Transflective digital holographic microscopy and its use for probing plasmonic light beaming

Yongjun Lim; Seung-Yeol Lee; Byoungho Lee

doi:10.1364/OE.19.005202

1. Introduction

Holographic microscopy is a sophisticated measurement technique which provides either an amplitude-contrast image or a phase-contrast image [1–4]. With the detected wavefront of the target objects, optical information emanating from them can be investigated and identified through numerical reconstruction methods [4–8]. For the last two decades due to the advancement of the charge-coupled devices (CCD) and the microscope objective with high numerical aperture, there have been intensive researches on the holographic microscopy techniques that provide various ways to perform three-dimensional imaging [9–16]. With these developments and advancements of hardware platforms, an accurate numerical reconstruction method for reconstructing detected coherent optical wavefront makes it more relevant for digital holographic microscopy to be applicable for nano-technology and bio-technology [9, 12, 13, 15, 17–21]. While wave nature of coherent light has played a central role in digital holographic microscopy, vectorial property of light waves represented as a polarization state is able to be implemented [22, 23]. Consequently, material properties such as birefringence and anisotropy were measured, and a multiplexing scheme has been introduced in the digital holographic microscopy [24–26]. Meanwhile, as novel photonic devices in nano scale regimes appear and the optical distributions accompanied by them require detecting in detail, measurement techniques that provide optical phenomena and their structural information are desirable especially when simultaneous detection of both of them are possible. Especially, in a recent emerging field of plasmonics, not a few works on plasmonic beaming phenomena have been reported [27–32]. On one hand, as is shown by those previously reported works, plasmonic beaming and the related phenomena occur at the optical far-field region, and we reported that holographic microscopy can effectively probe the beam path of plasmonic light beaming phenomena by adopting a phase-shifting technique [33]. Here, only the beam-path generated by plasmonic light beaming and focusing was detected by transmission-type holographic microscopy. On the other hand, various configurations showing plasmonic beaming phenomena have been demonstrated by inscribing periodic corrugation on metallic films circumventing a narrow slit structure or by modifying geometrical structures in subwavelength metal slit array configurations, but simultaneously measuring both the beam path and the corresponding base platform is hard to be achieved when referring to the previously used techniques such as confocal microscopy and scanning near field optical microscopy [34, 35]. In principle, the horizontally polarized light (p-polarized) is used to excite surface plasmons on metal-dielectric interface, so adopting the polarization property of light in digital holographic microscopy can induce a novel measurement technique adequate for measuring plasmonic devices, especially where both probing the beam propagation behaviors and viewing the corresponding platform structures are required to be measured. Hence, in this article, by separating the polarization state of the signal beam in conventional digital holographic microscopy, the optical distribution of the generated plasmonic light beaming is detected by transmission-mode holographic microscopy, and the base platform structure, i.e. façade of the metal structure, generating plasmonic light beaming phenomena is detected by reflection-mode holographic microscopy, both of which are launched simultaneously. To denote this concept, we use the term, transflective, a term borrowed from liquid crystal display systems [36], meaning a selectively-activated mode of transmission, reflection or both of them. Hence, we present digital holographic microscopy technique termed transflective digital holographic microscopy (TDHM), and its application for use as detecting a beam path and its platform structure in plasmonic light beaming is to be presented. After simply showing the fundamental relationships necessary for our TDHM, the experimental demonstration with a conventional USAF-1951 mask target is made, and then the application of our proposed technique is to be shown with planar metal slit array structures generating plasmonic light beaming phenomena. Although the term ‘transflective’ was also recently used by another group [37], the system used two CCDs and two piezo-electric devices, which is just a straightforward combination of two digital holographic microscopic systems. Preliminary version of our work was presented at a conference [38].

2. Fundamental concepts

Complex wavefront reconstruction is computationally performed in digital holographic microscopy, and the requisite numerical reconstruction methods have been widely suggested. Unlike conventional transmission mode and reflection mode activating independently, our TDHM follows the following relationships which are used in the polarization imaging by the use of digital holographic microscopy [22–24].

\begin{array}{l} I_{H} = {| Ψ_{R} + Ψ_{O T} + Ψ_{O R} |}^{2} \\ = {| Ψ_{R} |}^{2} + {| Ψ_{O T} |}^{2} + {| Ψ_{O R} |}^{2} + Ψ_{R} Ψ_{O T}^{*} + Ψ_{R}^{*} Ψ_{O T} + Ψ_{O T} Ψ_{O R}^{*} + Ψ_{O T}^{*} Ψ_{O R} + Ψ_{R} Ψ_{O R}^{*} + Ψ_{R}^{*} Ψ_{O R}, \end{array}

where

Ψ_{R}

,

Ψ_{O T}

and

Ψ_{O R}

are respectively the reference wave, the object wave from the transmission mode and the object wave from the reflection mode.

If two object waves, $Ψ_{O T}$ and $Ψ_{O R}$ , are orthogonal to each other, the following relation is valid:

Ψ_{O T}^{} Ψ_{O R}^{*} = 0,

which means two orthogonally polarized light do not interfere with each other. Accordingly, two terms indicating the interference between two object waves including the conjugate term of each object wave vanish as is shown below.

Ψ_{O T}^{} Ψ_{O R}^{*} + Ψ_{O T}^{*} Ψ_{O R}^{} = 0.

Hence, Eq. (1) can be simply arranged as follows.

\begin{array}{l} I_{H} = {| Ψ_{R} |}^{2} + {| Ψ_{O T} |}^{2} + {| Ψ_{O R} |}^{2} + Ψ_{R} Ψ_{O T}^{*} + Ψ_{R}^{*} Ψ_{O T} + Ψ_{R} Ψ_{O R}^{*} + Ψ_{R}^{*} Ψ_{O R} \\ = {| Ψ_{R} |}^{2} + {| Ψ_{O T} |}^{2} + {| Ψ_{O R} |}^{2} + Ψ_{R} (Ψ_{O T}^{*} + Ψ_{O R}^{*}) + Ψ_{R}^{*} (Ψ_{O T} + Ψ_{O R}), \end{array}

where

I_{H}

denotes the intensity of the recorded hologram on the CCD. From the above Eq. (4), it can be concluded that the recorded hologram excludes the interference between two object waves, and the conventional procedure is adopted to reconstruct the hologram. After the hologram intensity is captured by the CCD, the wavefront of the objective wave is reconstructed by a numerical method. Though several methods have been suggested to suppress or to effectively efface the quadratic DC term, we adopt phase shifting interferometry [39–43]. By referring to the previously shown methods in the polarization microscopy with phase-shifting interferometry configuration, Jones matrix formalism is applied to our numerical reconstruction relationships represented as follows.

Ψ_{R} = (\begin{array}{l} E_{x} \exp (i ϕ_{x} (x, y)) \\ E_{y} \exp (i ϕ_{y} (x, y)) \end{array}),

Ψ_{O T} = (\begin{matrix} 0 \\ E_{O T} \exp [i ϕ_{O T} (x, y)] \end{matrix}),

Ψ_{O R} = (\begin{matrix} E_{O R} \exp [i ϕ_{O R} (x, y)] \\ 0 \end{matrix}) .

Hence, the resultant interference intensity pattern recorded by the CCD is written as follows.

I_{H} (x, y) = E_{R}^{2} + E_{O T}^{2} + E_{O R}^{2} + 2 Re {E_{x} E_{O R}^{*} \exp (Δ_{X})} + 2 Re {E_{y} E_{O T}^{*} \exp (Δ_{Y})},

where

E_{R}^{2} = E_{x}^{2} + E_{y}^{2},

Δ_{X} = ϕ_{x} (x, y) - ϕ_{O R} (x, y),

and

Δ_{Y} = ϕ_{y} (x, y) - ϕ_{O T} (x, y) .

Here, we assume that $E_{x}^{2} = E_{y}^{2} .$ Consequently, with the 4-step phase-shifting interferometer, the object wave can be derived from the four different images with relative phase shift of $π / 2$ in tandem, and the resultant object wave at the CCD plane, $Ψ_{S} (x, y)$ , is given as follows:

Ψ_{S} (x, y) = \frac{1}{4 Ψ_{R}^{*}} [I_{H 1} - I_{H 3} + j (I_{H 4} - I_{H 2})],

where

I_{H i}

(i=1, 2, 3, 4) means

I_{H}

in Eq. (4) with relevant phase shifts in reference beam. By adopting Fresnel transformation, the resultant object wave at the image plane,

Ψ_{R E} (u, v, z)

, is given as follows.

Ψ_{R E} (u, v, z) = \iint Ψ_{S} (x, y) \exp (j k z) \exp [\frac{i k}{2 z} {{(u - x)}^{2} + {(v - y)}^{2}}] d x d y .

In addition, as we adopt off-axis geometry, the additional phase terms are added in Eqs. (10) and (11) and we apply an experimentally-detected reference wave rather than a digitally-given reference wave to Eq. (13). In frequency domain, we can arrange Eq. (13) as the following form while taking convolution algorithm into our considerations.

F . T . [Ψ_{R E} (u, v)] = F . T . [Ψ_{S} (x, y)] H (f_{x}, f_{y}),

where F.T. stands for Fourier transform. Numerical methods for retrieving the recorded wavefront are required as long as the above Fresnel integral formula, Eq. (13) is related, and we use the following reconstruction algorithm appropriate for relatively short distance range. If we regard

U_{R E}

and Uare respectively Fourier transform of

Ψ_{R E}

and

Ψ_{S}

, the following relationship can be adopted [6, 8].

\begin{array}{l} U_{R E} (f_{x}, f_{y}; s, t; z_{0}) = \sum_{m, n = - \infty}^{\infty} U (f_{x} - \frac{m}{Δ x}, f_{y} - \frac{n}{Δ y}; 0) H (f_{x} - \frac{m}{Δ x}, f_{y} - \frac{n}{Δ y}; s, t; z_{0}) \\ + \sum_{m, n = - \infty}^{\infty} U (f_{x} - \frac{m}{Δ x}, f_{y} - \frac{n}{Δ y}; 0) \sum_{\begin{array}{l} p, q = - \infty \\ p \neq m; q \neq n \end{array}}^{\infty} H (f_{x} - \frac{p}{Δ x}, f_{y} - \frac{q}{Δ y}; s, t; z_{0}), \end{array}

where

H (f_{x}, f_{y}; s, t; d) = \exp [i 2 π (f_{x} s + f_{y} t)] \exp [- i \frac{2 π d}{λ} {(1 - λ^{2} f_{x}^{2} - λ^{2} f_{y}^{2})}^{1 / 2}] .

Here, spatial frequencies, $(f_{x}, f_{y})$ are determined by the horizontal pixel size ( $Δ x$ ) and vertical pixel size ( $Δ y$ ) of the CCD, and $(s, t)$ denotes the arbitrary position at the CCD plane. In the next section, experimental demonstration for TDHM is made.

3. Experiments

In Fig. 1 , the schematic diagram for the proposed TDHM configuration is shown. As is shown in Fig. 1, the p-polarized light wave passing through the collimation optics configuration is firstly separated in two ways. One is the reference arm, and the other is the signal arm. At the beam splitter (B.S.) 2, the signal beam is split into the transmission-mode path and the reflection-mode path. And then, the p-polarized light illuminates the rear-side of the object at the transmission-mode path, and the s-polarized light used as a reflection light source is shown-up after passing through the half wave retarder placed in the reflection mode path. Hence, two orthogonally polarized light waves illuminate the rear side and the front side of the target object, respectively. In the reference arm, the circularly polarized light reaches the CCD after being reflected from the piezo-electric driven mirror. Consequently, two orthogonal linearly-polarized light waves and one circularly polarized light contribute to the resultant interference pattern which is to be captured by the CCD.

Fig. 1 Schematic diagram for the proposed TDHM.

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In our experiment, an Nd:YAG laser with a wavelength of 532 nm (Verdi, Coherent Corp.) is used as the light source. An XYZ-38 made by Piezosystem Jena is used as the piezo-electric driven stage for the phase shifter, and a SONY XCD-SX90 with 1280 (horizontal) × 960 (vertical) pixels is used as the CCD, each pixel size of which is 3.75 μm × 3.75 μm. Two SIGMA KOKI 65GR mechanical shutters are used to automatically block the signal waves depending on each activating-mode. In other words, the shutter 1 is open for the transmission mode, the shutter 2 is open for the reflection mode and both of them are open for the transflective mode. An Olympus BXFM is used for the microscopy, and a 100× LMPlanLN with numerical aperture of 0.85 is used as the microscope objective. The resultant field of view at the CCD plane is 24 μm(horizontal) × 18 μm(vertical). To experimentally verify our proposed TDHM, the conventional USAF target pattern is used, the minimum resolution of which is 228 lp/mm. According to the light-illumination mode, the detected object wavefronts are properly retrieved. In Fig. 2 , the retrieved images are shown according to each operating-mode. Figure 2(a), (b) and (c) are retrieved amplitude images of the transmission mode, reflection mode and transmission mode respectively, and Fig. 2(d), (e), and (f) are retrieved phase images of the transmission mode, reflection mode and transflective mode, respectively. As is shown by Fig. 2(c), the amplitude image acquired by the transflective mode contains the boundary line of the inscribed pattern. Even though unwanted phase aberration appears due to the small path-difference between two objective waves and the tilt of the target image, conventional methods can be used to compensate for these aberration-oriented problems. We use the negative lens in the reference arm before the beam splitter 4 as is seen in Fig. 1. As is seen in Fig. 2, our proposed concept is verified, and the transflective mode can provide both the transmitted and reflected wavefronts simultaneously. In Fig. 2(c), the amplitude image shows the distinct boundary line between the opaque area (surface of the USAF-1951 test target) and the transparent area. Due to the orthogonal property of two object waves, the retrieved amplitude image contains the optical information simultaneously given by the transmitted light (p-polarized) and the reflected light (s-polarized). Based on this fundamental experiment regarding our proposed TDHM, we use the TDHM to probe the optical far-field distribution of plasmonic light beaming phenomena and to view their platform structures in the following section.

Fig. 2 Experimental verification of TDHM using conventional USAF test target images. The amplitude image acquired by (a) the reflection mode, (b) the transmission mode, and (c) the transflective mode. The phase images obtained by (d) the reflection mode, (e) the transmission mode, and (f) the transflective mode.

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4. Application for plasmonic light beaming phenomena

In this section, we apply our TDHM for probing the beam path of plasmonic light beaming and viewing the corresponding platform structure. In Fig. 3 , the schematic diagram for generating plasmonic beaming phenomena is shown. Related to the physics of the generation of the plasmonic light beaming, not a few works have been reported [27–30, 32, 44]. In these previous works, controlling the intense radiation field accompanied with surface plasmon waves can effectively make beaming and focusing based on the geometrical modification of thin metallic films. As for the metal slit array structures, the number of slits inscribed in the metallic film can affect the radiation field. In other words, the more slits are placed in the metallic film, the more intense the plasmonic beaming field becomes. It was also shown that geometrical modification of metal slit array structures can make other optical phenomena such as beam focusing and off-axis (angled) beaming [44]. Hence, it is necessary to use an appropriate measurement technique probing the generated optical far-field distribution. More desirably, simultaneous measurement of the platform structure and the beam path can make a clear distinction among the fabricated plasmonic beaming structures. In this paper, we simply adopt plasmonic light beaming affected by the number of slits inserted in the thin metal film, where the period of the slit array, the thickness of the Ag film and the fill factor are respectively 400 nm, 500 nm, and 0.5. In our numerical analysis, rigorous coupled wave analysis (RCWA) technique is used to visualize the intensity pattern of plasmonic light beaming phenomena [45,46]. In our simulation, the p-polarized light with the wavelength of 532 nm is used to generate plasmonic beaming, and the indices of substrate and the silver layer are respectively 1.46 and 0.13+i3.2 at the given wavelength.

Fig. 3 Geometry for generating plasmonic light beaming phenomena.

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In Fig. 4 , the numerically calculated results are shown, and the number of slits inserted in the thin metal film in Fig. 4(a), (b) and (c) is 5, 7 and 9, respectively. As is seen in Fig. 4, the number of slits that are inserted in the silver layer affects the intensity distribution at the optical far-field regions. To identify these beam patterns and to view the difference between those constituting structures, our proposed TDHM is used. We use focused ion beam machining (Quanta 200 3D, FEI Corp.) to inscribe the narrow metal slit array structures after depositing a 500 nm Ag layer on the SiO₂ substrate, and the SEM images of the fabricated structures are shown in Figs. 5(a), (b) and (c) . As we are interested in optical field distributions and the images of the platforms structures, amplitude images are mainly retrieved as is shown in Figs. 5(d) through (l). Reconstructed images regarding the corresponding surface structure are given by the reflection mode, which are shown in Figs. 5(d), (e) and (f). Here, structures between each slit are not clearly shown because of the aliasing caused by the inherent diffraction limit of the system, i.e. the resolution limit of the microscope objective. However, it is expected that recently proposed concepts on improving resolution limits are expected to be adopted [47–49].

Fig. 4 Numerically calculated results for plasmonic light beaming depending on the number of inscribed slits in the Ag layer. The intensity distribution on the x-z plane when the number of slits is (a) 5, (b) 7, and (c) 9.

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Fig. 5 (a), (b) and (c) are SEM images of the fabricated metal slit array structures. (d), (e) and (f) are retrieved surface images obtained by the reflection mode. (g), (h) and (i) are x-z plane images showing the intensity distributions of plasmonic light beaming detected by the transmission mode. (j), (k) and (l) are amplitude images concurrently showing the optical beaming and the corresponding structure, obtained by the transflective mode.

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The beam-paths or the intensity distributions on the x-z plane acquired by the transmission-mode configuration are shown in Figs. 5(g), (h) and (i), respectively, and the retrieved images simultaneously showing the beams and the corresponding structures based on TDHM are shown in Figs. 5(j), (k) and (l). Figures 5(j) through (l) provide the optical information regarding the fabricated slit structures and optical field distributions centered around them at the same time. We clearly observe the generated beaming field emanating from the center of the fabricated metal slit array structures. This is the featuring property of our proposed TDHM in that two orthogonal waves can be retrieved at the same time. Due to this characteristic, we can identify that the generated beaming fields are distributed along the center of the fabricated slit array structures, while perceiving the boundary line between the fabricated structure and the surface of the silver film. In addition, we can observe that the generated plasmonic beaming field is different from one another and gradually increases according to the number of carved slits through our experimental results shown in Figs. 5(d) through (l). Compared to theoretical values, errors on fabrication such as surface damage caused by focused ion beam milling and roughness on the silver film during e-beam evaporation process mainly affect the radiation field at the exit region of each slit. Hence, the experimental results are not perfectly matched with those numerical ones. Additionally, as we use temporal phase shifting interferometry, errors such as intensity fluctuation of the light source, aberration of optics, unwanted multiple reflections of optics and vibration cause unwanted noises during holographic measurement process. Though we do not take into account those errors to improve numerical analysis results, we observe good agreement between numerical results and experimental results Figs. 5(g) through (i).

5. Conclusions and discussions

In this paper, we proposed transflective digital holographic microscopy, which is achieved by the separation of polarization of the incident light. By utilizing the polarization properties of light waves, we achieve the concurrent activation of transmission and reflection microscopy in the field of digital holography. By applying the proposed concept in the plasmonic beaming light phenomena, both the optical field distributions and the constituting platform metal structures are effectively and concurrently retrieved. Though we used mechanical shutters to activate each mode, alternative methods such as dividing phase steps into proper polarization states and placing a polarizer in front of the CCD as an analyzer may be used to achieve our proposed TDHM. We showed that three similar types of plasmonic beaming can be implemented by planar metal slit array structures, and we observed and demonstrated that there exists a difference between them according to the number of the slits by the use of transflective mode of digital holographic microscopy. We expect that our proposed configuration can be used to know how to correctly identify the difference between the transmission through slits and plasmonic beaming phenomena with extraordinary optical transmission, and the controversial questions regarding the generation of plasmonic beaming and the transmission through slits are expected to be unraveled by adopting our proposed method. We hope our suggested holographic microscopy technique can be used in the measurement of other optical phenomena and the detection of boundary area of various kinds of membranes in biology where both the surface measurement and the detection of beam path generated by the related structures are required at the same time.

Acknowledgment

The authors wish to acknowledge the support of the National Research Foundation and the Ministry of Education, Science and Technology of Korea through the Creative Research Initiative Program (Active Plasmonics Application Systems).

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Transflective digital holographic microscopy and its use for probing plasmonic light beaming

Abstract

1. Introduction

2. Fundamental concepts

3. Experiments

4. Application for plasmonic light beaming phenomena

5. Conclusions and discussions

Acknowledgment

References and links

Cited By

Figures (5)

Equations (16)

Optics Express