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  • VERSION 4.4

    Wave Optics ModuleModel Library Manual

  • C o n t a c t I n f o r m a t i o n

    Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information.

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    Part number: CM023503

    W a v e O p t i c s M o d u l e M o d e l L i b r a r y M a n u a l 19982013 COMSOL

    Protected by U.S. Patents 7,519,518; 7,596,474; 7,623,991; and 8,457,932. Patents pending.

    This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/sla) and may be used or copied only under the terms of the license agreement.

    COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/tm.

    Version: November 2013 COMSOL 4.4

  • Solved with COMSOL Multiphysics 4.4

    Beam Sp l i t t e r

    Introduction

    A beam splitter is used for splitting a beam of light in two. One way of making a splitter is to deposit a thin layer of metal between two glass prisms. The beam is slightly attenuated within the layer and then split into two paths. This example models the thin mre

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    etal layer using a transition boundary condition, which reduces the memory quirements. Losses in the metal layer are also computed.

    gure 1: A beam splitter composed of two prisms with a thin layer of metal between them.

    odel Definition

    odel the beam splitter in the 2D plane, as shown in Figure 1, under the assumption at the electric field is polarized perpendicular to the plane. A Gaussian beam of avelength 700 nm propagates in the x direction through the glass prism of refractive dex n 1.5. A 13 nm thin layer of silver sandwiched between the two prisms splits e beams.

    he model geometry is a square region around the region where the Gaussian beam osses the silver layer. The focus of the beam is at the left boundary, so the expression r the beam intensity at the focal plane can be used as the excitation. The expression r the relative electric field intensity at the focal plane of a Gaussian is

    Thin metal layer

    nput

    Output

    Output

  • Solved with COMSOL Multiphysics 4.4

    2 | B E A M S P L I T

    (1)

    where w = 3500 nm is the beam waist, and the y = 0 line is the centerline of the beam. Use this expression in a Port boundary condition on the left side to model the incident beam. Model all the other domain boundaries using Scattering Boundary Conditions. These conditions are appropriate when they are placed several wavelengths away from any scattering objects and the wave is known to be traveling at normal or almost n

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    ormal incidence.

    he thin silver layer is modeled using a Transition Boundary Condition. At a free-space avelength of 700 nm, the dielectric of silver is about r 16.5 1.06i, where the aginary part accounts for the losses. Thus, you can set the conductivity of the metal zero. This boundary condition allows for a discontinuity in the fields across the terface by splitting the mesh at the boundary. It can introduce both losses and a hase shift across the interface. It does not require a mesh of the thickness of the omain, and thus saves significant memory. Mesh the two domains with triangular ements, with the maximum size set such that there are six elements per wavelength the glass.

    esults and Discussion

    igure 2 shows the electric field intensity in the modeling domain. The beam is split to two beams, one propagating in the x direction and the other one in the

    direction. The splitting can be evaluated by computing the flux crossing the coming boundary and the two outgoing boundaries. Figure 3 plots the power ossing these boundaries as well as the losses at the mirror.

  • Solved with COMSOL Multiphysics 4.4

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    Fiw 3 | B E A M S P L I T T E R

    gure 2: The electric field intensity shows that the incoming beam is split into two beams approximately equal intensity.

    gure 3: The power flux crossing the input boundary and the two output boundaries as ell as the losses at the silver surface.

  • Solved with COMSOL Multiphysics 4.4

    4 | B E A M S P L I T

    Model Library path: Wave_Optics_Module/Optical_Scattering/beam_splitter

    Modeling Instructions

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    rom the File menu, choose New.

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    In the New window, click the Model Wizard button.

    O D E L W I Z A R D

    In the Model Wizard window, click the 2D button.

    In the Select physics tree, select Optics>Wave Optics>Electromagnetic Waves, Frequency Domain (ewfd).

    Click the Add button.

    Click the Study button.

    In the tree, select Preset Studies>Frequency Domain.

    Click the Done button.

    L O B A L D E F I N I T I O N S

    rametersOn the Home toolbar, click Parameters.

    In the Parameters settings window, locate the Parameters section.

    In the table, enter the following settings:

    ere, c_const is a predefined COMSOL constant for the speed of light in vacuum.

    ame Expression Value Description

    da0 700[nm] 7.000E-7 m Wavelength

    0 c_const/lda0 4.283E14 1/s Frequency

    _max 0.2*lda0 1.400E-7 m Maximum mesh size

    ps_Ag -16.5-1.06*i -16.5 - 1.06i Relative dielectric constant, Silver

  • Solved with COMSOL Multiphysics 4.4

    G E O M E T R Y 1

    1 In the Model Builder window, under Component 1 click Geometry 1.

    2 In the Geometry settings window, locate the Units section.

    3 From the Length unit list, choose m.

    Create a triangle using Polygon for one prism.

    Polygon 11 Right-click Component 1>Geometry 1 and choose Polygon.

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    In the Polygon settings window, locate the Coordinates section.

    In the x edit field, type -10 -10 10.

    In the y edit field, type -10 10 10.

    Click the Build Selected button.

    otate the triangle to create the other prism.

    otate 1On the Geometry toolbar, click Rotate.

    Select the object pol1 only.

    In the Rotate settings window, locate the Input section.

    Select the Keep input objects check box.

    Locate the Rotation Angle section. In the Rotation edit field, type 180.

  • Solved with COMSOL Multiphysics 4.4

    6 | B E A M S P L I T

    6 Click the Build All Objects button.

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    L E C T R O M A G N E T I C WA V E S , F R E Q U E N C Y D O M A I N ( E W F D )

    ow set up the physics.

    cattering Boundary Condition 1On the Physics toolbar, click Boundaries and choose Scattering Boundary Condition.

  • Solved with COMSOL Multiphysics 4.4

    2 Select Boundaries 2, 4, and 5 only.

    Po1

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    3 7 | B E A M S P L I T T E R

    rt 1On the Physics toolbar, click Boundaries and choose Port.

    Select Boundary 1 only.

    In the Port settings window, locate the Port Properties section.

  • Solved with COMSOL Multiphysics 4.4

    8 | B E A M S P L I T

    4 From the Wave excitation at this port list, choose On.

    5 Locate the Port Mode Settings section. Specify the E0 vector as

    6 In the edit field, type ewfd.k.Tr1

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    0 x

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    exp(-(y/3500[nm])^2) zT E R

    ansition Boundary Condition 1On the Physics toolbar, click Boundaries and choose Transition Boundary Condition.

    Select Boundary 3 only.

    In the Transition Boundary Condition settings window, locate the Transition Boundary Condition section.

    From the Electric displacement field model list, choose Relative permittivity.

    From the r list, choose User defined. In the associated edit field, type eps_Ag.From the r list, choose User defined. Leave the default value of 1.From the list, choose User defined. Leave the default value of 0.In the d edit field, type 13[nm].

  • Solved with COMSOL Multiphysics 4.4

    M A T E R I A L S

    Next, assign material properties. Use Glass (quartz) for all domains.

    1 On the Home toolbar, click Add Material.

    A D D M A T E R I A L

    1 Go to the Add Material window.

    2 In the tree, select Built-In>Glass (quartz).

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    In the Add material window, click Add to Component.

    Close the Add material window.

    E S H