LENS ANTENNAS. Oscar Quevedo-Teruel KTH Royal Institute of Technology

Transcription

1 LENS ANTENNAS Oscar Quevedo-Teruel KTH Royal Istitute of Techology

2 Outlie: Les ateas Part : Itroductio. Part : Homogeeous leses: Spherical. Part 3: Homogeeous leses: No-spherical. Part 4: Limitatios: Aberratios ad reflectios. Part 5: Graded idex leses. Part 6: New techiques: Trasformatio optics ad metasurfaces. KTH School of Electrical Egieerig

3 LENS ANTENNAS PART - INTRODUCTION KTH Royal Istitute of Techology

4 Les ateas A les atea is a atea which makes use of leses. Les ateas are cosidered a particular case of aperture ateas. Leses are well-kow for optical applicatios. Examples: Glasses: Telescopes: (Wikia.com) (Wikipedia.com) KTH School of Electrical Egieerig 4

5 Les ateas Leses have also bee used o microwave applicatios: They were popular decades ago, but they became i disuse. Why? They were bulky. They were expesive to be maufactured: Specially i 3D cofiguratios. - They became agai a research topic: New applicatios at higher frequecy bads ad THz: New geeratio of radio-telescopes. Commuicatios systems: 5G. Higher resolutio scaers. KTH School of Electrical Egieerig A. Neto et al. IEEE Trasactios o Ateas ad Propagatio, July 00. 5

6 Applicatio of microwave leses Leses are used to produce: Imagig systems: To create a image of a give object. Image Ateas: Receptio: Focus the fields comig from a give directio ito a sigle poit (receptor). KTH School of Electrical Egieerig 6 focus

7 Applicatio of microwave leses Leses are used to produce: Imagig systems: To create a image of a give object. Image Ateas: Receptio: Focus the fields comig from a give directio ito a sigle poit (receptor). Trasmissio: Radiate the eergy emitted from a sigle poit (emitter) ito a give directio. Emitter KTH School of Electrical Egieerig 7

8 Leses: Desig tools Leses as reflectors are large devices i terms of wavelegths. They are commoly desiged by ray or geometric optics, at least, i the first steps of the desig. After that, more accurate aalysis as physical optics ca be applied, although at the last step, physical theory must be used for a exact solutio. Durig this lecture, we will show the performace of leses from a atea desiger perspective, so full EM simulatios are employed to demostrate the operatio, performace ad limitatios of leses. KTH School of Electrical Egieerig 8

9 Reflectio ad refractio theory Icidet wave ito a differet propagatio material: Reflected ad trasmitted wave. S i θ i z θ t θ r S t S r si i si r v v si i si t v v si t v Whe the secod medium is deser that the first oe ( > ), there is always refractio. x Whe the secod medium is less dese, there is total reflectio whe: si i KTH School of Electrical Egieerig 9

10 Reflectio ad refractio theory Icidet way ito a differet propagatio material: Reflected ad trasmitted way. si i v si r v si t v = 3 S i = S t S r si i si t v v Whe the secod medium is deser that the first oe ( > ), there is always refractio. Whe the secod medium is less dese, there is total reflectio whe: si i KTH School of Electrical Egieerig 0

11 Fresel Formulae Takig ito accout the amplitude of the refracted ad reflected fields: Icidet Trasmitted Reflected E ( i) x A cos e i ir i E ( t) x T cos e t ir t E ( r) x cos e r ir r E E ( i) y ( i) z A e ir A si e i i ir i E E ( t) y ( t) z T T e ir t si e t ir t E E ( r) y ( r) z e ir si e r r ir r T T cosi A cos cos i cosi A cos cos i t t cosi cos cosi cos i i cost A cos cost A cos t t KTH School of Electrical Egieerig

12 LENS ANTENNAS PART - HOMOGENEOUS LENSES SPHERICAL LENSES KTH Royal Istitute of Techology

13 Homogeeous leses Oly oe dielectric material. They ca be covex or cocave. The most employed leses i ateas are: Elliptical (or Hyperhemispherical) Hyperbolic. f R R R Covex Bi-covex Plaar covex Cocave Bi-cocave Plaar cocave R f Meiscus leses KTH School of Electrical Egieerig 3

14 Bi-covex les It is composed of two covex leses: It has a focal poit i oe of the sides which produces a plae wave i the opposite side of the les. f f R R KTH School of Electrical Egieerig 4

15 Bi-covex les It is composed of two covex leses: It has a focal poit i oe of the sides which produces a plae wave i the opposite side of the les. source source f source f R R KTH School of Electrical Egieerig 5

16 Bi-covex les The les has, i theory, the same respose whe the frequecy is icreased. freq= freq=.5 f f R R freq= KTH School of Electrical Egieerig 6

17 Plaar covex les This is a particular case of the bi-covex les i which R is equal to. f source f R Radiatio patter KTH School of Electrical Egieerig 7

18 Bi-cocave les Lets assume a case i which R is equal to R. This is a divergig les with a virtual focal poit. f f R R Virtual focal poit KTH School of Electrical Egieerig 8

19 Plaar cocave les This is a particular case of the bi-cocave les i which R is equal to. f f R Virtual focal poit KTH School of Electrical Egieerig 9

20 Covergig ad divergig leses Which leses are covergig or divergig? Covex Bi-covex Cocave Bi-cocave Covergig leses Divergig leses Meiscus leses Covergig leses Composed of covex ad cocave shapes Divergig leses Plaar covex Plaar cocave KTH School of Electrical Egieerig 0

21 Combiatio of homogeeous spherical leses (I) Two equal covex leses: From plae wave to plae wave. KTH School of Electrical Egieerig

22 Combiatio of homogeeous spherical leses (II) Whe the size is differet, we ca cofie or expad plae waves: Expadig KTH School of Electrical Egieerig

23 Combiatio of homogeeous spherical leses (III) Whe the size is differet, we ca cofie or expad plae waves: Cofiig KTH School of Electrical Egieerig 3

24 Combiatio of homogeeous spherical leses (IV) Leses ca be combied to get certai performaces. f cocave f covex Photo take at the Palais de Découvert, Paris, 05. KTH School of Electrical Egieerig 4

25 LENS ANTENNAS PART 3 - HOMOGENEOUS LENSES NON-SPHERICAL LENSES KTH Royal Istitute of Techology

26 Elliptical leses A elliptical les produce a coheret radiatio i the opposite side of the focus. The eccetricity, e, of the ellipse is related to the les dielectric costat: e r f e R e R R R focus R focus KTH School of Electrical Egieerig 6

27 Hyper-hemispherical les The hyper-hemispherical les is a hemispherical dielectric shape which has attached a cylidrical extesio. Legth of the extesio depeds o the radius of the sphere ad the refractive idex employed. The maufacturig is easier tha a elliptical les. Extesio legth focus ε r =0 L R r Multiple reflectios iside the les KTH School of Electrical Egieerig 7

28 Hyperbolic les The hyperbolic les is a particular case of homogeeous covex les. It is the optimal case to reduce the spherical aberratio. ρ(θ) θ f ( ) ( ) f cos KTH School of Electrical Egieerig 8

29 Fresel leses It is a les with o spherical aberratios. Employed i lighthouses. Advatage: It is very thi. Disadvatages: it is arrow bad. Photo take at the Sciece Museum, Lodo, 03. Photo take at the Palais de Découvert, Paris, 05. KTH School of Electrical Egieerig 9

30 Fresel leses It is a les with o spherical aberratios. Employed i lighthouses. Advatage: It is very thi. Disadvatages: it is arrow bad. Photo take at the Sciece Museum, Lodo, 03. Photo take at the Museé des Art et Métiers, Paris, 05. KTH School of Electrical Egieerig 30

31 Implemetatio: Phase ceter cosideratios Your total atea is combiatio of a les ad feedig. Step : Estimate the phase cetre of your feedig. - This phase cetre ca chage with the frequecy. atea Step : Estimate the phase cetre of les. -This phase cetre ca chage with the frequecy. Step 3: Joi both i the phase cetre. atea f f R KTH School of Electrical Egieerig 3

32 LENS ANTENNAS PART 4 - LIMITATIONS ABERRATIONS AND REFLECTIONS KTH Royal Istitute of Techology

33 Aberratios Our leses ca have some distortios due to the imperfectios i the desig. Some moochromatic aberratios: Spherical: Coma: Astigmatism: All these types of aberratios produce, from the atea poit of view: Icrease of Side Lobe Levels (SLL). Decrease of directivity. KTH School of Electrical Egieerig 33

34 Aberratios: Astigmatism (I) The focal poit depeds o the plae of icidece. Icrease SLL KTH School of Electrical Egieerig 34

35 Aberratios: Astigmatism (II) The focal poit depeds o the plae of icidece. Higher SLL Distorted radiatio patter. KTH School of Electrical Egieerig 35

36 Aberratios: Chromatic aberratios Our leses ca have some distortios due to the imperfectios i the desig. Chromatic aberratios: Chromatic aberratios produce a differet respose depedig o the frequecy: From the atea poit of view, the respose is dispersive. This effect must be ormally avoided. KTH School of Electrical Egieerig 36

37 Fresel Formulae: Normal icidece KTH School of Electrical Egieerig Whe ormal icidece: 37 A T A T t i i t i i cos cos cos cos cos cos A A t i t i t i t i cos cos cos cos cos cos cos cos A T A T A A 0º t i Trasitios betwee differet media produce reflectios!!! Higher whe is much higher

38 Reflectios Oe of the most importat limitatios whe usig leses is the reflectios betwee material trasitios: = =3 λ 0 λ = λ 0 / Stadig wave KTH School of Electrical Egieerig 38

39 Reflectios The reflectio is higher whe the differece betwee materials is larger: = =3 A 0-5 = 3 = = = (db) Frequecy (GHz) KTH School of Electrical Egieerig 39

40 Limitatios: Reflectios Bi-covex les: Plaar covex les: source source KTH School of Electrical Egieerig 40

41 Reflectios ad matchig layers (I) Matchig layers are employed to reduce the reflectios i the borders of homogeeous leses. The easiest way is to use a sigle layer of quarter-wave. Narrow bad solutio. Quarter-wave impedace trasformer 3 0 λ /4 3 3 = 3 =3 = 3 3 =3 KTH School of Electrical Egieerig 4

42 Reflectios ad matchig layers (I) Matchig layers are employed to reduce the reflectios i the borders of homogeeous leses. The easiest way is to use a sigle layer of quarter-wave. Narrow bad solutio. 0-0 Quarter-wave impedace trasformer 3 λ /4 3 = 3 =3 (db) No matchig layers Quarter Impedace KTH School of Electrical Egieerig Frequecy (GHz) 4

43 Reflectios ad matchig layers (II) Matchig layers are employed to reduce the reflectios i the borders of homogeeous leses. A secod optio is to use a umber of layers: Ultra wide bad solutio. = 0GHz 3 =3 (db) LENS Three matchig layers 3 h =mm h =.mm h 3 =.mm 3 No matchig layers Matchig layers AIR ε r =6 ε r =4 ε r3 = Frequecy (GHz) KTH School of Electrical Egieerig 43

44 Reflectios: Effects ad limitatios The metioed techiques are oly valid for ormal icidece. The properties of the matchig layers are differet whe the icidet is ot ormal to the surface. If we do ot elimiate the reflectios i our homogeeous leses, we will obtai egative effects: 3 Icrease of the levels of cross-polarizatio. Icrease of the side lobe levels. Decrease o the maximum directivity. Decrease of the efficiecy. If we do ot cotrol our reflectios we ca deal with a very iefficiet atea KTH School of Electrical Egieerig 44

45 LENS ANTENNAS PART 5 GRADED INDEX LENSES KTH Royal Istitute of Techology

46 Path of the light: Graded idex leses The Fermat s priciple says that betwee two poits (x ad x ), the light takes the faster path betwee the two poits. The light path is: l x ds x (mi) l S( x, x) y A x A A x 0 -x A θ y A Beig the light metric: dl = ds y B x 0 x 0 θ The optical path: ds dx dy dz y B B x B x B -x 0 KTH School of Electrical Egieerig 46

47 Path of the light: Graded idex leses The Fermat s priciple says that betwee two poits (x ad x ), the light takes the faster path betwee the two poits. l AB x0 xa y A xb x0 y B x A A x 0 -x A l x AB 0 x x 0 0 x x A A y A xb x0 x x y B 0 B y A x 0 θ y A x l AB 0 si si y B x 0 θ x l AB 0 0 si si l AB x0 0 x B y B x B -x 0 B KTH School of Electrical Egieerig 47

48 Maxwell Fish Eye Les It is a les i which a source i ay excited poit of the circle surface will coverge exactly at the opposite size of the circle. It is a rotatioally symmetric les. Equivalet to a homogeeous sphere. D B C A A C B D R. C. Mitchell Thomas, O. Quevedo-Teruel, T.M. McMaus, S.A.R. Horsley, Y. Hao, Optics Letters, ( ) a ρ Homogeeous Flat KTH School of Electrical Egieerig 48

49 Maxwell Fish Eye Les: Demostratio Lets assume three poits, A, B ad P which defie a circumferece. P O A P Y O B Q OY PR=OP PQ Graphically: PQ = OP+OQ OY PR=OP +OP OQ Chord theorem: OP OQ = OA OB Maxwell, 854. R P Q Y Thales theorem: PQ/PR=OY/OP OY PR=OP PQ R OY PR=OP +AO OB Chord theorem: OA OB=a OY PR=OP +a KTH School of Electrical Egieerig 49

50 We kow that: Maxwell Fish Eye Les: Demostratio KTH School of Electrical Egieerig 50 A B P O Y R Q OY PR=OP +a We defie: PO = r OY=p PR = a a r pa a a r p (refractive idex) must be iverse to the distace p: a r ac p C We defie r, we have a r ac a r a r Now, we assume 0 whe r=0 0 a a r 0 r a a

51 Half-Maxwell Fish Eye Les A half Maxwell fish eye les ca be used to produce directive radiatio. However this techique has limitatios: The respose is ot the same i all the directios. There will be reflectios at the trasitios betwee the les ad free space. Maxwell Fish Eye les Half MFEL KTH School of Electrical Egieerig 5

52 Lueburg Les It was derived by Rudolf Lueburg i 944. It solves the previous problems: It has a completely rotatioally symmetric respose. It does ot have reflectios at the borders. C B R. C. Mitchell-Thomas, O. ρ Quevedo-Teruel, T.M. A McMaus, S.A.R. Horsley, Y. Hao, Optics Letters, 04. Flat ( ) 0 a There is also a equivalet surface which mimics the les behavior. Homogeeous M. Sarbort ad T. Tyc, Joural of Optics, /a KTH School of Electrical Egieerig 5 z/a z 4

53 Lueburg Les: Radiatio Patters Whe a Lueburg les is fed by a sigle radiator, we obtai a very directive beam i the opposite directio. The respose of a Lueburg les is UWB, limited oly by: Size at lower frequecy. Losses at higher frequecy. f = f =.5 = = = = f = KTH School of Electrical Egieerig 53

54 Lueburg Les: Radiatio Patters Whe a Lueburg les is fed by a sigle radiator, we obtai a very directive beam i the opposite directio. The respose of a Lueburg les is UWB, limited oly by: Size at lower frequecy. Losses at higher frequecy. = = = Directivity (dbi) = Agle (º) KTH School of Electrical Egieerig 54

55 Lueburg Les: Implemetatio Origially, it was coceived for a 3D implemetatio. It is difficult to place i some practical applicatios, such as vehicles. atea Lueburg les Photo take at KTH (Royal Istitute of Techology) facilities, 05. KTH School of Electrical Egieerig 55

56 Lueburg Les: Solutios O. Quevedo-Teruel, W. Tag ad Y. Hao, Optics Letters, 0. Lueburg les: r ( r) a Gutma les: f ( r) a f r Focal circle Focal circle f Feedig poit Feedig poit KTH School of Electrical Egieerig 56

57 Gutma les: Size reductio The total size of the les ca be reduced. The directivity is reduced. SLL are icreased. Part of the les is ot eeded. KTH School of Electrical Egieerig 57

58 Other graded idex leses: KTH School of Electrical Egieerig 58 ) ( r r M M r r r / / ) ( M. Eato les: Ivisible les Fissio les: 0 4 r r 90º rotatig les: 3 ) ( Q Q r /3 7 r r Q M Moopole les:

59 Refractive idex cosideratios Some of these leses required ifiite refractive idexes i their origi: They have sigularities. They ca be solved with trasmutatio or playig with the geometry o a surface. S. A. R. Horsley, I. R. Hooper, R. C. Mitchell Thomas ad O. Quevedo-Teruel, Scietific Reports, Eato Moopole /a /a /a /a Ivisible KTH School of Electrical Egieerig 59

60 Black holes They are leses which are able to attract all the fields to the ceter of the les: omidirectioal absorbers. The geeral formula for a black hole is: No Black Hole N< N=- N= r a r N r a r a A. V. Kildishev, L. J. Prokopeva ad E. E. Narimaov, Optics Express, 00. N= N=3 Black Hole N KTH School of Electrical Egieerig 60

61 LENS ANTENNAS PART 6 NEW TECHNIQUES: TRANSFORMATION OPTICS AND METASURFACES KTH Royal Istitute of Techology

62 Optical trasformatios Trasformatio Optics ca be used to chage the shape of leses. The oly feasible solutio is coformal mappig: - It is a approximate solutio. - It will be always worse tha the origial solutio. Example: - Lueburg les with plaar feedig. ' 0 x y x y 0 ' 0 0 ' 0 N. Kudtz ad D.R. Smith, Nature Materials, 00. KTH School of Electrical Egieerig 6

63 Optical trasformatios Aother possibility is to use Optical trasformatios to create completely ew type of leses. Trasformatio of a cylidrical wave i four directive beams. Refractive idex Cylidrical wave Squared les R. C. Mitchell-Thomas, M. Ebrahimpouri ad O. Quevedo-Teruel, Eucap 05. KTH School of Electrical Egieerig 63

64 3D implemetatio: Discretizatio A discretizatio is required for a pratical implemetatio. Ad the implemetatio ca be doe: With dielectric materials: Layers distributios y O x O. Quevedo-Teruel, W. Tag, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhag, S. Haq, Y. Hao, Scietific Reports, 03. With metamaterials (or trucated periodic structures): Y.G. Ma, S. Sahebdiva, C.K. Og, T. Tyc, ad U. Leohardt, New. J. Phys, 0. KTH School of Electrical Egieerig 64

65 D implemetatio: Metasurfaces Metasurfaces are thi metamaterial layers which ca be employed:. To produce uusual reflectio/refractio properties of icidet plae waves Similar approach of Fresel leses or trasmit-arrays to produce directive radiatio patters from a feedig source.. To guide surface waves i D cofiguratios. Feedig poit KTH School of Electrical Egieerig 65

66 Types of Metasurfaces Differet types of implemetatios: Metallic cofiguratios with oly. Dielectric implemetatios: Lower cost. The are ot arrow bad. k z eq k h= 0.5mm h= 0.8mm h=.5mm 3 GHz 4 GHz 6 GHz 8 GHz 0 GHz GHz 4 GHz 6 GHz 8 GHz 3 GHz 6 GHz GHz 8 GHz Frequecy (GHz) KTH School of Electrical Egieerig O. Quevedo-Teruel, M. Ebrahimpouri, M. Ng Mou Keh, Ultra Wide Bad Metasurface Leses Based o Off-Shifted Opposite Layers, i press IEEE Ateas ad Wireless Propagatio Letters,

67 Types of Metasurfaces Differet types of implemetatios: Metallic cofiguratios with oly. Dielectric implemetatios: Lower cost. The are ot arrow bad. k z eq k h= 0.5mm h= 0.8mm h=.5mm Frequecy (GHz) KTH School of Electrical Egieerig O. Quevedo-Teruel, M. Ebrahimpouri, M. Ng Mou Keh, Ultra Wide Bad Metasurface Leses Based o Off-Shifted Opposite Layers, i press IEEE Ateas ad Wireless Propagatio Letters,

68 LENS ANTENNAS PART 6 NEW TECHNIQUES: CONCLUSIONS KTH Royal Istitute of Techology

69 Summary: Les Ateas (I) Leses ca icrease the total directivity of our sigle ateas. The aperture of your atea is icreased. ρ(θ) Leses ca be classified as: Homogeeous leses (high reflectios). f Spherical. No-spherical: elliptical, hyperhemispherical, hyperbolic... Graded idex leses (reduced or o-reflectios). Implemetatios: 3D complex surfaces D metasurfaces. θ KTH School of Electrical Egieerig 69

70 Summary: Les Ateas (II) Limitatios: High frequecy applicatios oly!!! Losses ca be importat, depedig o the frequecy ad electrical size of your les. Reflectios (matchig layers). Aberratios: They ca decrease the directivity, ad icrease of our side lobe levels. Badwidth limited by: Dimesios (lower boud). Losses (higher boud). They are i geeral ultra wide bad. Fresel leses are arrow bad. KTH School of Electrical Egieerig 70

71 LENS ANTENNAS Oscar Quevedo-Teruel KTH Royal Istitute of Techology