 and 62.5 m for the rngs of 1 and 2 mm, respectvely, correspondng to Axcon angles of about and The bandwdth of the optcal X wave produced s determned by that of the exctaton sgnal and the transfer functons of the rng radators. The smulaton was performed for both broadband Ž1.5-cycle, see mages n the left column of Fg. 2. and narrower-band sgnals Ž1-cycle tone burst, see mages n the rght column.. In mcrowave and acoustc cases, short pulses can be produced. In optcs, tone bursts that are much longer than 1 cycles are usually used. The hybrd optcal X waves produced wth both the 1 and 2 mm radus rngs mmedately after the transmttng lens are shown n the top row of Fg. 2. Waves after propagaton over 6 m are shown n the mddle row, and waves at the detectng rngs are shown n the bottom row. Notce that because the optcal X waves produced by the 2 mm radus rng have a slghtly hgher phase velocty Ž larger Axcon angle., they are advanced n tme at the recever ste wx 2. The superlumnal nature of X waves has been dscussed elsewhere w2,4,7 x. From the optcal X waves shown n Fg. 2Ž. e and 2Ž. f, t s seen that rng felds are well recovered at the focal Fg. 2. Smulaton of optcal X wave communcaton systems. Ž. a, Ž. b ybrd optcal X waves produced wth both rngs of 1 and 2 mm rad. Ž. c, Ž. d ybrd optcal X waves before the recepton lens after propagatng over 6 m. Ž. e, Ž. f ybrd optcal X waves at the focal plane of the recepton lens. In Ž.Ž.Ž. a, b, c and Ž. d, the smulaton s carred out wth the Fresnel approxmaton, whle n Ž. e and Ž. f, wth the Raylegh-Sommerfeld dffracton formula. Images n the left and rght columns correspond to broadband Ž 1.5 cycles. and narrower band Ž 1 cycles. results, respectvely.

5 J. Lu, S. eroptcs Communcatons plane of the recever lens. Rng detectors are placed at the peaks of the rng felds correspondng to the transmttng rngs n the transmtter Ž Fg. 1. to recover the bnary sgnals of multple channels smultaneously. From Fg. 2Ž. e and 2Ž. f, t s clear that more transmttng rngs and detectors can be added to ncrease the number of channels of the optcal X wave communcaton system, ncludng to add a center pont transmtter and recever for conventonal communcatons. Assumng that the optcal X wave transmtter transmts uncorrelated symbols wth a lnear modulaton, e.g., quadrature phase-shft keyng Ž PSK., the nformaton that s carred by the optcal X waves from both channels can travel a mnmum dstance of 62.5 m, wthout sgnfcant dstortons. 5. Dscusson 5.1. Potentals of the X waõe communcaton systems The hgh carrer frequency and bandwdth potental of the optcal X wave communcaton systems make them attractve for wdespread use n future communcaton systems. Usng an X wave communcaton system, X waves carryng dgtal and analog nformaton can support real-tme nterconnectons between any two ponts on the globe at data rates of several ggabts per second or hgher. Ths data transfer can be realzed usng X wave array transmtters and recevers wth lower power requrements Žbecause the X wave propagaton energy concentrates n one drecton. than used n current rado frequency Ž RF. systems operatng at lower data rates. X waves generated by a fnte aperture are of practcal mportance due to three aspects when appled to the communcaton systems as dscussed n the Introducton: hgh speed, secure, and less senstve to multple-path effects. Therefore, the performance of communcaton systems can be mproved enormously by usng X waves Other orthogonal modes In addton to usng the Axcon angles Žthe example shown n the smulaton results., other parameters of X waves could also be used n combnaton wth the Axcon angles to further ncrease the capacty of X wave transmsson systems. For example, the parameter, m, n Eq. Ž. 2 may be used to separate channels because X waves of dfferent order, m, are also orthogonal Žfor m), X waves are not rotary symmetrc wx. 2. The advantage of usng asymmetrcal X waves s that they all have the same depth of feld as the zeroth-order X wave when the Axcon angle s the same. Smlarly, the ntal phase, f, n Eq. Ž. 2 could also be used to dstngush channels n combnaton wth the parameters, m and z. Of course, methods that may ncrease data rate of conventonal communcaton systems are also applcable to each channel of the X wave communcaton systems Array beams to further ncrease the number of channels It s worth notng that array beams w11x could also be used n the communcaton system. In ths case, pont sources and detectors are used to replace rngs. Ths wll greatly ncrease the number of channels. owever, the sgnal-to-nose rato may be reduced because the transmtter and detector szes wll be small and the detectors wll be phase nsenstve. w x n ymu Wth a rotatng X wave 2,8 multpled by e and summng over the order of the wave, m, broadband lmted dffracton array beams are obtaned that are also lmted dffracton solutons to the sotropc homogeneous scalar wave equaton w11 x: F r,t s cosk x cosk y e k zž zyc 1 t., Ž 18. Array x y where k zs k y k xqk y, and where k x and k y are wave numbers n the x and y drectons, respectvely. Pont sources that are placed at or away from the wave axs can be used to produce grd array beams of dfferent combnatons of k x and k y Algnment of the X waõe systems In Fg. 2, the rng detectors used are phase senstve. Ths requres that the transmttng rngs, lenses, and the rng detectors must be coaxally algned wth a precson of a fracton of a wavelength and perpendcular to the beam axs to avod phase cancellaton. Because of the phase senstvty, background nose from random radaton sources wll be largely cancelled and the system wll have a hgh securty Žntercepton wthout dsruptng the normal communcatons of such systems s dffcult Trade offs From Fg. 2, t s seen that the rng felds reconstructed from the X waves have a certan wdth that ncreases wth the decrease of the dameter of the recepton lens. In addton, sdelobes of the rng felds wll ncrease the effectve rng wdth. A larger wdth wll reduce the number of rngs that can be placed n the system. The number of rngs wll also be reduced f the communcaton dstance s ncreased. Ths s because a larger dstance decreases the largest usable dameter of the rngs. It s well known that the radus of the Ary pattern of a crcular wave source s gven by wx 8 ws.61lfra, 19 r

6 192 J. Lu, S. eroptcs Communcatons where l s the wavelength, F s the focal length, and ar s the radus of the lens aperture of the recever. Wth the X wave communcaton system dscussed n ths paper, the relatonshp between the Axcon angle and the radus of the rng can be obtaned wx 8, zssn y1 a rf, Ž 2. rng where arng s the radus of the transmttng rngs. The maxmum propagaton dstance wthout sgnfcant sgnal dstorton s gven by Ž depth of feld. wx 2 Z sa cotz. Ž 21. max t where at s the radus of the lens of the transmtter. Wth a wavelength of 1.55 mm and ars25 mm, the radus of the Ary pattern s about mm. Ths pattern wll be spatally convolved wth any rng responses from the X waves,.e., t wll ncrease the wdths of rngs at the recever because t s multpled wth the aperture of the ncdent X waves. Usng the example of ths paper, the maxmum number of rngs that can be placed wthn the 2 mm radus s about 1. Because the ncdent X waves n front of the recever have some dstortons from those mmedately after the transmsson lens, the actual number of rngs may be smaller Ž see Fg. 2.. When the communcaton dstance s determned, the Axcon angle of an X wave can be calculated wth Eq. Ž 21.. Then, from Eq. Ž 2., the maxmum radus of the rng can be calculated. Wth the radus of the Ary pattern ŽEq. Ž 19.., the maxmum number of rngs that can be placed n an X wave communcaton system can be estmated. From the dscusson above, t s clear that gven the wavelength of the carrer and the f-number ŽFrD, where D s the dameter of the aperture. of the transmtter and recever, the communcaton dstance s nversely proportonal to the maxmum number of channels or the data rate of the X wave communcaton systems McrowaÕe communcatons The current method could also be extended to a mcrowave communcaton system. Because a mcrowave wavelength s much larger than that of an optcal wave, a large aperture s requred to acheve a large communcaton dstance ŽEqs. Ž 19. Ž If the center frequency s 2 and 7 Gz, and the aperture dameters are 1 and 2 m, the rad of the Ary patterns of these systems wll be about 3.66 and.5229 mm, respectvely. For the frst system, f f-numbers1 and there are two transmsson rngs of rad of 5 and 1 mm Žcorrespondng Axcon angles of.2868 and.5738., respectvely, the maxmum communcaton dstance wll be 5 km Žthe maxmum number of rngs s about Wth the second system, the maxmum communcaton dstance s 115 km f the Axcon angle s.58 Ž a rng radus of mm. and f-numbers1. The maxmum number of rngs s about To construct a mcrowave X wave communcaton system, rng antennas wth proper focusng mechansms must be developed. 6. Concluson In ths paper, a new communcaton system wth lmted dffracton beams optcal X waves for parallel transmsson of dgtal bnary sgnals has been developed. An example has been gven to demonstrate the method. The use of optcal X waves for communcaton systems has several advantages over conventonal systems, such as larger capacty of communcatons, smaller mult-path effects, and hgh securty features. The theoretcal analyss and smulaton results show that optcal X waves can sgnfcantly mprove the performance of communcaton systems. Acknowledgements Ths work was supported n part by the grant L 631 from the Natonal Insttutes of ealth, USA. References wx 1 J.-y. Lu, n: S. Lees, L.A. Ferrar Ž Eds.., Acoustcal Imagng, vol. 23, Plenum Press, New York, 1997, pp wx 2 J.-y. Lu, J.F. Greenleaf, IEEE Trans. Ultrasoncs, Ferroelectrcs, Frequency Control 39 Ž wx 3 J.-y. Lu, J.F. Greenleaf, IEEE Trans. Ultrasoncs, Ferroelectrcs, Frequency Control 39 Ž wx 4 P. Saar, K. Revelt, Phys. Rev. Lett. 79 Ž wx 5 P. Saar, n: O. Svelto, S. De Slvestr, G. Denardo Ž Eds.., Ultrafast Processes n Spectroscopy, Plenum, New York, 1996, p wx 6 P. Saar,. Sonajalg, Laser Phys. 7 Ž wx 7 E. Recam, Physca A 252 Ž wx 8 J.-y. Lu, IEEE Trans. Ultrasoncs, Ferroelectrcs, Frequency Control 44 Ž wx 9 J.-y. Lu, IEEE Trans. Ultrasoncs, Ferroelectrcs, Frequency Control 45 Ž w1x J.-y. Lu, IEEE Trans. Ultrasoncs, Ferroelectrcs, Frequency Control 44 Ž w11x Jan-yu Lu, Int. J. Imagng System Technol. 8 Ž w12x S. e, T. Lo, J. Ltva, IEEE Trans. Crcuts Systems-II: Analog Dgtal Sgnal Processng 44 Ž