Homework-6 Due:

Transcription

1 Applied Optics H-464/564 ECE 594 rtland State niversity A. La Rsa Hmewrk-6 Due: Quarter wave plates and half wave plates The figures belw shw a calcite crystal plate lcated at the crdinate x=0. Calcite a birefringent material whse principal indices f refractin are n e = , n = The thickness d f the plate in each f the different cases cnsidered belw crrespnds t either a quarter wave plate ( QW, (n )d n e 2 ), r a half wave plate ( HW, 2 (n n e )d ). Here is the wavelength in vacuum. The ptical axis is riented alng the axis. In this questin we analyze the different effect the calcite plate has n incident light f different plarizatins. 1A. Case: Incident light is linearly plarized. The calcite material is a half wave plate. S r ut i, r ut Calcite, HW Sketch yur als

2 i) rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x <0. rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x >d. ii) Evaluate the fields E y and E z at x=0, and use the diagram abve t sketch their Evaluate the fields E y and E z at x =d, and use the diagram abve t sketch their 1B. Case: Incident light is linearly plarized. The calcite material is a quarter wave plate. S r ut i, r ut Calcite QW Sketch yur als i) rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x <0. rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x >d. ii) Evaluate the fields E y and E z at x=0, and use the diagram abve t sketch their Evaluate the fields E y and E z at x =d, and use the diagram abve t sketch their

3 1C. Case: Incident light is linearly plarized. The calcite material is a quarter wave plate. S Calcite QW Sketch yur als i) rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x <0. rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x >d. ii) Evaluate the fields E y and E z at x=0, and use the diagram abve t sketch their Evaluate the fields E y and E z at x =d, and use the diagram abve t sketch their

4 1D. Case: Incident light is circularly plarized. The calcite material is a half wave plate. S r ut i, r ut Calcite HW Sketch yur als i) rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x <0. rvide an expressin fr the fields E y (x,t) and E z (x,t) in the regin x >d. ii) Evaluate the fields E y and E z at x=0, and use the diagram abve t sketch their Evaluate the fields E y and E z at x =d, and use the diagram abve t sketch their

5 Image 2. larizatin by birefringent materials A ptical device is made ut f tw sectin f calcite (n = 1.658, n e = 1.486) as shwn in the figure. In Regin-1 the ptical axis () is riented alng the -axis. In regin-2 the O is riented alng the -axis. 2A Cnsider an incident wave linearly plarized alng the -axis and prpagating in the -directin. u u B 1 C Incident wave A 20 Figure fr questin 2A 2 D Nrmal t the interface AC i) Draw a few wavelets emanating frm the AB interface, cnstruct the crrespnding wavefrnt, and indicate the speed f such a wavefrnt. What is the net index f refractin that this wavefrnt sees as it prpagate thrugh regin-1? Nte: Fr clarity, prvide yur answers t i), ii) and iii) in different and separated figures. Nte: In yur drawings, indicate explicitly (with a label) whether yur wavelets are spherical r elliptical. ii) As the wavefrnt frm regin-1 arrives t the interface AC, draw a few wavelets emanating frm the AC interface, cnstruct the crrespnding wavefrnt, and calculate the speed f such a wavefrnt. What is the net index f refractin that this wavefrnt sees as it prpagates thrugh regin-2? iii) Based n i) and ii) abve, trace the path (in the plane) f an incident ray as it travels thugh the ptical device, indicating and calculating the crrespnding angles f refractin at the AB, AC and DC interfaces.

6 Image Nte: Fr clarity, prvide yur answers t i), ii) and iii) in different and separated figures. Nte: In yur drawings, indicate explicitly (with a label) whether yur wavelets are spherical r elliptical. 2B Cnsider an incident wave linearly plarized alng the -axis and prpagating in the -directin. B 1 C Incident wave u A 20 Figure fr questin 2B 2 D Nrmal t the interface AC i) Draw a few wavelets emanating frm the AB interface, cnstruct the crrespnding wavefrnt, and indicate the speed (if any) f such a wavefrnt. What is the net index f refractin if any) that this wave sees as it prpagates thrugh regin-1? Nte: Fr clarity, prvide yur answers t i), ii) and iii) in different and separated figures. Nte: In yur drawings, indicate explicitly (with a label) whether yur wavelets are spherical r elliptical. ii) As the wavefrnt frm regin-1 arrives t the interface AC, draw a few wavelets emanating frm the AC interface, cnstruct the crrespnding wavefrnt, and indicate (calculate) the speed (if any) f such a wavefrnt. What is the net index f refractin (if any) that this wave sees as it prpagate thrugh regin-2? iii) Based n i) and ii), trace the path (in the plane) f an incident ray, indicating and calculating the crrespnding angles f refractin at the AB, AC and DC interfaces. Nte: Fr clarity, yu may want t prvide yur answers t i), ii) and iii) in different and separated figures.