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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 7744–7755
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Spontaneous emission of electric and magnetic dipoles in the vicinity of thin and thick metal

R. Hussain, D. Keene, N. Noginova, and M. Durach  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 7744-7755 (2014)
http://dx.doi.org/10.1364/OE.22.007744


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Abstract

Strong modification of spontaneous emission of Eu3+ ions placed in close vicinity to thin and thick gold and silver films was clearly demonstrated in a microscope setup separately for electric and magnetic dipole transitions. We have shown that the magnetic transition was very sensitive to the thickness of the gold substrate and behaved distinctly different from the electric transition. The observations were described theoretically based on the dyadic Green’s function approach for layered media and explained through modified image models for the near and far-field emissions. We established that there exists a “near-field event horizon”, which demarcates the distance from the metal at which the dipole emission is taken up exclusively in the near field.

© 2014 Optical Society of America

1. Introduction

The effects of the local environment on spontaneous emission are commonly discussed in terms of the Purcell effect [1

1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

] accounting for a modification of the photonic mode density and a subsequent alteration of the dipole emission rate [2

2. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Progress in Optics XII, 162–231 (1974).

5

5. W. Lukosz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation,” JOSA 69(11), 1495–1503 (1979). [CrossRef]

]. Depending on the degree of modification of electric and magnetic components of optical modes, electric and magnetic dipoles can be affected in a different manner. This was discussed theoretically [4

4. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” JOSA 67(12), 1607–1615 (1977). [CrossRef]

8

8. Z. Xi, Y. Lu, P. Yao, W. Yu, P. Wang, and H. Ming, “Controllable directive radiation of a circularly polarized dipole above planar metal surface,” Opt. Express 21(25), 30327–30335 (2013). [CrossRef] [PubMed]

] and shown experimentally by observing changes in luminescence spectra of rare earth ions such as Eu3+ [9

9. P. T. Worthing, R. M. Amos, and W. L. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59(1), 865–872 (1999). [CrossRef]

18

18. R. Hussain, C. Whitefield, C. Carroll, J. Vella, A. Urbas, and N. Noginova, “Emission of electric and magnetic dipoles in plasmonic systems,” in CLEO Technical Digest, paper QM4H.7 (2012).

], having both magnetic and electric dipole transitions. It was suggested that Eu3+ ions can be used as a spectroscopic tool for probing the effect of optical magnetic resonance in plasmonic nanostructures [19

19. S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the Interplay of Electric and Magnetic Modes via Fano-Like Plasmon Resonances,” Nano Lett. 11(9), 3927–3934 (2011). [CrossRef] [PubMed]

], and for mapping local distributions of optical magnetic and electric fields in plasmonic metamaterials [15

15. X. Ni, G. V. Naik, A. V. Kildishev, Y. Barnakov, A. Boltasseva, and V. M. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B 103(3), 553–558 (2011). [CrossRef]

]. It was established that losses in nanostructured materials and changes in radiation patterns, which are different for magnetic and electric dipoles, are important factors for these applications [10

10. N. Noginova, R. Hussain, M. A. Noginov, J. Vella, and A. Urbas, “Modification of electric and magnetic dipole emission in anisotropic plasmonic systems,” Opt. Express 21(20), 23087–23096 (2013). [CrossRef] [PubMed]

12

12. S. Karaveli and R. Zia, “Spectral tuning by selective enhancement of electric and magnetic dipole emission,” Phys. Rev. Lett. 106(19), 193004 (2011). [CrossRef] [PubMed]

].

Modification of electric and magnetic dipole emission associated with the presence of metal is an open problem in nano-optics and has recently attracted a lot of attention [12

12. S. Karaveli and R. Zia, “Spectral tuning by selective enhancement of electric and magnetic dipole emission,” Phys. Rev. Lett. 106(19), 193004 (2011). [CrossRef] [PubMed]

, 13

13. S. Karaveli and R. Zia, “Strong enhancement of magnetic dipole emission in a multilevel electronic system,” Opt. Lett. 35(20), 3318–3320 (2010). [CrossRef] [PubMed]

]. If an emitter is placed in the vicinity of an ideal mirror and oriented parallel to the interface, one can expect a reduction of an electric and an enhancement of a magnetic dipole emission normal to the interface due to the boundary conditions for optical electric and magnetic fields [8

8. Z. Xi, Y. Lu, P. Yao, W. Yu, P. Wang, and H. Ming, “Controllable directive radiation of a circularly polarized dipole above planar metal surface,” Opt. Express 21(25), 30327–30335 (2013). [CrossRef] [PubMed]

, 17

17. N. Noginova, Yu. Barnakov, H. Li, and M. A. Noginov, “Effect of metallic surface on electric dipole and magnetic dipole emission transitions in Eu3+ doped polymeric film,” Opt. Express 17(13), 10767–10772 (2009). [CrossRef] [PubMed]

]. However, in very close vicinity to real metals at distances of about 30 nm, the opposite behavior has been recently observed: the emission of the electric dipole was enhanced while magnetic dipole emission was decreased near thin gold films and nano-strip arrays [10

10. N. Noginova, R. Hussain, M. A. Noginov, J. Vella, and A. Urbas, “Modification of electric and magnetic dipole emission in anisotropic plasmonic systems,” Opt. Express 21(20), 23087–23096 (2013). [CrossRef] [PubMed]

, 18

18. R. Hussain, C. Whitefield, C. Carroll, J. Vella, A. Urbas, and N. Noginova, “Emission of electric and magnetic dipoles in plasmonic systems,” in CLEO Technical Digest, paper QM4H.7 (2012).

].

The goal of the current work is to provide a better understanding of the effects of close vicinity of metal on electric and magnetic emitters. Here we restrict ourselves to planar geometry, considering dipoles very close to the surface of thin and thick metal films. The paper is organized as follows. First, we describe an experiment where the distinctly different behavior of electric and magnetic emitters located near thin gold films was visualized in an optical microscope setup. Then, we provide a theoretical description where we show that the contribution of Eu3+ emitters to far-field radiation demonstrates a threshold-like behavior dependent upon the distance between the emitters and the metal surface. In very close vicinity to the metal, all of the energy imparted on the emitter is required to establish a near field image within the metal, leaving nothing for radiation into the far field, which we refer to as being beyond the “near-field event horizon”. Our model establishes a theoretical framework for the estimation of this threshold as a function of the thickness of the metal film. Also we show that it provides an adequate description of the effects observed in far field emission, which was originated from emitters located outside of this “event horizon.”

2. Experiment

Highly luminescent Eu(TTA)3(L18) chromophore material was synthesized in house, following [20

20. K. Wang, L. Gao, and C. Huang, “Optical properties of the highly ordered Langmuir-Blodgett film of a strongly luminescent Eu(III) complex,” J. Photochem. Photobiol. Chem. 156(1-3), 39–43 (2003). [CrossRef]

]. The emission spectrum of Eu3+ has several well-distinguishable spectral lines, Fig. 1.
Fig. 1 Emission spectrum of Eu(TTA)3(L18) amphiphilic complex. The excitation wavelength is 330 nm. Schematic of the levels is shown in insert.
The transition 5D0 - 7F1 with the emission at the wavelength, λ = 590 nm is associated primarily with a magnetic dipole [21

21. J. G. Reifenberger, G. E. Snyder, G. Baym, and P. R. Selvin, “Emission polarization of europium and terbium chelates,” J. Phys. Chem. B 107(46), 12862–12873 (2003). [CrossRef]

] while the rest of the lines are primarily electric dipole transitions, including the strongest line, 5D0 - 7F2 with λ = 611 nm, originating at the same energy level.

The idea behind our experiment was to use the microscope setup where one could simultaneously observe the emission of Eu3+ placed in different surroundings: near thin metal, thick metal, and glass, which would be used as a reference. Then we would record and compare the effects of the different placement on the emission intensity separately for magnetic and electric transitions.

The substrates were fabricated with thermal deposition of gold or silver on a glass substrate through a standard STM mesh, 656-300-AU, purchased from Ted Pella Inc. Such a deposition produced 7 μm x 7 μm square patches of metal with 2 μm distances between each other, arranged in square blocks of ~50 x 50 μm size with 15 μm distances between blocks. The thickness of metal after the first step of deposition was ~50 nm as measured with the Bruker DektakXT profilometer. In order to obtain metal squares of two different thicknesses on the same substrate, we covered a half of the sample, and continued the thermal deposition. After the second phase, the thickness of squares at the exposed part was in the order of 170 nm.

Solutions of Eu(TTA)3(L18) complex and polystyrene in chloroform were mixed in the proportion 1:5. 30-microliter drop of the mixture solution was spread on a water surface. After evaporation of chloroform, a thin polymeric film was formed on the water surface [22

22. F. Monroy, F. Ortega, and R. G. Rubio, “Dilatational rheology of insoluble polymer monolayers: Poly(vinylacetate),” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7629–7641 (1998). [CrossRef]

]. Such a process produced films with practically uniform thickness (which was confirmed with the profilometer after transferring the film to a flat surface). Immersing the substrate with metal squares, the film was transferred to the substrate covering both squares and a space between them. The thickness of the Eu3+ polymeric films was in the range of 30-40 nm.

The microscope images were recorded using Zeiss Imager Z2m microscope equipped with Axiocam camera. The luminescence of Eu3+ was excited with UV light at λ = 325 nm, which was brought to the sample with the optical fiber from the CW He-Cd laser. In order to record the emission signals at electric and magnetic transitions separately, interferometric filters for 610 nm and 590 nm correspondingly were inserted in the recording channel. The signal at 590 nm was relatively weak, that restricted us to use the 20x resolution objective of microscope.

Fig. 2 (a) A substrate with thin gold squares in a standard reflection mode. Eu3+ luminescence: (b) total (c) at 610 nm and (d) at 590 nm.
The images obtained in the sample with thin gold are shown in Fig. 2. In Fig. 2(a), the golden squares seen in the standard reflection mode (using the microscope light source) correspond to square arrangements of small gold patches. The total emission, Fig. 2(b), is brighter on the gold than on glass between them. However, the image clearly shows the presence of the luminescent film on both gold and glass.

Fig. 3 (a) Thick and thin (as indicated with circles) patches of gold on glass in reflected light; (b) and (c) Eu3+ luminescence at 610 nm and 590 nm correspondingly.
Images taken at 610 nm (strong electric transition) and 590 nm (magnetic transition) are shown in Fig. 3(c) and Fig. 3(d) correspondingly. As one can see, the image recorded at the electric dipole transition (Fig. 3(c)) is similar to the image with the total emission (Fig. 3(b)), which can be expected taking into account that the transition at 610 nm contributes of ~70% to the total signal. For the magnetic dipole emission, the contrast between gold and glass is the opposite (Fig. 3(d)): the film on gold is darker than on glass interspacing.

Such a difference in contrasts for magnetic and electric dipole emission exists only if gold is thin (50 nm). At larger thicknesses of metal, both electric and magnetic dipoles show similar behavior. In order to clear demonstrate this, the polymeric film with Eu3+ was deposited onto a substrate having both thick and thin metal patches in such a way that the polymeric film of almost uniform thickness covered both thick and thin metal patches and bare glass.

The image recorded at the electric dipole transition (shown in Fig. 3(b)) shows much stronger emission intensity from the Eu3+ placed on the top of gold squares than that on the glass (inter-square spacing). The character of contrast does not depend on the thickness of gold: gold brighter than glass is seen for both thin and thick patches.

The magnetic transition (in Fig. 3(c)) shows the negative contrast (gold is darker than glass) only for the thin gold (see the bottom circle). The contrast between thick gold and glass was similar to what was observed for the electric transition (gold is brighter than glass, see squares in the top circle).

We repeated the same experiment using a similar substrate having thin and thick silver patches, Fig. 4. In opposite to the observations with gold, the contrast was the same in all cases. For both electric and magnetic transitions, thick and thin silver squares looked brighter than glass, however, the magnetic dipole emission was significantly weaker on the top of thin silver than that on thick silver. Note that non-uniformity which can be seen in Figs. 3 and 4 is due to the combined effects of films roughness, illumination from the side and possibly to a non-uniform distribution of Eu3+ ions in the polymeric films.

3. Theory

Our formulation is based on the dyadic Green’s function approach for layered media [23

23. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105(2-3), 489–504 (1981). [CrossRef]

]. Consider the structure composed of a glass substrate with refraction index ng, a metal film with thickness a and a polymer layer with thickness d and refraction indexnp, containing a dipole separated by distance h from the metal (see Fig. 5). We show that the behavior of the emitters is strikingly different depending on the parameter h.
Fig. 5 Schematic of the structure.

The experiments are performed at CW UV excitation, which implies a steady state condition Puv=Pe+Pm+Pnonem where the excitation power Puvis equal to the power released by the ions in the form of electric dipole emission Peat the transition 5D0 - 7F2, magnetic dipole emissionPm at the transition 5D0 - 7F1 as well as Pnonem released through other radiative and non-radiative channels.

In this paper we use normalized emission rates Fe and Fm defined through Pe=ωeΓ0eFe and Pm=ωmΓ0mFm. Here the spontaneous emission rate for electric and magnetic dipoles in a homogeneous polymer medium are Γ0e=4k03|de|2/(3np2) and Γ0m=4k03|dm|2/(3) [7

7. L. Novotny and B. Hetcht, Principles of Nano-optics, (Cambridge University, 2007).

]. The normalized emission rates are equal to the integrals Fe=0ρ˜e(k)dk and Fm=0ρ˜m(k)dk over the density of states ρ˜(k) per interval dkof the component kof the wave vector parallel to the layers of the structure [23

23. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105(2-3), 489–504 (1981). [CrossRef]

, 24

24. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

]. Note that the integrals not only include the density of states involving radiation of photons, but also the states involving near-field fork>k0. Generic expressions forρ˜e(k)dPe/dk and ρ˜m(k)dPm/dkare provided in the Appendix (please see Eqs. (8) and (10)) and were derived following [23

23. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105(2-3), 489–504 (1981). [CrossRef]

, 24

24. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

].

Formation of the electric dipole image and the dominant contribution of this relaxation channel can be confirmed by the fact that the normalized relaxation rate Fe is directly proportional to h3 for h<10nmas can be seen from Fig. 6(a). Interaction of the electric dipole with its image results in an increased relaxation rate as well as strong quenching of radiation from emitters positioned near metal films.

Interaction of the magnetic dipole with the near-field created by it is different from that of the electric dipole. The dependence of Fm on h approximately corresponds toh0.8, which first of all means that in the plane geometry there is no near-field image in the form of a magnetic dipole. The near-fields created by a magnetic dipole near plasmonic metal nanostructures is a very interesting problem of optical magnetism, which will be considered elsewhere.

The intensity of radiation emitted by the dipoles toward the microscope at an angle θ to the normal of the structure per solid angle dΩ is given by
dIedΩ=PuvPe+Pm+PnonemωeΓ0eρe(θ)=Puvρe(θ)Fe+(Γ0m/Γ0e)Fm+β,
(2)
dImdΩ=PuvPe+Pm+PnonemωmΓ0mρm(θ)=Puvρm(θ)(Γ0m/Γ0e)Fe+(Γ0m/Γ0e)Fm+β,
(3)
where it is assumed thatωmωe, andβ=Pnonem/(ωeΓ0e). Here ρ(θ)is the local density of states involving emission of a photon in the interval of emission angles dθnormalized to the density of photons in the vacuum (see Appendix). In our calculations below, we use Γ0e/Γ0m8 for the ratio between the rates of emission of electric dipole transition (5D0 - 7F2) and magnetic dipole transition (5D0 - 7F1) in free space, which we estimate as ratio of relative areas under the corresponding spectral lines in Fig. 1. We use βas the only fitting parameter for our theory.

The numerators in Eqs. (2) and (3) correspond to the far field formation, while the denominators are responsible for the quenching. To illustrate how the quenching is included into our theory we introduce factorf, which represents the denominators in Eqs. (2) and (3). The physical meaning of fcorresponds to the ratio between the full relaxation rate of emitters on glass to emitters on the metal films. We normalize fby the full relaxation rate on the glass substrate, since this rate is practically independent of h

f=(Fe+(Γ0m/Γ0e)Fm+β)|a0(Fe+(Γ0m/Γ0e)Fm+β).
(4)

The factor fis plotted in Fig. 6(b). It can be seen that for emitters with h<10nm f0. This is due to strong quenching, which was described above. Quenching is also stronger for very thin metal films, where it is effective even for emitters separated by h30nmfrom the metal. The divide between green and red areas in Fig. 6(b) defines what we call the “near-field event horizon”, beyond which emitters cannot radiate and be detected in the far field.

We explain the properties of the observed emission based on these images. The complex factors in front of the amplitudes lead to a lag in the oscillations of the images with respect to the original dipoles. The radiation emitted by the images travels toward the original dipoles and acquires the corresponding phase. At arrival to the position of the original dipole the emission constructively or destructively interferes with the emission from the original dipole. Since we observe the emission in the direction normal to the interface most of the emission comes from dipoles oriented parallel to the interface and this is where we will place our focus in the discussion.

Now let us turn to the magnetic dipole emission. For a magnetic dipole on top of thick metal films enhancement is observed, while emission is decreased on top of thin films. If one reduces the thickness of the metal film to be on the order of the skin-depth ls the reflection coefficient is changed to rp=itanh(a/ls) [28

28. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

] and the far-field image described above is modified, so that its magnitude becomes reduced. Taking this into account the intensity of the magnetic dipole radiation normal to the structure is modified as

|1+itanh(a/ls)e2iφh|21+tanh(a/ls)22sin(2φh)tanh(a/ls).

It can be easily seen that, for example, for φhπ/15 this function represents enhancement for thick metal films als and reduction of intensity for thin films als. It needs to be noted that the reflection characteristics of our actual structure (see Fig. 5) are more complex than the ones we use for the explanations we provide above, first of all, because the emission frequencies of Eu3+ transitions are somewhat detuned from the plasmonic resonance. Another factor is the additional reflections from the polymer-air and metal-glass substrate interfaces.

Now having established the groundwork for the theoretical description we turn to the exact situation with which we are presented experimentally. To find the intensities Ie and Im measured by the microscope, we integrate Eqs. (2) and (3) over the radiative angle from 0 to θm corresponding to the numerical aperture of the microscope NA=0.5using Eqs. (13)-(17) from Appendix. We also average the result over the position h of the emitters within the polymer films. We define the intensity contrast between emitters on metal films and emitters placed directly on the glass substrate as

η(a)=Ie(a)Ie(a=0)1andμ(a)=Im(a)Im(a=0)1
(7)

With this definition a positive value of contrast means that the signal coming from the emitters placed on gold films is stronger than the signal coming from those on the glass substrate. Negative contrast signifies the opposite situation.

The contrast ratiosηandμare shown as functions of the metal film thickness a, for gold and silver, in Fig. 7.
Fig. 7 (a) The contrast ratios η and μ (see Eq. (7)) for electric and magnetic transitions for gold film as a function of film thickness; (b) The same for silver film.
The contrastηis positive for gold films thicker thana20nmand is higher for thicker films, which agrees with the experimental results. One can also see that the contrast ratioμis negative for thin gold films with a70nmand is positive for thicker films. We have placed orange and green dots in Fig. 7 to highlight the theoretical values corresponding to metal thickness, a=50nmanda=170nm, at which the experiments were conducted. It can be easily seen from Fig. 3(b) and (c) that these contrast ratios correspond nicely to the experimental values. At the same time both ηandμare positive for silver films thicker than 20nmin accordance with the experiments shown in Fig. 4(b) and (c). It is through varying the fitting parameterβthat we establish a curve for the functionμshown in Fig. 7(a) that fits the experimental data for gold (Fig. 3(c)), therefore locking down the value forβ=12, which seems to be reasonable for our highly luminescent material. Such sensitivity of magnetic dipole radiation to changes in the optical nanoscale environment can serve as yet another proof of the importance of investigations into the field of optical magnetism. Note that in the current study, the sign of the contrast is clearly demonstrated in different surroundings simultaneously and is in agreement with theoretical results. Experimental estimation of the exact values of contrasts in the dependence of the gold/silver film thickness is the subject of a separate study which will be published elsewhere.

4. Conclusions

In conclusion, we have studied the effects of close vicinity to metal on spontaneous emission of electric and magnetic dipole sources through an optical microscope setup. Distinctly different behavior of electric and magnetic dipoles was demonstrated near gold films of a nanoscale thickness. We described the results theoretically based on the dyadic Green’s function approach for layered media and proposed an interpretation based on modified image models for the near and far-field.

These results can find applications in probing and mapping of optical field distributions in plasmonic systems by spectroscopic methods.

Appendix

The electric local density of statesρ˜e(k)per interval dkof the component k of the wave vector parallel to the layers of the structure can be found to be
ρ˜e(k)=1ωeΓ0edPedk,
(8)
where Pe=ck0/2Im(deG^e(r0,r0)de), andG^is the electric dyadic Green’s function at the position of the emitterr0. Using the Fourier representation of the Green’s function we find
dPedk=ck02np2Re[kkz(de||2k02np22(1+r1se2ikz(dh))(1+r2se2ikzh)1r1sr2se2ikzd+de||2kz22(1r1pe2ikz(dh))(1r2pe2ikzh)1r1pr2pe2ikzd+de2k2(1+r1pe2ikz(dh))(1+r2pe2ikzh)1r1pr2pe2ikzd)].
(9)
Herekz=k02np2k2, r1p and r1sare reflection coefficients from the polymer-air interface for TM and TE polarized radiation, while r2pand r2sare corresponding reflection coefficients for reflection from the metal films ([28

28. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

] has detailed description of reflection from films).

The magnetic local density of statesρ˜m(k)can be found as
ρ˜m(k)=1ωmΓ0mdPmdk,
(10)
wherePm=ck0np2/2Im(dmG^m(r0,r0)dm), andG^is the magnetic dyadic Green’s function. Finally, we find that

dPmdk=ck02Re[kkz(dm||2k02np22(1+r1pe2ikz(dh))(1+r2pe2ikzh)1r1pr2pe2ikzd+dm||2kz22(1r1se2ikz(dh))(1r2xe2ikzh)1r1sr2se2ikzd+dm2k2(1+r1se2ikz(dh))(1+r2se2ikzh)1r1sr2se2ikzd)].
(11)

The intensity of radiation emitted into the air by the electric dipole with moment deand frequencyω=ck0into a solid angledΩat angleθ to the normal in the far-field zone is
dIedΩ=c4π|E(θ)|2¯r2=ωΓ0eρe(θ).
(12)
Here |E|2¯is the electric field at distance r from the sample averaged over the orientation of the dipoles. The spontaneous emission rate in a homogenous polymer medium is Γ0e=43np2k03|de|2 and the local density of states involving emission of a photon into the air in the interval of emission angles dθnormalized to the density of photons in the vacuum for the electric dipole is
ρe(θ)=116πcos2θ(np2sin2θ)(|ts+|2+|tp+|2sin2θ+|tp|2(np2sin2θ)).
(13)
Similarly, the intensity of radiation by the magnetic dipole reads as
dImdΩ=c4π|H(θ)|2¯r2=ωΓ0mρm(θ).
(14)
Here the spontaneous emission rate for a magnetic dipole in a homogeneous polymer medium is Γ0m=43k03|dm|2and the normalized density of states for the magnetic dipole is
ρm(θ)=116πcos2θ(np2sin2θ)(np4|tp+|2+|ts+|2sin2θ+|ts|2(np2sin2θ)).
(15)
The amplitudes of the detected radiation tp,s± in Eqs. (12)-(15) are
tp,s±=t21eiφdh[1±R(a)e2iφh]1+r12R(a)e2iφd,
(16)
R(a)=r23+r34eϕm(a)1+r23r34eϕm(a),
(17)
where phases are given byφx=k0npx, andϕm(a)=2k0εma2a/ls. The skin-depth is equal tols=(k0Reεm)125nmat optical frequencies. The subscripts in the Fresnel coefficients for p-polarization rij=ninjni+nj and tij=2njni+njcorrespond to the notations given in Fig. 5, while the Airy coefficient R(a)represents reflection from the metal film [28

28. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

]. The coefficients tp,s±contain all the information about the environment in which the emitters are located.

Acknowledgments

The work was partially supported by the NSF PREM grant # DMR 1205457, NSF IGERT grant #DGE 0966188, AFOSR grant # FA9550-09-1-0456 and a student research grant from College Office of Undergraduate Research (COUR)at Georgia Southern University.

References and links

1.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

2.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Progress in Optics XII, 162–231 (1974).

3.

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60(7), 2744–2748 (1974). [CrossRef]

4.

W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” JOSA 67(12), 1607–1615 (1977). [CrossRef]

5.

W. Lukosz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation,” JOSA 69(11), 1495–1503 (1979). [CrossRef]

6.

R. R. Chance, A. H. Miller, A. Prock, and R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63(4), 1589–1595 (1975). [CrossRef]

7.

L. Novotny and B. Hetcht, Principles of Nano-optics, (Cambridge University, 2007).

8.

Z. Xi, Y. Lu, P. Yao, W. Yu, P. Wang, and H. Ming, “Controllable directive radiation of a circularly polarized dipole above planar metal surface,” Opt. Express 21(25), 30327–30335 (2013). [CrossRef] [PubMed]

9.

P. T. Worthing, R. M. Amos, and W. L. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59(1), 865–872 (1999). [CrossRef]

10.

N. Noginova, R. Hussain, M. A. Noginov, J. Vella, and A. Urbas, “Modification of electric and magnetic dipole emission in anisotropic plasmonic systems,” Opt. Express 21(20), 23087–23096 (2013). [CrossRef] [PubMed]

11.

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, “Quantifying the magnetic nature of light emission,” Nat Commun 3, 979 (2012). [CrossRef] [PubMed]

12.

S. Karaveli and R. Zia, “Spectral tuning by selective enhancement of electric and magnetic dipole emission,” Phys. Rev. Lett. 106(19), 193004 (2011). [CrossRef] [PubMed]

13.

S. Karaveli and R. Zia, “Strong enhancement of magnetic dipole emission in a multilevel electronic system,” Opt. Lett. 35(20), 3318–3320 (2010). [CrossRef] [PubMed]

14.

S. Karaveli, A. J. Weinstein, and R. Zia, “Direct modulation of lanthanide emission at sub-lifetime scales,” Nano Lett. 13(5), 2264–2269 (2013). [CrossRef] [PubMed]

15.

X. Ni, G. V. Naik, A. V. Kildishev, Y. Barnakov, A. Boltasseva, and V. M. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B 103(3), 553–558 (2011). [CrossRef]

16.

N. Noginova, G. Zhu, M. Mavy, and M. A. Noginov, “Magnetic dipole based systems for probing optical magnetism,” J. Appl. Phys. 103(7), 07E901 (2008). [CrossRef]

17.

N. Noginova, Yu. Barnakov, H. Li, and M. A. Noginov, “Effect of metallic surface on electric dipole and magnetic dipole emission transitions in Eu3+ doped polymeric film,” Opt. Express 17(13), 10767–10772 (2009). [CrossRef] [PubMed]

18.

R. Hussain, C. Whitefield, C. Carroll, J. Vella, A. Urbas, and N. Noginova, “Emission of electric and magnetic dipoles in plasmonic systems,” in CLEO Technical Digest, paper QM4H.7 (2012).

19.

S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the Interplay of Electric and Magnetic Modes via Fano-Like Plasmon Resonances,” Nano Lett. 11(9), 3927–3934 (2011). [CrossRef] [PubMed]

20.

K. Wang, L. Gao, and C. Huang, “Optical properties of the highly ordered Langmuir-Blodgett film of a strongly luminescent Eu(III) complex,” J. Photochem. Photobiol. Chem. 156(1-3), 39–43 (2003). [CrossRef]

21.

J. G. Reifenberger, G. E. Snyder, G. Baym, and P. R. Selvin, “Emission polarization of europium and terbium chelates,” J. Phys. Chem. B 107(46), 12862–12873 (2003). [CrossRef]

22.

F. Monroy, F. Ortega, and R. G. Rubio, “Dilatational rheology of insoluble polymer monolayers: Poly(vinylacetate),” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7629–7641 (1998). [CrossRef]

23.

J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105(2-3), 489–504 (1981). [CrossRef]

24.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

25.

M. Durach, A. Rusina, V. I. Klimov, and M. I. Stockman, “Nanoplasmonic renormalization and enhancement of Coulomb interactions,” New J. Phys. 10(10), 105011 (2008). [CrossRef]

26.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

27.

R. M. A. Azzam, “Transformation of Fresnel’s interface reflection and transmission coefficients between normal and oblique incidence,” JOSA 69(4), 590–596 (1979). [CrossRef]

28.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

OCIS Codes
(160.5690) Materials : Rare-earth-doped materials
(240.0310) Optics at surfaces : Thin films
(240.6680) Optics at surfaces : Surface plasmons
(260.2510) Physical optics : Fluorescence
(260.3800) Physical optics : Luminescence
(260.3910) Physical optics : Metal optics

ToC Category:
Surface Plasmons

History
Original Manuscript: February 18, 2014
Revised Manuscript: March 14, 2014
Manuscript Accepted: March 17, 2014
Published: March 26, 2014

Citation
R. Hussain, D. Keene, N. Noginova, and M. Durach, "Spontaneous emission of electric and magnetic dipoles in the vicinity of thin and thick metal," Opt. Express 22, 7744-7755 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-7744


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References

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  2. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Progress in Optics XII, 162–231 (1974).
  3. R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60(7), 2744–2748 (1974). [CrossRef]
  4. W. Lukosz, R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” JOSA 67(12), 1607–1615 (1977). [CrossRef]
  5. W. Lukosz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation,” JOSA 69(11), 1495–1503 (1979). [CrossRef]
  6. R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems,” J. Chem. Phys. 63(4), 1589–1595 (1975). [CrossRef]
  7. L. Novotny and B. Hetcht, Principles of Nano-optics, (Cambridge University, 2007).
  8. Z. Xi, Y. Lu, P. Yao, W. Yu, P. Wang, H. Ming, “Controllable directive radiation of a circularly polarized dipole above planar metal surface,” Opt. Express 21(25), 30327–30335 (2013). [CrossRef] [PubMed]
  9. P. T. Worthing, R. M. Amos, W. L. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59(1), 865–872 (1999). [CrossRef]
  10. N. Noginova, R. Hussain, M. A. Noginov, J. Vella, A. Urbas, “Modification of electric and magnetic dipole emission in anisotropic plasmonic systems,” Opt. Express 21(20), 23087–23096 (2013). [CrossRef] [PubMed]
  11. T. H. Taminiau, S. Karaveli, N. F. van Hulst, R. Zia, “Quantifying the magnetic nature of light emission,” Nat Commun 3, 979 (2012). [CrossRef] [PubMed]
  12. S. Karaveli, R. Zia, “Spectral tuning by selective enhancement of electric and magnetic dipole emission,” Phys. Rev. Lett. 106(19), 193004 (2011). [CrossRef] [PubMed]
  13. S. Karaveli, R. Zia, “Strong enhancement of magnetic dipole emission in a multilevel electronic system,” Opt. Lett. 35(20), 3318–3320 (2010). [CrossRef] [PubMed]
  14. S. Karaveli, A. J. Weinstein, R. Zia, “Direct modulation of lanthanide emission at sub-lifetime scales,” Nano Lett. 13(5), 2264–2269 (2013). [CrossRef] [PubMed]
  15. X. Ni, G. V. Naik, A. V. Kildishev, Y. Barnakov, A. Boltasseva, V. M. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B 103(3), 553–558 (2011). [CrossRef]
  16. N. Noginova, G. Zhu, M. Mavy, M. A. Noginov, “Magnetic dipole based systems for probing optical magnetism,” J. Appl. Phys. 103(7), 07E901 (2008). [CrossRef]
  17. N. Noginova, Yu. Barnakov, H. Li, M. A. Noginov, “Effect of metallic surface on electric dipole and magnetic dipole emission transitions in Eu3+ doped polymeric film,” Opt. Express 17(13), 10767–10772 (2009). [CrossRef] [PubMed]
  18. R. Hussain, C. Whitefield, C. Carroll, J. Vella, A. Urbas, and N. Noginova, “Emission of electric and magnetic dipoles in plasmonic systems,” in CLEO Technical Digest, paper QM4H.7 (2012).
  19. S. N. Sheikholeslami, A. García-Etxarri, J. A. Dionne, “Controlling the Interplay of Electric and Magnetic Modes via Fano-Like Plasmon Resonances,” Nano Lett. 11(9), 3927–3934 (2011). [CrossRef] [PubMed]
  20. K. Wang, L. Gao, C. Huang, “Optical properties of the highly ordered Langmuir-Blodgett film of a strongly luminescent Eu(III) complex,” J. Photochem. Photobiol. Chem. 156(1-3), 39–43 (2003). [CrossRef]
  21. J. G. Reifenberger, G. E. Snyder, G. Baym, P. R. Selvin, “Emission polarization of europium and terbium chelates,” J. Phys. Chem. B 107(46), 12862–12873 (2003). [CrossRef]
  22. F. Monroy, F. Ortega, R. G. Rubio, “Dilatational rheology of insoluble polymer monolayers: Poly(vinylacetate),” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7629–7641 (1998). [CrossRef]
  23. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105(2-3), 489–504 (1981). [CrossRef]
  24. G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]
  25. M. Durach, A. Rusina, V. I. Klimov, M. I. Stockman, “Nanoplasmonic renormalization and enhancement of Coulomb interactions,” New J. Phys. 10(10), 105011 (2008). [CrossRef]
  26. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  27. R. M. A. Azzam, “Transformation of Fresnel’s interface reflection and transmission coefficients between normal and oblique incidence,” JOSA 69(4), 590–596 (1979). [CrossRef]
  28. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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