I. Theory introduction

A. Fresnel Equations

Since we have decided to build up an plasmonics sensor in which the amplitude of the reflected beam (reflected intensity or reflectance) from gold-dielectric interface is detected, and also a more precise way to detect surface plasmon resonance is to detect phase changing. Where both the theory of reflected amplitude and phase changing are based on Fresnel equations. Hence we would like to introduce the theory for our master project starting from Fresnel equations.

Let us first consider an incident beam at the boundary between two materials with different index of refraction (for example, air: n1 and glass: n2). We will discuss two different conditions for both TM (transverse magnetic) and TE (transverse electric) mode waves.

Figure 1[1] shows the picture of the incident, reflected and transmitted waves at an planar interface for TE (left) and TM (right) mode respectively.

Figure 1. Left: incident wave of TE mode (electric field is perpendicular to the plane of incidence) at the interface; Right: incident wave of TM mode (magnetic field is perpendicular to the plane of incidence). We can see that “E” represents electric field, “B” represents magnetic field, “Xr” represents the reflected components, “Xt” represents the transmitted components.

On the basis of law of reflection and law of refraction (Snell’s law):

  r 

nr sinr  nt sint 

We first introduce the definition of the required boundary condition: the components (both electric field and magnetic field) parallel to the interface should be continuous when crossing the boundary.

The boundary conditions for TE waves:

 E  Er  Et   B cos  Br cos  Bt cost The boundary conditions for TM waves:

  B  Br  Bt   E cos  Er cos  Et cost

Taking account of the relation between electric field and magnetic field:

 c  E B   B   n 

Then the above boundary conditions for both wave modes can be presented as following:

 E  Er  Et TE :   n1E cos  n1Er cos  n2 Et cost

  n1E  n1Er  n2 Et TM :   E cos  Er cos  Et cost

If we further employ Snell’s law to eliminate the angle of refraction θt while introducing the relative refractive index n=n2/n1 as shown below:

2 2 2 ncost  n 1 sin t  n  sin  

In this way we can finally get the reflection coefficient r=Er/E and transmission coefficient t=Et/E for two modes as following:

 E cos  n2  sin 2  r  r   E 2 2 TE :  cos  n  sin   E 2cos t  t   E cos  n2  sin 2 

 E  n2 cos  n2  sin 2  r  r   E 2 2 2 TM :  n cos  n  sin   E 2ncos  t  t   E n2 cos  n2  sin 2 

The above equations (9) and (10) are known as Fresnel equations. For non-planar interface, the scattering losses should be also taken into consideration when calculating both reflection and transmission coefficients.

B. Total internal reflection and evanescent wave

1). Total internal reflection (TIR) After having got the coefficients for both reflection and transmission, we now turn to discuss the energy issue at the planar interface between two materials, that is, the power of incident beam Pi will be separated into reflected part Pr and transmitted part Pt, and the proportion for each part compared with the total energy of the incident wave is called reflectance (represented by R) and transmittance (represented by T) respectively. Here we give their mathematical expression without proof:

2 P  E  R  r  r 2   r   Pi  E 

P cos T  t  r 2  n t t 2  Pi cosi

As we plot the incident angle θ versus R, and take the boundary between air (n=1) and glass(n=1.5) for instance, the reflectance R for both external and internal can be shown as below:

[1] Figure 2. The reflectance of TM and TE modes for both external and internal reflection, nair=1, nglass=1.5.

From Figure 2 we can see the external and internal Brewster angle, or so called polarizing angle, which is -1 expressed by θp=tan (nt/ni), in which nt and ni represent the index of refraction for the material of incident space and transmitted space separately. Additionally, we could also find that under the condition of internal reflection, the reflection coefficient rTM and rTE reaching to unity value not occurs at normal incidence. This -1 phenomenon is known as total internal reflection, in which the corresponding incident angle is θc=sin (nt/ni), the subscript ‘c’ indicates the specific name of this angle: critical angle.

2). Phase change of TIR mode

Let us continue the topic of internal reflection. However, when the incident angle θ>θc, it means sinθ>n, with n=nt/ni, then the expression of reflection coefficient should be rewritten as followings: 2 2 Er cos  i sin   n rTE    E cos  i sin 2   n2

2 2 2 Er n cos  i sin   n rTM     E n2 cos  i sin 2   n2

For (13) and (14) either equation, r could be taken the form of r=±(a-ib)/(a+ib), then the phase of can be expressed by polar form:

ei r    ei2  ei

Where the expression for r (polar form) and β in each mode are presented as followings:

 r  ei2   2 2  TE : 1 sin   n    tan     cos    

 r  ei2  ei2     2 2  TM : 1 sin   n    tan     n2 cos    

Now we take the phase change of the E-field of the reflected wave into consideration with respect to the original phase of the incident wave, and we represent it as φ, then using the reflection coefficient and the wave equation of incident wave, the E-field of the reflected wave now is:

i ik.rt  ik.rt  Er  rE  r e E0e  r E0e 

Hence if we combine equations (16) - (18), we could get the phase change for each wave mode at interval of total internal reflection (θc<θ<π/2):

  sin 2   n2     2  2 tan 1  TE      cos  c    :   2  2 2   1 sin   n   2   2 tan     TM  n2 cos    

3). Evanescent wave However, when under TIR mode, the electromagnetic field should be still continuous at the boundary of two mediums, akin to the transmitted wave, we call it as the “evanescent wave”. We will investigate the properties of evanescent wave by first looking at its wave equation as shown below.

ik t .rt  Et  E0te  We assume that the evanescent wave is propagating at x-z plane as shown in Figure 1, in which the E-field could be presented by x-y coordinate, then we can get:

k t .r  kt sint , cost , 0.x, y, 0  kt xsint  y cost  

For the case of TIR mode, the angle of refraction θt can be presented by:

sin 2  sin 2  cos  1 sin 2   1  i 1  t t n2 n2

So now the exponential factor is shown as following:

sin sin 2  k .r  k x  ik y 1  t t n t n2

For convenience, we could also define a real and positive value:

sin 2    k 1  t n2

Then the transmitted wave can be rewritten as:

sin ixk it t n y Et  E0te e e 

From equation (25) it is obvious that the evanescent wave has harmonic functions with invariable amplitude along x direction, but also decreasing exponentially along y direction. There exists a range that the energy of the evanescent wave will return to the first medium after having propagated at the second medium, this range is called penetration depth, which can be represented by equation (26), in which the wave amplitude is decreased to the 1/e of the original value.

1  y     sin 2  2 1 n2

An exception occurs that the energy of evanescent wave can continue forward propagation, which is realized by placing an extra medium in contact with the medium of the evanescent wave, then the total internal reflection can be frustrated. The most common way to have frustrated TIR is to put two right-angle prism together with the diagonal surface facing to each other, as shown in Figure 3, in this way, the evidence of the evanescent fields, in which the field that leaks through the TIR surface, is provided.

Figure 3. Comparison of TIR and frustrated TIR. C. Optical properties of materials

1). Dielectric a). Polarization of dielectric materials When we apply electromagnetic field (EM field) to dielectric material, there will be tiny displacement for electron regarding the position of nuclei, which will further produce an induced dipole. Then we introduce the dipole moment p which is the product of the displaced charge and the separated distance of negative and positive charge as below:

p  qr 

As we can see, the vector of the dipole moment is pointing from electrons to nuclei. Then we introduce another important notion, the polarization P, which represents the total dipole moment per unit volume, its expression is given by equation (28) as shown below, N is the number of dipole pairs per unit volume, e is the charge amount of a single electron.

P  Ner 

As the magnitude of the nuclei mass is far higher than that of electron mass, we can consider that the electrons are bind by nuclei via elastic force given by Hooke’s law. Furthermore, in an alternating EM field, electrons also oscillate, and the oscillation is actually a damping process because the kinetic energy of electron will decrease when colliding with other electrons. Therefore, we can use Newton’s classical mechanics to interpret the motion of oscillating electron by adding the above conditions into consideration, hence we can get the following equation to describe oscillation model of electron:

dr d 2r  Kr  m  eE  m  dt dt 2

In equation (29), K is the spring constant of the elastic model; m is the mass of electron; γ is a frictional constant, of which reciprocal is the relaxation time (time period between two collisions) of the free electron. Additionally, the Lorenz force (ev×B) for the moving charge can be omitted due to the negligible magnitude of magnetic field compared to E-field.

-iωt Considering E-field and the motion of oscillator as harmonic wave, which can be written as E=E0e and -iωt r=r0e respectively, then equation (29) can be solved as following:

 eE r    m 2  im  K

Therefore the polarization can be expressed by:

 Ne2  P   E   2    m  im  K 

However, the E-field in the above equation actually represents the local field Eloc of dipole, which is the superposition of the applied field Eapp and the field that caused by the interaction with other dipoles, the latter component is given by P/3ε0, therefore: P Eloc   Eapp  3 0

Next we rewrite the expression of polarization as following:

 Ne2  P  P   E     2     m  im  K  3 0 

Now we can see polarization appears at both side of equation (33), before solving the above equation to get the expression of polarization, let us define the resonance frequency of the medium dipole:

2 2 K Ne 0    m 3m 0

Thus the equation for polarization can be written as:

Ne2 / m P  2 2 E  0   i

And the magnitude of P can be presented by:

Ne2 / m P  E  2 2 2 2 2 0    

From equation (36) we can see that when ω«ω0, P has the same sign with E, hence the oscillations of dipoles are in phase with E-field; On the contrary, when ω»ω0, P has the opposite sign against E, hence the oscillations of dipoles have a phase difference of 180° compared with E-field. Furthermore, at resonance frequency (ω=ω0), the polarization becomes maximum, here the damping term (iωγ) can not be negligible now, meanwhile inducing a 90° phase shift between polarization and E-field.

b). Propagation of light waves in dielectric materials Let us consider about the charge density ρ of dielectric material. Normally, the charge in a certain material are made of free charge and bound charge. But the free charge is thought to be zero in dielectric, therefore the charge density of dielectric is simply bound charge density, and it could be also associated with polarization P as shown below:

  b   f  b  0  b    b  P

In the above equation, ρb and ρf are the bound and free charge density respectively. And the same condition is also applicable for current density J as shown:

J  J  J  J  0  J  b f b b  P  J   b t Combined with equation (37) and (38), we can write Maxwell's equations for dielectric as followings:

   P  E     0 B  E    t    B  0  2 E 1 P c B    t  0 t

We assume the dielectric material is homogeneous, then there is a net surface charge density caused by polarization, but the internal charge density is still zero, according to Gauss’s law for E-field,  E  0 . So we can get:

 E   E 2E  2E    B    E      B   t  t

Then Ampere’s law in Maxwell's equations can be rewritten as:

2 2 2 2  E 1  P c  E  2  2  t  0 t

And now we can apply the expression of polarization P using equation (35) into the above equation:

2 2 2 2  Ne   E c  E  1 2 2  2   m 0 0   i  t

i(kz-ωt) 2 Considering E-field as harmonic wave: E=E0e , the solution for k becomes:

2 2 2   Ne 1  k  2 1 2 2   c  m 0 0   i 

Obviously the propagation constant k is a complex number, so k can be further presented by its real and imaginary part: k=kR+ikI. Hence now the E-field harmonic wave can be rewritten as:

ikR zikI zt  kI z ikR zt  E  E0e  E0e e 

2 Therefore kI determines the damping rate of the E-field harmonic wave. Moreover, since AE  I E , in which A and I are amplitude and intensity of E-field separately, then we can get Beer-Lambert law:

z I  I0e 

In which α=2kI is the attenuation coefficient of the medium. Additionally, now the refractive index becomes complex number as well, using the relation: n=(ck/ω), we can get the complex refractive index n=nR+inI (nI is also called extinction coefficient) and also the corresponding relative permittivity εr:  c2  Ne2 1    n  in 2   k 2 1 r    R I   2  2 2    m 0 0   i    Ne2  2  2   Ne2    1 0   i  m 2 2 2 2 2 m 2 2 2 2 2  0 0       0 0     

Let us further discuss the complex refractive index of dielectric, if we plot the complex n derived from equation (46), as shown in Figure 4[1]:

16 Figure 4. Graph of angular frequency ω versus nR and nI. Parameters are chosen as followings: ω0=1×10 /s, γ=1×1014/s, N=1×1028/m3.

From the above graph we can see that nR experiences a drastic rising up and dropping down and meanwhile nI is changing from a negligible number to a significant value when the angular frequency ω is falling into the neighborhood of resonance frequency ω0:

     0 2

The region mentioned above is the region of anomalous dispersion, and nR becomes unit value when it passes through this region to higher frequency. In addition, the physical meaning for resonance frequency ω0 of a dielectric according to the above graph is that, the material suddenly has a great chance to absorb photons when the frequency of incident beam is located at ω0. Moreover, ω0 here for dielectric indicates a related incident beam wavelength around the magnitude of 101 nm, in which the wavelength is rather short compared to visible spectrum.

Normally, for ω«ω0, the damping term of equation (46) can be neglected (γ=0) so that we can get the expression of the refractive index at low frequency: Ne2  1  n2 1     2 2  m 0  0  

In which the refractive index at low frequency for dielectric is found to only have real part. Furthermore, if we rewrite the component in the bracket of equation (48) to series as below:

1 1 1   2  1   2  4   1   1  ...  2 2 2  2  2  2 4  0  0  0  0  0 0 

Then equation (48) can be rewritten as:

Ne2   2  4  n2 1 1  ...  2  2 4  m 00  0 0 

Next if we apply ω=2πc/λ and consider about taking square root for both sides of equation (50), the so called Cauchy dispersion equation is got as below:

B C n  A   ...  2 4

By using Cauchy dispersion equation, it is quite convenient for us to determine the refractive index of different wavelength at low frequency region.

2). metal a). Conduction current in metal On the contrary, in metals, only free electrons exist, no electron bounds to nuclei by elastic force - the force constant K=0, hence electron motion equation of metal can be presented by:

dr d 2r  m  eE  m  dt dt 2

Here we introduce the notion of conduction current density J, which can be defined by:

dr J  Ne  dt

-iωt -iωt Consider the conduction current density J also as harmonic wave, so J=J0e , as well as E=E0e , then we can rewrite the electron motion equation of metal as following:

 Ne2   i   J   E   m 

Here we define the static conductivity σ, in which “static” means frequency ω=0, then we get:  Ne2  J  0   E  E   m 

The above equation is also the description of Ohm’s law for DC condition, finally we present conduction current density in frequency domain:

   J   E  1 i / 

b). Propagation of light waves in metal Let us first rewrite Ampere’s law for metal in Maxwell's equations by adding the form of conduction current density J into it:

E J c2B    t  0

Then we use the conclusion of equation (40) combined with equation (57) to get the following result:

1   2E  1    E 2E        2  2  2   c  t   0c 1 i /  t

i(kz-ωt) Since E-field in the above equation is in the form of harmonic wave given by: E=E0e , next we would like to get the expression of propagation constant k for metal:

 2    k 2   i 0   2   c 1 i / 

In which μ0 is the permeability of vacuum. In addition, it is obvious that the propagation constant k for metal is also a complex number, and especially its coefficients for real part and imaginary part are the same:

  k  k  ik  1 i 0  R I 2

With the complex propagation constant k, the harmonic wave equation for metal has the same form as that of dielectric given by equation (44) before, hence there still exists the damping term ekI z . Then we often define a penetrated depth corresponding to the remained 1/e amplitude of E-field, this depth is specially called skin depth δ, where:

1 2     kI 0

Normally, we can use skin depth to identify the conductivity of a certain type of metal, in which smaller skin depth indicates larger conductivity. c). Plasma frequency Before we start the derivation, we would like to introduce an important notion called “plasmon”: if we compare the free electron gas in metal to the real gas of molecules, when the metal is expected to have fluctuation of electron gas densities, electron gas density waves can be generated, then this phenomena is called plasmon.

Next we introduce the complex refractive index of metal which is derived from equation (59), then we get:

 2  c2 n2  k 2 1 0  c2  2  i

Here we also would like to introduce the notion of plasma frequency, which is given by:

 Ne2  1  Ne2  Ne2 2 2 2      p  0c   0c     0       m  0 0  m  m 0

Hence now equation (62) can be rewritten as:

 2 n2  n  in 2 1 p  R I  2  i

If we plot the refractive index n of metal using equation (64), the resulted graph is shown in Figure 5[1]:

Figure 5. Graph of angular frequency ω versus nR and nI of metal. Here value of parameters are given: 16 14 ωp=1.63×10 /s, γ=4.1×10 /s.

2 2 Theoretically, the crossover of the above graph occurs at    p  . However, because ωp»γ, so the crossover can be regarded as occurring at ω=ωp. The physical meaning for this crossover is that it forms the boundary between optically transparent region and opaque (with high reflection coefficient) region. For ω<ωp, complex refractive index is kept and the light wave is damping in metals; on the other hand, for ω>ωp, the refractive index becomes a pure real number and the radiation can be transparent in metal. Therefore, it can be conclude that above plasma frequency, metals allow EM wave propagation and become transparent, this phenomenon can be also classified as a type of plasmon, the so called bulk plasmon or volume plasmon.

D. Surface plasmon polaritons

1). The wave equation of surface plasmon polaritons Let us first rewrite Maxwell's equations for macroscopic EM field (also known as Maxwell’s equations in matter) as followings:

  D  ext   B  0  B  E     t D  H  J   ext t

In which the equations elaborate the relation among four macroscopic fields as listed below:

 E: electric field;  B: magnetic induction (or magnetic flux density);  D: dielectric displacement (D=ε0εrE);  H: magnetic field (B=μ0μrH, μr is relative permeability).

Additionally, ρext and Jext represent the external charge density and external current density respectively. Here we would like to investigate the wave equations for the medium which is nonmagnetic (hence the relative permeability μr=1) and no external charge (ρext=0) / external current (Jext=0) existed either. Next let us assume that the wave here is a harmonic time-dependence wave, and we also assume the propagation geometry that should be one-dimensional with propagation along x-axis and no spatial variation in x-y plane, the assumed propagation geometry is shown in Figure 6:

Figure 6. Propagation geometry of a planar waveguide under a Cartesian coordinate system.

Then the harmonic time-dependent, one-dimensional wave gives:

  t  i : indicates harmonic time-dependence;

  x  i : indicates wave propagating along x axis, and β=kx is the corresponding propagation constant;   y  0 : indicates homogeneity along y axis. Next, by using the above definitions and assumptions, we further expand the two curl equations from Maxwell’s equations in matter, then we got (for convenience, we would like to replace symbol of relative permittivity εr to ε in the following deductions, and we also define k0=ω/c as the wave vector in vacuum):

  Ey    i0 H x   z  H Ex E  0    iEz  i0 H y  t  z   iEy  i0 H z       H  y  i E   0 x  z  E H x  H   0    iH z  i 0Ey  t  z i H i E    y    0 z  

For TM mode wave, the nonzero components are: Ex, Ez and Hy, hence we can get the wave equation for TM mode:

 2 H y  k 2   2 H  0  z 2 0 y

For TE mode wave, the nonzero components are: Hx, Hz and Ey, hence we can get the wave equation for TE mode:

 2 E y  k 2   2 E  0  z 2 0 y

2). Surface plasmon polariton at single interface Let us first define a most simple geometry that could maintain surface plasmon polaritons (for convenience, we use “SPPs” as the abbreviation of surface plasmon polaritons in the following text), which is a smooth planar interface between a dielectric with positive real dielectric constant ε2 at half space z>0, and a metal with dielectric function ε1(ω) at half space z<0.

In addition, the propagation of waves is along x-direction with evanescent decay in z-direction. Here we would like to give the component of wave vector parallel to z axis for two media separately: ki=kz,i (i=1,2), so now it is possible to know the confined vertical distance for wave propagation in two media which is the reciprocal of kz: z=1/|kz|. Hence the defined geometry is shown in Figure 7:

Figure 7. A simple geometry for supporting SPPs. Firstly we give the solution for the wave equation of TE mode wave:

   ix k z  E z  Ae e 2   y  

  1 ix k2 z dielectric(z  0) : H x z  iA k2e e     0   ix k z  H z  A e e 2  z     0      ix k1z  Ey z  Ae e    1 ix k1z  metal(z  0) : H x z  iA k1e e   0    ix k z H z  A e e 1   z     0

Two components Ey and Hx need to be continuous at the interface, which requires:

Ak1  k2   0 

Since Re[kz]>0, so the above condition is only valid when A=0, hence no amplitudes for waves leading to no SPPs excitation at all. Therefore SPPs can not be excited for TE polarization.

Secondly we give the solution for the wave equation for TM mode wave:

   ix k z  H z  Ae e 2   y  

  1 ix k2 z dielectric(z  0) : Ex z  iA k2e e      0 2   ix k z  E z  A e e 2  z      0 2      ix k1z  H y z  Ae e    1 ix k1z  metal(z  0) : Ex z  iA k1e e    01    ix k z E z  A e e 1   z      01

Two components Hy and Ez need to be continuous at the interface, which requires:

k  2   2  k1 1

Since we have known that Re[kz]>0, so positive ε2 of dielectric needs Re[ε1]<0, which indicates the metallic character of the related medium. Then here comes an important conclusion: the surface waves could only propagate at the interface between two media with opposite signs of Re[ε][2]. Next, by further combining the expression of Hy in the solution with the original wave equation of TM mode wave, we ultimately reach to the key result in this section:

1 2   k0  1   2

The above equation interprets the dispersion relation of SPPs in TM mode at smooth planar interface which is between two media.

3). Dispersion relation of surface plasmon polaritons Now we can get the dispersion relation of SPPs for different modes at the interface between a conductor and an insulator, here we assume that the collision frequency of the conductor(metal) is negligible so that γ=0, which comes out the Drude model for ideal conductor:

 2   1 p  1  2

The plot for whole dispersion relation is plotted in Figure 8[3].

Figure 8. Dispersion relation of SPPs.

From the above plot we can find three modes for dispersion relation:

 Bound mode: the mode which corresponds to SPPs excitation, it is further presented in Figure 9[4]. Under this mode, the propagation constant β is expressed by combining equation (73) - (74), then we can get:

2 2   2   p  kx    2 2  c 1  2   p Figure 9. SPPs in bound modes.

 Quasi-bound mode: theoretically, if we assume the ideal conductor with Im[ε1]=0, then this mode is just corresponding to a frequency gap and the propagation constant β is a pure imaginary number, thus the wave propagation is prohibited. For real metal, this mode is related to the leaky part between radiation modes and bound modes, thus it is called “quasi-bound”. We will discuss about SPPs under the real metal case in next section.

 Radiation mode: as we have mentioned before, this modes indicate the transparency regime, and volume plasmons is excited. In addition, the two components of wave vector kz and kx are both becoming pure real number now.

4). Surface plasmon If we introduce the Laplace equation for electrical potential φ at the interface of SPPs excitation, as shown below:

ix k2 z z  0 : z  A2e e

 ix k1z  z  0 : z  A1e e   2     0

The former two formulas are the solutions of the third formula, we can see that the solution of φ is a kind of wave which is propagating along x axis and exponentially damping along z axis. The reason that we introduce the electrical potential here is that in order to sustain the continuity of φ and its 1st derivative, it needs:

1  2  0 

If we apply equation (77) to equation (73), it can be found that now the surface wave propagation constant β becomes infinity, which leads to the group velocity νg of electron gas to zero:

d    0  g d

Therefore, the mode of this electrostatic phenomenon is called surface plasmon, and it can be fulfilled at the surface plasmon frequency ωsp:

 p sp   1  2

However, for real conductor, we should concern about the interaction between electrons in electron gas, therefore the collision frequency γ can not be zero, thus the relative permittivity ε1(ω) is actually a complex number with both real and imaginary parts being nonzero. Figure 10[5] gives one example for the dispersion relation of real metal.

Figure 10. An example of dispersion curve with damping term γ.

From the above graph the leaky part between radiation mode and bound mode can be seen as we have mentioned before. Now the wave vector at surface plasmon frequency becomes a finite value, and some parameters of surface plasmon can be obtained as below:

 Wavelength of surface plasmon λsp:

2    sp Re[ ]

 Propagation length Lsp along x direction (or so called energy attenuation length):

1 Lsp  2Im[ ] 

 Penetration depth dsp,m in conductor medium:

1 1 1 1  2 dsp,m     k 2 2 k  2  1   k0 1 0 1

5). Excitation of surface plasmon polaritons by prism coupling However, there is no direct excitation of surface plasmon polaritons at planar conductor/insulator interface by incident beam, since for a certain type of dielectric: β>k, in which k is the wave vector of the light at dielectric medium. As a result, when the incident light a dielectric with an angle θ to the vertical axis of the interface, the components of k which is along the interface: kx=ksinθ, is even smaller than β, hence phase-matching is unachievable in this way.

Fortunately, there is one way to realize phase-matching, that is a tri-layer system with the thin metal film at the middle and two insulators of different relative permittivity at two sides. For simplicity, we will set the insulator with lower relative permittivity to be air (εair=1), when the light beam is reflecting between the insulator with higher relative permittivity ε and metallic thin film (with incident angle θ), it will generate the wave vector which is along the interface: kx  k  sin 

Now the in-plane wave vector is bigger than the propagation constant of surface wave: kx>β, the light line of the in-plane wave is located between the light lines of two insulators, as shown in Figure 11[6][7][8]. Therefore, in this way the excitation of SPPs at metal/air interface is achievable.

Figure 11. Excitation of SPPs using phase-matching method. εd is the lower relative permittivity (in our case: air), and εp is the higher relative permittivity (prism).

The most common configuration to achieve the tri-layer structure is the Kretschmann method, in which a metallic thin film is evaporated on the hypotenuse side of a right-angle prism, as shown in Figure 12. The purpose of using prism is to create a rather bigger incident angle than total internal reflection angle on the interface of metal/prism, which is further aimed to have evanescent wave propagation along metal/air interface, thus SPPs propagation can be generated.

Figure 12. Kretschmann configuration II. Simulations for surface plasmon polaritons

A. MATLAB simulation

1). Simulations for pure gold layer a). Outline for simulation Since we have two types of laser source used for SPPs excitation:

 Diode laser: wavelength 795nm, maximum power 40mW;  Helium-Neon laser: wavelength 633nm, maximum power 5mW.

We have also decided to use Kretschmann configuration with a BK7 glass prism, and the Titanium adhesion layer between gold thin film and prism is applied, we set the thickness of this adhesion layer to be constant (3nm). All in all, the thickness of gold layer and the wavelength of laser source are two main parameters which we would like to investigate, the aim for the investigation is to find the most suitable thickness of gold layer with the better laser wavelength so that we can eventually get the best observation result of SPPs.

The criteria for the good observation for SPPs is that the groove of the reflectance graph (x axis: incident angle on gold layer, y axis: reflectance) should be deep enough and not too wide. Firstly, deeper the groove the better contrast between the reflectance at angle of surface plasmon and that of the other incident angles, which means the difference between the reflectances at two vertices of the groove and the reflectance at the bottom of the groove (the minimum value at the angle of surface plasmon) is big enough, then better contrast helps the better observation. Secondly, too wide groove indicates a more wide range of incident angle could have possibility to excite SPPs, therefore it will lead to a worse sensitivity for our sensor.

In addition, we also want to simulate the condition that the prism is surrounded by water instead of air just for comparison, which means we would like to change the subphase to water as well. Hence we finally summarized the parameters to change during simulations:

 Laser source: Diode (795nm) / Helium-Neon (633nm);  Subphase: air (n=1) / water (n=1.33);  Gold layer thickness: 10 - 100;

Note that for different wavelength of incident beam, the refractive index is also changed. Therefore we have searched the refractive index for BK7 prism, Titanium and Gold under the wavelength of 795nm and 633nm respectively (the refractive index of water and air also changes with wavelength, but the difference is so little that could be negligible), which is shown in Table 1. It should be mentioned that these refractive index are from the specific literature, which we have collected them in “Bibliography” section.[9][10][11][12][13]

Refractive index Gold Titanium BK7 glass Diode N 0.18693 3.126 1.5109 795nm K 4.666 4.01 9.2489e-9 Helium-Neon N 0.19591 2.7043 1.5151 633nm K 3.2578 3.7657 1.2126e-8

Table 1. Refractive index of gold, Titanium and BK7 glass for two different wavelengths. b). Process for simulation The simulation is realized by MATLAB GUI (graphical user interface) programming with “uicontrol” module. In this way, we can build up an user interface under MATLAB to real-time choose and input the parameters (subphase, wavelength of laser source, gold layer thickness) which can further change the reflectance. In addition, “uicontrol” module is applied in different way for each parameter:

 Subphase: the pull-down menu with two options (air | aqua);  Laser source: the pull-down menu with two options (Diode-795nm | Helium-Neon-633nm);  Gold layer thickness: the slide bar, the input value is ranging from 10nm to 100nm with a step of 0.05nm;  End calculation: the press-button for termination of iteration, then the parameters which are set at last and the related calculated values (reflectance etc.) will be stored in MATLAB Workspace, which can be further extracted to a .txt or .xls file if needed.

Additionally, we also present the current refractive index of these three materials in real-time on the graph of the interface. So finally the user interface for calculation of SPPs is designed as below:

Figure 13. User interface for SPPs calculation realized by MATLAB GUI programming.

The corresponding MATLAB source code is given in “Appendix” section, which is used to generate surface plasmon resonance. The algorithm is inspired by Masahiro Yamamoto’s online self-study note: “Surface Plasmon Resonance (SPR) Theory”.[14] c). Results of simulation

Figure 14. Simulation result for Helium-Neon laser (633nm) with air subphase. Figure 15. Simulation result for Diode laser (795nm) with air subphase. Figure 16. Simulation result for Helium-Neon laser (633nm) with water subphase. Figure 17. Simulation result for Diode laser (795nm) with water subphase. Figure 14 to 17 have shown all the simulation results for SPPs generation on pure gold layer. The simulations are divided to four parts which investigate the combination of the conditions of two different laser source and two different subphase separately, and the thickness of gold layer is ranged from 10nm to 100nm within each part.

Note that the calculated data from simulation are first extracted to .txt files and then implemented into SciDAVis - the free scientific data analysis and visualization software to plot the reflectance graph (x axis: incident angle on gold layer, y axis: reflectance).

For two different laser sources, we can see that the incident angle of surface plasmon resonance for each wavelengths are totally different. Furthermore, it is also obvious that the dark spot in the reflectance curve of Helium-Neon laser is generally wider than that of Diode laser’s.

For two different subphases, it is shown that there is no obvious SPPs excitation with water subphase. We can only conclude that the gold thin film and the Diode laser with wavelength of 795nm is not suitable for SPPs excitation when water plays the role of subphase.

From the two graph of air subphase, we further choose 35nm to 55nm thickness of gold layer to explore the best thickness for SPPs excitation. We will quantify the criteria we mentioned before by first looking at one graph of reflectance:

Figure 18. Demonstration of the evaluation of SPPs quality.

The parameters marked on the above graph are:

 ΔRx (x=1,2): the reflectance difference between the maximum and minimum value, the incident angle of ΔR1 is smaller than SPPs angle, the incident angle of ΔR2 is bigger than SPPs angle;  Δθ: the difference between two incident angles, in which the two angles correspond to ΔRx/2.

Hence we define the quality index of SPPs Qspp, where: R R 1  2 Q  2 2  spp 

The evaluation results of 35nm to 55nm gold layer of both laser sources are given in Table 2.

Laser source Au thickness ΔR1 ΔR2 Δθ Qspp 35nm 0,91214745 0,63540803 1,7 0,444257657 40nm 0,88757353 0,66845591 1,15 0,67542699 Diode laser 45nm 0,86787727 0,68985055 0,9 0,852984698 795nm 50nm 0,84672059 0,70968995 0,7 1,032606227 55nm 0,82902754 0,72456091 0,6 1,063143108

35nm 0,84877662 0,43690948 4,8 0,127570289 Helium-Neon 40nm 0,81155226 0,48060078 3,6 0,178278703 laser 45nm 0,78264978 0,51021099 2,9 0,222451806 633nm 50nm 0,75215024 0,53811189 2,3 0,269223873 55nm 0,72687003 0,5590118 1,95 0,288376806

Table 2. Evaluation of SPPs quality.

From the above results we can find that SPPs quality of diode laser is far better than that of Helium-Neon laser’s. Moreover, since the inputs of gold layer thickness in simulation are a series of discrete values with interval of 0.05°, thus the evaluation results just roughly indicate the best thickness range, not a precise thickness. Therefore we conclude that in our project, it is better to adopt diode laser and choose gold layer thickness from 45nm to 55nm to excite good quality surface plasmon resonance.

2). Trial of functionalised gold layer surface plasmon resonance simulation Here we just try to simulate SPPs at functionalised gold layer, we would like to say that the simulation is based on several assumptions. Hence we can not use this simulation to guide our experimental part, but can help us to predict some possible phenomenon of experimental results. Some key points of this simulation are highlighted as shown below:

 Since we can not find the exact refractive index of the material for functionalization - Cyclam (1,4,8,11-tetraazacyclotetradecane). Fortunately, we have found a predicted value of Cyclam[15], where: n=1.43, and we also assume that Cyclam simply adheres on gold layer.  The thickness range of Cyclam on gold layer is unknown, and is probably depending on the concentration of Cyclam solution. Therefore we choose four different order of magnitude of Cyclam layer thickness: d=5nm, 50nm, 500nm, 5μm.  We will still use the MATLAB source code for pure gold layer SPPs generation to do functionalised gold layer simulation, in which we just need to add 5th layer to the configuration, and the assumed refractive index and thickness of Cyclam should be defined as well.  The gold layer here is chosen to be 50nm, and diode laser is applied. We also plot surface plasmon resonance for pure gold layer just for comparison.

The simulation results are presented in Figure 19. Figure 19. Simulation results for pure and functionalised gold layer with different Cyclam thickness.

From the above results, we can see that as Cyclam thickness increases from 5nm to 500nm, there exists only one resonance frequency for each thickness. However, when the thickness of Cyclam reaches 5μm, multi resonance frequencies occurs. Unfortunately, we can not give a reasonable interpretation for this result due to the lack of theoretical knowledge. It is worthy to making investigation further on this phenomenon after this project.

B. MEEP simulation

1). Brief introduction and installation of MEEP In addition to MATLAB simulations, we also try to use MEEP to do surface plasmon resonance simulations. MEEP (MIT Electromagnetism Equation Propagation) is a free software under GNU/Linux system specially used for finite-difference time-domain (FDTD) simulation. It contains the packages for photonic calculation algorithm, and the user has to call the specific algorithm by coding in certain programming languages to get the raw data of simulations. It supports the libraries of C++, python and Scheme. Here we decide to use Scheme programming language, which is a type of functional programming, to write the code for photonic simulation, then the source code will be saved in .ctl file. However, in order to run simulation programs in MEEP, we have to firstly install a type of Linux distributions, here we choose to install VMware player first, which is a free platform (this is different from VMware workstation, which is more powerful and requires payment) for virtual machines. Then we choose to install one of the most common Linux distributions called Debian, which the newest stable release (Debian 7.8 “wheezy”) is installed. The reason we choose to use Debian Linux is because there is already prepared a precompiled packages of MEEP software under Debian Linux, we just need to input: apt-get install meep h5utils[16] under Root Terminal window in the system, and all the needed packages can be installed. Note that except for MEEP package, other packages are also needed to assist the simulations, for example, we need packages to form .gif dynamic map or plot the photonic graph.

After the .ctl file is written. We can run the .ctl file under Root Terminal window of Debian linux. After the source code is finished running, one can further extract the data, plot the graph and draw pictures by input the specific commands under the terminal. Some common-used commands for MEEP is summarized as following:

 meep filename.ctl |tee filename.out; Execute .ctl file and save the compile results in .out file.  grep parameters: filename.out > filename.dat; extracte the specific parameters from the compile results and export them into data file.  h5topng filename.h5; Convert .h5 file to .png format picture. Normally, when compiling .ctl source code, MEEP will generate an HDF5 output file (.h5).

The coding interface of .ctl file under Debian Linux is shown below:

Figure 20. Coding interface under Debian Linux. 2). Code structure of MEEP Normally, the parameters (refractive index, polarization, permittivity, etc) of materials used for MEEP simulation have to be defined by users, except for air, since we can just use the predefined optical parameters of air in MEEP. Here we have to define the parameter of gold layer, the adhesion layer using Titanium and BK7 glass. For two metals (Au & Ti), we would like to apply a more complicated Lorenz-Drude model[17][18], in which the dielectric function ε(ω) is the superposition of inter-band εinter(ω) and free-electron εfree(ω) with several resonance frequencies, the corresponding equations is presented below:

             int er   free   2   p   free  1     i0  k 2  f j p  int er    2 2  j1  j   ij

The parameters in above equations are:

 Γ: the damping coefficient;  Ωp: plasma frequency specially for the condition of inter-band transitions;  ωp: plasma frequency for free electrons;  f: strength of oscillators.

The values of the above parameters are summarized as below:

j 1 2 3 4 5 6 Omega ωp,j 1e-20 0.33472 0.66944 2.3947 3.4714 10.743

Gamma Γj 0.042747 0.19438 0.27826 0.7017 2.0115 1.7857

Sigma σj 4.0314e+41 11.363 1.1836 0.65677 2.6455 2.0148

Table 3. Parameters for a complex Lorenz-Drude model of gold.

j 1 2 3 4 5 Omega ωp,j 1e-20 0.62669 1.2461 2.0236 1.5671

Gamma Γj 0.066137 1.8357 2.0309 1.3413 1.4211

Sigma σj 5.1166e+40 79.136 8.7496 1.5787 0.014077

Table 4. Parameters for a complex Lorenz-Drude model of Titanium.

For the definition of the optical parameters of BK7 glass, the Sellmeier Equation is applied[19], which is specially used for computing the refractive index of transparent media, the equation is presented as below:

2 2 2 2 B10 B20 B30 n 0  1 2  2  2  0  C1 0  C2 0  C3

The coefficients Bi and Ci for BK7 glass is presented as below:

Coefficient B1 B2 B3 C1 C2 C3 Value 1.03961212 0.231792344 1.01046945 6.00069867e-3 2.00179144e-2 1.03560653e2 Table 5. Parameters for Sellmeier equation of BK7 glass. Here we also summarize some key components that we should define when coding the simulations:

 lattice: the dimensions of the frame for the simulation, for example, if we want to define the lattice of a cylinder waveguide, we should define the length and diameter of the cylinder;  geometry-list: determine where we should place the certain type of the material, for example, we have to define the size and center for each material in 3-dimensions;  Resolution: the resolution for the simulation, which determines the precision of the simulation results, normally we set it from 10 to 50;  Source: normally we have three different sources to use, continuous source, user-defined source and Gaussian beam source. In our simulation, we adopt Gaussian beam source, in which we have to further define the center frequency, bandwidth and the position of the Gaussian beam.  PML thickness: PML is the abbreviation of “perfect-match-layer”, this layer is defined to 100% absorb the incident wave in order to pretend reflection. Normally we will place this type of layer along the boundary(lattice) in the simulated condition to make sure the beam will not reflected to the configuration again so that the precision of the simulation can be guaranteed.

3). MEEP simulation results a). Dispersion relation We have tried to do simulations to get the dispersion relation at Au-Bk7 glass interface (in this simulation, Titanium adhesion layer is not included). For comparison, we also plot the corresponding theoretical solutions of this dispersion relation, in which a simple MATLAB code is applied, then we extract the results to a .dat file. On the other hand, for MEEP simulation, first we execute the .ctl file and extract the complied results to .out file, then we further extract the data of frequencies to a .dat file, finally we plot the values of two .dat file in on graph using gnuplot under Debian Linux. The Scheme source code (.ctl file) for MEEP simulation and the corresponding theoretical solutions using MATLAB code are presented in “Appendix” section. The The graph of both theoretical and simulation values of dispersion relation is shown as below:

Figure 21. Theoretical solution and Simulation result of dispersion relation at gold-BK7 glass interface. Unfortunately, it seems like the simulated dispersion curves for different resonance frequencies are not confined to the stable value (ωspp), it is worthy to do more research on how to use MEEP to demonstrate more precise simulations.

b). Plane wave interactions with metal-dielectric interface We also try to simulate the condition that the plane wave is interacting with the gold-BK7 glass interface, this time Titanium adhesion layer is applied. We set the incident angle of of plane wave to be π/4 to see the resulting E-field strength distribution. A Scheme code (.ctl file) is firstly compiled under the Root Terminal window of Debian Linux, and then the compiled results will be extracted to a HDF5 file (.h5 file), then the program will automatically export the data of .h5 file to draw the .png picture showing E-field strength distribution. The Scheme source code has been added to “Appendix” section.

For comparison, we first give a picture which show the pure plane wave propagating in air with an incident angle π/4 to the boundary. Note that more red color means the E-field strength is reaching closer to the positive maximum value, while more blue color means the E-field strength is reaching closer to the negative maximum value. Then we make the picture which shows the E-field strength when the plane wave is interacting with the gold-BK7 glass interface with an incident angle of π/4. In Figure 23, we can see the horizontal white line boundary in the middle of the picture, which refers to the Au + Titanium layer, the upper space from the boundary is BK7 glass, while the space below the boundary is air. Unfortunately the simulation result fails to demonstrate a well-organized confined E-field distribution along two sides of the interface. We assume that the reflected and transmitted waves may have more complex interaction or maybe some nonlinear photonic phenomenons occur. In addition, the code aimed for this simulation should be further modified as well.

Figure 22. Plane wave propagating in air.

Figure 23. Plane wave interacting with gold-BK7 glass interface. III. Experimental preparation

A. Optical setup

1). Overview At first Helium-Neon laser source (λ=633nm, 5mW) is used, the optical setup is shared by two projects, the laser beam is divided by a beam splitter used for two projects separately. The configuration of the optical components is rather compact. Soon after the Helium-Neon laser is approved to be not suitable for SPPs excitation for 50nm thickness gold metal layer, we build up the new optical setup using Diode laser source (λ=795nm, 40mW), which is the optical setup we have used until the master project is finished, this time optical components are placed within wider intervals, which facilitates to have more free space to add extra optical components in order to try more assumptions and experiment. For the last part of the project, the optical sensor is used to detect Cadaverine molecule, since Cadaverine is irritant and toxic, the whole optical configurations are moved to the lab with fumehood installed in.

2). Configuration overview Here we would like to show our ultimately adopted optical configuration used for SPPs excitation, in which the two key components are chosen: 795nm-wavelength Diode laser and BK7 prism with 50nm gold layer deposited on. Figure 24 and Figure 25 present the sketch diagram and the real picture of the whole optical setup respectively. Note that the serial numbers in the below two figures should be corresponded.

Figure 24. Sketch diagram of the optical setup

Figure 25. Real picture of the optical configuration 3). Components description a). Diode laser source The picture of the highly sophisticated Diode laser source generator is shown below. The procedures for starting the laser generator should be noticed:

Step 1: Unlock the laser generator by clockwise turn the key at the backside; Step 2: Press the yellow button at the left bottom of the front; Step 3: Press the black button beside the temperature display panel to switch it to “T set” mode, check the set temperature (in our case Tset=23.3°C); Step 4: Wait until the real-time-display temperature to be stable at Tset, now the green indicator light under the label “Temp ok” is on, which indicates now we can open the laser beam; Step 5: Press the red button under the label “LD on”, laser beam is turned on, switch the knob which is above the “LD on” label to set the current of the laser beam (in our experiments, the current is set to 100mA).

Figure 26. Control panel of the Diode laser source beam generator

b). Half wave plate Let us first talk about the principle of half wave plate. For some crystal structures, where the atoms are arranged in a certain order, different included angle between E-field vector and the crystal axes may cause different refractive index of the incident beam, therefore now the multiple resonance frequencies of the material are determined by different crystal polarization.

When the medium material with right asymmetric crystal structure is chosen, one crystal axis (fast axis) which supports the fastest wave propagation speed, and the other axis (slow axis) which supports the slowest wave propagation speed will have a π/2 included angle. Therefore, when an unpolarized light beam is propagating through such an asymmetric crystal structure medium, double refraction will occur, which is known as “birefringence”, as shown in the left picture of Figure 27, indicating the range of the refractive index.

This physical phenomenon can be used to design the wave plate. The wave plate is made of the above mentioned material which can induce birefringence effect. If two waves with the same angular frequency and the same phase but different in polarization, in which one is parallel to the fast axis and another is parallel to the slow axis, are propagating perpendicularly through the wave plate. The phase difference between the faster wave (along fast axis) and slower wave (along slow axis) can be expressed as:

n  n L   slow fast  c

The equation should be Where Γ is the phase difference between the fastest wave and the slowest wave, L is the thickness of the wave plate. When Γ equals to π, the wave propagating along slow axis will have a half wave retardation compared with the wave propagating along the fast axis, therefore now the wave plate is a half wave plate. Note that wave plate is designed specifically for a certain wavelength, here we choose the λ/2 plate for λ=800nm.

If we further let a plane-polarized wave beam propagating perpendicularly through the half wave plate, the polarization of the wave can be divided into two components which are parallel to the fast axis and slow axis respectively. Let us track a fixed point on the wave, before penetrating through the half wave plate, the vector of this point might be the vector sum of the positive maximum of the wave components along both fast axis and slow axis. Since the wave component which is propagating along the slow axis will have a half wave retardation (180° phase difference) compared with the other one propagating along the fast axis, now the vector on the same point is the vector sum of the positive maximum of the wave component along fast axis and the negative maximum of wave components along slow axis as shown in the right picture of Figure 27.

Figure 27. Schematic diagrams of birefringence effect (left)[20] and half wave plate (right)[21].

In Figure 27, θ refers to the included angle between the polarization of the incident wave and the fast axis, we can see that after passing through the half wave plate, the polarization of the incident wave has a variation of 2θ, thus the polarization of the incident wave beam has changed. As a consequence, we can change θ by rotating the half wave plate in order to set our desired polarization of the wave beam.

c). Beam splitting polarizer The polarizer is used to divide the unpolarized light wave into TM mode and TE mode components. In our optical configuration, the polarizer is actually a beam splitting polarizer cube glued into the center of an optical rotation mount. Normally, a beam splitting polarizer consists of two prisms adhering together, the gap between the prisms is usually filled with one type of transparent glue or just air gap, the refractive index of the gap material should be smaller than that of prisms’ anyway. The prisms are made from birefringent material.

When unpolarized light wave propagating through the beam splitting cube, as shown in Figure 28[22]. The p-polarized wave will propagate along slow axis and s-polarized wave will propagate along fast axis, since nslow>nfast, p-polarized wave has a bigger total internal reflection angle than that of s-polarized wave’s, where -1 θc=sin (ngap/nslow,fast), therefore at the interface between the gap and the prism, the incident angle θi of both wave modes is specifically designed, so that s-polarized wave will have total internal reflection and the direction of propagation is changed, on the other hand, the incident angle θi is still smaller than the TIR angle of p-polarized wave, therefore the p mode wave will still propagate along the original direction.

Figure 28. Beam splitting polarizer.

For our optical configuration, the wave beam coming out from the polarizer will be pure TM mode wave beam (p-polarization). In addition, by rotating the λ/2 plate we can change the polarization of the incident laser beam to be totally parallel with the slow axis on beam splitting polarizer, in this way the maximum fraction of TM wave will be generated, and now the coming out TM wave beam will certainly get the maximum power as well.

d). Convex lens Since the angle range of surface plasmon resonance excitation is quite narrow, the black line in the reflected light spot on a screen is sometimes too narrow to recognize. Therefore a convex lens can be applied before the prism, the distance between the convex lens and the prism glass surface should be around the focal length of the lens, then the laser beam will be first focused on the gold-prism interface and then diffusing to the CCD camera, in this way, the black line of SPPs can be distinguished on the screen. The principle of using convex lens in our optical configuration is shown below:

Figure 29. Comparison of SPPs excitation with and without convex lens.

e). Absorptive filter In order to get the clear image of the light spot with SPPs black line in the middle, a Thorlabs neutral density filter (NE10A Ø25 mm Absorptive ND Filter with Optical Density=1.0) is applied. The neutral density (ND) filter can reduce the intensity of incident light within a long range of wavelength, especially the intensities for different wave lengths will be reduced equally. Therefore we can utilize this property of the neutral density filter to reduce the reflected light intensities, in which the corresponding incident angles are closely in either sides of SPPs angle. In this way the light intensities between the SPPs black line on the screen will be weakened, causing the SPPs black line easier to be recognized. The optical property of this ND filter is presented in Figure 30[23] which is obtained from Thorlabs official website. From the following transmission graph we can see that the transmission coefficient at λ=800nm is around 13.5%, which means around 86.5% intensity of the reflected beam has been filtered using this neutral filter.

Figure 30. Transmission coefficient graph of NE10A Ø25 mm Absorptive ND Filter.

4). Optical setup for Helium-Neon laser source Here we also give the original version of the optical configuration using Helium-Neon laser source, note that this setup is originally shared by two master projects. The real picture of the optical setup based on Helium-Neon laser is shown in Figure 31, in which the marked components and the green light path are applied by our project.

Figure 31. Optical setup based on Helium-Neon laser source

The components marked in the above picture are listed : 1. Helium-Neon laser source (λ=633nm); 2. Mirror; 3. Polarizer; 4. Beam splitting cube; 5. Mirror; 6. Half wave plate; 7. Rotation mount with prism; 8. Ruler used for beam height calibration; 9. CCD camera. Note that before assembling the polarizer (component No.3), the laser gun of Helium-Neon laser source should be rotated in order to have two same power beams after the incident wave propagating through the beam splitting cube. Figure 32 shows the Helium-Neon laser source used in the original optical setup.

Figure 32. Helium-Neon laser source generator.

B. Gold thin film deposition on prism

1). Prism cleaning The cleaning procedures for BK7 glass prism is summarized below, each steps is shown in Figure 33 as well.

Step 1: Put the prism into a beaker of Acetone at least 15 minutes; Step 2: Put the prism in a second beaker filled with Isopropanol, use ultrasound to clean the prism surface at least 10 minutes; Step 3: Rinse the prism with distilled water, then use nitrogen to dry the prism.

Figure 33. Procedures for prism cleaning. 2). Metal thin film deposition on prism a). Prism mounting The E-beam system (Cryofox Explorer 600) is used to deposit metallic thin film on the hypotenuse surface of BK7 prism. Before the deposition starts, the prism should be mounted and stabilized with a holder. Since prism can not be mounted with a planar holder, here we choose to use a bracket which has the vertical wall to stick the prism, then we use tapes to fix the prism on the wall of the bracket, as shown in Figure 34.

Figure 34. Mounting the prism.

b). Titanium and gold layer deposition First, a 3nm thickness Titanium layer will be deposited on prism surface as an adhesion layer, following by a 50nm gold layer deposition. The recipe on the Cryofox system is shown below:

Figure 35. E-beam Ti+Au deposition recipe on Cryofox system screen.

The procedures for operating the Cryofox Explorer 600 is summarized as below: Step 1: Set the needed recipe, always remember to “Append Recipe” when altering it, press “Use Recipe” until the check-mark appears. Step 2: When Cryofox is in standby mode, the pressures in two chambers are: Load-lock chamber: ~10-3 mbar; Main chamber: ~10-7 mbar. Step 3: ”Coating Process”; when the load-lock chamber pressure goes to ~103 mbar, open the load-lock chamber, put the sample in. Step 4: “Start / Stop Process”, use hands to push the load-lock chamber. Step 5: When the pressure of load-lock chamber goes down to ~10-3 mbar, it will be detected by a sensor in main chamber. Step 6: The system itself will choose the certain mode (E-beam / DC Sputter / RF Sputter) regarding the recipe. Step 7: Load-lock chamber will connect to main chamber regarding the certain mode (E-beam / DC Sputter / RF Sputter). Step 8: When pressures of both load-lock chamber and main chamber together go down to 5×10-5 mbar, press “Start Layer”. Step 9: Two chambers’ pressure will go up to ignition pressure. Step 10: When deposition finished, system will automatically vent, then take out the sample, close the load-lock chamber. Step 11: Press “Coating Process” (light off), and “Standby Vacuum” (light on).

One thing should be highlighted is that when mounting the prism to the vertical wall of the bracket, the upper end of the vertical wall should be aligned with the edge of the hypotenuse surface of the prism. If the edge of the prism is lower than the upper end of the wall, it will cause anisotropic scattering of gold atoms during E-beam deposition, as shown in the left picture of Figure 36, hence the nonuniform thickness gold layer and even the contamination of gold layer might happen. An unsuccessful gold deposited prism is shown in the right picture of Figure 36, we can see some contamination occur on the part of the gold layer marked by blue frame.

Figure 36. Investigation of nonuniform gold layer thickness and contamination.

C. Determination of SPPs angle on pure gold layer

1). Preparation The position for placing the BK7 glass prism on the rotation mount should be chosen carefully, in which to make sure the rotating angle of the rotation mount is exactly the rotating angle of the incident beam on the prism. The position for the prism on the rotation mount is shown in Figure 37. Note that the purple-line triangle refers to the position for placing the prism. Figure 37. The position for placing the prism on the rotation mount.

The calculation for the incident angle on the gold-prism interface according to the incident angle read from the rotation mount is applied. Note that we would like to build up an .xls table file to record the raw data and do computations, the recorded angle from the rotation mount is deg form and .xls file supports rad form, therefore the transform between two forms should be noticed. Figure 38 shows the principle of incident angle calculation and the corresponding equations is shown below:

          sin 1      180 180     sin 1     3  4  n     prism    

The parameters in the above equation are:

 θ⊥: The perpendicular incident angle on prism, indicating a 45° incident angle on gold layer;

 θ1: The incident angle on prism;  θ3: The incident angle on gold-BK7 glass interface.

Figure 38. Geometry for calculating the incident angle on gold layer. 2). Finding the SPPs angle by power meter First we should determine the rotation angles of the λ/2 plate and the polarizer. Normally, the rotation angle for the polarizer is around 90° (also 180° is suitable). Then the power meter can be placed after the polarizer, by rotating the angle of the λ/2 plate to find the maximum power measured by the power meter, we can roughly determine the rotation angle of the λ/2 plate. Note that after introducing the convex lens and absorptive filter into the light path, in order to get the clearest real-time video of the black line at SPPs angle, the polarizer and the λ/2 plate will be further adjusted precisely. Hence finally the rotation angle for polarizer is determined to be 89°, and 239° for λ/2 plate.

Next we can roughly find the angle at SPPs by checking whether there is a red light spot appearing on the gold layer when rotating the rotation mount, as shown in Figure 39, in which the red light spot indicates the confinement and propagation of surface wave at SPPs incident angle.

Figure 39. Red spot light on gold layer indicating the surface plasmon resonance.

Then rotating the rotation mount to a smaller angle until the red spot light disappears. Now we can place the power meter on the other side of the prism surface with respect to the prism plane of the incident wave, and increase the angle of the rotation mount slowly for each step, the accuracy of the rotating angle can be both 0.2 degree (12’) or 0.04 degree (2’24’’), the reflected light intensity is recorded by power meter, as shown in Figure 40. Note that we do not apply the absorptive filter and the convex lens when during the section of determination the SPPs angle, since convex lens will change the light distribution on the cross-section profile of the Gaussian beam (the laser beam is actually one type of Gaussian beam), hence causing the measurement results to be inaccurate. Besides, the light intensity measured behind the absorptive filter is quite sensitive to the included angle between the reflected beam and the planar of the filter, thus it is quite inconvenient to make measurements when applying the absorptive filter.

Figure 40. Measurements of the reflected light intensity by power meter. Note that the mainframe and the detector has been marked in the above picture, the reading on the screen of the mainframe is always fluctuating since it is quite sensitive to the surrounding natural light. Hence one should move the detector slightly to find the maximum reflected intensity and wait until the reading is stable value then record the date for each time measurement.

One thing should be also mentioned is that we choose to measure and calculate the normalized reflected intensities instead of measured reflectance, since part of the laser beam energy will be transformed to thermal energy during propagation, therefore the measured reflectance does not have so much reference value.

We have done two measurements in order to find SPPs angle for Diode laser source, the related graphs are shown in Figure 41.

Figure 41. The 1st and 2nd SPPs measurement on pure gold layer using Diode laser source (795nm).

It can be seen that the SPPs angle found in two measurement are slightly different, and we also compared the two measured values with the simulation value (Diode laser - subphase: air - gold layer thickness: 50nm):  Simulation value: θspp=41.6°; st  The 1 measurement value: θspp=42.43°, with polarizer angle (97°) and λ/2 plate angle (220°); nd  The 2 measurement value: θspp=42.5°, with polarizer angle (89°) and λ/2 plate angle (239°).

Note that the rotation angles of polarizer and λ/2 plate are different between the 1st and 2nd measurement, we assume that these differences of polarizer and λ/2 might be the reason to explain why the SPPs angle got from two measurements are not critically equal. Furthermore, the simulated value of SPPs angle has slightly less than 1 degree difference compared with two measured values, in which the corresponding explanation can be diverse, for example: the deposited gold layer might not ensured to be 100% pure; the way we determine the 45° incident angle on gold layer is not absolutely right; the refractive index of air should be altered with the changing laser source wavelength in the simulation, etc.

In addition, the surface plasmon polariton excited by Helium-Neon laser source is also measured, as shown in Figure 42.

Figure 42. SPPs excitation on pure gold layer using Helium-Neon laser (633nm).

This time the measured angle of SPPs (43.97°) is quite close to related simulation value (43.7° for 50nm gold layer thickness). What’s more, the measurement and simulation of SPPs excited by Helium-Neon laser both demonstrate that the reflected intensity contrast at SPPs angle and other angles is smaller than that of the excitation by Diode laser, in other words, the gaps in the graph of both simulation and measurement are still wider than that of Diode laser. Therefore it can be totally confirmed that the quality of SPPs excitation using Helium-Neon laser is worse than that of Diode laser.

3). Video collection of the SPPs spot light using CCD camera The CCD camera is used as an image sensor to record the real-time video of the light spot shooting at its photo-sensitive array, then the binary data collected by the camera will be transported to the PC via a special data cable, the video is recorded in the PC using UC480 Viewer software, the process is shown in Figure 43. Note that the light intensity will be quantified as the pixel intensity in the software.

The light spots generated in different situations are recorded. Firstly the video of light spot without convex lens or absorptive filter is recorded. Then two videos are recorded where convex lens and absorptive filter are singly added into the light path. And three types of convex lenses with different focal length (50mm, 75mm and 100mm) are chosen to find the best solution. Figure 43. Video collection for SPPs light spot by CCD camera and UC480 Viewer user interface on PC.

Firstly the comparisons are made for four different conditions, note that the focal length of the used convex lens here is 50mm, the focal point is roughly adjusted on the surface of prism.

Figure 44. Collected images of light spot reflected at SPPs angle in 4 different conditions

The optical configuration for each picture in Figure 44 are given as following:

 SPPs excitation reflected light spot 1: without convex lens and absorptive filter;  SPPs excitation reflected light spot 2: only with absorptive filter;  SPPs excitation reflected light spot 3: only with convex lens;  SPPs excitation reflected light spot 4: with both convex lens and absorptive filter.

We can see that when simply adding the absorptive filter to the light path, the contrast ratio of the light spot is strengthened, in other words, the black-colored part in the image now becomes darker compared with picture 1. If we simply add the convex lens, the size of the light spot will be enlarged as shown in picture 3, but the gray level of the dark part is still too low. Then by adding both absorptive filter and convex lens, we can eventually get the high contrast SPPs light spot with black line (indicating the surface plasmon) in the middle. Also, images of light spots with convex lenses of different focal lengths are captured and investigated, as shown in Figure 45, in which picture 1 to 3 are using 50mm 75mm and 100mm focal length convex lenses respectively.

Figure 45. SPPs excitation light spots of 50mm 75mm and 100mm focal length convex lenses.

Note that the distance between each convex lens and the prism is roughly controlled around corresponding focal length. We can see that the convex lens with 50mm focal length result in the best SPP light spot image since it has the biggest amplification factor among these three lenses when the light path is limited.

Moreover, when using isopropanol to distill at the red spot on the gold layer during SPPs excitation, now the current 2nd medium is isopropanol instead of air, following by the change of refractive index of the 2nd medium, then the surface plasmon frequency ωspp and the wave vector β=kx propagating along gold-air interface have also changed, hence eventually there will be a different SPPs angle for this area, namely the black line in the light spot will disappear since this angle is currently not the SPPs angle. However, after isopropanol has been evaporated at all, the refractive index at gold-air interface has been recovered, and SPPs excitation occurs again, so the black line will appear again in the light spot as well, as shown in Figure 46.

Figure 46. SPPs light spot distilled with isopropanol (left) and then isopropanol is evaporated (right).

Particularly worth mentioning is that we can use the light spot of SPPs excitation to examine the purity of gold layer. Figure 47 gives the comparison between two SPPs light spots excited at different areas on the gold layer, in which gold layer on these two areas have obvious difference in purity. We can see that purer gold layer can result in better contrast of SPPs spot light with black line in the middle.

Figure 47. Comparison of two SPPs light spots related to difference gold layer purity. In the end, we also would like to give two graphs of reflected intensities at SPPs angle, as shown in Figure 48, the 1st graph simply applies convex lens (with 50mm focal length), and SPPs are excited by using both convex lens and absorptive filter in the 2nd graph.

From the 1st graph, we can see that the power intensity in the cross-section profile of the Gaussian beam has been dispersed, now the contrast between normalized maximum and minimum intensity has become smaller, since the light intensity of the black line at the precise SPPs angle should ideally stay at zero, the light intensities at other incident angles have been generally reduced. From the 2nd graph, the aspect ration is roughly the same with that of the 1st graph, so we can see that adding absorptive filter just causing another distortion of the light beam before it goes to the detector (CCD camera).

Figure 48. SPPs excitation with singly convex lens and with both convex lens and absorptive filter. IV. Functionalization of gold layer

A. Introduction

1). Overview The gold layer on the inclined surface of the prism is functionalised by a special reagent. The reagent is the mixture of an organic compound Cyclam (white powder) and 2-Ethoxyethanol solvent. The aim of the functionalization is to form the crystal structure of Cyclam on the gold layer no matter the related regime is chemical or physical absorption, then the angle of SPPs excitation for functionalised gold layer is supposed to be changed compared with that of the pure gold layer, finally after the functional groups of Cyclam have bonded with Cadaverine molecule, the SPPs angle is desired to be further shifted.

2). Investigation method We mainly use two different methods to investigate the properties of functionalised gold layer. The 1st method is to simply apply the optical microscope together with the CCD camera and related user interface software on PC to capture the real time images of the functionalised gold layer. The 2nd method is to use the optical configuration (mainly the λ/2 plate, beam splitting polarizer, absorptive filter) with the Diode laser source (795nm) to excite surface plasmon resonance on functionalised gold layer.

The ultimate aim for our investigation is to find the most suitable parameters for functionalization in order to have the best quality of SPPs excitation, here we summarize several investigated issues for functionalization:

 Concentration of Cyclam, or the ratio between Cyclam (mg) and 2-Ethoxyethanol (ml);  Different physical configuration for functionalization;  Replication of functionalization.

3). Basic concepts a). Surface functionalization Functionalization, is defined as the process that one or more certain chemicals with special functional groups[24] are introduced to the surface of a material, the interface between the mono-or-multi layer chemicals and substrate surface can be chemical bonds or just physical-absorption[25]. Hence new properties and functions can be added to the bulk material and combined with the inherent features of the substrate.

b). Cyclam 1,4,8,11-Tetraazacyclotetradecane (synonym: Cyclam), is classified to a type of macrocyclic amines, in which its Nitrogen Alkyls play the role as ligands and have notable capacity to bind with transition metal[26], such as Ni(II), Cu(II), Co(III) and Au (III) ions[27]. To be specific, the fourteen membered tetraamine macrocycles demonstrate the superb ability to “form highly thermodynamic and kinetically stable metal complexes compared with metal ion dissociation”[28]. Note that up til now we have not searched out the convincing evidence which can show the chemical absorption between Cyclam and pure gold thin film. The chemical formula of Cyclam can be written as (NHCH2CH2NHCH2CH2CH2)2 or just C10H24N4. A 2D molecular structure of Cyclam is shown in Figure 49. In addition, it should be mentioned that Cyclam is white-colored powder or fiber[29] at standard state (25°C at 100kPa). For solubility of Cyclam, it is soluble in Acetone, Ethyl Acetate, Ethanol, Chloroform, Cyclohexane, Methanol and water[30]. Figure 49. 2D molecular structure of Cyclam.

c). 2-Ethoxyethanol 2-Ethoxyethanol is a colorless, odorless but toxic solvent at standard state which is fabricated by the reaction between ethylene oxide and ethanol. Its chemical formula can be presented as HOCH2CH2OC2H5, the molecular structure of 2-Ethoxyethanol is shown in Figure 50. Here we use 2-Ethoxyethanol as the solvent for Cyclam.

Figure 50. 2D molecular structure of 2-Ethoxyethanol.

There are mainly two reasons for us choose to use 2-Ethoxyethanol as solvent. First, since Cyclam’s solubility in 2-Ethoxyethanol is not as high as in water or Ethanol, this can increase the possibility for gold-Cyclam binding instead of being completely dissolved in the solvent so that no crystal structure of Cyclam can bond to gold layer. Second, meanwhile 2-Ethoxyethanol can be a good cleaner for removal of the chemical impurities on gold layer.

Figure 51. Reagent preparation for functionalization. Picture 1: Commercial packing of 2-Ethoxyethanol (big dark glass bottle) and Cyclam (small white plastic bottle); Picture 2: Mass measurement for Cyclam powder using high accuracy electronic scale; Picture 3: Volume measurement of 2-Ethoxyethanol by using glass graduate and the plastic disposable dropper. B. Preparation

1). Preparation for the reagent First, the reagent for functionalization should be prepared. The white powder of Cyclam is weighed using an 1×10-4 g accuracy electronic scale, in which the empty white plastic container for later loading the Cyclam is put on on the electronic scale, the digit on the screen can then be returned to zero by press the “Menu” key once. The plastic disposable dropper (accuracy 0.25ml) and graduate (accuracy 1ml) are used to measure and get the desired volume of the 2-Ethoxyethanol. A small beak for holding the reagent is first cleaned by Acetone, Isopropanol and distilled water in sequence. It is better to dry the beaker by Nitrogen flow. Then the 2-Ethoxyethanol in the graduate with certain volume is poured into the beaker, following by adding into the Cyclam white powder. A cleaned glass rod can facilitate to speed up the mixing. The preparation of the functionalization reagent is shown in Figure 51.

2). Different physical configuration for functionalization

Figure 52. Different physical configurations for functionalization. Picture 1: The prism is put vertically in the beaker of reagent (for big volume reagent condition); Picture 2: The prism with beaker is put with a tilted angle (for small volume reagent condition); Picture 3: Gold layer of the prism is facing to the bottom of beaker; Picture 4. A funnel is used to stabilize the prism, and the prism is covered with reagent; Picture 5. The reagent is just distilled on the vertical gold layer.

Next the prepared reagent for functionalization should be transferred to the gold thin film surface of the prism. Here we list several way to process this step, as shown in Figure 52. The effect and quality of functionalization for each physical configuration will be discussed later. Different physical configurations of functionalization in Figure 52 are:

 Picture 1: For lower Cyclam concentration, the volume of 2-Ethoxyethanol is larger, so that by simply putting the prism into the beaker with gold layer being perpendicular, the prism can totally merged into the reagent.  Picture 2: For higher Cyclam concentration, the volume of 2-Ehoxyethanol is smaller, and its liquid level is lower than the top edge of the prism. Therefore the beaker is putting in a tilted angle with respect to the vertical direction so that now the gold layer can be totally merged into the liquid. As shown in the first two pictures in Figure 53. In addition, two side edges of the gold layer can support the prism by touching with the curved wall of the beaker, then the main part of the gold layer will not contact with the inner surface of the beaker, so that the gold layer can be protected, as shown in the last picture of Figure 53.  Picture 3: We assume that the vertical gold layer can not have a frequent contacting with Cyclam molecules. Therefore the gold layer is placed to be faced to the beaker inner bottom in order to try to make a better absorption between gold thin film and Cyclam.  Picture 4: Since Cyclam is a quite expensive chemical compound product. Therefore the way of functionalization by using less amount of reagent is investigated. A funnel is used to stabilize the prism, and the gold layer is directly distilled with reagent, forming a thin layer of liquid.  Picture 5: This configuration is used to examine the quick functionalization. After the gold layer is distilled with the reagent, the prism will be directly taken out and processed with further measurements.

Figure 53. Placing the beaker together with the prism tilted with respect to the table top.

3). Clean the glass surface After the reagent has contacted with the gold layer of the prism with a certain time period. The the two glass right-angle side should be cleaned by distilled water, since the impure glass surface will affect the experiment precision. Note that distilled water will destroy the functionalised gold layer to a great extent, hence in order to clean the glass sides without influencing the functionalised gold layer, the prism is put on a piece of clean tissue, in which the gold layer is perpendicular to the horizontal table top, the tissue is used for absorbing the redundant distilled water, then use a plastic disposable dropper to carefully drop the distill water at the top horizontal edge of the glass side, the distilled water will flow down along the wall of the glass side so that the glass surface can be cleaned. The process is shown in Figure 54.

Figure 54. Glass surface of the prism is cleaned by distilled water after functionalization. 4). Observations For observation of the functionalised gold layer, the optical microscope with CCD camera and the corresponding user interface software on PC is applied. In addition, the bracket with vertical wall used for gold deposition on the inclined surface of the prism is also implemented. As shown in Figure 55.

Figure 55. Observation of functionalised gold layer using optical microscope, the prism is mounted on the vertical wall of a special bracket.

Note that the excitation and measurement methods of the functionalised gold layer is using the same optical configuration as that of the pure gold layer before.

C. Results and discussion

We hereby screen out some typical samples to discuss further, as shown in Table 6.

Sample No. Cyclam (mg) 2-Ethoxyethanol (ml) Time period Placing vertical (V) or horizontal (H) 1 60 20 10min V 2 25 20 10min H 3 25 20 7h V 4 25 20 10min V 5 100 10 10min V 6 100 20 10min V

Table 6. Some typical samples of functionalised gold layer, note that Cyclam and 2-Ethoxyethanol are measured in milligram (mg) and milliliter (ml) respectively. The gold layer surface of the prism is placed both vertically or horizontally after finishing functionalization.

1). Physical configuration, Cyclam concentration and crystalline appearance For one physical configuration that the gold layer is being faced to the inner bottom of the beaker (sample No.5 - 100mg-10ml-10min-V). It seems like inevitable scratches are formed on the gold layer since gold layer has contact with the bottom, as shown in Figure 56. Therefore this kind of configuration is not applicable. Figure 56. Left picture: gold layer is being faced to the inner bottom of the beaker during functionalization; Right picture: Some scratches are caused since gold layer has contact with beaker bottom.

One more thing to be mentioned in the right picture of Figure 56 is that after the prism is being taken out from the beaker, the prism surface deposited with gold layer is then placed perpendicularly to the table top. As the reagent for functionalization is evaporating and flowing along the gold layer from top edge down to the bottom, the remainder Cyclam molecules form the thickness gradient on the gold layer. However, when functionalization finished, if we use a plastic disposable dropper to take out all the reagent from the beaker and place the beaker horizontally so that the gold layer is now horizontal as well, as shown in Figure 57, then it turns out that no obvious thickness gradient is formed on the gold layer.

Figure 57. Gold layer surface is kept horizontally after finishing functionalization.

It can be seen that in Figure 56, when the gold layer has formed Cyclam thickness gradient, for upper part of gold layer, white dots are formed, on the other hand, only white layer with non-uniform thickness is formed on the lower part. On the other hand if the gold layer surface is put horizontally after functionalization, there will be difference for Cyclam molecules distribution on gold layer. Figure 58 shows the captured pictures of sample No.2 and No.4 by optical microscope, the former three parameters for these two samples are the same (25mg-20ml-10min) but differ at the the last parameter (No.2 horizontal / No.4 vertical). In Figure 58, picture 1 shows the uniform white layer of sample No.2, picture 2 and 3 show the upper (white dots) area and lower (white layer) area on the gold layer of sample No.4 separately. Note that all three pictures are in amplification factor of 50x. It is found that the upper part with white dot mainly consists of the radial shape crystalline appearances, while the lower part with white layer mainly consists of meander-like crystalline appearances.

However, it is also interesting to find that even on the white layer, thickness variation also indicates the size changing of the Cyclam crystalline on gold layer. It can be directly recognized by human eye that even on the white layer of the functionalised gold, the transparency differs, then we resort to optical microscope to get further details, as shown in Figure 59, the general (amplification factor 5x) and partial (amplification factor 50x) pictures of the white layer of sample No.6 (100mg-20ml-10min-V), have demonstrated that the crystalline in the more white-colored area seems to be in smaller size but more amount, on the contrary, the crystalline in the more transparent area seems to be in bigger size but less amount. Moreover, same evidence is also found in sample No.1 (60mg-20ml-10min-V), as shown in Figure 60. Where more white-colored area also indicates denser and smaller size crystalline (left picture) while more transparent area indicates thinner but bigger size crystalline (right picture) as well. In addition, we can further find out that more white-colored area demonstrate radial pattern crystalline on gold layer, while the more transparent area demonstrates meander-like crystalline both in Figure 59 and 60.

Figure 58. Picture 1: the uniform white layer of sample No.2; Picture 2 and 3: the upper (white dots) area and lower (white layer) area on the gold layer of sample No.4 separately. Sample No.2 and 4 share three same parameters (Cyclam 25mg / Ethoxyethanol 20ml / time period 10min), while No.2 is placed horizontally and No.4 is placed vertically after functionalization. All three pictures are in amplification factor of 50x.

Figure 59. Pictures of the two areas with different transparencies on the white layer of sample No.6 (Cyclam 100mg / 2-Ethoxyethanol 20ml / time period 10min / placing vertically). The first picture is in 5x magnification while the rest two pictures are in 50x.

Figure 60. Two different areas (on white layer) on the functionalised gold layer (Cyclam 60mg / 2-Ethoxyethanol 20ml / time period 10min / placing vertically). Left picture shows the detail of the more white-colored area, while the right picture shows the detail of the more transparent area of gold layer. Note that both picture are at amplification factor of 50x. As the concentration goes high enough as sample No.5, the functionalised gold layer becomes roughly uniform appearance with entirely white-colored surface to naked eye even it is placed vertically to the table top. We present the captured picture of sample No.5 in magnification of 20x as shown in Figure 61.

Figure 61. Functionalised gold layer (sample No.5) with Cyclam 100mg / 2-Ethoxyethanol 10ml / time period 10min / placing vertically presented in magnification of 20x.

The white dots on the upper part of the gold layer can be treated as the isolated crystalline structure which could not even form the monolayer Cyclam; Besides, it is predictable that the pure white layer at lower part of the gold surface could probably be the multilayer of Cyclam molecule.

Moreover, for the more transparent white layer also at lower part of gold, we can just assume that the meander-like crystalline appearances at more transparent white molecular layer might be the kind of transition layer between the isolated crystalline and the overlapping crystalline layers before the concentration of Cyclam has not reached high enough.

Another assumption can be given is that the meander-like crystalline represents the monolayer of Cyclam on gold surface, which plays the role of basic level for multilayer formation of Cyclam molecules, then the smaller crystalline appearances are formed on the meander-like crystal structure. However, since the concentration of Cyclam is high enough for sample No.5 (100mg in 10ml 2-Ethoxyethanol), the entire gold surface are covered by Cyclam multilayer.

Unfortunately due to the limited schedule for the project, the thickness of the white dots, meander-like crystalline and pure white layer can be measured by atom force microscope (AFM) further after this semester.

2). Cyclam concentration and SPPs excitation Both the upper part (Figure 58, picture 2) and lower part (Figure 58, picture 3) of the gold surface of sample No.4 and the uniform pure white layer on sample No.5’s gold surface (Figure 61) are processed with SPPs excitation by the previously used optical configuration, the reflected light beam intensities have been measured for each SPPs excitation. Note that these three crystalline appearances are the predicted isolated crystal structure, monolayer and multilayer of Cyclam molecules in sequence. The measurement results is found in Figure 62. Note that the interval between the neighboring two sampled incident angles for sample No.5 SPPs measurement (the last graph in Figure 62) is quite big compared to that of the the former two measurements, this is because when trying to find the brightest red spot on the gold layer (sample No.5) when rotating the rotation mount, no obvious and bright red spot are found, namely no high quality SPPs excitation occurs. Therefore no sudden drop down of reflected intensity will happen, hence big interval is okay. Figure 62. Measurement of reflected laser beam intensity during SPPs excitation for both upper and lower part of functionalised gold layer of sample No.4 (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 10 min / placing vertically) and the pure white functionalised gold layer of sample No.5 Cyclam 100mg / 2-Ethoxyethanol 10ml / time period 10 min / placing vertically). From the measurement results, it is interesting that the angle of SPPs excitation shifts towards λ/2 when the crystalline appearance of the functionalised gold layer changing from isolated crystal to meander-like structure and ultimately to the possible multilayer of Cyclam molecule, and minimum reflectance is also rising with respect to this sequence. This finding is quite inspiring since it is in accordance with the simulation results in Chapter “Simulations for surface plasmon polaritons”. As we have given a predicted refractive index for Cyclam (roughly equals to 1.43), when Cyclam layer becomes thicker, SPPs angle is supposed to shift towards λ/2 in the simulation.

However, the simulation can not explain the rising minimum reflected intensity as the functionalised layer becomes thicker. Nevertheless, as long as once we can ensure that the extinction coefficient (the imaginary part of the refractive index) of Cyclam is negligible, the simulation can proof the positive shifting of the SPPs angle for increasing thickness of functionalised layer.

In addition, the reflected intensity measurement result for upper part of functionalised gold layer of sample No.4 is quite similar to the related measurement result for 50nm pure gold layer, this is a bit tricky since the isolated crystalline appearances are distributed loosely on the upper part of gold layer, then there is a big chance that SPPs excitation occurring at the pure gold layer among these isolated structures. Therefore the SPPs excitation under the condition of Cadaverine binding with Cyclam is need to be achieved and measured in order to proof whether SPPs excitation happens to pure gold layer or isolated Cyclam crystalline.

The spot light images at SPPs angle for these three measurements are presented in Figure 63. Since we are not 100% sure that SPPs excitation does occur just on the isolated Cyclam crystalline, we can only say that the SPPs quality on meander-like crystalline appearance is worse than that of pure gold layer but far better than the pure white functionalised gold layer with higher Cyclam concentration, hence too high concentration of Cyclam in the reagent is not good for optimization of SPPs quality for functionalised gold layer.

Figure 63. SPPs light spots for: 1. Upper part of gold layer (isolated Cyclam crystalline) of sample No.4; 2. Lower part of gold layer (meander-like Cyclam crystalline) of sample No.4; 3. Pure white functionalised gold layer of sample No.5.

3). Time period for functionalization The captured pictures of the upper part gold layer of both sample No.3 and No.4 are presented in Figure 64, in which each upper part is presented in two different magnification factors (20x and 100x). Unfortunately the lower part of the gold layer of sample No.3 could not form the meander-like crystalline since the recycled gold layer, which is cleaned after 1st time functionalization, is used for the preparation of sample No.3, is no longer pure gold layer making Cyclam more difficult to absorbed on it, this issue will be discussed further. The light spot at SPPs angle of the upper part gold layer of both sample No.3 and No.4 are also presented in Figure 64.

From Figure 64, no obvious difference between two sets of results can be found. Also, from all along the experience for doing functionalization, we give an experiential assumption that the real start point for functionalization occurs is at the beginning when the thin liquid layer of the reagent starts to evaporate, hence when the prism is simply merged in the reagent, functionalization is seemed not to be processed, or the progress of functionalization is negligible.

Figure 64. Two captured images by optical microscope and image of SPPs light spot for both sample No.3 (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 7 hours / placing vertically) (picture 1-3) and sample No.4 (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 10min / placing vertically) (picture 4-5).

4). Replication of functionalization Since it is quite time and cost consuming to clean up the functionalised gold layer and then deposit new gold layer on the cleaned prism, plus we also want to build up the sensor which is reusable. Therefore, some effort is also spent on investigation of the feasible method to clean the functionalised layer and make the gold layer to be highly pure again. Here two materials are investigated for the potential ideal remover of functionalised layer: distilled water and hot Chloroform. The method used to examine the effect of cleaning is to do functionalization again on the recycled gold layer to observe the crystalline appearance on it, if the the crystalline remains the same appearance, indicating a thorough and successful cleaning process.

a). Distilled water The functionalised gold layer is simply rinsed by distilled water for at least 3 minutes, followed by a second time functionalization. Note that the parameters of functionalization remain the same for the former and latter ones (25mg - 20ml - 10min - V). A pure BK7 prism without gold thin film deposited on is also functionalised just used for comparison. The results are shown in Figure 65.

Figure 65. Left picture: the functionalised (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 10min / placing vertically) gold layer is firstly rinsed by distilled water and then processed with functionalization again using the same parameters. Right picture: pure BK7 glass prism without gold layer is processed with functionalization use the same parameters as that of the right picture’s. Note that both pictures are set to amplification factor of 10x.

It is obvious that distilled water is not capable for cleaning the functionalised gold layer. Small amout of solid phase reagent for functionalization is just remained on the gold layer and no binding happens at all. More evidence can also be found on the second time functionalization using other parameters. Figure 66 shows two pictures of the second time functionalised gold layer with different parameters (left 25mg / right 100mg - 20ml - 24hours - placing vertically). It is easy to see that higher concentration of Cyclam results in larger size of the solidified structures.

Figure 66. Left picture: the functionalised (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 24h / placing vertically) gold layer is firstly rinsed by distilled water and then processed with functionalization again using the same parameters. Right picture: same condition with that of the left picture, which only differs in mass of Cyclam (100mg). Note that both pictures are set to amplification factor of 50x.

b). Hot Chloroform It is searched that hot Chloroform and hot Ethanol can be used for removal of the functionalised layer on gold[31]. Since the boiling point of Chloroform is 61.15°C at standard state[32], we decide to firstly put the prism in the beaker, the prisms is merged with Chloroform, then heat up the Chloroform to 110°C for 20min, and finally go down to 60°C for 10min to clean the functionalised layer on the prism. The configuration for this method is presented in Figure 67. Note that when processing with Chloroform, the air exhaust fan must be open and the respirator should be worn.

Figure 67. Configurations for removing the functionalised surface from gold layer using hot Chloroform.

Then it turns out that Chloroform has better effect to remove the functionalised layer from gold, since sample No.3 in Table 6 is the product of second time functionalization and the reused gold layer is firstly cleaned by hot Chloroform.

5). Other findings However, another reused prism which is also cleaned by hot Chloroform fails to have successful functionalization, the reagent used for this functionalization is to dilute the former reagent (Cyclam 25mg / 2-Ethoxyethanol 20ml) ten times, that is distill 10ml extra 2-Ethoxyethanol into 1ml former reagent, the physical configuration is the one shown in picture 4 of Figure 52 (the one using the funnel to stabilize the prism facing to the top). The time period for this functionalization is set to be half an hour. The result of this functionalization is shown in Figure 68, note that the left picture is enlarged in 20x, while the right one is 100x.

Figure 68. Functionalization on reused gold layer firstly cleaned by hot Chloroform, the reagent used for this time has nearly 1/10 of the concentration used for the functionalization of sample No.3 and No.4 It is also interesting to find that the failed functionalised layer will not inhibit SPPs excitation. As we can see that there either larger size or smaller size of solidified reagent material remained on the the gold surface, by slightly changing the convex lens in optical configuration, we can locate SPPs excitation at our desired area on the gold layer, hence we have got different pattern of light spot of SPPs excitation by locating the laser beam spot in different areas on gold layer. The results are summarized in Figure 69.

Figure 69. SPPs excitation at four different areas on the functionalised gold layer, the reagent used for this time has nearly 1/10 of the concentration used for the functionalization of sample No.3 and No.4 (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 10min / placing horizontally). Picture 1: the area with less amount of dots with smaller size; Picture 2: the area of thick functionalised layer; Picture 3: Transitional area between dots and layer; Picture 4: area with relatively larger amount of big sized dots.

The chosen areas for SPPs excitation in Figure 69 are:

 Picture 1: SPPs excitation at the area with less amount of dots, also the dots are in smaller size;  Picture 2: SPPs excitation at the area with the formed thick layer of solidified reagent;  Picture 3: SPPs excitation at the transitional area between dots and layer of the solidified reagent;  Picture 4: SPPs excitation at the area with full of larger-sized dots.

The variation of the SPPs pattern is hard to explain, but one can now make an assumption that the solidified reagent which have not been absorbed by gold layer (chemically or physically) can be seen as an dielectric medium adhered with gold layer.

Additionally, we also try to achieve functionalization by Cyclam evaporation directly at the gold thin film. Since the melting point of Cyclam is 185°C[33], we set the temperature of the heater to reach to 240°C. A beaker with its caliber being specially chosen to be shorter than the hypotenuse edge of the prism is used, so that the prism can directly put on the top of the beaker with the gold layer facing to the bottom. The time period for evaporation is counted from the time point when Cyclam starts evaporation, whole evaporation process is controlled to be around 10 minutes. The configuration for Cyclam evaporation is shown in Figure 70. Figure 70. Configurations for Cyclam evaporating directly on gold layer in order to have a fast and efficient functionalization process.

Note that almost 50mg Cyclam has been evaporated, but the captured pictures of the gold layer have shown that the functionalization is not as good as our expectations. The overall picture of the functionalised gold layer is shown in Figure 71, in which we can see that some black spots are loosely distributed on the gold layer. Then the black spots are found to be the crystalline appearance as we use a larger amplification factor lens in microscope to make observations, see Figure 72, it is interesting to see that by slightly adjusting the focal length, different layers on the gold surface have been highlighted. In the left picture, the radial shape crystalline of Cyclam are clear to recognize, while in the right picture, plenty of droplets shape solidified structures which is quite similar to the residual solidified reagent for functionalization as we have seen before in Figure 66 and Figure 68 are found.

From Figure 72, it is obvious that the crystalline structure and the residual solidified structure are formed in different layer, which indicates the Cyclam molecule evaporated on gold layer may have formed 3D structure rather than 2D structure, or it is possible that the crystalline is first formed on gold layer, and then it is covered by the residual solidified structure, followed by the formation of droplets shape structure on top of the layer. We hold the opinion that the droplet shape structure widely distributed on the gold layer may caused by two reasons: Firstly when processing this experiment, the beaker with the prism placing on the top are surrounded by air and water vapor, and it is obvious to see that evaporation of Cyclam is closely accompanying with water vaporization, therefore some water droplets may reside on the gold layer; Secondly, since the evaporation is processing on an reused gold layer, therefore the gold layer may not be perfectly cleaned.

One more thing should be also mentioned that, after we further try to excite SPPs on this gold layer evaporated with Cyclam molecule. It is easy to find the brightest red light spot on gold layer, indicating there does have apparent SPPs excitation, but not black line in the image of the light spot at SPPs angle as shown in Figure 73. Since the residual solidified structures on this gold layer is quite similar as the droplets shape we presented in Figure 68, in which the related black line for SPPs excitation could be found in Figure 69. Hence we assume that larger thickness of the functionalised gold layer by Cyclam molecule evaportation could be a reason responsible for bad quality SPPs excitation. Figure 71. Functionalised gold layer using Cyclam molecule evaporation in air atmosphere, amplification factor of the captured image: 20x.

Figure 72. Captured images in magnification of 100x of the functionalised gold layer by Cyclam evaporation. In the left picture, Cyclam crystalline is highlighted, while in the right picture, droplets shape residual solidified structures are clear to see, and the ambiguous deep color spots in the right picture are the unclear Cyclam crystalline.

Figure 73. SPPs light spot of functionalised gold layer evaporated with Cyclam molecules. V. Build the Cadaverine sensor

A. Introduction

1). Brief introduction about Cadaverine Cadaverine, also called pentane-1,5-diamine[34], is an organic compound which can be released from animal tissue degradation, in which the interior process is actually the protein hydrolysis of the tissue, hence it is good to use Cadaverine as an indicator for whether the meat product has gone bad or not. Cadaverine is special for its strong rancidity. In standard state, Cadaverine is syrupy liquid with light yellow color, it can be fuming in air atmosphere and forming hydrate with water vapor. Note that Cadaverine is toxic. Its chemical formula can be written as NH2(CH2)5NH2, the molecular structure of Cadaverine is shown in Figure 74.

Figure 74. Molecular structure of Cadaverine

2). Description of the Cadaverine sensor The gas-phase Cadaverine will be heated in the beaker and then transported throw the tube to the sealed physical configuration (prism holder) in which the BK7 prism with functionalised gold thin film is mounted. Before sensing process starts, there have been already SPPs excitation on functionalised gold layer, the whole optical configuration is the same as the one used for SPPs excitation on pure gold layer before, the reflected beam is collected by CCD camera, the light spot of SPPs is shown on the PC screen using the related interface software linked to CCD camera. It is expected that when the gas-phase Cadaverine is transported on the functionalised gold layer, the black line of SPPs on the screen will have an obvious shift instead of disappearance, indicating the formation of chemical bond between Cyclam and Cadaverine molecules, the distance of SPPs black line shifting under the same amount of Cadaverine molecules represents the precision of the Cadaverine sensor.

B. Mechanical design and assembly of the prism holder

1). Modification of the design of the prism holder The prism holder is designed by my co-supervisor assistant professor James Hoyland, the open source 3D computer graphic software[35] - Blender 3D is used to make the design. The reason for making a prism holder for the Cadaverine sensor is that since Cadaverine is toxic, it has to be used in a sealed space, on the other hand the sealed space is applied to collect Cadaverine molecules and facilitate sensing process. The original design of the prism holder is shown in Figure 75. Note that the holder is fabricated by 3D printing.

Figure 75. Original design of the prism holder by Blender 3D. However, since we plan to transport gas-phase Cadaverine into the prism holder, a cylindrical port should be designed on the back wall of the prism holder. The pipe for transporting Cadaverine is chosen with diameter of 5.80mm. One more thing to be mentioned is that the size of the trench designed for holding the prism is a little bit narrow compared to prism’s real dimension, as shown in Figure 76, the real dimension of the prism is measured by caliper. Fortunately, since in 3D printing system, the dimension of the design can enlarged in each axis, therefore here we choose to keep the original dimension of Z-axis (the height of the prism) but multiplying a modification factor of 1.05x along X and Y axis, in addition, since the chosen diameter of the pipe is 5.80mm, hence when we further modify the design, the diameter should be set to 5.8/1.05=5.524mm. Finally the design of the prism holder is modified by adding a cylindrical port, this is realized in Blender by applying a Boolean function, the modified design in user interface of Blender is shown in Figure 77.

Figure 76. Real dimensions of the BK7 prism measured by caliper (precision 0.05mm).

Figure 77. User interface of Blender, it can be seen that now the prism holder has been modified by adding a cylindrical port in order to let gas phase Cadaverine go into the sealed space via a transportation pipe.

It is found that the modified design of the prism holder now is consistent with the real dimension of the prism. The captured picture of a real prism holder by 3D printing is shown in Figure 78.

Figure 78. Real picture of the modified prism holder fabricated by 3D printer, we can see that now the dimension is consistent with the real prism.

2). Assembly of the prism holder

Figure 79. Machining the Aluminum plates for sealing the prism holder, the holder is assembled at last. The main procedures for prism holder assembly is shown in Figure 79, the related steps are summarized:

Step 1: Two aluminum plates have already been cut, make screw thread (M5) in four screw holes; Step 2: Fasten one aluminum plate with the prism holder, use a drill to mark four places on aluminum plate through the screw hole of the prism holder, doing exacting the same thing by using another aluminum plate; Step 3: Use nail and hammer to make the four marker on aluminum plate bigger and easier to recognize; Step 4: Use electric drill to make the hole (M4) at four marker on aluminum plate, then the grinding drill is applied to make the plate to be flat without undesired topology, make screw thread (M5) for the plate. Two extra holes are made in the center of the plate, one hole is using M4 (screw thread), another one is using a screw with 2.2mm diameter; Step 5: Mount the bottom plate on the rotation mount, two screw holes on the plate should be corresponded to the other two screw holes on the rotation mount; Step 6: Assemble the prism holder and two aluminum plates together, note that the back of the bottom plate is totally flat since no screw is used in that side.

C. Test the Cadaverine sensing system

1). Setup for Cadaverine sensor The entire system assembled for Cadaverine sensor is presented below:

Figure 80. Whole setup for Cadaverine sensor system. 2). Sensor testing We want to test whether the sensor is able to detect pure gas phase of Cadaverine, this is the method which is used to test the most basic function of the sensor. Some key points here are highlighted:

 Cadaverine is carefully extracted using a plastic disposable dropper, here we just evaporate 1ml pure Cadaverine and transport its gas phase towards the functionalised gold layer through the pipe. Since the boiling point of Cadaverine is 179.1°C, we plan to heat the beaker with Cadaverine to 200°C.  The gold layer is functionalised using the parameters of sample No.4 in Table 6 (Cyclam 25mg / 2-Ethoxyethanol 20ml / time period 10min / placing vertically), which has the best quality of SPPs excitation among all the functionalised samples.  SPPs have been excited on functionalised gold layer before, when the temperature of the heater reaches to 200°C, we start to record the video of the light spot of SPPs angle, the length of the video is around 12 minutes.

Unfortunately, the results are seemed to be unsuccessful, the black line at SPPs light spot has no shifting at all. As shown in Figure 81, the pictures are captured in every two minutes.

Figure 81. Sensor is tested with pure gas-phase Cadaverine, in which Cadaverine is kept heating and evaporating, the images are captured at certain time point of heating Cadaverine, the start point for counting is from the heater reaching to 200°C.

3). Results discussion The reason to explain why the sensor fails to detect Cadaverine molecule can be variable. Here we list three possible reason responsible for this failure:

 Firstly, Cadaverine may be decomposed during being heated under 200°C, since Cadaverine will “emit toxic fumes of nitroxides”[36], and we do smell a little bit irritant gas during sensor testing. Therefore it it possible that before Cadaverine is transported on the functionalised gold layer, it has already been decomposed, therefore no bonding between Cadaverine and Cyclam molecules at all.  Second, as we have said in the introduction of Cadaverine, that Cadaverine is volatile in air atmosphere and could form hydrate with vapor water, making Cadaverine bond with water molecule prior to bonding with Cyclam.  Third, Cadaverine may not be successfully transported to the functionalised gold layer, since the beaker is not 100% sealed and we can see that water vapor can easily leak from the top edge of the beaker. Therefore the same leakage may also happen to Cadaverine since the heating temperature is higher than its boiling point.

However, all the explanations are build on the basic viewpoint that Cadaverine could really have chemical bond with Cyclam. We start to doubt about this common view. Hence a second experimental trial is done to proof that Cadaverine is capable to form chemical bond with Cyclam molecule. Therefore we try to use liquid-phase pure Cadaverine to distill it on gold layer to examine our assumption, if the black line shifts instead of disappearing after the gold layer contacting with Cadaverine liquid, it can proof that Cadaverine could really have chemical bond with Cyclam, on the other hand, if the black line disappears and appears again after Cadaverine is evaporated at all, then it can be concluded that Cadaverine can not bond with Cyclam molecules, then the functionalised gold layer can not be used to detect Cadaverine molecules.

Two captured pictures are shown in Figure 82, it can be found that when Cadaverine is firstly distilled on gold layer, black line of SPPs disappears, after Cadaverine is evaporated at all, the black line of SPPs appear again, in which the same phenomenon occurs just like the experiment using Isopropanol as before.

Figure 82. Cadaverine is directly distilled on functionalised gold layer. Left: Cadaverine is staying at the red spot of the gold layer; Right: Cadaverine is evaporated at all and black line of SPPs appears again.

However, more methods and multiple experimental conditions should be considered to demonstrate the rigorous proof that Cadaverine can not form chemical bond with Cyclam. Since in the second experiment, Cadaverine and the functionalised gold layer are in room temperature, it can be only assumed that Cadaverine can not have chemical bonding with Cyclam at room temperature.

On the other hand, the quality of functionalization of gold layer is also worthy investigating, since the visible black spot at SPPs excitation angle can be only recognized at the white dots area on functionalised gold layer, it is difficult to distinguish whether the SPPs excitation happens on the surrounding pure gold layer or just right on the isolated Cyclam crystalline. Here we can have two methods for further investigation: the first one is just to use a new BK7 prism with gold layer deposited on, then doing functionalizaiton on this gold layer in order to form meander-like crystalline and pure white layer, although SPPs excitation is not obvious on these two types of surface structure, the power meter can be applied to measure the reflected intensity before and after contacting with Cadaverine molecule. Not only that, by further applying SPPs detection using phase change measurement instead of beam amplitude detection, the even subtle difference on optical properties between Cyclam crystalline and Cyclam-Cadaverine bond can be found out. VI. Bibliography

[1] Pedrotti, F. L., & Pedrotti, L. S. (1993). Introduction to Optics 2nd Edition.Introduction to Optics 2nd Edition by Frank L. Pedrotti, SJ, Leno S. Pedrotti New Jersey: Prentice Hall, 1993, 1. [2] Maier, S. A. (2007). Plasmonics: fundamentals and applications: fundamentals and applications. Springer Science & Business Media. [3] Surface plasmon polaritons, Justin White, March 19, 2007 - (Submitted as course work for AP272, Stanford University, winter 2007). Link: http://large.stanford.edu/courses/2007/ap272/white1/ [4] Bozhevolnyi, S. I. (2008, October). Plasmonic nano-guides and circuits. InPlasmonics and Metamaterials (p. MWD3). Optical Society of America. [5] Baltar, H. T., Goldys, E. M., & Drozdowicz-Tomsia, K. (2012). Propagating Surface Plasmons and Dispersion Relations for Nanoscale Multilayer Metallic-Dielectric Films. INTECH Open Access Publisher. [6] “Metal Optics”, Prof. Vlad Shalaev, Purdue Univ., ECE Department, Link: http://shay.ecn.purdue.edu/~ece695s/ [7] Raether, H. (1988). Surface plasmons on smooth surfaces (pp. 4-39). Springer Berlin Heidelberg. [8] “Surface-plasmon-polariton waveguides”, Hyongsik Won, Ph.D Thesis, Hanyang Univ, 2005. [9] Refractive index database, link: http://refractiveindex.info/ [10] For gold: Rakic, A. D., Djurišic, A. B., Elazar, J. M., & Majewski, M. L. (1998). Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied optics, 37(22), 5271-5283. [11] For Titanium: Johnson, P. B., & Christy, R. W. (1972). Optical constants of the noble metals.Physical Review B, 6(12), 4370. [12] SCHOTT optical glass data sheets 2012-12-04, link: http://refractiveindex.info/download/data/2012/schott_optical_glass_collection_datasheets_dec_2012_us.pdf [13] SCHOTT Zemax catalog 2012-12-04, link: http://refractiveindex.info/download/data/2012/schottzemax-20121204.agf [14] Masahiro Yamamoto’s online self-study note: “Surface Plasmon Resonance (SPR) Theory”, link: http://www.chem.konan-u.ac.jp/applphys/web_material/spr_tutorial/sprtheory.html [15] Santa Cruz Biotechnology - 1,4,8,11-Tetraazacyclotetradecane (CAS 295-37-4), link: http://www.scbt.com/datasheet-253995-1-4-8-11-tetraazacyclotetradecane.html [16] Meep Installation, link: http://ab-initio.mit.edu/wiki/index.php/Meep_Installation [17] Markovic, M. I., & Rakic, A. D. (1990). Determination of the reflection coefficients of laser light of wavelengths λ∊ (0.22 µm, 200 µm) from the surface of aluminum using the Lorentz-Drude model. Applied optics, 29(24), 3479-3483. [18] Marković, M. I., & Rakić, A. D. (1990). Determination of optical properties of aluminium including electron reradiation in the Lorentz-Drude model. Optics & Laser Technology, 22(6), 394-398. [19] Raymond C. Rumpf, Electromagnetic Properties of Materials – Part I Lorentz and Drude Models, ECE 5390 Special Topics: 21st Century Electromagnetics. Link: http://emlab.utep.edu/ee5390em21/Lecture%202%20--%20Lorentz%20and%20Drude%20models.pdf [20] Birefringence - Wikipedia, link: http://en.wikipedia.org/wiki/Birefringence [21] Half-Wave Plates - Polarization - Newport, link: http://www.newport.com/Polarization/144921/1033/content.aspx [22] Linear polarizer principles - Meadowlark optics, link: http://www.meadowlark.com/store/catalog/Polarizers_Oct_18_2012.pdf [23] Graphs - Mounted Absorptive Neutral Density Filters, link: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=266 [24] Lapshin, R. V., Alekhin, A. P., Kirilenko, A. G., Odintsov, S. L., & Krotkov, V. A. (2010). Vacuum ultraviolet smoothing of nanometer-scale asperities of Poly (methyl methacrylate) surface. Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques, 4(1), 1-11. [25] Functionalization - The Science of Aerogel - Learn - Blog - AEROGEL.ORG, link: http://www.aerogel.org/?p=1918 [26] Barefield, E. K. (2010). Coordination chemistry of N-tetraalkylated Cyclam ligands—A status report. Coordination Chemistry Reviews, 254(15), 1607-1627. [27] Suh, M. P., Kim, I. S., Shim, B. Y., Hong, D., & Yoon, T. S. (1996). Extremely facile template synthesis of Gold (III) complexes of a saturated azamacrocycle and crystal structure of a six-coordinate Gold (III) complex. Inorganic Chemistry, 35(12), 3595-3598. [28] Füzerová, S., Kotek, J., Císařová, I., Hermann, P., Binnemans, K., & Lukeš, I. (2005). Cyclam (1, 4, 8, 11-tetraazacyclotetradecane) with one methylphosphonate pendant arm: a new ligand for selective copper (II) binding.Dalton transactions, (17), 2908-2915. [29] SPECIFICATION SHEET (PDF) - 1,4,8,11-Tetraazacyclotetradecane 98% (GC), Sigma-Aldrich, link: http://www.sigmaaldrich.com/Graphics/COfAInfo/SigmaSAPQM/SPEC/25/259160/259160-BULK______ALDRI CH__.pdf [30] Cyclam - Material Safety Data Sheet - CheMatech, link: http://www.chematech-mdt.com/uploads/Products/cyclam.pdf [31] Makowska-Janusik, M., Kassiba, A., Errien, N., & Mehdi, A. (2010). Mesoporous Silica Functionalized by Cyclam–Metal Groups: Spectroscopic Studies and Numerical Modeling. Journal of Inorganic and Organometallic Polymers and Materials, 20(4), 761-773. [32] Chloroform - Wikipedia, link: http://en.wikipedia.org/wiki/Chloroform [33] Cyclam - Wikipedia, link: http://en.wikipedia.org/wiki/Cyclam [34] Cadaverine - Compound Summary, National Center for Biotechnology Information. PubChem Compound Database; CID=273, http://pubchem.ncbi.nlm.nih.gov/compound/273 (accessed May 31, 2015). [35] Blender (software) - Wikipedia, link: http://en.wikipedia.org/wiki/Blender_%28software%29 [36] Sax, N. I. (1979). Dangerous properties of industrial materials. VII. Appendix

A. MATLAB source code for the simulation of surface plasmon polaritons

%This MATLAB code is used for generating surface plasmon resonance %The user interface control object - 'uicontrol' is applied for inputting %For BK7 glass prism, Titanium adhesion layer and gold layer, two sets of %refractive indexes are given for two different laser sources: Helium-Neon %laser <633nm> and diode laser <795nm> separately. %by Yi WEI, May 2015 clear all

%initialization for constants termination=0; pi=acos(-1); img_i=complex(0,1);

%define the wavelengths of two different laser sources lambda_he=633e-9;%Helium Neon laser lambda_di=795e-9;%Diode laser

%build up the frame of the graph figure(1) clf axes('position',[.05 .25 .9 .7])

%BK7 glass prism n_bk7_he=1.5151; %refractive index for Helium-Neon laser source (633nm) k_bk7_he=1.2126e-8; n_bk7_di=1.5109; %refractive index for Diode laser source (795nm) k_bk7_di=9.2489e-9;

%Titanium (adhesion layer between prism and gold) n_ti_he=2.7043; %refractive index for Helium-Neon laser source (633nm) k_ti_he=3.7657; n_ti_di=3.126; %refractive index for Diode laser source (795nm) k_ti_di=4.01; d_ti=1e-9*3; %thickness of Titanium layer

%gold n_au_he=0.19591; %refractive index for Helium-Neon laser source (633nm) k_au_he=3.2578; n_au_di=0.18693; %refractive index for Diode laser source (795nm) k_au_di=4.666;

%build up the user interface control of gold layer thickness d_gold=uicontrol('style','slider','min',10,'max',100,'value',50); set(d_gold,'units','normalized','position',[.27 .06 .15 .03]); uicontrol('style','text','string','Gold_layer_thickness','units','normalized','position',[. 14 .07 .12 .02]);

%laser source source=uicontrol('style','popup','string','Diode-795nm|Helium Neon-633nm'); set(source,'units','normalized','position',[.69 .12 .1 .05]) uicontrol('style','text','string','Laser source wavelength','units','normalized','position',[.58 .14 .1 .02]);

%subphase (air or aqua) subphase=uicontrol('style','popup','string','air|aqua'); set(subphase,'units','normalized','position',[.27 .12 .07 .05]) uicontrol('style','text','string','Subphase','units','normalized','position',[.2 .14 .06 .0 2]);

%end calculations stop=uicontrol('style','pushbutton','string','End_calculation','callback','termination=1;') ; set(stop,'units','normalized','position',[.58 .05 .1 .05]); while termination==0;

clear angle_range reflectance

angle_range(:,1)=(30:.05:60)';

%choose the laser source and the corresponding refractive indexes if get(source,'value')==1 %Diode laser lambda=lambda_di;

%layer 1: BK7 glass prism n(1)=n_bk7_di; %real part refractive index - prism k(1)=k_bk7_di; %imaginary part refractive index - prism

%layer 2: adhesion layer n(2)=n_ti_di; %real part refractive index - adhesion layer k(2)=k_ti_di; %imaginary part refractive index - adhesion layer

%layer 3: gold layer n(3)=n_au_di; %real refractive index - gold layer k(3)=k_au_di; %imaginary refractive index - gold layer

else %Helium Neon laser lambda=lambda_he;

%layer 1: BK7 glass prism n(1)=n_bk7_he; %real part refractive index - prism k(1)=k_bk7_he; %imaginary part refractive index - prism

%layer 2: adhesion layer n(2)=n_ti_he; %real part refractive index - adhesion layer k(2)=k_ti_he; %imaginary part refractive index - adhesion layer

%layer 3: gold layer n(3)=n_au_he; %real refractive index - gold layer k(3)=k_au_he; %imaginary refractive index - gold layer

end

%input the metal layer thickness d(2)=d_ti; %Titanium adhesion layer thickness (nm) d(3)=1e-9*get(d_gold,'value'); %gold layer thickness (nm)

%layer 4: subphase below if get(subphase,'value')==1 %air n(4)=1.00; k(4)=0; else %aqua n(4)=1.33; k(4)=0; end

%angular range on which to count theta_abs_deg=angle_range(:,1); %calculating dielectric constants e_real=n(1)^2-k(1)^2; e_img=2*n(1)*k(1); epsilon(1)=complex(e_real,e_img);

e_real=n(2)^2-k(2)^2; e_img=2*n(2)*k(2); epsilon(2)=complex(e_real,e_img);

e_real=n(3)^2-k(3)^2; e_img=2*n(3)*k(3); epsilon(3)=complex(e_real,e_img);

e_real=n(4)^2-k(4)^2; e_img=2*n(4)*k(4); epsilon(4)=complex(e_real,e_img);

%determine the incident angle theta_abs=theta_abs_deg/180*pi; theta_ref=pi/4+asin(1/n(1)*sin(theta_abs-pi/4));

%start iteration for count_theta=1:length(theta_ref);

incident_angle=theta_ref(count_theta); m1=sqrt(epsilon(1)-n(1)^2*sin(incident_angle)^2)/epsilon(1); mn=sqrt(epsilon(end)-n(1)^2*sin(incident_angle)^2)/epsilon(end);

for i=2:(length(epsilon)-1) alpha=d(i)*2*pi/lambda*sqrt(epsilon(i)-n(1)^2*sin(incident_angle)^2); q=sqrt(epsilon(i)-n(1)^2*sin(incident_angle)^2)/epsilon(i); emf(i,1,1)=cos(alpha); emf(i,1,2)=-img_i*sin(alpha)/q; emf(i,2,1)=-img_i*sin(alpha)*q; emf(i,2,2)=cos(alpha); end

emf_all=[1 0;0 1];

for i=2:(length(epsilon)-1) emtot(:,:)=emf(i,:,:); emf_all=emf_all*emtot; end index_r=((emf_all(1,1)+emf_all(1,2)*mn)*m1-(emf_all(2,1)+emf_all(2,2)*mn))/... ((emf_all(1,1)+emf_all(1,2)*mn)*m1+(emf_all(2,1)+emf_all(2,2)*mn));

reflectivity=index_r*conj(index_r); reflectance(count_theta)=reflectivity; end

plot(theta_abs_deg,reflectance) title('Plot of surface plasma polariton on gold layer'); xlabel('incident angle at the interface of gold layer and dielectric'); ylabel('Reflectance');

data=reflectance'; ca=axis;

%notes for the graph text(ca(1)+(ca(2)-ca(1))*.5,ca(3)+(ca(4)-ca(3))*.2,... ['BK7 glass prism: n=',num2str(n(1)),'+i',num2str(k(1)),... '\newline Ti layer: n=',num2str(n(2)),'+i',num2str(k(2)),' d=',num2str(d(2)*1e9),'nm',... '\newline Au layer: n=',num2str(n(3)),'+i',num2str(k(3)),' d=',num2str(d(3)*1e9),'nm']);

pause(.05) end B. Source codes for MEEP simulations

1). MATLAB code for generating dispersion relation %This MATLAB code is used for generation of dispersion relation at gold-BK7 %glass interface. Note that the Drude model for ideal metal is applied. %by Yi Wei, April 2015 omega_p=1;%plasma frequency c=1;%normalized speed of light epsilon_d=2.2827;%relative permittivity of BK7 glass omega_spp=omega_p/sqrt(1+epsilon_d); %calculating the surface plasmon resonance frequency omega=[0.01:0.01:omega_p/sqrt(1+epsilon_d)]; %range of the angular frequency of the incident wave epsilon_m=1-omega_p^2*omega.^-2; %Drude model for ideal metal k=(omega./c).*sqrt(epsilon_m*epsilon_d.*(epsilon_m+epsilon_d).^-1); %calculating the propagation constant along the gold-BK7 glass interface plot(k,omega);

%export the data of theoretical dispersion relation to .dat file temp=[k;omega; ones(1,length(omega))*omega_spp]'; save('analytical_solution.dat','temp','-ASCII')

2). Scheme code in MEEP for simulation of dispersion relation The .ctl file is presented below, note that the green text after the semicolon is the annotations for the code.

(define-param rsl 5);resolution of the simulation (define-param size_z 2); dimension in z axis (define-param fp 1); normalized plasma frequency of drude model (define-param glass 2.2827); relative permittivity of BK7 glass (define-param tpml 1); PML thickness (define-param fgau 0.5); frequency at Gaussian beam center (define-param bwg 2); bandwidth of the Gaussian beam

;define the optical properties of gold (define Au (make dielectric (epsilon 1) (polarizations (make polarizability (omega 1e-20) (gamma 0.042747) (sigma 4.0314e+41)) (make polarizability (omega 0.33472) (gamma 0.19438) (sigma 11.363)) (make polarizability (omega 0.66944) (gamma 0.27826) (sigma 1.1836)) (make polarizability (omega 2.3947) (gamma 0.7017) (sigma 0.65677)) (make polarizability (omega 3.4714) (gamma 2.0115) (sigma 2.6455)) (make polarizability (omega 10.743) (gamma 1.7857) (sigma 2.0148)) )))

;define the optical property of BK7 glass (define BK7 (make dielectric (epsilon glass)))

;define the dimension of lattice (set! geometry-lattice (make lattice (size no-size no-size (+ size_z (* 2 tpml))))) ;placing the materials in the lattice (set! geometry (list (make block (center 0 0 0) (size infinity infinity size_z) (material Au)) (make block (center 0 0 (* 0.25 size_z)) (size infinity infinity (* 0.5 size_z)) (material BK7))))

(set! pml-layers (list (make pml (direction Z) (thickness tpml))))

;define the Gaussian beam source (set! sources (list (make source (src (make gaussian-src (frequency fgau) (fwidth bwg))) (component Ez) (center 0 0 0)) ; ) )

(set! resolution rsl);define the resolution for this simulation

;define Bloch periodic boundary conditions (define-param k-points (list (vector3 0 0 0) (vector3 2.0 0 0) ) )

;define several k-points (set! k-points (interpolate 20 k-points))

;make calculations on these k-points (run-k-points 300 k-points)

3). Scheme code in MEEP for plan wave interaction simulation The .ctl file is presented below, the thickness of gold layer is 50nm and thickness of Titanium adhesion layer is 3nm, note that the green text after the semicolon is the annotations for the code.

(define-param dx 10); cell size in x axis (define-param dy 5); cell size along y axis (define-param d_au 0.05); gold layer thickness (define-param d_ti 0.003); Titanium layer thickness (define-param d_gls 4); BK7 glass thickness (define-param d_air 5); air thickness (define-param gls 2.2827); permittivity of BK7 glass (define-param fp 1); high frequency dielectric of Drude model (define-param bwg 4); bandwidth of the Gaussian pulse (define-param tpml 0.50); PML thickness (define-param theta (/ pi 4)); incident angle of the plane wave

(set! resolution 50);define the resolution for simulation domain

;define the optical properties of gold (define Au (make dielectric (epsilon 1) (polarizations (make polarizability (omega 1e-20) (gamma 0.042747) (sigma 4.0314e+41)) (make polarizability (omega 0.33472) (gamma 0.19438) (sigma 11.363)) (make polarizability (omega 0.66944) (gamma 0.27826) (sigma 1.1836)) (make polarizability (omega 2.3947) (gamma 0.7017) (sigma 0.65677)) (make polarizability (omega 3.4714) (gamma 2.0115) (sigma 2.6455)) (make polarizability (omega 10.743) (gamma 1.7857) (sigma 2.0148)) )))

;define the optical properties of Titanium (define Ti (make dielectric (epsilon 1) (polarizations (make polarizability (omega 1e-20) (gamma 0.066137) (sigma 5.1166e+40)) (make polarizability (omega 0.62669) (gamma 1.8357) (sigma 79.136)) (make polarizability (omega 1.2461) (gamma 2.0309) (sigma 8.7496)) (make polarizability (omega 2.0236) (gamma 1.3413) (sigma 1.5787)) (make polarizability (omega 1.5671) (gamma 1.4211) (sigma 0.014077)) )))

;define the optical property of BK7 glass (define BK7 (make dielectric (epsilon gls)))

;define the lattice (set! geometry-lattice (make lattice (size (+ dx (* 2 tpml)) (+ dy (* 2 tpml)) no-size)))

;define the geometry of the materials (set! geometry (list (make block (center 0 (+ (/ d_au 2) (/ d_ti 2)) 0) (size infinity d_au infinity) (material Au)) (make block (center 0 0 0) (size infinity d_ti infinity) (material Ti)) (make block (center 0 (+ (/ d_gls 2) (+ d_au (/ d_ti 2))) 0) (size infinity d_gls infinity) (material BK7)) (make block (center 0 (/ (- 0 d_air) 2) 0) (size infinity d_air infinity) (material air)) ))

;define PML thickness (set! pml-layers (list (make pml (thickness tpml))))

;define the wave vector (define ky (* fp (sin theta)))

;give the amplitude function (define (f_amp p) (exp (* 0+2i pi ky (vector3-y p)))) (set! k-point (vector3 0 ky 0))

;define the simulation domain to be complex field (set! force-complex-fields? true)

;define the Gaussian beam (set! sources (list (make source (src (make continuous-src (frequency fp))) (component Ez) (center 5 0) (size 0 dy) (amp-func f_amp))))

(set! pml-layers (list (make pml (thickness tpml) (direction X))))

;extract the data to .png file (run-until 50 (at-beginning output-epsilon) (at-end (output-png Ez " -Zc bluered")))