Survival of the orbital angular momentum of light through an extraordinary optical transmission process in the paraxial approximation

We report on the extraordinary optical transmission (EOT) of an orbital angular momentum (OAM) state of light in the paraxial approximation. The OAM state transmits through a subwavelength metal hole array with a square structure, and then is analyzed by using a Mach-Zehnder interferometer. In the experiment, the transmitted light well conserves the OAM information while the transmission efficiency of the OAM mode is much greater than 1 (i.e., EOT works). Further study shows that the OAM mode has no significant influence on the transmission spectrum of the EOT paraxial process under our experimental configuration. Our work can be useful for future plasmon-based OAM devices. ©2016 Optical Society of America OCIS codes: (050.4865) Optical vortices; (310.6628) Subwavelength structures, nanostructures; (100.3175) Interferometric imaging; (240.6680) Surface plasmons. References and links 1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. 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Introduction
The phenomenon of extraordinary optical transmission (EOT) was first reported in 1998 by Ebbesen et al., who studied the light passing through subwavelength metal hole arrays [1].What strongly attracts researchers is its greatly enhanced far-field transmission efficiency at #262997 certain wavelengths.Such phenomenon is contradictive to Bethe's classical aperture theory [2].Several theoretical models based on surface plasmon polaritons (SPPs) have been proposed to explain the fundamental aspects of the EOT effect in the past two decades [3][4][5].The EOT process is usually described as a photon-SPP-photon process, i.e., photons couple with free electrons to generate SPPs, which tunnel through the subwavelength holes and then convert back to photons.Recently, the quantum nature of SPPs has been studied in the EOT process with various quantum sources [6][7][8][9].Due to its easily-controlled spectral properties and its excellent sensitivity to the dielectric constant in interfaces, the EOT effect has been widely applied in optical filters, optical lithography, chemical and biological sensing, and other photonic devices [10][11][12][13][14][15].
The orbital angular momentum (OAM) of light was first proposed and demonstrated by Allen et al. in 1992 [16].Their pioneering work shows that the OAM is one of the important properties of photons.Typical OAM state in a Laguerre-Gaussian mode carries the azimuthal phase of ( ) exp ilϕ , where ϕ is the angular coordinate and l can be any integer value.l is also the so-called "topological charge (TC)" distinguishing different OAM states.OAM states have been widely used in optical tweezers, optical communication, quantum information processing and optical imaging [17][18][19][20][21].Its conversion to short-wavelength photons through nonlinear optical processes is an interesting topic in recent years [22][23][24][25].Much work has been done to investigate the polarizing and dynamic properties of an EOT process [26][27][28][29], however, a few authors discuss the case with an input of a spatial optical mode [30][31][32][33][34][35].In this letter, we present the experimental observation of the EOT effect with an OAM state.The OAM states passing through the subwavelength metal hole arrays are analyzed by using a standard configuration based on the Mach-Zehnder interferometer [36].Our experimental demonstration presents the direct evidence to show whether the collective electron oscillations during the EOT paraxial process in a metal hole array will change the OAM states.Also, by measuring the transmission spectrums of a Gaussian state and an OAM state, we study the influence of TC on the transmission efficiency.

Experiment and results
The optical components used to generate the OAM states are vortex phase plates (VPP-m633, RPC Photonics Inc.) working at a wavelength of 633 nm, which can produce OAM beams with TCs from l = 1 to l = 8 [Fig.1(a)].In order to match the working wavelength of the VPPs, a sample of subwavelength square hole array is fabricated in a 135 nm-thick Ag film sputtered on a SiO 2 substrate.The size of the sample is 64 µm × 64 µm.As shown in the insert of Fig. 1(b), each circular hole in the array has a diameter of 300 nm, which is spaced by a distance of 550 nm.Above parameters including the thickness of the Ag film, the array period and the hole size are optimized by the FDTD method [37].The dielectric constant of Ag used is −18.66 + 2.33i.
The transmission spectrum of the sample is characterized by using a normally-incident unpolarized white light source, which is reshaped to a near-parallel beam with a size of ~300 μm.The transmission peak locates at 633 nm [Fig.1(b)].The deviations from the corresponding simulation may result from the non-perfect fabrication of the sample.Figure 2 shows the schematic experimental setup based on the Mach-Zehnder interferometer.A linearly-polarized light beam from a He-Ne laser is divided by a beam splitter into a signal beam and a reference beam.After being reshaped, the signal beam passes through the VPP and carries a specific TC.The efficiency of the VPP is ~90%, which produces a good OAM mode.Then, the signal beam is focused by a 20X objective normally onto the sample, which is placed at the focal point of the objective.The objective has a numerical aperture of N.A. = 0.45 to decrease the size of the signal beam so that it can match the sample area.The optical alignment in this experiment is optimized for the Gaussian beam, which has a diameter of 40 μm at the sample surface [Fig.3(a)].The output intensity pattern after the EOT sample is imaged by another objective (10X, N.A. = 0.3) on a CCD camera.The transmitted OAM beam is turned paraxial after this objective.It can be replaced by a power meter (PM) to measure the transmitted light.The reference beam is first reshaped by a telescope system, and then is recombined with signal beam at another beam splitter for the mode analysis.The interference pattern is recorded by the CCD camera.At first, the reference beam is blocked to measure the directly-transmitted pattern after the metal hole array.By changing the VPP, the signal beams carrying TCs from l = 0 to l = 4 are generated.The corresponding input patterns are shown in Figs.3(a)-3(e), respectively.Clearly, the diameters of the patterns become bigger as the TC increases.Figures 3(f)-3(j) show the intensity patterns after passing through the sample, which are corresponding to l = 0, 1, 2, 3, and 4, respectively.The output intensity patterns are almost the same as the input ones under the paraxial experimental configuration.The small divergence may be caused by the scattering inside the sample.To find out whether the OAM modes change during the transmission process, it is necessary to measure the spatial phase distribution of the output patterns, which is closely associated with the TC of an OAM mode.The standard measurement of an OAM mode is to introduce a reference wave to interfere with it [36,38].Figures 3(k)-3(o) show the interference patterns after introducing the reference beam.In Fig. 3(k), the input mode carries no OAM information, i.e. l = 0.The Newton's rings indicate that the signal beam has a spherical wavefront, which is introduced by the focusing objective.When the input signal beam carries an OAM of l > 0, one can obtain the TC from the interference pattern by simply counting the number of the curves originating from the singularity of the signal beam [38].It is equal to the carried TC of the mode.As shown in Figs.3(l)-3(o), the transmitted optical modes carries the same TC as the input ones.Our results directly demonstrate that the OAM mode exists in the paraxial EOT process after it passes through such subwavelength metal hole array.Also, we performed a measurement of the transmission efficiency to show that the EOT effect works for all the TC numbers under our experimental configuration.Here, the transmission efficiency η is defined by ( ) , where out p , in p and σ are the output power, the input power, and the fraction of surface area occupied by the holes, respectively.Usually, the EOT effect can be identified when η > 1.In the experiment, we measured out p and in p of different OAM modes.The results are displayed in Table 1.All the transmission efficiencies normalized to the area of the metal holes are bigger than 1, which is a clear indicator of the EOT process [1].Based on above experimental results, we can claim that the OAM of light survives during a plasmon-assisted EOT paraxial process.From Table 1, it seems that the transmission efficiency deceases as the TC increases.After carefully observations of Fig. 3, one can find that the diameters of the signal beams are much smaller than the sample area when l = 0, 1, and 2. In these cases, most of the signal intensities experience the EOT process, which result in similar transmission efficiencies as shown in Table 1.When the input TC is increased to 3 or 4, the diameter of the OAM mode is close to or bigger than the array area, which results in considerable intensities of the input modes being blocked by the Ag film.Correspondingly, the measured transmission efficiencies are much lower than its actual values.In order to accurately measure the transmission efficiency, the optical alignment should be carefully optimized so that the whole input patterns transmit through the array area when changing the TC number in the experiment.
To further clarify the role of the TC in the EOT process, we measured the transmission spectrum of a Gaussian mode with l = 0 and an OAM mode with l = 3 [Fig.4(a)].The light source is a Ti:sapphire tunable laser.Its wavelength ranges from 690 nm to 1050 nm.The OAM mode is generated by using a spatial light modulator (SLM) at various input wavelengths.An incident beam from the laser is reflected on the SLM and is diffracted into different orders.A pinhole is used to select the first diffraction order, whose TC is decided by the loaded fork-grating on the SLM.Then, a 50X objective with N.A. = 0.42 is used to decrease the size of the signal beam to ~60 μm so that it can match the sample area.A 20X objective and a CCD camera form a monitoring system to guarantee that the whole beam transmits through the sample.The sample is a square metal hole array fabricated on a 130 nm-thick Ag film.Each circular hole is 300 nm in diameter with a period of 500 nm. Figure 4(b) shows the transmission spectrums between the wavelengths of 700 nm and 900 nm with input modes of l = 0 and l = 3.The measurement is performed with a wavelength interval of 5 nm.The measured curves of l = 0 and l = 3 well coincide with each other.The results clearly demonstrate that TC does not change the performance of an EOT paraxial process under our experimental scheme.

Conclusion
In conclusion, we experimentally demonstrate the survival of an OAM state of light during an EOT paraxial process.By using a Mach-Zehnder interferometer, the OAM state passing through a subwavelength metal hole array is analyzed.The experimental result shows that the OAM information is well conserved after such EOT process in the paraxial approximation.In addition, we investigate the transmission spectrum of the EOT paraxial process with an OAM mode, which has no obvious difference from that with a Gaussian input.Our work investigates the characteristics of a plasmon-assisted transmission of an OAM state, which has potential applications in integrated devices for OAM multiplexing and detection in optical communication.

Fig. 1 .
Fig. 1.(a) Phase patterns of VPPs with l = 1 to l = 8.(b) The experimental (red line) and simulated (blue line) transmission spectrums of the sample.The inserted picture in (b) is the SEM image of the sample.

Fig. 2 .
Fig. 2. The schematic experimental setup for the EOT of various OAM modes.A He-Ne laser generates a linearly-polarized Gaussian beam at the wavelength of 633 nm, which is divided into two beams by a beam splitter (BS).The signal beam carrying certain TC is focused by a 20X objective on the sample.The transmitted signal is imaged on the CCD by a 10X objective or collected by a power meter (PM).The reference beam is reshaped by a telescope to interfere with the signal beam.

Fig. 3 .
Fig. 3. Experimental observations of the OAM states during the EOT process.Columns from left to right correspond to the TCs from l = 0 to l = 4, respectively.The first row is the input intensity patterns.The second row is the output intensity patterns passing through the sample.The interference patterns between the signal beams and the reference beam are shown in the third row, where the number of the curves in the spiral patterns indicates the TC.

Fig. 4 .
Fig. 4. (a) The schematic setup for the measurement of the transmission spectrum.A light beam from a Ti:sapphire tunable laser is reflected by a SLM with a fork-grating loaded on it.The first-order diffraction beam carrying certain TC is focused on the sample.The transmitted signal is optimized by an imaging system and then is measured by a power meter (PM).The inserted picture in (a) is the hologram picture of the fork-grating.(b) Experimental results of the transmission spectrums with a Gaussian mode of l = 0 (red line) and an OAM mode of l = 3 (green line).Both are normalized to the area of the metal holes.The inserted picture in (b) is the SEM image of the sample.