Properties of induced polarization evanescent reflection with a solid immersion lens (SIL)

doi:10.1364/OE.15.001191

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Properties of induced polarization evanescent reflection with a solid immersion lens (SIL)

Tao Chen and Tom D. Milster »View Author Affiliations

Optics Express, Vol. 15, Issue 3, pp. 1191-1204 (2007)
http://dx.doi.org/10.1364/OE.15.001191

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▸ Article Outline
– Abstract
1. Introduction
2. Generation of the induced polarization signal
3. Characteristics of the induced polarization signal for different substrates and optical configurations
4. Conclusion
Appendix
– References and links

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Abstract

Properties of the induced polarization signal with a solid immersion lens (SIL) are investigated by experiments and simulations. A LaSFN9 SIL (NA=1.5) is used in the experiment. Physics of the induced polarization signal are described for several configurations of optical systems and substrates. Induced polarization signals from evanescent-wave coupling to dielectric, semiconductor and metal substrates are studied in detail. It is shown that surface plasmon waves are excited with Au substrates and the induced polarization signal is affected by the surface plasmon waves. Simulation results of the induced polarization signal for a gallium phosphide SIL (NA=2.64) are discussed.

1. Introduction

Since the solid immersion lens (SIL) was invented by Mansfield and Kino in 1990, [1

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57,2615–2616 (1990). [CrossRef]

] it has been used in various areas, such as microscopy [2

Q. Wu, L. Ghislain, and V. B. Elings, “Imaging with Solid Immersion Lenses, Spatial Resolution, and applications,” Proc. IEEE ,88,1491–1498 (2000). [CrossRef]

], Raman spectroscopy [3

C. D. Poweleit, A. Gunther, S. Goodnick, and J. Menéndez, “Raman imaging of patterned silicon using a solid immersion lens,” Appl. Phys. Lett. 73,2275–2277 (1998). [CrossRef]

], lithography [4

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. ,74,501–503 (1999). [CrossRef]

], data storage [5

T. D. Milster, “Near-field optical data storage: avenues for improved performance,” Opt. Eng. 40,2255–2260 (2001). [CrossRef]

] and other applications [6

K Sendur, C Peng, and W Challener,“Near-field radiation from a ridge waveguide transducer in the vicinity of a solid immersion lens,” Phys. Rev. Lett. 94,043901 (2005). [CrossRef] [PubMed]

]. The SIL is a high-refractive-index, image-centric hemisphere, as shown in Fig. 1. A small gap h between the flat side of the hemisphere and the object provides a path for evanescent coupling of light between the SIL and the sample. Numerical aperture (NA) in this case is NA=nsinθ_m , where n is SIL’s index of refraction, and θ_m is the marginal ray angle. With a SIL, the NA is greater than what is achieved with an optical system in air by a factor of n. For example, NA can reach over 2.0 with special lens materials. [7

M. Lang, T. D. Milster, T. Minamitani, G. Borek, and D. Brown, “Fabrication and characterization of sub-100 km diameter gallium phosphide solid immersion lens arrays,” Jpn. J. Appl. Phys. 44,3385–3387 (2005). [CrossRef]

, 8

Q. Wu, G. D. Feke, Robert D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. ,75,4064–4066 (1999). [CrossRef]

] The lateral resolution and focused spot size, which are proportional to λ/NA, are also improved by a factor of n in the SIL system compared to using the same objective lens in air, due to the increase of NA. The nature of this resolution improvement and spot size decrease is enabled by the evanescent waves generated in the focus region and their coupling between the SIL and the substrate. [9

T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, and Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. 38,1793–1794 (1999). [CrossRef]

]The evanescent waves beyond critical angle θ_c =sin^-1(1/n) exponentially decay from the flat bottom side of the SIL. An expression for the 1/e decay distance z_1/e of the evanescent energy at the marginal ray angle θ_m is

z_{\frac{1}{e}} = \frac{λ}{4 π} \frac{1}{\sqrt{n^{2} \sin^{2} θ_{m} - 1}} .

(1)

Recently, a novel method to control h was presented through the application of an induced polarization signal from the frustrated total internal reflection (FTIR) at the SIL/air interface. As demonstrated for a spinning substrate, the system is capable of dynamically controlling gap variations to less than ±2nm. [10

T. Ishimoto, K. Saito, M. Shinoda, T. Kondo, A. Nakaoki, and M. Yamamoto, “Gap servo system for a biaxial device using an optical gap signal in a near field readout system,” Jpn. J. Appl. Phys. 42,2719–2724 (2003). [CrossRef]

] In addition, a new near-field imaging system with the SIL, which is based on the induced polarization evanescent reflection principle, experimentally demonstrated the ability of obtaining image contrast enhancement, high lateral resolution and topographical imaging with nanometer-scale height resolution. [11

T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32,124–126 (2007). [CrossRef]

] However, to date, the physics and general characteristics of the induced polarization signal have not been completely described. This paper discusses the physics and characteristics of the induced polarization evanescent reflection, with respect to different SIL materials, substrate materials, and optical configurations. Theoretical, simulation and experimental results are presented.

The following sections describe the induced polarization reflection in detail. In Section 2, generation of induced polarization evanescent reflection is explained. Section 3 discusses characteristics of the induced polarization signal for different substrates and optical configurations. In Sec. 4, conclusions of this study are presented. Appendix lists a mathematical description of the simulation.

2. Generation of the induced polarization signal

The induced polarization signal is generated by using a SIL mounted on an inverted Olympus IX70 microscope, which is described in detail in a separate publication. [12

T. Chen, T. D. Milster, J. K. Park, B. McCarthy, D. Sarid, C. Poweleit, and J. Menendez “Near-field solid immersion lens (SIL) microscope with advanced compact mechanical design,” Opt. Eng. 45,103002 (2006). [CrossRef]

] The schematic diagram of this setup is shown in Fig. 1. The illumination source is a laser diode with λ=650nm. A 100^×, 0.8-NA Olympus objective lens is used with a LaSFN9 SIL (n=1.84 at 650nm), where NA=nsinθ_m =1.84×0.8≈1.5. The laser light is expanded and collimated with a pinhole spatial filter and collimation lens. The collimated laser beam passes through linear polarizer 1 that establishes the native polarization state in the plane of the figure. After passing through the non-polarizing beam splitter, the light is focused by the objective lens into the SIL. Upon reflection from the SIL’s flat surface, the phase and amplitude differences between p and s polarization states produce an induced polarization state at the pupil of the objective lens, which is orthogonal to the native polarization state. After reflection from the non-polarizing beam splitter, the induced polarization energy is integrated onto a photodiode (PD) with polarizer 2 oriented perpendicularly to the native polarization. This induced polarization signal can be also investigated by observing the reflected-light distribution at the pupil with a CCD camera refocused to image the pupil of the objective lens.

Fig. 1. Schematic diagram of a SIL induced-polarization near-field microscope. Linearly polarized collimated coherent illumination is used at the entrance pupil. With the flat surface of the SIL located very close to the sample, an orthogonal component of polarization is induced upon reflection from the flat surface of the SIL through frustrated total internal reflection.

The pupil dependence of the illumination is illustrated in Fig. 2. For example, at the entrance pupil, all light is linearly polarized along the horizontal direction, as shown in Fig. 2(a). In the horizontal direction, as shown in Fig. 2(b), the incident light is oriented as p polarization. In the vertical direction, as shown in Fig. 2(c), the incident light is oriented as s polarization. In the diagonal direction, as shown in Fig. 2(d), the incident light is both s and p polarized. Since n>1, frustrated total internal reflection occurs at the focus for plane waves incident at angles larger than the critical angle θ_c =sin^-1(1/n). S and p polarized light are not equally reflected in this case, because there are phase and amplitude differences between s and p polarization states. These differences result in elliptically polarized reflected light along the diagonal direction. An illustration of the amplitude and phase differences versus angle of incidence is shown in Fig. 3 for the case of large h, such that the reflections are essentially TIR.

The elliptically polarized light is quantified by observing the reflected light distribution in the exit pupil of the objective lens. For a flat glass substrate (N_s =1.67 at λ=650nm) and LaSFN9 SIL (NA=1.5), Fig. 4 shows simulated polarization pupil maps for different h.

Fig. 2. Schematic of polarized illumination in a SIL optical system. (a) Top view of the entrance pupil, native polarization state at the entrance pupil is along the horizontal direction. (b) p polarization along the horizontal direction of entrance pupil, (c) s polarization along the vertical direction of entrance pupil, (d) Mixed p and s polarization along diagonal direction of entrance pupil.

Fig. 3. S and p polarized light reflection verses incident angle at glass (n=1.84) and air interface, λ=650nm and h»λ; (a) Amplitude coefficients of r_p and r_s (b) Phase difference between r_p and r_s .

The elliptical polarization results in an induced polarization signal reaching the CCD through polarizer 2 with its axis perpendicular to the native polarization state. Both measurement and simulation CCD images are shown in Fig. 5 for three values of h. (Details of the simulation are provided in the Appendix.) From these results, it is observed that most of the energy in the induced component is beyond the critical angle of the SIL/air interface, and it is a maximum value in the diagonal quadrants. Therefore, the gap induced polarization phenomenon is mainly due to evanescent energy generated by FTIR.

In Fig. 5(c) h=1500nm, and there are several bright thin rings inside the TIR radius, which are due to interference between the flat bottom of SIL and the flat substrate. Because the air gap is very large, there is no evanescent coupling between the SIL and the glass sample. However, the surfaces are close enough to form a Fabry-Perot cavity. As shown in Fig. 3, light in the focus cone with angles of incidence just below the critical angle exhibit significant reflection from both surfaces. Except where these waves add with a phase difference of π, a strong reflection is observed. As the angle of incidence decreases toward the center of the pupil, this effect is significantly reduced due to the lower reflection coefficients. The Fabry-Perot rings shown in the white box of Fig. 5(c) are not observed for the light beyond θ_C , because this light is TIR.

Fig. 4. Reflected light polarization pupil maps. LaSFN9 SIL, NA=1.5, refractive index of substrate N_s =1.67. The inner dashed circle indicates Brewster’s angle and the outer dashed circle indicates TIR angle. Axes correspond to n × direction cosine in the pupil. (a) Air gap h=100nm, (b) air gap h=1000nm.

Fig. 5. Near-field induced polarization signal at the lens pupil for different gap heights. The white dash circles on the pupil pictures indicate the boundary of total internal reflection (TIR) critical angle, which shows that most of the induced energy is due to evanescent waves beyond the critical angle. The grayscale is linearly proportional to optical power. The box indicates regions of Fabry-Perot fringes. As rings inside the TIR boundary.

3. Characteristics of the induced polarization signal for different substrates and optical configurations

In order to properly describe the induced polarization signal, several terms are defined. Firstly, the integrated PD signals are normalized to the induced polarization value obtained with large (several micrometer) h. This normalized detector signal is called S. As shown in Fig. 6, for induced polarization signal S, h_c is the beginning of far-field region C at 90% of the far-field asymptote. h₀ is the operating point, which is typically at 40% of far-field asymptote. h_t is the threshold, where the extension of the tangent line at h₀ meets S=0. Region A (foot region) is from h=0nm to h_t . Region B (operating region) is from h_t to h_c . Region C (far-field region) is from hc into the far-field. As shown in Fig. 6, the far-field asymptote is defined by the constant level of the induced polarization signal in the far field. When the bottom of the SIL is far away from the flat substrate, there is no evanescent coupling between the SIL and the substrate. Only TIR occurs. Therefore, the induced polarization signal doesn’t change significantly in region C. However, the native polarization signal exhibits oscillation behavior in this far-field region. Since the native polarization signal is mainly from light with incident angle smaller than θ_C , light reflected to the pupil has characteristics of a Fabry-Perot cavity formed between the two surfaces. When h changes, the reflected native polarization signal oscillates with h. Gain g is defined by g=ΔS/Δh, with units of μm^-1, which is the slope of S at tangent h₀ . S_min is the minimum induced polarization signal in region A. Minor modification to these definitions are necessary in some geometries, as demonstrated in the following paragraphs.

Fig. 6. The calculated induced and native polarization signal S for a Si substrate with a LaSFN9 SIL (NA=1.5) at 650nm, and sinθ_m =0.8.

3.1 Low absorption substrates

One type of substrate that exhibits certain characteristic behavior is low-absorption material. Typical response of the induced-polarization signal for low-absorption material is shown in Fig. 7, for NA=1.5 illumination at λ=650nm with n=1.84. Glass, with substrate complex refractive index N_S =1.67+0i, exhibits a smooth, mono tonic increase as h is increased from h=0 to h=500nm. S_min at h=0nm is nearly zero. Silicon, with N_S =3.85+0.02i, shows a similar response, except S_min at h=0nm has an offset and the region B exhibits higher gain. The characteristic values are shown in Table 1. The higher g is caused by silicon’s high real component of the refractive index and the offset is caused by silicon’s imaginary component of the refractive index.

Fig. 7. Simulation and measurement data obtained using a λ=650nm laser beam for the illumination light with n=1.84 for LaSFN9. The solid and dashed black curves are the induced polarization signals versus air gap height h for glass and Si flat substrates respectively, with θ_m ,=53.13°. The green line is the simulation of GaP (n=3.3) SIL material with a glass substrate, where θ_m =26.49° . In the measurements, gap height was determined by use of a calibrated bimorph that holds the SIL. [12

]

Table 1. The characteristic values h_t , h_c , h_c -h_t , S_min , and g of glass, Si and Au substrates with LaSFN9 and GaP SILs.

SIL	sinθ _m	NA	Substrate	N_s	h_t (nm)	h_c (nm)	h_c -h_t (nm)	S_min (a.u.)	g (μm^-1)
LaSFN9	0.8	1.5	Glass	1.67	15	250	235	0.005	5.93
LaSFN9	0.8	1.5	Si	3.85+0.02i	9	165	156	0.019	10.05
LaSFN9	0.8	1.5	Au	0.17+3.15i	28	125^*	97	0.001	14.29
GaP	0.8	2.6	Glass	1.67	__	100	__	0.8	1.61^**
GaP	0.8	2.6	Si	3.85+0.02i	0	50	50	0.005	27.9
GaP	0.8	2.6	Au	0.17+3.15i	5	15	10	0.027	87.53
ZnS	0.8	2.2	Photoresist	___	__	90	__	0.577	6.49^***
GaP	0.446	1.5	Glass	1.67	2	250	248	0.076	6.58

^* h_c defined at 80% of far-field asymptote.

^** h_o defined at 85% of far-field asymptote.

^*** h_o defined at 70% of far-field asymptote.

Simulation and experimental results indicate that the induced polarization signal for low-absorption substrates is a monotonic function of h. A heuristic explanation of this phenomenon is based on the behavior of evanescent waves. When the bottom of SIL is contact with the object, the air gap is zero. There is almost no evanescent energy reflected. It mostly couples into the object at these contact points, except for a very small amount due to residual Fresnel reflection. Most of this reflected light is blocked by the crossed polarizer, because there is little phase shift between p and s reflections in this condition. When the gap height increases, more evanescent energy is reflected until the exponential decay lengths of the evanescent waves are exceeded. After that distance, the light is totally internally reflected (TIR). Further increase of the gap height produces no increase in the induced signal.

The induced polarization signal for low absorption substrates can be expressed by the following parametric fitting curve:

f (h) = C_{1} {1 - \exp (- C_{2} h^{C_{3}})}^{C_{4}} + C_{5} .

(2)

The values of C₁ to C₅ are obtained through a numerical algorithm. Equation (2) can be used to calibrate the air gap height if the intensity of induced polarization is known. [11

T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32,124–126 (2007). [CrossRef]

] For example, coefficients for glass and Si substrates verses gap height h in are given Table 2 for the conditions measured in Fig. 7.

Table 2. Parametric values of induced polarization signal for a LaSFN9 SIL glass and Si substrate verse gap height h in Fig. 7.

Substrate	C₁	C₂	C₃	C₄	C₅
Glass	1.006	0.0441	0.7842	3.3332	0.0058
Si	0.955	0.2299	0.5851	8.1426	0.0218

3.2 Metal substrates

Metal substrates exhibit high absorbance, which results in more complicated induced polarization behavior than is observed with low-absorbance substrates. In this section, the characteristics of a Au (N_s =0.17+3.15i) substrate with an LaSFN9 SIL is examined in detail.

The induced polarization signal for a Au substrate is calculated and measured at the PD and pupil with the configuration shown in Fig. 1. As shown in Fig. 8(a), the induced polarization signal with a Au substrate is more complicated than that of dielectric and semiconductor substrates. Characteristic values are shown in Table 1. The Au substrate has the highest g and smallest S_min compared with glass and Si. In addition, associated with the complicated signal is a dark ring that appears in the pupil distribution, as shown in Fig. 8(b). The curve shape and ring pattern are due to surface plasmon (SP) wave excitation.

Fig. 8. Simulation and measurement data obtained using λ=650nm laser light with NA=1.5 and a Au substrate. (a) Induced polarization signals versus air gap height h. (b) Induced polarization signals at the pupil for h=400nm.

As a brief review of SP excitation, one arrangement for generation of a SP wave is the Otto configuration [13

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216,398–410 (1968). [CrossRef]

] as shown in Fig. 9(a), where p-polarized light is incident on the flat bottom of prism. When the incident angle is bigger than the TIR angle, an evanescent field is generated along the prism/air interface. If the angle of incidence is appropriate, a metallic substrate, such as gold, silver or aluminum, placed in the vicinity of the prism will excite a SP wave along the air/metal interface. [14

D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, and J. J. Fasano, “Optical field enhancement by long-range surface-plasma waves,” Appl. Opt. 21,3993–3995 (1982). [CrossRef] [PubMed]

,15

B. Ran and S. G. Lipson, “Comparison between sensitivities of phase and intensity detection in surface plasmon resonance,” Opt. Express 14,5641–5650 (2006). [CrossRef] [PubMed]

,16

A. Otto, “The surface polariton response in attenuated total reflection,” in Polaritons: Proceedings of the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. Demartina, ed.(Pentagon, New York, 1974), pp.117–121.

] At the surface plasmon resonance (SPR) angle, incident light energy is strongly coupled into the SP wave, which leads to a dramatic decrease in reflectivity and phase jump between the s and p polarization reflections. [15

B. Ran and S. G. Lipson, “Comparison between sensitivities of phase and intensity detection in surface plasmon resonance,” Opt. Express 14,5641–5650 (2006). [CrossRef] [PubMed]

] When the SIL is placed very close to a Au substrate, as shown in Fig. 1, it meets the Otto condition to excite SP wave for certain angles of incidence in the focus cone.

Fig. 9. (a). Otto configuration geometry for exciting a surface plasmon wave (b) Schematic diagram of three layers calculation of reflection coefficient. ϵ₀, ϵ₁ and ϵ₂ are the dielectric constants of SIL, air and Au, respectively. θ is the incident angle and θ_C is the critical angle of the TIR.

In order to understand the effect of a SP wave on induced polarization, the reflectivity and phase change of a SIL with a Au substrate is calculated with standard Maxwell’s equations and Fresnel coefficients for electromagnetic propagation through one-layer media, [16

] as shown in Fig. 9(b). The reflection coefficients for p and s polarized light are

r_{q} = \frac{r_{01}^{q} + r_{12}^{q} \exp ({2 ik}_{1 z} h)}{1 + r_{01}^{q} r_{12}^{q} \exp ({2 ik}_{1 z} h)}, q = p, s

(3)

where

r_{i, i + 1}^{q} = \frac{X_{i}^{q} - X_{i + 1}^{q}}{X_{i}^{q} + X_{i + 1}^{q}}, i = 0,1

(4)

X_{j}^{q} = {\begin{matrix} \frac{ε_{j}}{k_{jz}} q = p \\ k_{jz} q = s \end{matrix} j = 0,1,2

and

k_{iz} = \sqrt{{(\frac{ω}{c})}^{2} ε_{i} - {(\frac{ω}{c} \sin θ)}^{2} ε_{0} .}

i and j represent different layers; 0 is the prism layer, 1 is the air gap layer in the middle, and 2 is the metal layers. θ is the incident angle in the SIL , ϵ is the dielectric constant, c is speed of light in the vacuum, and ω is angular frequency. Complex reflection coefficients are defined as r_p = |r_p |e^iϕ_p and r_s = |r_s |e^iϕ_s . The phase difference of p and s polarizations is Δϕ =ϕ _p -ϕ _s .

In the calculation, ϵ₀=3.3856 (glass), ϵ₁=1 (air) and ϵ₂= -9.8936 + 1.0710i (Au), λ=650nm, θ_c =sin^-1(1/1.84) ≈ 32.92°, and the maximum marginal angle θ_m = sin^-1(0.8) ≈ 53.13°.

The calculation results of p polarized reflectivity R_P =|r_p |² and phase difference Δϕ_S are shown in Fig. 10. The coupling strength between the evanescent wave and the SP wave is characterized by the dip in R_p , which changes with the air gap height, as shown in Fig. 10(a). When the incident angle θ is smaller than θ_C , R_p has similar behavior for all h. However, when h=400nm and θ=34.89°, SPR occurs and R_p exhibits a sharp resonant dip. Most incident light energy is coupled into the SP wave under these conditions, and there is much less light reflected back into the optical system. The dark ring in the pupil distribution, as shown in Fig. 8(b), occurs at this SPR angle.

Since the induced polarization signal is generated by the phase difference between p and s polarized light, Fig. 10(b) gives a good explanation of the induced polarization signal in Fig. 8(a). When h=0nm, there is still adequate Δϕ to produce an elliptically polarized reflection, which produces an induced polarization signal offset at this point, shown in Fig. 8(a). When h=17nm, Δϕ is very small, which corresponds exactly to the minimum value of S at h=17nm in region A of Fig. 8(a). As h increases, Δϕ increases along with S. Because of the SP effect at h=150nm, the reflectivity has a wide dip, as shown in Fig. 10(a), which causes S to stop increasing as h increases. When h=400nm, although there is SPR, Rp has a sharp dip only at the resonance angle. Therefore, the total induced polarization signal is larger than that at /z=150nm. In addition, at /z=400nm and incident angle from 18° to 34°, Δϕ is large, which results in a strong induced polarization signal. This condition is also clearly observed in Fig. 8(b). The quadrantal pupil distribution inside the dark ring is caused by the Δϕwithin this incident angle range.

If the metal is a thin metal film coated on a dielectric substrate, the SP wave can also be excited at certain conditions. [14

] This geometry is similar to read-only optical disc (a metal reflection layer coated on plastic substrate).

Fig. 10. Otto configuration for SPR with ϵ₀=3.3856 (glass), ϵ,=₁ (air) and ϵ₂= -9.8936 + 1.0710i (Au). (a) Calculation of p polarized light reflection coefficient for different air gap heights. (b) Calculation of phase difference Δϕ between p polarized and s polarized light for different air gap heights.

3.3 Induced polarization signal with a NA =2.6 SIL system

If gallium phosphide (GaP) is used as SIL material, n=3.3 at 650nm, and NA=nsinθ_m =3.3×0.8≈2.64. The induced polarization signals for glass, Si and Au substrates are shown in Fig. 11 under this illumination condition. Characteristic values are shown in Table 1. The critical angle between the SIL/air interface is θ_c =sin^-1(1/3.3) ≈ 17.64°, which is smaller than that of a LaSFN9 SIL. Therefore, with the same objective lens in the microscope, more evanescent waves are generated because more incident light is beyond the critical angle. This condition results in a shorter operating region, which is about 50nm for a Si substrate. g≈27.9μm^-1, which is higher than that in Fig. 7. With a glass (n=1.67) substrate, the induced polarization signal is very different than observed in Fig. 7, where n=1.84. S_min at h=27nm is about 75% of the maximum intensity at h=0nm. Even when h =0nm, there is a large amount of light reflected back to the microscope. Since the critical angle between the SIL and the glass substrate is θ_c =sin^-1 (1.67/3.3) ≈ 30.4°, and θ_m = sin^-1 (0.8)≈ 53.13°. The induced polarization signal for the Au substrate is also very different compared to Fig. 7. For example, there is a peak at h=35nm, due to a large SPR phase difference between s and p polarized light on reflection. A dip appears in the foot region of induced polarization signal, and S_min is at h=6nm because of the minimum phase difference between s and p polarized light at h=6nm, as shown in the inset of Fig. 11.

3.4 Optical systems with equal NA and λ but different n and sinθ_m.

The induced polarization signals for two optical systems with the same NA are examined in this section. A LaSFN9 SIL with NA=nsinθ_m = 1.84×0.8≈1.5 exhibits the same NA as a GaP SIL with NA=nsinθ_m =3.3×0.446≈1.5. The induced polarization signals are calculated for λ=650nm with a glass (N_s =1.67+0i) substrate. The results are shown in Fig. 7 and Table 1. The far-field asymptote of the GaP SIL in this case is approximately a factor of 10 smaller than that of the LaSFN9 SIL, although it is not shown in Fig. 7 due to normalization. For the GaP SIL,θ_c =sin^-1(1/3.3)≈17.64° at the SIL/air interface, θ_m = sin^-1 (0.446) ≈ 26.49°, and Δθ=θ_m -θ_c =8.85°. For the LaSFN9 SIL, θ_c =sin^-1(1/1.84)≈32.92°, θ_m = sin^-1 (0.8) ≈ 53.13° and Δθ=θ_m -θ_c =20.21°. Therefore, evanescent energy is generated in the LaSFN9 SIL system with a wider incident light angle range Δθ for producing evanescent waves. The length of region B and g of the GaP SIL are larger than with the LaSFN9 SIL. The S_min of the GaP SIL is also larger than that of the LaSFN9 SIL. This comparison demonstrates that two different optical systems can have the same focused spot size and lateral resolution, which are proportional to λ/NA, but different induced polarization signals.

3.5 Illumination with circularly polarized light.

The induced polarization signal is investigated with circularly polarized illumination conditions in this section. Circularly polarized light is generated from the linearly polarized light E ₀ x̑ of the laser diode by passing it through a quarter wave plate (QWP). The circularly polarized illumination light at the entrance pupil of Fig. 1 is proportional to E ₀ x̑ + jE ₀ y̑ . If the action of focusing, reflection off the SIL interface and recollimation is treated like an optical filter, the resulting pupil field can be described with complex coefficients r_n and r_i , which describe the native and induced reflections, respectively. Of course, these coefficients are functions of pupil position and gap characteristics. For example, the x-polarized component of the illumination light yields two output components, r_nE _o x̑ + rjE _o y̑ .Likewise, the y-polarized component of the illumination light yields two output components jr_iE _o x̑ + jr_nE _o y̑ . Combination of these reflected values at the pupil and transmission back through the QWP yields an output field of the form r_iE _o x̑ + r_nE _o y̑ . The native and induced components can be easily separated with a linear polarizer or a polarization beam splitter. Therefore, circularly polarized illumination doesn’t change the characteristics of the induced polarization signal when compared to using linearly polarized illumination.

3.6 Photoresist thin film on Si substrate.

The induced polarization signal of a photoresist multi-layer thin film on a Si substrate is studied with a ZnS SIL (n=2.72 at 365nm). [17

D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE ,5754,1049–1055 (2004). [CrossRef]

] In this case, NA=nsinθ_m =2.72×0.8≈2.18. The first layer is photoresist (N ₁=1.689+0.028i at 365nm) with thickness 150nm. The second layer is an antireflection layer (N ₂=1.81+0.34i at 365nm) with thickness 180nm, and the substrate is Si (N_s =6.55+2.66i at 365nm). The calculated induced polarization verses air gap height is shown in Fig. 11, and characteristic values are listed in Table 1. Results are similar to the induced polarization signal for a glass substrate with NA=2.64. S_min is at h=10nm because of the minimum phase difference between s and p polarized light, and h_c =90nm. From h_t = 10nm to h=90nm, the induced polarization signal increases as h increases, which can be used as an air gap control signal between the SIL and the photoresist multi-layer thin film structures.

Fig. 11 Calculated induced polarization signals versus air gap height h for glass, Si and Au flat substrates (GaP SIL, λ=650nm, NA=2.64) and photoresist thin film (ZnS SIL, λ=365nm, NA=2.18). Insert shows an expanded scale near h=0nm.

4. Conclusion

Properties of the induced polarization signal generated with a SIL are studied with simulation and experiment. The induced polarization signal is obtained experimentally through a SIL mounted on an inverted Olympus IX70 microscope. A 100^×, 0.8-NA Olympus objective lens is used with a LaSFN9 (n=1.84 at 650nm) SIL. The effective NA=1.5. The simulation model is based on a vector plane-wave decomposition of light emitted from the exit pupil and thin-film theory. With linearly polarized light at the entrance pupil, characteristics of the induced polarization signal are understood by investigation of light reflected from the bottom of the SIL. When FTIR occurs, there is phase difference between p and s polarized light, which leads to elliptical polarization. The induced polarization signal is measured from this elliptically polarized light through a linear polarizer that is perpendicular to the polarization state at the entrance pupil. Experimental and simulation results show that for glass and Si substrates, the induced polarization signal is a monotonic function of the gap height within the near-field coupling region. The induced polarization signal is mainly generated by evanescent waves, which is also clearly shown by pupil distributions both in simulation and experimental results. For an Au substrate, a surface plasmon (SP) wave is excited in the SIL system, which is similar to the Otto configuration. Under certain conditions, surface plasmon resonance (SPR) appears and is observed in the pupil distribution. Complex reflection properties of the metal and excited SP wave affect the induced polarization signal. The induced polarization signal of a GaP SIL (n=3.3 at 650nm and NA=2.64) is studied by simulation, and the results show a much shorter operating region due to a large fraction of evanescent waves. When the refractive index of the substrate is much smaller than that of the SIL, a large induced polarization signal is generated at 0nm air gap height. SIL optical systems with the same NA but different n and sinθ_m show different induced polarization signals because of the different amounts of evanescent energy generated in each case. Circularly polarized illumination doesn’t change the characteristics of the induced polarization signal compared to using linearly polarization illumination. The induced polarization signal of a photoresist multi-layer thin film structure exhibits similar behavior to a glass substrate.

Appendix

The induced polarization signal is simulated by utilizing vector diffraction and thin-film theories. The simulation model is based on a vector plane-wave decomposition of light emitted from the illumination optical system exit pupil. [18–20

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system.2. Structure of the image field in an aplanatic system,” Proc. R.Soc.Londaon-A ,253 (1274), pp.358–379 (1959). [CrossRef]

] Light emitted from each sample point in the exit pupil reference sphere arrives as a vector plane wave at the flat side of the SIL inside index n. The vector interaction of each plane wave with the thin-film stack composed of the incident index n, air gap and homogeneous thin-film structure of a the sample is governed by known thin-film relationships. [21

H. A. Macleod Thin Film Optical Filters (McGraw-Hill, New York, 1989)

] For calculation of the reflected field, the plane-wave reflections are combined in the entrance pupil reference sphere of the collection lens optical system. This light distribution propagates through the collection optical system from entrance pupil to the exit pupil. Then, the detector signal is found by integrating the signal at the exit pupil of the collection optical system.

The electrical field E at the exit pupil of the collection optical system is described in matrix notation as

E (α_{0}, β_{0}) = Q (α_{0}, β_{0}) A (α_{0}, β_{0})

(5)

where both E(α₀, β₀) and A(α₀, β₀) have dimensions 3×1 pertaining to x, y and z Cartesian coordinates. Q(α₀, β₀) is a 3×3 transform matrix used to map the electrical field from the entrance pupil to the exit pupil, which is

Q = [\begin{matrix} \frac{m' β_{0}^{2} + m' α_{0}^{2} β_{0} {γ'}_{EXP}}{\sqrt{(1 - γ_{0}^{2}) (1 - {γ'}_{EXP}^{2})}} & \frac{- m' α_{0} β_{0} + m' α_{0} β_{0} γ_{0} {γ'}_{EXP}}{\sqrt{(1 - γ_{0}^{2}) (1 - {γ'}_{EXP}^{2})}} & \frac{m' α_{0} {γ'}_{EXP} \sqrt{1 - γ_{0}^{2}}}{\sqrt{(1 - {γ'}_{EXP}^{2})}} \\ \frac{- m' α_{0} β_{0} + m' α_{0} β_{0}^{2} {γ'}_{EXP}}{\sqrt{(1 - γ_{0}^{2}) (1 - {γ'}_{EXP}^{2})}} & \frac{m' α_{0}^{2} + m' β_{0}^{2} γ_{0} {γ'}_{EXP}}{\sqrt{(1 - γ_{0}^{2}) (1 - {γ'}_{EXP}^{2})}} & \frac{m' β_{0} {γ'}_{EXP} \sqrt{1 - γ_{0}^{2}}}{\sqrt{(1 - {γ'}_{EXP}^{2})}} \\ \frac{- α_{0} β_{0} \sqrt{1 - {γ'}_{EXP}^{2}}}{\sqrt{1 - γ_{0}^{2}}} & \frac{- β_{0} γ_{0} \sqrt{1 - {γ'}_{EXP}^{2}}}{\sqrt{1 - γ_{0}^{2}}} & - \sqrt{(1 - γ_{0}^{2}) (1 - {γ'}_{EXP}^{2})} \end{matrix}],

(6)

where α₀, β₀ and γ₀ are the direction cosines in the exit pupil reference sphere of the illumination optical system and entrance pupil of the collection optical system,

γ_{0} = \sqrt{1 - α_{0}^{2} - β_{0}^{2}},

, $α ´$ , EXP,

β ´

EXP and γ´EXP are the direction cosines in the exit pupil of the collection optical system, and

{γ'}_{EXP} = \sqrt{1 - {α'}_{EXP}^{2} - β_{EXP}^{2}} .

. Assuming that the optical system meets the sine condition, $α ´$ EXP =ḿα₀ and

β ´

EXP=ḿβ₀. ḿ is the transverse system magnification for the collection optical system. A(α₀, β₀) is the general vector plane wave amplitude in matrix notation and it is calculated as described in reference [20

T. D. Milster, J. S. Jo, and K. Hirota,“Roles of propagating and evanescent waves in solid immersion lens system,” Appl. Opt. 38,5046–5057 (1999). [CrossRef]

Mathematically,

A (α_{0}, β_{0}) = M_{F} (α_{0}, β_{0}) M_{p} (α_{0}, β_{0}) O ({mα}_{0}, {mβ}_{0}) Ψ (α_{0}, β_{0}),

(7)

where M _F (α₀, β₀) is the film function matrix, M _P (α₀, β₀) is a polarization matrix describing the vector transformation between the entrance and exit pupils of the illumination system, O (mα₀, mβ₀) is the vector field that illuminates the entrance pupil of illumination system, and Ψ(α₀, β₀) is a function that contains only the scalar elements of the optical system.

M _F (α₀, β₀) has dimensions 3 × 5 with elements given by F_l such that

M_{F} (α_{0}, β_{0}) = [\begin{matrix} F_{S} & F_{P} & 0 & 0 & 0 \\ 0 & 0 & F_{S} & F_{P} & 0 \\ 0 & 0 & 0 & 0 & F_{zP} \end{matrix}],

(8)

where

F_{l} = {(\begin{matrix} \frac{τ r_{II}}{τ_{II}} \end{matrix})}_{l} \exp (- iϕ),

(9)

and

F_{zP} = \frac{n γ_{0}}{γ_{1}} {(\begin{matrix} \frac{τ r_{II}}{τ_{II}} \end{matrix})}_{P} \exp (- iϕ),

(10)

γ_{1} = {[1 - n^{2} (1 - γ_{0}^{2})]}^{\frac{1}{2}},

ϕ = - 2 πh γ_{1} .

(11)

The subscript l in Eq. (9) refers to either the s or p polarization direction,τ_II and r_II are the transmission and reflection coefficients of the air/substrate interface respectively, τ is the transmission coefficient of the SIL/air interface, and full expressions of τ,τ_II and r are shown in reference 21.

M _P (α₀,β₀)is given by

M_{P} (α_{0}, β_{0}) = [\begin{matrix} \frac{β_{0}^{2}}{1 - γ_{0}^{2}} & \frac{- α_{0} β_{0}}{1 - γ_{0}^{2}} \\ \frac{γ_{0} α_{0}^{2}}{1 - γ_{0}^{2}} & \frac{α_{0} β_{0} γ_{0}}{1 - γ_{0}^{2}} \\ \frac{- α_{0} β_{0}}{1 - γ_{0}^{2}} & \frac{α_{0}^{2}}{1 - γ_{0}^{2}} \\ \frac{α_{0} β_{0} γ_{0}}{1 - γ_{0}^{2}} & \frac{γ_{0} β_{0}^{2}}{1 - γ_{0}^{2}} \\ - α_{0} & - β_{0} \end{matrix}],

(12)

Ψ(α₀,β₀) is given by

Ψ (α_{0}, β_{0}) = T (α_{0}, β_{0}) \times \exp [i 2 πW (α_{0}, β_{0})] \sqrt{\frac{γ_{ENP}}{γ_{0}}},

(13)

where α_ENP, β_ENP and γ_ENP are the direction cosines at entrance pupil of illumination system,

γ_{ENP} = \sqrt{1 - α_{ENP}^{2} - β_{ENP}^{2}}

, α_ENP = mα₀ and β_ENP = mβ₀, and m is the transverse system magnification for the illumination optical system. T (α₀, β₀) is the exit pupil transmittance function, W (α₀, β₀) is the wavefront aberration function. Since the object-side conjugate on the objective lens is usually much lower numerical aperture than the SIL-side conjugate, the state of polarization in the entrance pupil of illumination system is given by a 2 × 1 matrix

O (α_{ENP}, β_{ENP}) = [\begin{matrix} O_{x} (α_{ENP}, β_{ENP}) \\ O_{y} (α_{ENP}, β_{ENP}) \end{matrix}] .

(14)

Acknowledgments

This work is supported by contract # DMR-0216601 from the National Science Foundation, an Imaging Fellowship from the University of Arizona, and a gift from Intel Corporation.

References and links

1.	S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57,2615–2616 (1990). [CrossRef]
2.	Q. Wu, L. Ghislain, and V. B. Elings, “Imaging with Solid Immersion Lenses, Spatial Resolution, and applications,” Proc. IEEE ,88,1491–1498 (2000). [CrossRef]
3.	C. D. Poweleit, A. Gunther, S. Goodnick, and J. Menéndez, “Raman imaging of patterned silicon using a solid immersion lens,” Appl. Phys. Lett. 73,2275–2277 (1998). [CrossRef]
4.	L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. ,74,501–503 (1999). [CrossRef]
5.	T. D. Milster, “Near-field optical data storage: avenues for improved performance,” Opt. Eng. 40,2255–2260 (2001). [CrossRef]
6.	K Sendur, C Peng, and W Challener,“Near-field radiation from a ridge waveguide transducer in the vicinity of a solid immersion lens,” Phys. Rev. Lett. 94,043901 (2005). [CrossRef] [PubMed]
7.	M. Lang, T. D. Milster, T. Minamitani, G. Borek, and D. Brown, “Fabrication and characterization of sub-100 km diameter gallium phosphide solid immersion lens arrays,” Jpn. J. Appl. Phys. 44,3385–3387 (2005). [CrossRef]
8.	Q. Wu, G. D. Feke, Robert D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. ,75,4064–4066 (1999). [CrossRef]
9.	T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, and Y. Zhang, “The nature of the coupling field in optical data storage using solid immersion lenses,” Jpn. J. Appl. Phys. 38,1793–1794 (1999). [CrossRef]
10.	T. Ishimoto, K. Saito, M. Shinoda, T. Kondo, A. Nakaoki, and M. Yamamoto, “Gap servo system for a biaxial device using an optical gap signal in a near field readout system,” Jpn. J. Appl. Phys. 42,2719–2724 (2003). [CrossRef]
11.	T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32,124–126 (2007). [CrossRef]
12.	T. Chen, T. D. Milster, J. K. Park, B. McCarthy, D. Sarid, C. Poweleit, and J. Menendez “Near-field solid immersion lens (SIL) microscope with advanced compact mechanical design,” Opt. Eng. 45,103002 (2006). [CrossRef]
13.	A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216,398–410 (1968). [CrossRef]
14.	D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, and J. J. Fasano, “Optical field enhancement by long-range surface-plasma waves,” Appl. Opt. 21,3993–3995 (1982). [CrossRef] [PubMed]
15.	B. Ran and S. G. Lipson, “Comparison between sensitivities of phase and intensity detection in surface plasmon resonance,” Opt. Express 14,5641–5650 (2006). [CrossRef] [PubMed]
16.	A. Otto, “The surface polariton response in attenuated total reflection,” in Polaritons: Proceedings of the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. Demartina, ed.(Pentagon, New York, 1974), pp.117–121.
17.	D. Nam, T. D. Milster, and T. Chen, “Potential of solid immersion lithography using I-line and KrF light source,” Proc. SPIE ,5754,1049–1055 (2004). [CrossRef]
18.	B. Richards and E. Wolf, “Electromagnetic diffraction in optical system.2. Structure of the image field in an aplanatic system,” Proc. R.Soc.Londaon-A ,253 (1274), pp.358–379 (1959). [CrossRef]
19.	D. G. Flagello, T. Milster, and A. E. Rosenbluthk, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13,53–64 (1996). [CrossRef]
20.	T. D. Milster, J. S. Jo, and K. Hirota,“Roles of propagating and evanescent waves in solid immersion lens system,” Appl. Opt. 38,5046–5057 (1999). [CrossRef]
21.	H. A. Macleod Thin Film Optical Filters (McGraw-Hill, New York, 1989)

OCIS Codes
(210.0210) Optical data storage : Optical data storage
(240.6680) Optics at surfaces : Surface plasmons
(260.0260) Physical optics : Physical optics
(260.6970) Physical optics : Total internal reflection

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 11, 2006
Revised Manuscript: January 24, 2007
Manuscript Accepted: January 25, 2007
Published: February 5, 2007

Citation
Tao Chen and Tom D. Milster, "Properties of induced polarization evanescent reflection with a solid immersion lens (SIL)," Opt. Express 15, 1191-1204 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-1191

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References

S. M. Mansfield and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett. 57, 2615-2616 (1990). [CrossRef]
Q. Wu, L. Ghislain, and V. B. Elings, "Imaging with solid immersion lenses, spatial resolution, and applications," Proc. IEEE 88, 1491-1498 (2000). [CrossRef]
C. D. Poweleit, A. Gunther, S. Goodnick, and J. Menéndez, "Raman imaging of patterned silicon using a solid immersion lens," Appl. Phys. Lett. 73, 2275-2277 (1998). [CrossRef]
L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999). [CrossRef]
T. D. Milster, "Near-field optical data storage: avenues for improved performance," Opt. Eng. 40, 2255-2260 (2001). [CrossRef]
K. Sendur, C. Peng, and W. Challener, "Near-field radiation from a ridge waveguide transducer in the vicinity of a solid immersion lens," Phys. Rev. Lett. 94, 043901 (2005). [CrossRef] [PubMed]
M. Lang, T. D. Milster, T. Minamitani, G. Borek, and D. Brown, "Fabrication and characterization of sub-100 km diameter gallium phosphide solid immersion lens arrays," Jpn. J. Appl. Phys. 44, 3385-3387 (2005). [CrossRef]
Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, "Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens," Appl. Phys. Lett. 75, 4064-4066 (1999). [CrossRef]
T. D. Milster, J. S. Jo, K. Hirota, K. Shimura, and Y. Zhang, "The nature of the coupling field in optical data storage using solid immersion lenses," Jpn. J. Appl. Phys. 38, 1793-1794 (1999). [CrossRef]
T. Ishimoto, K. Saito, M. Shinoda, T. Kondo, A. Nakaoki, and M. Yamamoto, "Gap servo system for a biaxial device using an optical gap signal in a near field readout system," Jpn. J. Appl. Phys. 42, 2719-2724 (2003). [CrossRef]
T. Chen, T. D. Milster, S. H. Yang, D. Hansen, "Evanescent imaging with induced polarization by using a solid immersion lens," Opt. Lett. 32,124-126 (2007). [CrossRef]
T. Chen, T. D. Milster, J. K. Park, B. McCarthy, D. Sarid, C. Poweleit, and J. Menendez, "Near-field solid immersion lens (SIL) microscope with advanced compact mechanical design," Opt. Eng. 45, 103002 (2006). [CrossRef]
A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398-410 (1968). [CrossRef]
D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, and J. J. Fasano, "Optical field enhancement by long-range surface-plasma waves," Appl. Opt. 21, 3993-3995 (1982). [CrossRef] [PubMed]
B. Ran and S. G. Lipson, "Comparison between sensitivities of phase and intensity detection in surface plasmon resonance," Opt. Express 14, 5641-5650 (2006). [CrossRef] [PubMed]
A. Otto, "The surface polariton response in attenuated total reflection," in Polaritons: Proceedings of the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. Demartina, ed. (Pentagon, New York, 1974), pp. 117-121.
D. Nam, T. D. Milster and T. Chen, "Potential of solid immersion lithography using I-line and KrF light source," Proc. SPIE 5754, 1049-1055 (2004). [CrossRef]
B. Richards and E. Wolf, "Electromagnetic diffraction in optical system.2. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959). [CrossRef]
D. G. Flagello, T. Milster, and A. E. Rosenbluthk, "Theory of high-NA imaging in homogeneous thin films," J. Opt. Soc. Am. A 13, 53-64 (1996). [CrossRef]
T. D. Milster, J. S. Jo, and K. Hirota, "Roles of propagating and evanescent waves in solid immersion lens system," Appl. Opt. 38, 5046-5057 (1999). [CrossRef]
H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1989).

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