WO2009087573A1 - Device for modifying and/or controlling the state of polarisation of light - Google Patents
Device for modifying and/or controlling the state of polarisation of light Download PDFInfo
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- WO2009087573A1 WO2009087573A1 PCT/IB2009/000235 IB2009000235W WO2009087573A1 WO 2009087573 A1 WO2009087573 A1 WO 2009087573A1 IB 2009000235 W IB2009000235 W IB 2009000235W WO 2009087573 A1 WO2009087573 A1 WO 2009087573A1
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B11/00—Recording on or reproducing from the same record carrier wherein for these two operations the methods are covered by different main groups of groups G11B3/00 - G11B7/00 or by different subgroups of group G11B9/00; Record carriers therefor
- G11B11/10—Recording on or reproducing from the same record carrier wherein for these two operations the methods are covered by different main groups of groups G11B3/00 - G11B7/00 or by different subgroups of group G11B9/00; Record carriers therefor using recording by magnetic means or other means for magnetisation or demagnetisation of a record carrier, e.g. light induced spin magnetisation; Demagnetisation by thermal or stress means in the presence or not of an orienting magnetic field
- G11B11/105—Recording on or reproducing from the same record carrier wherein for these two operations the methods are covered by different main groups of groups G11B3/00 - G11B7/00 or by different subgroups of group G11B9/00; Record carriers therefor using recording by magnetic means or other means for magnetisation or demagnetisation of a record carrier, e.g. light induced spin magnetisation; Demagnetisation by thermal or stress means in the presence or not of an orienting magnetic field using a beam of light or a magnetic field for recording by change of magnetisation and a beam of light for reproducing, i.e. magneto-optical, e.g. light-induced thermomagnetic recording, spin magnetisation recording, Kerr or Faraday effect reproducing
- G11B11/10532—Heads
- G11B11/10534—Heads for recording by magnetising, demagnetising or transfer of magnetisation, by radiation, e.g. for thermomagnetic recording
- G11B11/10539—Heads for recording by magnetising, demagnetising or transfer of magnetisation, by radiation, e.g. for thermomagnetic recording using electromagnetic beams, e.g. polarised light
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/28—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising
Definitions
- the present invention relates to the field of optics and more particularly to the enhanced transmission of light through a surface structure, such as a metal film, with at least one miniature subwavelength through hole or aperture.
- a surface structure such as a metal film
- SPPs surface plasmon polaritons
- electromagnetic surface waves existing at the interface between a dielectric and a metal are particularly sensitive to tiny variations in their local electronic environments. This creates new opportunities and applications for photonics (see [2]) by simply texturing a metal surface.
- metal films structured with two dimensional subwavelength hole arrays present remarkable properties such as the so- called “extraordinary optical transmission” (EOT) which is a clear signature of SPP-light interaction (see [3 - 5]).
- EOT extraordinary optical transmission
- Linear birefringence is absolutely central in optics since it allows full control of the state of polarisation (SOP) of light without absorption.
- the aim of the present invention is to propose a simple miniature device which allows to convert and tailor the state of polarisation (SOP) of light, without any loss of light coherence. Therefore, in accordance with the invention, a device for modifying and controlling the state, of polarisation of light is proposed.
- SOP state of polarisation
- Said device comprises a light impervious surface structure provided with at least one through hole or aperture and with a surface topography comprising one or several surface features which are arranged periodically or quasi-periodically around said hole or aperture or around each of said holes or apertures and designed to interact in a resonant manner with the transmitted light.
- Said device is characterised in that the surface topography around the or each hole consists of a grating selected among elliptical and chiral gratings.
- the invention relies on a modified version of a circular nano-aperture surrounded by periodic circular corrugations, also known as a "bull's eye” structure (see [10]).
- a circular nano-aperture surrounded by periodic circular corrugations also known as a "bull's eye” structure (see [10]).
- Such an optical grating acts as a miniature antenna presenting huge EOT for optical wavelength inside a narrow band centered on the SPP resonance (see also [11]).
- the specificity of the claimed device is its unique ability to control the SOP of the electromagnetic field going through the aperture. This is achieved by introducing a well defined eccentricity in the grating geometry which in turn modifies the phase of the excited SPP and consequently the polarisation of the transmitted light.
- the inventors have found that one can actually use the shape of the grating surrounding the central aperture to tailor and fully control the SOP of the electromagnetic field going through the associated aperture.
- the invention relies essentially on the grating conversion of light into SPP (and back) and not on the properties of localised electromagnetic modes in the aperture or hole to change the SOP of the transmitted light.
- the device is such that it comprises one subwavelength through hole or aperture of circular shape, that the light impervious surface structure is made of metal and that the surface feature(s) consist(s) of (a) depressed feature(s) like (a) corrugation(s) or groove(s) milled into the surface structure or of (a) raised feature(s) like (a) rib(s) formed on the surface structure and defining (a) groove(s) between them.
- the present invention encompasses two embodiments of the resonant device, each adapted to a specific way of controlling the state of polarisation of light, namely a first embodiment based on an elliptical grating and a second embodiment based on a chiral grating. .
- the invention will be better understood thanks to the following description and drawings of different embodiments of said invention given as non limitative examples thereof.
- Fig. l(a) is a microscopy image of a practical realisation of the first embodiment of the invention
- Fig. l(b) shows comparative [Intensity vs. Wavelength] curves obtained with the device of Fig. l(a) and by theoretical prediction based on 2D dipoles model;
- Fig. 2(a) is a schematical representation of the optical polarisation tomography setup used by the inventors;
- Fib. 2(b) is an image provided by the camera of Fig. 2(a) when using the inventive device of Fig. l(a);
- Fig. 2(c) is a cross cut of the intensity profile along the dotted line of Fig. 2(b);
- Fig. 3 (a) represents [Intensity vs. angle] curves as results of the SOP analysis of the output beam of the device of Fig. l(a) for a linearly polarised input beam;
- Fig. 3(b) represents the image of the input Poincare sphere through the transformation by the Mueller matrix of the device of Fig. l(a);
- Fig. 4(a) represents microscopy images of left (L) and right (R) handed chiral surface topographies of two surface structures of devices according to the second embodiment of the invention;
- Fig. 4(b) shows [Intensity vs. Wavelength] curves of the chiral topographies of the surface structures of Fig. 4(a);
- Fig. 5 shows [Intensity vs. angle] curves as results of the SOP analysis of the output beam of the chiral surface structures of Fig. 4(a) for an input light with variable linear polarisation;
- Fig. 6 is a representation of the same type than Fig. 3(b) in relation to the devices of Fig. 4(a).
- n is the length of the long axis
- b n is the length of the short axis
- n is an integer varying from 1 to the maximum number of elliptical grooves of the surface topography
- m is a number greater than 0
- P is the period of the grating, the value of which is close to the wavelength of the incident - A - light to be treated, more particularly equal to the surface plasmon polaritons wavelength for the considered light wavelength.
- Two especially advantageous practical realisations of this first embodiment consist of a half-wave plate which rotates the plane of polarisation and of a quarter wave-plate which converts linear polarised light into a circular one, the combination of the two enabling a complete exploration of all polarisation states.
- the hole diameter is 260 nm and the grooves width and depth are 370 and 80 nm respectively.
- P 760 nm is the period of the grating (which equals the SPP wavelength ⁇ SPP for a laser excitation at 785 nm (see (15]) and n is an integer going from 1 to 8 (see Fig. l(a)).
- Fig. l(b) Also shown in Fig. l(b) is the transmission spectra of the structure with a resonant peak at ⁇ ⁇ 777 nm.
- the measured extraordinary transmission efficiency (larger than 1) is a direct signature of the involvement of SPP.
- the choice for the grating symmetry can be justified on theoretical grounds.
- the grooves were discretised into a sum of point dipoles P M proportional to the local electric field at M. Each dipole is excited coherently by the light impinging normal to the metal film and SPPs are launched in the direction of the central nanohole where they excite an in-plane radiating dipole (see [16]).
- the principle of the inventive device can be illustrated by considering only the point dipoles located along the short and long axes of the ellipses.
- the coupling between the incident light and SPPs depends on the cosine of the angle w between the radial vector MO and P M (Fig. l(a)). It means that if the incident linear polarisation is switched from a direction parallel to the x axis to a direction parallel to the y axis then the radiating central dipole will change from ⁇ ic (where ⁇ is a constant) to e l ⁇ /2 ⁇ j> .
- the intensity is thus defined by taking the maximum of the Airy spot shown on Fig. 2(b).
- SOP of light is prepared and analysed with half wave plates, quarter wave plates, and polarisers located before and after the objectives (see [21] to [23]).
- the isotropy of the bare setup was checked by measuring the Mueller matrix M with a glass substrate.
- M ⁇ is practically identical to the identity matrix / with individual elements deviating from it by no more than 0.02. It implies that the optical setup does not induce depolarisation and that consequently it can be relied on the used measurement procedure for obtaining M.
- Optical depolarisation i.e., losses in polarisation coherence
- the incident illumination spot size on the sample was varied between 2 and 20 ⁇ m without affecting the matrix, i.e., without introducing additional depolarisation.
- the matrix Af xp ' exhibits several interesting symmetrical features which relate to the polarisation properties of the device.
- p and ⁇ measure respectively the relative dichroism (i.e. the relative absorption) and the birefringence of this biaxial 2D medium.
- the Mueller matrix predicted by the 2D dipole model can be numerically calculated: f 1.000 0.089 0.000 0.000 ⁇
- JVl 2D 0.000 ⁇ ooo 0.000 0.446 -0.890 (3)
- the operator M *xp ⁇ defines a geometrical transformation connecting this Poincare sphere to an output surface with a characteristic radius D(hf xp ).
- this angle measures directly the inclination of the output circle shown on Fig. 3(b).
- the grating forming the surface topography of the device can also be of a chiral type and the groove forming said grating can have the shape of an Archimed spiral defined by the polar formula:
- P P x ⁇ /2 ⁇ , where P is the period of the spiral, the value of which is close to the wavelength of the incident light to be treated, more particularly equal to the surface plasmon polaritons wavelength for the considered light wavelength.
- Such surface structures can be called "Archimedian bull's eye”.
- the period P of the spiral is chosen so that efficient [SPP to light] and [light to SPP] couplings are achieved.
- the hole diameter is 270 ⁇ m and the grooves width and depth are 280 and 80 nm respectively.
- Fig. 4(a) two enantiomers of the same system are shown.
- the left (L) and right (R) handed spirals are obtained after application of an in plane mirror symmetry relatively to the y axis.
- Fig. 4(b) the light transmission spectra through the L and R Archimedian bull's eye structures (was recorded). It shows that the systems are acting like resonant antennas.
- the surface topography mentioned hereinbefore in relation to any of the two embodiments is located on the side of the entry opening of the hole of the surface structure, be it an elliptical grating (first embodiment) or a chiral grating (second embodiment).
- the surface feature(s) (groove(s), rib(s)) of the surface topography of the inventive device can show, as represented on Fig. l(a) and on Fig.
- discontinuous structure(s) wherein the chiral feature or each elliptical feature is composed of segments or portions which are shaped and arranged in order to follow, at least roughly in shape, the general configuration of the concerned feature (ellipse, spirale).
- a second surface topography can be provided on the surface structure and located on the side of the exit opening of the hole of the surface structure (not shown).
- This possible second surface topography can allow to apply an additional treatment to the transmitted light, for example a controlled directionality and optical divergence to the emitted or transmitted light (see for example WO-A-03/019243).
- the SPP control over the polarisation provided by the device according to the invention has many possible applications in photonics and in information technology.
- the present invention also encompasses, among other applications, a detector unit, a display unit and a read/write head for opto- magnetic data storage media, each of which comprises at least one device as described before, using advantageously the advantageous properties of the claimed device in any of its embodiments.
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Abstract
The present invention concerns a device for modifying and/or controlling the state of polarisation of light, said device comprising a light impervious surface structure provided with at least one through hole or aperture and with a surface topography comprising one or several surface features which are arranged periodically or quasi-periodically around said hole or aperture or around each of said holes or apertures and designed to interact in a resonant manner with the transmitted light. Device characterised in that the surface topography around the or each hole consists of a grating selected among elliptical and chiral gratings.
Description
Device for modifying and/or controlling the state of polarisation of light
The present invention relates to the field of optics and more particularly to the enhanced transmission of light through a surface structure, such as a metal film, with at least one miniature subwavelength through hole or aperture. It is known that surface plasmon polaritons (SPPs), electromagnetic surface waves existing at the interface between a dielectric and a metal (see [I]), are particularly sensitive to tiny variations in their local electronic environments. This creates new opportunities and applications for photonics (see [2]) by simply texturing a metal surface. For example, metal films structured with two dimensional subwavelength hole arrays present remarkable properties such as the so- called "extraordinary optical transmission" (EOT) which is a clear signature of SPP-light interaction (see [3 - 5]).
In the present invention, reference is also expressly made to WO-A-03/019245, US patent No. 6,236,033 to Ebbesen et al., US patent
No. 5,973,316 to Ebbesen et al., US patent No. 6,040,936 to Kim et al., US patent No. 6,052,238 to Ebbesen et al. and US patent No. 6,285,020 to Kim et al.
In this particular context, several studies have started to address polarisation issues, discussing in this respect the influence of the individual hole shapes. Elliptical or rectangular apertures can behave like polarisers, following the Malus law (see [6 - 8]).
However these known structures do not show linear birefringence. Linear birefringence is absolutely central in optics since it allows full control of the state of polarisation (SOP) of light without absorption.
The aim of the present invention is to propose a simple miniature device which allows to convert and tailor the state of polarisation (SOP) of light, without any loss of light coherence. Therefore, in accordance with the invention, a device for modifying and controlling the state, of polarisation of light is proposed.
Said device comprises a light impervious surface structure provided with at least one through hole or aperture and with a surface
topography comprising one or several surface features which are arranged periodically or quasi-periodically around said hole or aperture or around each of said holes or apertures and designed to interact in a resonant manner with the transmitted light. Said device is characterised in that the surface topography around the or each hole consists of a grating selected among elliptical and chiral gratings.
Thus, the invention relies on a modified version of a circular nano-aperture surrounded by periodic circular corrugations, also known as a "bull's eye" structure (see [10]). Such an optical grating acts as a miniature antenna presenting huge EOT for optical wavelength inside a narrow band centered on the SPP resonance (see also [11]).
The specificity of the claimed device is its unique ability to control the SOP of the electromagnetic field going through the aperture. This is achieved by introducing a well defined eccentricity in the grating geometry which in turn modifies the phase of the excited SPP and consequently the polarisation of the transmitted light.
The inventors have found that one can actually use the shape of the grating surrounding the central aperture to tailor and fully control the SOP of the electromagnetic field going through the associated aperture. In contrast to aforementioned previous solutions [6 - 8], the invention relies essentially on the grating conversion of light into SPP (and back) and not on the properties of localised electromagnetic modes in the aperture or hole to change the SOP of the transmitted light. Preferably, the device is such that it comprises one subwavelength through hole or aperture of circular shape, that the light impervious surface structure is made of metal and that the surface feature(s) consist(s) of (a) depressed feature(s) like (a) corrugation(s) or groove(s) milled into the surface structure or of (a) raised feature(s) like (a) rib(s) formed on the surface structure and defining (a) groove(s) between them.
The present invention encompasses two embodiments of the resonant device, each adapted to a specific way of controlling the state of polarisation of light, namely a first embodiment based on an elliptical grating and a second embodiment based on a chiral grating. . The invention will be better understood thanks to the following description and drawings of different embodiments of said invention given as non limitative examples thereof. In the drawings:
Fig. l(a) is a microscopy image of a practical realisation of the first embodiment of the invention;
Fig. l(b) shows comparative [Intensity vs. Wavelength] curves obtained with the device of Fig. l(a) and by theoretical prediction based on 2D dipoles model;
Fig. 2(a) is a schematical representation of the optical polarisation tomography setup used by the inventors;
Fib. 2(b) is an image provided by the camera of Fig. 2(a) when using the inventive device of Fig. l(a); Fig. 2(c) is a cross cut of the intensity profile along the dotted line of Fig. 2(b);
Fig. 3 (a) represents [Intensity vs. angle] curves as results of the SOP analysis of the output beam of the device of Fig. l(a) for a linearly polarised input beam; Fig. 3(b) represents the image of the input Poincare sphere through the transformation by the Mueller matrix of the device of Fig. l(a); Fig. 4(a) represents microscopy images of left (L) and right (R) handed chiral surface topographies of two surface structures of devices according to the second embodiment of the invention; Fig. 4(b) shows [Intensity vs. Wavelength] curves of the chiral topographies of the surface structures of Fig. 4(a);
Fig. 5 shows [Intensity vs. angle] curves as results of the SOP analysis of the output beam of the chiral surface structures of Fig. 4(a) for an input light with variable linear polarisation; Fig. 6 is a representation of the same type than Fig. 3(b) in relation to the devices of Fig. 4(a).
According to a first embodiment of the invention and as shown on Fig. l(a), the grating forming the surface topography of the device can be made of elliptical grooves and said successive concentric elliptical grooves forming the grating have then respective dimensions such that their respective long axis and short axis are as follows: an = n x P + P/m and bn = n x P. wherein an is the length of the long axis, bn is the length of the short axis, n is an integer varying from 1 to the maximum number of elliptical grooves of the surface topography, m is a number greater than 0 and P is the period of the grating, the value of which is close to the wavelength of the incident
- A - light to be treated, more particularly equal to the surface plasmon polaritons wavelength for the considered light wavelength.
Two especially advantageous practical realisations of this first embodiment consist of a half-wave plate which rotates the plane of polarisation and of a quarter wave-plate which converts linear polarised light into a circular one, the combination of the two enabling a complete exploration of all polarisation states.
As it results from the analysis of the experiments described hereinafter, the increment or difference of length between the long axis and the short axis of each ellipse formed by the surface features δL = an — bn is advantageously determined by extrapolation on the basis of a computed value inducing theoretically the requested phase shift (φ) increased by a value depending on the material(s) forming the device and/or the shape and/or dimensions of the surface features. More particularly, Fig. l(a) shows a practical realisation of this first embodiment of the invention, for which m = 4.
In order to fully characterise the optical behaviour of the invention, a genuine polarisation tomography of the isolated subwavelength aperture has been implemented by the inventors. Furthermore, they have also developed a microscopic (dipolar) model to link structural design with change of SOP.
As a practical example of a device according to the invention and as an experimental subject in the following, one should consider a "bull's eye" structure made of 8 grooves and fabricated by FIB milling in a 300 nm thick Au film, as shown on Fig. l(a).
The hole diameter is 260 nm and the grooves width and depth are 370 and 80 nm respectively.
The groove shape is chosen to be elliptical with the long axis an = n . P + P/4 and the short axis bn = n . P. Here P = 760 nm is the period of the grating (which equals the SPP wavelength λSPP for a laser excitation at 785 nm (see (15]) and n is an integer going from 1 to 8 (see Fig. l(a)).
Also shown in Fig. l(b) is the transmission spectra of the structure with a resonant peak at λ ∞ 777 nm. The measured extraordinary transmission efficiency (larger than 1) is a direct signature of the involvement of SPP. The presence of this peak proves that, despite the small increment of δL = P/4 between the long and short axis of the ellipses, the structure still behaves like a miniature or nano antenna.
The choice for the grating symmetry can be justified on theoretical grounds. In the used model, the grooves were discretised into a sum of point dipoles PM proportional to the local electric field at M. Each dipole is excited coherently by the light impinging normal to the metal film and SPPs are launched in the direction of the central nanohole where they excite an in-plane radiating dipole (see [16]).
To reproduce completely the system, a second transmission channel is introduced in which the central dipole is excited directly by the incident light. The interference between these two channels leads to a Fano like effect (see [17]) resulting in the observed transmission peak. The relative (complex) amplitude between these two channels was fitted to reproduce the spectra of Fig. l(b) (see [18]).
The good agreement between the used model and the data (see Fig. l(b)) allows to use it for predicting the optical behavior of the structure at a given λ.
The principle of the inventive device can be illustrated by considering only the point dipoles located along the short and long axes of the ellipses.
It is thus clear that δ L corresponds to a phase shift φSPP = 2πδL/λSpp = π/2 between SPPs propagating along the long (y) and the short (x) axes.
Additionally the coupling between the incident light and SPPs depends on the cosine of the angle w between the radial vector MO and PM (Fig. l(a)). It means that if the incident linear polarisation is switched from a direction parallel to the x axis to a direction parallel to the y axis then the radiating central dipole will change from αic (where α is a constant) to elπ/2 αj> .
From the point of view of this idealised picture (which neglects damping), it can be deduced that the system behaves like a birefringent biaxial medium, i.e., a perfect quarter wave plate, with fast and slow axes parallel respectively to the x and y axes. Obviously if one now takes into account all the dipoles as well as the Fano interference effect and the finite value of the SPP propagation length LSpp (damping) in the structure the actual result will naturally deviate from this idealised case (see [19] and [20]).
In order to study experimentally the SOP conversion by the considered device, a complete polarisation tomography (see [21]) was
caπied out using the optical setup sketched in Fig. 2(a). A laser beam at λ = 785 nm is focused normally onto the structure by using an objective L1. The transmitted light is collected by a second objective L2 forming an Airy spot on the camera (see Fig. (2b-c)). This was expected since the hole behaves like a point source in an opaque gold film.
In the herein described experiments, the intensity is thus defined by taking the maximum of the Airy spot shown on Fig. 2(b). The
SOP of light is prepared and analysed with half wave plates, quarter wave plates, and polarisers located before and after the objectives (see [21] to [23]).
The complete knowledge of the SOP requires 6 intensity projection measurements (Lj) = <|E . S1I2) made along the 4 linear polarisation vectors x,y,p = (x+y)l4l , m = (x-y)/-j2 , and along the two circular polarisation vectors L = (x+iy)/-j2) , R = {x + iy)l 4Z) . It is convenient [22] to introduce the four Stokes parameters S1 = (l^ -I^ ,
S2 = (Ip -I*), S3 = (/z -/A), and S0 = (/* +/,) = (llolal) ■
The goal of this polarization tomography is then the determination of the 4 x 4 Mueller matrix M characterising the transformation of the input Stokes parameters during the interaction of the laser light with the structure. In order to write down the full Mueller matrix, 6 x 6 intensity projections were measured corresponding to the 6 previously mentioned unit vectors for the input and the output polarisations (see [24]).
At first, the isotropy of the bare setup was checked by measuring the Mueller matrix M with a glass substrate. Up to a normalisation constant, one can deduce that M^^ is practically identical to the identity matrix / with individual elements deviating from it by no more than 0.02. It implies that the optical setup does not induce depolarisation and that consequently it can be relied on the used measurement procedure for obtaining M. Optical depolarisation (i.e., losses in polarisation coherence) can be precisely quantified through the degree of purity of the Mueller matrix defined by (see (25]):
The residual depolarisation (1-D~2%) was imputed to the lenses and to alignment errors.
It should be noted that the incident illumination spot size on the sample was varied between 2 and 20 μm without affecting the matrix, i.e., without introducing additional depolarisation.
In the following experiment, the case of a large gaussian spot with FWHM = 20 μm was considered in order to illuminate the whole structure (see [26]). When measuring the Mueller matrix of the considered device, it was found that:
^ LOOO a 107 -0,008 0.000 ^ jM«φt = 0411 0,972 -0,002 -0,004
0,004 -0,002 0.306 -0,932 , (D
^0,001 -0,017 0,934 0.294 J which is clearly block diagonal, up to experimental errors.
It is also remarkable that D(Af***) = 0.981. This means that despite the existence of the SPP transmission channel, the polarisation coherence is not lost during the propagation through the structure. This situation contrasts with previous SOP tomography measurements on metallic hole arrays in which the polarisation degrees of freedom were mixed with spatial information responsible for SPP-induced depolarisation (see [27]).
Beside these two points, the matrix Afxp' exhibits several interesting symmetrical features which relate to the polarisation properties of the device.
First, it can be observed that in the described experimental procedure the polarisation in the Airy spot (see Fig. 2(b)) is homogeneous (see [28]). This means that in the conducted analysis, the polarisation tomography of the central radiating dipole is actually performed, i.e., we are dealing only with the SU(2) point symmetry of the Mueller matrix. In this context, the rectangular point symmetry group C2v of the ellipse imposes that the 2 x 2 Jones matrix J (see [22]) connecting the incident electric field (E'",Ey ) to the transmitted electric field (E°'" ,E°"') must be diagonal in the x and y basis, i.e.,
where β = peiφ is a complex number.
In analogy with bulk optics, p and φ measure respectively the relative dichroism (i.e. the relative absorption) and the birefringence of this biaxial 2D medium.
Clearly φ is reminiscent of φSpp discussed above.
Using the previous Jones Matrix J the theoretical Mueller matrix can be obtained:
(2) which is similar to ftfxp' and in particular satisfies the symmetries:
M0I = M10,
M00 = M11,
M22 = M33,
M23 = -M32, which were observed experimentally. It can be deduced that:
Using Eqs. 1,2, it results in p « 0.898 and φ » 72.5°
Reciprocally by injecting the previous values for p and φ in M°2v the result do not differ from M2^' by more than 2 %, in agreement with the value obtain for the residual depolarization.
Then, using the fitting parameters already considered in the transmission spectrum Fig. l(b), the Mueller matrix predicted by the 2D dipole model can be numerically calculated:
f 1.000 0.089 0.000 0.000 ^
0.089 1.000 0.000
JVl 2D = 0.000 αooo 0.000 0.446 -0.890 (3)
V 0.0000 0.000 0.890 0.446 J which is close to lf2v and M"*- and corresponds to D(M2D) = 1.
This numerical model is sensitive to small variations of the fitting parameters and the agreement with the experiment could be probably improved by going beyond the paraxial approximation for the incident light (see [29]).
Finally, closer consideration was given to the consequence of the transformation defined by Afxp~ by varying the linear polarisation θ of the input state every 10° from -90° to +90°. Fig. 3 (a) shows the transmitted intensity analysed along the 6
(six) fundamental polarisations x, y, p, m, L and R as a function of θ.
The interference fringes observed were compared with the predictions given by the 2D dipole model (dotted curves) and with the intensity deduced from the Mueller matrix M3^' (continuous curves). In both cases the agreement is very good showing once again the consistency of the different measurements and deductions. Furthermore, this can be geometrically illustrated by using the Stokes vector (see [22]) defined by S = [S1X+ S2y+ S3Z]IS0.
The surface drawn by the input Stokes vector is called a Poincare sphere and has the radius D = 1. As shown in Fig. 3(b), the operator M*xp~ defines a geometrical transformation connecting this Poincare sphere to an output surface with a characteristic radius D(hfxp).
This experimental surface is very close to the ideal sphere D = 1 in agreement with the absence of net depolarisation as discussed earlier. The experiment shown on Fig. 3 (a) is also represented on this sphere.
From Eq. 2, it can be deduced that if the input Stokes vector explores the equator corresponding to linear polarisations, then the output
Stokes vector draws a circle of radius D « 1 which is contained in the plane y/z = M33IM32 making the angle 90° - φ = 17.5° with the z axis. These predictions are directly consistent with the observations.
Additionally, for a pure left circular input SOP, one does experimentally obtain S = OA 123.x - 0.8984 y + 0.3104z in agreement with the value deduced from MC2v : S'= 0Λ067x-0.9272y + 0.2949z .
From the foregoing analysis and description in relation to the first embodiment of the invention, based on both experimental and theoretical results, the person skilled in the art has a clear understanding of the inventive device incorporating the SPP structure.
To sumerise the previous analysis, it should first be noted that p » 1 which implies that the device acts essentially as a birefringent medium with the Jones Matrix
J / 1 0 \ ~ \0 eiφ / i.e., as a wave plate. Second, the value obtained for φ shows that the device differs slightly from an ideal quarter waveplate for which φ = 90°.
From the point of view of the Poincare sphere, this angle measures directly the inclination of the output circle shown on Fig. 3(b).
For a perfect quarter wave plate this circle would go through the poles, i.e., a complete conversion from linear to circular polarisation becomes possible if the input SOP is polarised along p or m .
In this context, numerical calculations with the 2D dipoles model show that by changing slightly the value for the long axis increment δL, the phase φ can be changed continuously. This means than with such a SPP device one can in principle tailor and generate any kind of SOP conversion on the Poincare sphere going from the equator (linear polarisation) to the poles (circular polarisation) or vice versa.
According to a second embodiment of the invention, and as shown on figure 4(a), the grating forming the surface topography of the device can also be of a chiral type and the groove forming said grating can have the shape of an Archimed spiral defined by the polar formula:
P = P x θ/2π, where P is the period of the spiral, the value of which is close to the wavelength of the incident light to be treated, more particularly equal to the surface plasmon polaritons wavelength for the considered light wavelength. Such surface structures can be called "Archimedian bull's eye".
In the practical realisations of Fig. 4(a), the period P of the spiral is chosen so that efficient [SPP to light] and [light to SPP] couplings are achieved.
In figure 4(a), surface features fabricated by FIB milling in a 300 nm thick Au film are shown, for which P = λSPP = 760 nm which
corresponds to the laser excitation at λ0 = 780 nm. The hole diameter is 270 πm and the grooves width and depth are 280 and 80 nm respectively.
In Fig. 4(a), two enantiomers of the same system are shown. The left (L) and right (R) handed spirals are obtained after application of an in plane mirror symmetry relatively to the y axis. As shown in Fig. 4(b), the light transmission spectra through the L and R Archimedian bull's eye structures (was recorded). It shows that the systems are acting like resonant antennas.
One should also note that the two resonant peaks observed are identical for both structures. This means that the chirality does not affect the spectrum.
In order to determine the SOP conversion obtained with the spiral topographies, the Mueller Matrix of each of them was recorded.
For the L-structure:
'1.000 0.031 -0.107 -0.028N
0.029 0.96 0.044 -0.251
Jl/- =
-0.105 0.037 0.953 0.287
0.029 0.261 -0.282 0.809
For the R-structure:
1.000 0.035 0.111 0.023 λ 0.026 0.95 -0.051 -0.246
M* = 0.096 -0.034 0.943 0.267 -0.011 -0.254 -0.277 0.745
These non diagonal matrices show that the SOP conversion is important and different for the two enantiomers. This is a clear signature of the chirality. Additionally, the degree of depolarisation are D(M1) = 0.967 and D(M1*) = 0.939 showing that the structures do not disturb the polarisation coherence of the incident light state. A theoretical analysis similar to the one done for the "elliptical bull's eye" of the first embodiment show that the Jones matrices for the two enantiomers are given in the circular polarisation basis by:
* .22 f|
and
It can be emphasized that there is a strong symmetry between the two matrices. Indeed, we have
and
in agreement with known properties of planar chiral structures.
The properties of this second embodiment of the invention and its way of working are explained in more details in [29], which is incorporated herein by reference. According to the invention, the surface topography mentioned hereinbefore in relation to any of the two embodiments is located on the side of the entry opening of the hole of the surface structure, be it an elliptical grating (first embodiment) or a chiral grating (second embodiment). The surface feature(s) (groove(s), rib(s)) of the surface topography of the inventive device can show, as represented on Fig. l(a) and on Fig. 4(a), continuous structure(s) or, as an alternative realisation not represented on the drawings, also discontinuous structure(s), wherein the chiral feature or each elliptical feature is composed of segments or portions which are shaped and arranged in order to follow, at least roughly in shape, the general configuration of the concerned feature (ellipse, spirale).
Furthermore, a second surface topography can be provided on the surface structure and located on the side of the exit opening of the hole of the surface structure (not shown).
This possible second surface topography can allow to apply an additional treatment to the transmitted light, for example a controlled directionality and optical divergence to the emitted or transmitted light (see for example WO-A-03/019243).
The SPP control over the polarisation provided by the device according to the invention has many possible applications in photonics and in information technology.
Thus, the present invention also encompasses, among other applications, a detector unit, a display unit and a read/write head for opto- magnetic data storage media, each of which comprises at least one device as described before, using advantageously the advantageous properties of the claimed device in any of its embodiments.
Examples of types of detector or display units or read/write heads which can possibly incorporate a device according to the invention are already known (see [12] to [14]).
The teachings of the following documents/publication/ information are incorporated by reference in the present specification:
[I] H. Raether, Surface Plasmons (Springer, Berlin, 1988).
[2] C. Genet and T. W. Ebbesen, Nature (London), 445, 39 (2007).
[3] T. W. Ebbesen et al., Nature (London) 391, 667 (1998). [4] W. L. Barnes et al., Phys. Rev. Lett. 92, 107401 (2004).
[5] L. Martin-Moreno et al., Phys. Rev. Lett. 86, 1114 (2001).
[6] R. Gordon et al., Phys. Rev. Lett. 92, 037401 (2004).
[7] J. Elliott et al., Phys. Rev. B 70, 233403 (2004).
[8] A. Degiron et al., Opt. Commun. 239, 61 (2004). [9] W. Gotschy et al., Opt. Lett. 21, 1099 (1996).
[10] H. J. Lezec et al., Science 297, 820 (2002).
[I I] E. Laux et al., Nat. Photon. 2, 161 (2008).
[12] T. Ishi et al., Jpn. J. Appl. Phys. 44, L364 (2005). [13] G. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge University Press, Cambridge, England, 1997).
[14] C. D. Stanciu et al., Phys. Rev. Lett. 99, 047601 (2007).
[15] P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[16] C. Genet, M. P. van Exter, and J. P. Woerdman, J. Opt. Soc. Am. A 22, 998 (2005). [17] C. Genet, M. P. van Exter, and J. P. Woerdman, Opt.
Commun. 225, 331 (2003).
[18] Additionally we modeled the transmission spectra of the central isolated hole alone by using a fit of experimental spectrum.
[19] D. S. Kim et al., Phys. Rev. Lett. 91, 143901 (2003). [20] In our model we used LSPP = 0.95 μm to fit Fig. 2(b). This value agrees with the formula [19] LSPP = λo /(2πnSPP x FWHM) » 0.93 μm where nSPP « 1.05 is the SPP index and FWHM is the full width at half maximum of the transmission peak.
[21] F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron . 21, 109 (1997).
[22] M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, England, 1999), 7th ed.
[23] Y. Gorodetski et al., Opt. Lett. 30, 2245 (2005). [24] Actually only 16 measurements are needed to determine M [21]. Our systematic procedure is thus more than sufficient to obtain M. [25] J. J. Gill, J. Opt. Soc. Am. A 17, 328 (2000). [26] For spot size FWHM « 20 μm the effective numerical aperture of the incident beam at λ = 785 nm is only λ/FWHM » 0.04. At this low numerical aperture regime, the parameters used for the fit of the 2D dipole model at normal incidence are still pertinent.
[27] E. Altewischer et al., Opt. Lett. 30, 90 (2005). [28] Given the fact that M^355 » /, this is directly verified by using a pair of crossed polarisers in the input and output beam, i.e., measuring the extinction. [29] Aurelien Drezet et al., Optics Express, 12559-12570,
Vol. 16, No. 17, 18 August 2008.
Claims
1. Device for modifying and/or controlling the state of polarisation of light, said device comprising a light impervious surface structure provided with at least one through hole or aperture and with a surface topography comprising one or several surface features which are arranged periodically or quasi-periodically around said hole or aperture or around each of said holes or apertures and designed to interact in a resonant manner with the transmitted light, device characterised in that the surface topography around the or each hole consists of a grating selected among elliptical and chiral gratings.
2. Device according to claim 1, characterised in that it comprises one subwavelength through hole or aperture of circular shape, in that the light impervious surface structure is made of metal and in that the surface feature(s) consist(s) of (a) depressed feature(s) like (a) corrugation(s) or groove(s) milled into the surface structure or of (a) raised feature(s) like (a) rib(s) formed on the surface structure and defining (a) groove(s) between them.
3. Device according to anyone of claims 1 and 2, characterised in that the successive concentric elliptical grooves forming the grating have respective dimensions such that their respective long axis and short axis are as follows: an = n x P + P/m and bn = n x P, wherein an is the length of the long axis, bn is the length of the short axis, n is an integer varying from 1 to the maximum number of elliptical grooves of the surface topography, m is a number greater than 0 and P is the period of the grating, the value of which is close to the wavelength of the incident light to be treated, more particularly equal to the surface plasmon polaritons wavelength for the considered light wavelength.
4. Device according to claim 3, characterised in that the increment or difference of length between the long axis and the short axis of each ellipse formed by the surface features δL = an - bn is determined by extrapolation on the basis of a computed value inducing theoretically the requested phase shift (φ) increased by a value depending on the material(s) forming the device and/or the shape and/or dimensions of the surface features.
5. Device according to anyone of claims 1 and 2, characterised in that the unique continuous chiral groove forming the grating has the shape of an Archimed spiral defined by the polar formula: p = P x θ/2π, where P is the period of the spiral, the value of which is close to the wavelength of the incident light to be treated, more particularly equal to the surface plasmon polaritons wavelength for the considered light wavelength.
6. Device according to anyone of claims 1 to 5, characterised in that the surface topography is located on the side of the entry opening of the hole of the surface structure.
7. Device according to claim 6, characterised in that a second surface topography is located on the side of the exit opening of the hole of the surface structure.
8. Detection unit characterised in that it comprises at least one device according to anyone of claims 1 to 7.
9. Display unit characterised in that it comprises at least one device according to anyone of claims 1 to 7.
10. Read/writer head for opto-magnetic data storage media characterised in that it comprises at least one device according to anyone of claims 1 to 7.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US1049408P | 2008-01-09 | 2008-01-09 | |
| US61/010,494 | 2008-01-09 |
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| WO2009087573A1 true WO2009087573A1 (en) | 2009-07-16 |
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ID=40592033
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/IB2009/000235 Ceased WO2009087573A1 (en) | 2008-01-09 | 2009-01-09 | Device for modifying and/or controlling the state of polarisation of light |
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4712881A (en) * | 1985-06-21 | 1987-12-15 | The United States Of America As Represented By The Secretary Of The Army | Birefringent artificial dielectric structures |
| EP1128372A2 (en) * | 2000-02-28 | 2001-08-29 | NEC Research Institute, Inc. | Surface plasmon-enhanced read/write heads for optical data storage media |
| JP2004127389A (en) * | 2002-09-30 | 2004-04-22 | Toshiba Corp | Recording / reproducing head and recording / reproducing device |
| US20040190116A1 (en) * | 2001-08-31 | 2004-09-30 | Lezec Henri Joseph | Optical transmission apparatus with directionality and divergence control |
| US20050161589A1 (en) * | 2003-12-05 | 2005-07-28 | University Of Pittsburgh | Metallic nano-optic lenses and beam shaping devices |
| WO2008075763A1 (en) * | 2006-12-20 | 2008-06-26 | Nec Corporation | Light distributor |
-
2009
- 2009-01-09 WO PCT/IB2009/000235 patent/WO2009087573A1/en not_active Ceased
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4712881A (en) * | 1985-06-21 | 1987-12-15 | The United States Of America As Represented By The Secretary Of The Army | Birefringent artificial dielectric structures |
| EP1128372A2 (en) * | 2000-02-28 | 2001-08-29 | NEC Research Institute, Inc. | Surface plasmon-enhanced read/write heads for optical data storage media |
| US20040190116A1 (en) * | 2001-08-31 | 2004-09-30 | Lezec Henri Joseph | Optical transmission apparatus with directionality and divergence control |
| JP2004127389A (en) * | 2002-09-30 | 2004-04-22 | Toshiba Corp | Recording / reproducing head and recording / reproducing device |
| US20050161589A1 (en) * | 2003-12-05 | 2005-07-28 | University Of Pittsburgh | Metallic nano-optic lenses and beam shaping devices |
| WO2008075763A1 (en) * | 2006-12-20 | 2008-06-26 | Nec Corporation | Light distributor |
Non-Patent Citations (1)
| Title |
|---|
| EBBESEN, THOMAS ET. AL.: "Miniature Plasmonic Wave Plates", PHYSICAL REVIEW LETTERS, vol. 101, no. 043902, 25 July 2008 (2008-07-25), pages 1 - 4, XP002527467 * |
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