August 15, 2004 / Vol. 29, No. 16 / OPTICS LETTERS 1867
Tunable diffraction of magnetic fluid films and its potential
application in coarse wavelength-division multiplexing
Yen-Wen Huang, Ssu-Tse Hu, Shieh-Yueh Yang, and Herng-Er Horng*
Institute of Electro-Optical Science and Technology, National Taiwan Normal University, Taipei 116, Taiwan
Jung-Chun Hung and Chin-Yih Hong
Department of Mechanical and Automation Engineering, Da-Yeh University, Chang-Hwa 515, Taiwan
Hong-Chang Yang
Department of Physics, National Taiwan University, Taipei 106, Taiwan
Cha-Hsin Chao and Ching-Fuh Lin†
Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei 106, Taiwan
Received February 27, 2004
When an external magnetic field is applied parallel to the film surface of a magnetic f luid film, a high-quality one-dimensional periodic chain structure is formed when the field strength reaches a certain level. With a periodic chain structure in the magnetic f luid film, an incident light is diffracted onto the magnetic thin film. The results show that the one-dimensional periodic chain structure in the magnetic f luid film can serve as an optical grating. Further investigations reveal the feasibility of developing tunable coarse wavelength-division multiplexing by utilizing a periodic chain structure. © 2004 Optical Society of America
OCIS codes: 160.3820, 260.3160, 230.1950.
As a result of the agglomeration of magnetic particles, many types of structural pattern, such as a disordered
column structure,1,2
a two-dimensional hexagonal structure,3,4 and a column splitting state,4are formed
in magnetic f luid films when an external magnetic field is applied perpendicularly to a f ilm surface. A number of published papers have shown that the structural patterns can be manipulated by
adjust-ment of the control parameters.5,6
Some research has also discussed relevant physical interactions in these tunable structural patterns.4,7,8
Because of the versatility of these tunable structures, magnetic f luid films under perpendicular f ields exhibit many optical properties, such as tunable transmission,9,10
a tunable refractive index,11
and magnetochromatics.3,12
These particular optical characteristics of magnetic f luid films show promise for the development of photonic devices such as tunable optical attenuators, optical modulators, switches, filters, and photonic crystals.13
When an external magnetic f ield is applied par-allel to the f ilm surface, a randomly distributed chain structure is obtained in a magnetic f luid film.14 – 16
Many researchers have pointed out that the magnetic chains are optically anisotropic,10,14 – 16
and hence birefringence or dichroism is generated for magnetic f luid f ilms. With the recent success in the formation of a high-quality one-dimensional periodic chain structure in a magnetic f luid film under parallel fields, new optical effects can be generated. In this Letter we explore the diffraction behavior of a one-dimensional periodic chain structure in a magnetic f luid f ilm under parallel magnetic fields and study
the feasibility of a tunable wavelength demultiplexer by using the diffraction effect.
The magnetic f luid used here is kerosene-based MnFe2O4. To obtain a f ilm we inject the f luid into a rectangular cell with an area of 10 mm 3 1000 mm and a depth of 0.3 mm on a glass plate. The magnetic f luid film is then covered with another glass plate and put into a Helmholtz coil that provides a uniform magnetic f ield parallel to the f ilm surface. The structural patterns in the film were observed by use
of an optical microscope and a CCD. Thus the
struc-tural images could be recorded and analyzed. For investigation of the diffraction effect of the magnetic f luid film under parallel fields, a parallel white light is normally incident upon the f ilm. The transmitted light is monitored with a CCD, and its spatial intensity distribution is probed by feeding the transmitted light into a spectrometer and a photomultiplier.
When an external magnetic field H is applied par-allel to the surface of a magnetic f luid f ilm, magnetic particles in the magnetic f luid film start to agglomer-ate to form a one-dimensional periodic magnetic-chain structure as the f ield strength exceeds a certain value. A typical one-dimensional periodic chain structure in
a magnetic f luid f ilm under a magnetic f ield 共H 苷
150Oe兲 is shown in Fig. 1. Chain width a and chain
spacing Dx (i.e., the period of the structure) were 1.2 and 2.32 mm, respectively.
We investigate the diffraction effect of the ordered structure shown in Fig. 1 by use of a parallel white light that is normally incident upon the magnetic film, as shown in Fig. 2. The image of the transmitted
1868 OPTICS LETTERS / Vol. 29, No. 16 / August 15, 2004
Fig. 1. One-dimensional periodic chain structure in the magnetic f luid f ilm under a parallel magnetic f ield. The concentration Ms of the f luid is 15.5 emu兾g, the film thick-ness L is 0.3 mm, the width of the cell, W , is 10 mm, the applied f ield strength H is 150 Oe, and the sweep rate of applying the f ield is 10 Oe兾s.
Fig. 2. Schematic cross section of the magnetic f luid f ilm possessing a one-dimensional periodic chain structure and a diffracted image of the transmitted light through the f ilm. Each black dot in the schematic represents the cross section of a magnetic chain. The Cr f ilm shown here blocks the incident light outside the cell. The parallel white light is normally incident upon the f ilm. The white spot at the center of the diffracted image is located at a certain distance above the f ilm and is in the normal line of the f ilm. Angle u denotes the diffracted angle of the transmitted light.
light is shown in Fig. 2. The white spot was found at the center of the image along the normal (incident) line of the f ilm (incident) light. In addition, colorful images were obtained on both sides of the white spot. Note that a color sequence from purple to red resulted along directions outward from the white spot. According to the image of the transmitted light shown in Fig. 2, the white spot corresponds to the zeroth-order diffracted light, and the colorful parts are of the first-order diffraction for various wavelengths of visible light. This color sequence is attributed to the fact that the wavelength of purple light is the shortest whereas that of red is the longest in visible light.
To identify the diffracted angle of the first-order diffraction for a given wavelength l, say, 600 nm, we detected the spatial intensity distribution, shown in Fig. 3, in which angle u is the span from the normal line of the f ilm to the detected point. It was found that the first-order diffraction peaks are located at
uexp苷 615.00±. We then used the grating equation
Dx sin uth苷 nl (1)
to calculate the theoretical value of the first-order
diffraction angle uth for l 苷 600 nm in the case
where n is 1 for the first-order diffraction. With
Dx 苷 2.32 mm from Fig. 1, uth is 14.99±, which is
consistent with the experimental angle, uexp.
Consis-tency between uth and uexp was also found for other
wavelengths. Therefore the one-dimensional periodic chain structure in a magnetic f luid film under a parallel magnetic f ield is an optical grating.
According to the diffraction image shown in
Fig. 2, the f irst-order diffraction angles of various wavelengths are different. This reveals that the one-dimensional chain structure is able to split light with different wavelengths. A signif icant application that can be achieved by use of this property is wave-length-division multiplexing. Here we lay out the potential for using a tunable one-dimensional periodic chain structure in a magnetic f luid film for tunable coarse wavelength-division multiplexing (CWDM).
To fulfill the requirements of CWDM, the device should be able to resolve two lights with wavelengths that differ by 20 nm. To test this ability, we scanned the spatial intensity distributions of the first-order diffraction peaks of various wavelengths (580, 600, 620, and 640 nm), and the results are plotted in Fig. 4. These four peaks are clearly resolvable.
From Eq. (1) the peak separation between two
first-order diffractions of various wavelengths l1 and
l2can be calculated as
Dup苷 uth, l12 uth, l2苷 sin21共l1兾Dx兲 2 sin21共l2兾Dx兲 , (2) where uth, l1 and uth, l2 are the calculated first-order
diffraction angles for l1 and l2, respectively.
Ex-perimentally, Dx in Eq. (2) becomes smaller under a
higher field. Thus Dup should increase. Figure 5
il-lustrates the experimental observation of the increase
Fig. 3. Spatial intensity distribution of the diffracted light with a wavelength of 600 nm.
August 15, 2004 / Vol. 29, No. 16 / OPTICS LETTERS 1869
Fig. 4. Spatial intensity distributions of the f irst-order diffraction peaks for various wavelengths l. The concen-tration of the f luid 共Ms兲 is 15.5 emu兾g, the film thickness 共L兲 is 0.3 mm, the width of the cell 共W兲 is 20 mm, the ap-plied f ield strength 共H兲 is 150 Oe, and the sweep rate of the f ield application is 10 Oe兾s.
Fig. 5. Spatial intensity distributions of the two f irst-order peaks of the diffracted light with wavelengths of 620 and 640 nm under 150 and 200 Oe, respectively. The separation Dup between the two peaks is increased from 0.57± to 0.94± when the f ield H increases from 150 to 200 Oe.
in Dupwhen the f ield strength is increased. Dup was
0.57± under 150 Oe, whereas Du
p increased to 0.94±
under 200 Oe. The variation in Dup with changes in
field strength def initely demonstrates the tunability of
CWDM through the use of a one-dimensional periodic structure in a magnetic f luid f ilm under parallel magnetic f ields.
In conclusion, the one-dimensional periodic chain structure in a magnetic f luid f ilm under parallel magnetic f ields acts as an optical grating. It has further been demonstrated that the resolution of the wavelength division of the optical grating satisf ies
the requirements of CWDM. With the tunability
of the periodic chain structure, one can tune the characteristics of magnetic-f luid CWDM by adjusting the external field strength.
This work was supported by the National Science Center of the Republic of China (ROC) under grant NSC92-2112-M-003-010 and NSC92-2112-E-212-011 and was partially supported by the Ministry of Educa-tion of the ROC under grant 91-N-FA01-2-4-2. H.-E. Horng’s e-mail address is phyfv001@scc.ntnu.edu.tw.
*Also with the Department of Physics, National Taiwan Normal University, Taipei 116, Taiwan.
†Also with Graduate Institute of Electronics
En-gineering, National Taiwan University, Taipei 106, Taiwan.
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