LAB 7: Refractive index, geodesic lenses and leaky wave antennas

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Hilary Underwood
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$EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas LAB 7: Refractive idex, geodesic leses ad leaky wave$ $Purpose: The mai goal of this laboratory how to characterize the effective refractive idex of materials, ray tracig of$ $. Refractio idex measuremet: Before startig with the measuremet of the radiatio patter.$ $The, based o the agle i which you will start to have total reflectio, you will calculate the refractive idex.$

1 EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas LAB 7: Refractive idex, geodesic leses ad leaky wave ateas. Purpose: The mai goal of this laboratory how to characterize the effective refractive idex of materials, ray tracig of geodesic leses, ad how to uderstad the mai parameters of leaky wave ateas by usig a ear field scaer.. Refractio idex measuremet: Before startig with the measuremet of the radiatio patter. You will develop a fast measuremet of the refractive idex of water. You will fill half of a cylider with water. The, based o the agle i which you will start to have total reflectio, you will calculate the refractive idex. si i v si v t Total reflectio whe: si i This techique is used for guidig the light i optical fibers. Laser illumiatig a trasitio betwee air ad water. As alterative method, you will characterize the refractive idex of water ad glass, by comparig two differet plaar covex leses made of water ad glass: Without water With water With glass

$EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas To proceed with this techique, you will calculate the focal distace accordig$ Geodesic leses: I this sectio, we will study how geodesic leses i a homogeous material ca be costructed.

Geodesic leses: I this sectio, we will study how geodesic leses i a homogeous material ca be costructed.

surfaces. For example, a Maxwell fish-eye les ca be represeted as a sphere. Equivalet shape of a Maxwell fish-eye les.

2 EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas To proceed with this techique, you will calculate the focal distace accordig to the theory depedig o the refractive idex: f R 3. Geodesic leses: I this sectio, we will study how geodesic leses i a homogeous material ca be costructed. As we cocluded i the theory lectures, a huge umber of leses ca be trasformed from dielectric twodimesioal shapes to three-dimesioal equivalet surfaces. For example, a Maxwell fish-eye les ca be represeted as a sphere. Equivalet shape of a Maxwell fish-eye les. Equivalet shape of a Lueburg les. I the lab, we are goig to study a umber of leses ad we will represet their equivalet refractive idexes with wood shapes. For example, i the followig figure, the strigs represet the shortest path i physical dimesios, which is equivalet to the path of the light i a homogeous les:

$EI400 Applied Atea Theory LAB7: Refractive idex ad$ $This is because the refractive idex is costat i$ all the les, so the physical path is equivalet to

wood shapes to represet the path of the light i

agle of radiatio of a covetioal leaky wave atea ad

First of all, we are goig to measure the agle of

3 EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas Represetatio of the rays for a homogeous Lueburg les. This is because the refractive idex is costat i all the les, so the physical path is equivalet to the optical path (=): l x ds We will use differet wood shapes to represet the path of the light i differet leses: x Lueburg les Maxwell fish-eye les Eato les 90deg rotatig les 4. Leaky wave ateas: I this sectio, we will study the agle of radiatio of a covetioal leaky wave atea ad its radiatio atteuatio. 4.. Agle of radiatio. First of all, we are goig to measure the agle of radiatio of the followig microstrip leaky wave atea: Descriptio of the microstrip leaky wave Practical realizatio 3

$EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas The ateas has a substrate with two layers, a lower PP (εr =.$ It has two regios, oe i which it is maily the radiatio, ad two taperig regios to match the ports.

It has two regios, oe i which it is maily the radiatio, ad two taperig regios to match the ports.

This agle ca be derived as: cos Where β is the phase of the propagatio i the air, β is the phase of the propagatio i the

GHz f = 4.4 GHz f = 4.6 GHz f = 4.8 GHz f = 5.0 GHz f = 5.

4 EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas The ateas has a substrate with two layers, a lower PP (εr =.) of 4 mm thickess; ad upper FR4 (εr = 4.5). It has two regios, oe i which it is maily the radiatio, ad two taperig regios to match the ports. Sice the phase of the propagatio costat chages with the frequecy, the agle or radiatio will chage with frequecy. This agle ca be derived as: cos Where β is the phase of the propagatio i the air, β is the phase of the propagatio i the waveguide, ad γ is the elevatio agle. The simulated radiatio patters for this structure are, whe fed from the right side: / f = 4. GHz f = 4.4 GHz f = 4.6 GHz f = 4.8 GHz f = 5.0 GHz f = 5. GHz Radiatio patter measuremets ad estimatio of the phase costat: Coect oe of the ports of the atea to a load (50 Ω), ad excite the other port with the sigal geerator at the previous frequecies. Measure the radiatio patter with the ear field scaer (do ot forget that you must chage the frequecy maually i the computer): Near field scaer: RFxpert. 4

$EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas Corroborate the results that were obtaied with the simulator.$ I this case, we are goig to cosider the previous atea, i which we have itroduce argo bars i betwee the metallic layers. This meas that the substrate will be bars of plastic with argo iside.

I this case, we are goig to cosider the previous atea, i which we have itroduce argo bars i betwee the metallic layers. This meas that the substrate will be bars of plastic with argo iside.

The leaky wave atea has a measured trasfer S parameter as follows: 0-0 S -0-30 Therefore, the atea is radiatig faster at lower frequecies tha at higher oes.

5 EI400 Applied Atea Theory LAB7: Refractive idex ad leaky wave ateas Corroborate the results that were obtaied with the simulator. Calculate the propagatio costat with respect to the frequecy ad report it i a graph. 4.. Atteuatio costat. I Sectio, you will see the effect of atteuatio i a leaky wave atea. I this case, we are goig to cosider the previous atea, i which we have itroduce argo bars i betwee the metallic layers. This meas that the substrate will be bars of plastic with argo iside. The groud pla is metallic grid, so we will observe the electric field amplitude i the argo bars. Experimet cofiguratio. The leaky wave atea has a measured trasfer S parameter as follows: 0-0 S Therefore, the atea is radiatig faster at lower frequecies tha at higher oes. Questio: This atea will be more directive at 3.5 GHz or at 5 GHz. Explai why. This waveguide is goig to be excited with high power. We will use a amplifier; ad our experimet will be held betwee 4-5GHz. I order to avoid radiatios to us, a absorber layer will be placed i the top of the structure. This high power will be employed to excite a eo lamp iside the waveguide. The purpose of this Sectio, is to observe the atteuatio ad visualize how the light is extiguished alog the waveguide Frequecy (GHz) High radiatio costat Low radiatio costat 5

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