guided mode resonance filters

7/31/2019 Guided Mode Resonance Filters

1/19

PHOTONICSRESEARCHLABORATORY

GMR Filters

18th July, 2012

Vivek Raj Shrestha

Department of Electronic Engineering, Kwangwoon Univ., Seoul, S.Korea


2/19


GRATING ANOMALIES

In 1902. R. W. Wood observed that the intensity of light diffracted by a grating

generally changed slowly as the wavelength was varied, but occasionally a sharp

change in intensity was observed at certain wavelengths. Called anomalies, these

abrupt changes in the grating efficiency curve were later categorized into two

groups: Rayleigh anomaliesandresonance anomalies

Rayleigh anomalies :Lord Rayleigh predicted the spectral locations where a certain set of anomalies would be found: he

suggested that these anomalies occur when light of a given wavelength and spectral orderm'is

diffracted at | | = 90 from the grating normal (i.e., it becomes an evanescent wave, passing over the

grating horizon).

For wavelengths < ', | | < 90, so propagation is possible in orderm'(and all lower orders), but

for > 'no propagation is possible in orderm'(but it is still possible in lower orders). Thus there is a

discontinuity in the diffracted powervs. wavelength in orderm'at wavelength , and the power that

would diffract into this order for > 'is redistributed among the other propagating orders. This

causes abrupt changes in the power diffracted into these other orders.

These Rayleigh anomalies, which arise from the abrupt redistribution of energy when a diffracted order

changes from propagating (| | < 90) to evanescent (| | > 90), or vice versa, are also

called threshold anomalies


3/19


GRATING ANOMALIES(2)

Resonance anomalies

The second class of anomalies, which are usually much more noticeable than Rayleigh

anomalies, are caused by resonance phenomena, the most well-known of which are

surface excitation effects. At the interface between a dielectric and a metal, there are

specific conditions under which a charge density oscillation ("electron wave") can be

supported, which carries light intensity away from the incident beam and therefore

decreases the diffraction efficiency of the grating. The efficiency curve would show asharp drop in intensity at the corresponding conditions (see Figure 9-20).


4/19


Basic Concepts of GMR


5/19


Propagation Constant of waveguide grating


6/19


Resonance Regimes of Waveguide Grating

Rayleigh Anomaly


7/19PHOTONICSRESEARCHLABORATORY



HIGHLY EFFICIENT COLOR FILTER INCORPORATING

A THIN METALDIELECTRIC RESONANT STRUCTURE

Yeo-Taek Yoon, Chang-Hyun Park, and Sang-Shin Lee

Applied Physics Express 5 (2012) 022501



Abstract and Introduction

A highly efficient color filter that takes advantage of an

ultrathin metal (Al)-dielectric (TiO2) resonant structure,

where a subwavelength metallic grating is deposited as

cladding in a planar dielectric waveguide, is

demonstrated.

A selective spectral response was obtained by virtue ofthe guided mode resonance between the diffracted mode

and waveguide mode.

Devices Center

Wavelength(nm)

3dB bandwidths(nm)

Red 430 67

Green 520 84

Blue 630 80



Design Considerations

Initially, we fixed grating pitch, grating height, and dielectric thickness at 350,

50, and 80 nm, respectively and investigated the dependence of the spectralresponse on the refractive index nd of the dielectric layer in the range from

1.3 to 3.5.

Calculated spectral response for varying refractive indices of the

dielectric layer.

The center wavelength of the color filter

can be tailored by varying the grating pitch,

which is one of the major factors

determining the GMR condition[5,13].

The grating height is closely related to

the spectral shape.[16]



Results from simulation

When the dielectric film has a much greater refractive index of nd = 3.5 compared with the

substrate, however, higher order diffracted modes in addition to the first-order mode may resonantly

couple to the waveguide mode, resulting in multiple peaks.15).

In the case where nd = 2.5, the magnetic field is drastically reinforced inside the dielectric layer at

the resonant wavelength of 550 nm, as shown in Fig. 2(c). In contrast, as shown in Fig. 2(d), no

significant enhancement in the field is observed at the off-resonance position of= 450 nm, where

the transmission is relatively low.

When nd is less than or equal to the refractive index of the

substrate, as indicated in Fig. 2(a), no noteworthy resonance is

observed due to the lack of phase matching between the guidedmodes of the waveguide and the diffracted modes. For instance, in

the case where nd=1.5, the magnetic field distribution is observed

to be localized very slightly inside the dielectric layer, as shown in

Fig. 2(b) for the H-field intensity distribution (|Hy|2) at = 470 nm



Results

Theoretical spectral response of the designed color filters.

Measured and calculated spectral responses for (a) Dev B, (b) Dev G, and (c) DevR. The color images for input white light are included together with the SEM

images of the devices.



A NEW THEORY OF WOOD'S ANOMALIES ON OPTICAL GRATINGS



Wood's anomalies are an effect observed in the spectrum oflight resolved by optical diffraction gratings; they manifest

themselves as rapid variations in the intensity of the various

diffracted spectral orders in certain narrow frequency bands.

They were first discovered by Wood in 1902 in experiments on

reflection gratings, and were termed anomalies because the

effects could not be explained by ordinary grating theory.

The new theory presented here is based on a guided wave appro

ach, in which all multiple-scattering effects are implicitly account

ed for.



Woods Anomalies

It is pointed out that the anomalies may be of two types, one associated with the

Rayleigh wavelengths and the other related to a resonance effect. These two types of

anomalies may occur separately and independently, or they may almost coincide, as

one finds in most optical reflection gratings. The Rayleigh wavelength type is well

known. The resonance type is the one which is shown to be related to the guided

complex waves supportable by the grating.

In 1902, Wood discovered the presence of unexpected narrow bright and dark bandsin the spectrum of an optical reflection grating illuminated by a light source with a

spectral intensity distribution which was only slowly varying. He noted, furthermore,

that these bands could be weakened or abolished completely in some cases, but not

in others, by simply rubbing the tops of the gratings (we understand this now to be a

groove depth effect, rather than an edge effect). In addition, he found that the

occurrence of these bands was dependent on thepolarization of the incident light.The bands were present only for S polarization, when the electric vector was

perpendicular to the rulings of the gratings. Since these effects could not be explained

by means of ordinary grating theory, Wood termed them "anomalies".



Rayleighs Analysis

The first theoretical treatment of these anomalies is due to Rayleigh in 1907. His

"dynamical theory of the grating" was based on an expansion of the scattered

electromagnetic field in terms of outgoing waves only. With this assumption, he finds

that the scattered field is singular at wavelengths for which one of the spectral orders

emerges from the grating at the grazing angle. He then observed that these

wavelengths, which have come to be called the Rayleigh wavelengths R, correspond

to the Wood anomalies. Furthermore, these singularities appear only when the

electric field is polarized perpendicular to the rulings, and thus account for the S

anomalies; for P polarization, his theory predicts a regular behavior near R. Thus,

Rayleighs theory correctly predicted the major features observed experimentally at

that time: the wavelengths at which the S anomalies occurred, and the absence of P

anomalies.

Limitations in Rayleigh's theory: It indicates a singularity at the Rayleigh wavelength,and, therefore, does not yield the shape of the bands associated with the anomaly.

Wood's later papers, however, suggest that P anomalies can sometimes be observed.

Anomalies of both the S and P type are obtainable, but P anomalies are found only on

gratings with deep grooves. Rayleigh's approximation with initial assumption of includi

ng outgoing waves only, and this approximation is valid for shallow grooves only.



About the paper

The new theoretical approach which is given in the presentreport is phrased in such a way as to yield new insight into the

character of Wood's anomalies.

It is not an extension of the multiple-scattering approach it is a

new guided wave viewpoint which formally may be viewed as an

extension of the earlier work of Rayleigh and Artmann, but

which contains a number of new elements.

It readily explains both the occurrence of P anomalies under

appropriate conditions, and the new effect described by Stewart

and Gallaway.



Woods Anomaly

Two types of anomalous effects occur:

(1) a rapid variation in the amplitudes of the diffracted spectral

orders, corresponding to the onset or disappearance of a

particular spectral order, and

(2) a resonance type of behavior in these amplitudes.

Effect (1), related to the Rayleigh wavelength, is well,

understood and requires no further discussion. Effect (2), the

resonance effect, is the one which has heretofore beenincompletely appreciated and which is shown here to be related

to the leaky (complex) waves supportable by the grating.


19/19PHOTONICS RESEARCH LABORATORY

A WIDE-ANGLE TRANSMISSIVE FILTER BASED ON AGUIDED-MODE RESONANT GRATING

guided mode resonance filters

Documents