Guided-mode propagation loss with different parameters
Controlling and guiding light with planar waveguide has a great potential to fabricate attractive optical devices such as modulators , filters  and sensors . Although many studies use planar waveguide made of dielectric materials or semiconductors, metals also play an important role in this field. Metals have been usually used as mirror in the visible or infrared regions. By constructing the dielectric layer sandwiched by two metal layers and forming the metal-dielectric-metal (MDM) structure, we can obtain the unique optical properties which the dielectric planar waveguides do not have. Recently, Shin
This type of MDM can be expected to have the interesting optical features not only in the negative refraction index but also in the mode properties. The above mentioned waveguide structure can commonly accommodate only surface plasmon mode. When the thickness of guiding layer is increased to millimeter-scale, such waveguide can accommodate thousands of guided modes, and ultrahigh-order modes (UHM) can be excited. In this case the MDM is commonly called symmetrical metal-cladding waveguide (SMCW) . To our knowledge, however, there have been few investigations about the UHM properties of the SMCW. In this chapter, we have reported the UHM properties of the SMCW and their applications on optical devices. The UHM of SMCW can be excited by free space coupling  in small incident angle. In section 2, we present some details of the UHM properties such as large mode spacing, sensitive to the change of waveguide parameters, and slow wave effect. Section 3 introduces applications on optical devices such as modulators, filters and sensors, which are closely related to the UHM in guiding layer.
2. Properties of SMCW
The SMCWs are the millimeter-scale guiding layers (dielectric constant
2.1. The attenuated total reflection spectrum
When a laser beam cast on the upper metal layer with resonant conditions, a large part of the light energy is transferred in the guiding layer, resulting in the attenuated total reflection (ATR) spectrum, which describes the relation between reflectivity and incident angle or wavelength of the reflected light. We take TE mode for example. The reflection coefficient of the four-layer optical system for TE mode is written as 
here rij=(κi-κj)/(κi+κj), is the complex Fresnel reflection coefficient for the boundary between media i and j, in which the normal components of the wave vectors and propagation constant of guided modes are, respectively, expressed as follows:
here k0=2π/λ is the wavenumber in vacuum; ε3 is the dielectric constant at medium in which the light incident and reflected;
The experimental arrangement for measuring ATR spectrum is shown schematically in Fig.4. The SMCW is fixed on a computer controlled
2.2. Ultrahigh-order mode
Disregarding the effects resulting from the limited thickness of the metal film, dispersion equation of the guided modes in SMCW can be written as
where attenuated coefficient in the metal α2=iκ2, m is the mode ordinal number of guided mode. The parameters relevant to polarization are given by:
According to Eq. (4), we can deduce an approximate formula:
Furthermore, when d reaches millimeter-scale, the waveguide can accommodate thousands of guided modes. For example, use the parameters: ε2 = −28 + i1.8, ε1 = 2.278, λ= 859.8nm,
where N =
Because UHMs have a short retention time in waveguide layer, any tiny change of
From above mentioned three equations, sensitivity is in inverse proportion to effective index
Finally, according to Eq. (4), tiny change of wavelength can generate great change of effective index, illustrating that UHM has strong dispersion property and consequent slow light effect. Using Eq. (7), we can also obtain the group velocity of UHM:
In the equation, group velocity expression is totally different from those conventional slow light schemes, which is composed of two contributions that are shown in Eq. (12): one originates from the first-order dispersion resembling the conventional slow light system, and factor
2.3. Propagation loss
Once SMCW is used to achieving optical devices, the important concern relating to the SMCW is that metallic structures exhibit high losses at optical wavelengths. An issue arising is whether the UHMs could be efficiently confined to the guiding layer over a long distance transmission. To see this clearly, four types of metal cladding waveguides have been considered as shown in Fig.5. Fig.5(a) is a structure of three-layer metal cladding waveguide without considering metal and radiative loss. By using three-layer waveguide theory, for TE mode, propagation constant,
where m0 is mode order.
Fig.5(b) is a structure of SMCW only with considering radiative loss. Comparing Fig.5(b) with Fig.5(a) by using weak-coupling condition, which is satisfied with four-layer system , the radiative damping, Im(Δ
Where is the absorption constant of the cladding layer, is the vertical guiding wave vector of three-layer metal cladding waveguide without considering the metal absorption,
Fig.5(c) is a structure of three-layer metal cladding waveguide only with considering metal loss. Comparing Fig.5(a) with Fig.5(c) under the condition of |ε2r|>>ε2i at visible and near infrared wavelength, we can obtain that metal loss only affects the imaginary part of propagation constant in three-layer metal cladding waveguide. Then the intrinsic damping, Im(
2.4. The enhanced Goos–Hänchen effect
When the weak coupling condition |exp(2i
According to stationary phase method, the Goos-Hänchen (GH) shift L is expressed as:
With the parameters ε3=1, ε1=2.278, ε2=-28+1.8j,
To measure the shift while avoiding small spurious displacement, we use the wavelength interrogation-based method by combining a tunable laser and a one-dimensional position sensitive detector (PSD). The position of the incident light can be determined by the PSD through the photocurrents from the output electrodes x1 and x2 (see Fig.7):
here I1 and I2 are the photocurrents of the output electrodes x1 and x2, respectively. V1 and V2 are the voltages converted from I1 and I2 after amplifier circuit. The analog voltages V1 and V2 are further converted into digital signals and collected by the computer (PC). Light displacement measurement using PSD can achieve high sensitivity and accuracy and will not be affected by the change of the light intensity.
The experimental arrangement for measuring GH shift is shown in Fig.7 . After passing through two apertures (A1, A2) and a splitter (S1), a large part of the Guassian beam from a tunable laser was introduced onto the SMCW. Another part of the beam, which is reflected from S1, irradiated the second splitter (S2) and is detected by a wavemeter connected to a computer. We choose to excite the UHMs, because of the polarization independence of the UHMs, TE and TM incidences have nearly the same characteristics. The reflected light from the SMCW was first detected by a photodiode (PD). Angular scan was performed by rotating the goniometer and the ATR spectrum was generated. We selected the operation angle to be located at the maximum reflectivity near a certain dip of the spectrum (Position 1). The GH effect is not remarkable at this position due to the deviation of the resonance condition. The position of the reflected beam was set as the reference at this point. Then we moved the PD out of the light path (Position 2) without changing any position of the incident beam and let the reflected light beam cast onto the center of the PSD perpendicularly. Then by changing the wavelength through temperature tuning, the variation of
3. Optical devices based on SMCW
The above mentioned properties of UHM in SMCW have been widely used to applications on optical devices. Here, we list several practical application examples, such as filter, sensor, modulator and slow wave device. Due to its excellent performance and simple structure, optical devices based on SMCW have the potential applications in many fields.
3.1. Tunable comb filters
As mentioned above, a sub-millimeter SMCW is capable of coupling the incident light with a fixed wavelength from free space into the glass slab directly. As the excitation of the guided modes results in resonant transfer of energy from the incident light, guided modes manifest themselves by a series of resonant dips in the reflectivity when the incident angle is varied. On the other hand, if a polychromatic light is used instead of a single-wavelength light, resonant dips at a fixed incident angle can also be achieved in a spectral plot of the reflectivity. In this way, a comb filter is built . For a better understanding of how it works, we consider the UHMs of the sub-millimeter SMCW in the case of free space coupling. Eq. (7) can be rewritten as
It is found that
From Fig.9, we can see equally spaced loss peaks with a 3 dB line-width of 0.1 nm appear in the spectral plot from 1551 to 1556 nm. The wavelength spacing of these peaks is just 0.8 nm. The channel isolation, which is closely related to the thickness of the upper gold film of the waveguide, has been found to be 12 dB. Insertion loss is characterized by the maximum reflectivity, which is greater than 95% (~0.2 dB). The tunability of the filter can be obtained simply by slightly rotating the waveguide with respect to the incident light. Tuning of the center wavelength in the range of channel spacing can be easily obtained by changing several degrees of the incident angle according to Eq. (26).
3.2. Optical sensors
In this section, we propose oscillating wave sensors using SMCW structure. The thickness of guiding layer can be expanded to millimeter scale, which it can contain very sensitive UHM. The high sensitivity can be detected by measuring the intensity variation of the reflected light due to the movement of the corresponding synchronous angle by an optical sensor. In addition, an alternative approach is presented via measuring the enhanced GH shifts at excitement of UHM. This approach enables the possibility to obtain a higher resolution and prevent the disturbance caused by the power fluctuation of the light source.
3.2.1. Sensitivity analysis
If we using the intensity measurement interrogation to observe the response of the sensor, the sensitivity in SMCW can be defined as the rate of change of the reflectivity to center characteristics parameters which is expressed as:
Using the phase matching condition of resonance energy transfer, the effective refractive index N can be expressed as
Combined (28) with (29), the sensitivity
where SN is defined as the rate of change of the effective refractive index N with respect to certain characteristic parameter and determined by Eq.(9)-(11). As described in section 2.2, optical waveguide oscillating field sensor exhibits the substantial improvement: the UHMs of the SMCW with millimeter scale is selected to act the sensing probe, so
Taking wavelength sensing for example , use the parameters: ε2 = −28 + i1.8,
Similarly, in the GH shift interrogation, the sensitivity of the sensor is defined by the change rate of the GH shift (L) with respect to center characteristics parameters and it can be written as
Compared with the intensity interrogation, the only difference is the replacement of SR by SL. According to Eq. (22), if the intrinsic damping of the UHM is close to the radiative damping, a large GH shift can be observed . The dependence of the GH shift on the effective index for a selected mode forms a resonance peak. High sensitivity
Moreover, the thickness of the upper metal cladding is also an important factor that must be considered when analyzing the sensitivity. The thicknesses of upper and bottom metal films are essential parameters in the determination of the sensitivity. If thickness
3.2.2. Refractive index sensing
In the intensity interrogation (as illustrated in Fig. 11(a)), the sample is sealed by an O-ring sandwiched between two gold films that deposited on glass substrates. The two gold films and the sample cell form the SMCW structure. The upper gold film (35 nm in thickness) is deposited on a thin glass slide. The glass slide is 0.178 mm in thickness, with a RI of 1.50. The lower gold film (300 nm) is deposited on a glass plate. The lower glass plate’s thickness is 2 mm with an RI of 1.50. The dielectric constants of the gold films are −11.4+i1.50 at the wavelength of 650 nm. The sample cell serves as the guiding layer of the waveguide sensor, and the thickness of the sample cell is governed by the thickness of the O-ring of about 1.99 mm. The aqueous sample could be pumped in and out of the sample cell by a peristaltic pump through the inlet and outlet on the lower substrate. The water sample with an RI of 1.333 can be used as the guiding layer of the waveguide. The guided wave concentrates and propagates in the sample layer as the oscillating field and hence a magnification in sensitivity is expected. Fig.11(b) is the sensor sample .
Based on sensitivity analysis, SI can be cast in the form of
Then we can see that the use of a smaller incident angle (1.69° in the experiment) as a sensing probe can achieve higher sensitivity. The experimental results are shown in Fig.12. In this case, a 20 ppm NaCl concentration change (corresponding to 2.6×10−6 RIU) can cause a reflectance change of around 3%.With a standard error of 0.2% for the measurement of the optical intensity, its resolution with 1% noise level can reach up to 0.88×10-6 RIU for the ideal case.
In the GH shift interrogation (as illustrated in Fig. 13), a glass prism is coated with a 20 nm thick gold film to serve as the coupling layer. A 300 nm thick gold film is sputtered on a glass slab to act as the substrate. The air gap of 0.7 mm sandwiched between two gold films works as the guiding layer, where a gasket is used to form a sealed sample cell. With the help of a peristaltic pump, sample liquids to be detected flow into the cell through the inlet and the outlet tubes embedded in the substrate glass plate.
The expression of sensitivity SGH is similar to Eq. (36) by replacing SR with SL. So UHM is also selected as a sensing probe. Experiments are carried out with the waveguide parameters as follows:
3.2.3. Displacement sensing
In the experimental setup, we propose to use a variable air gap produced by a calibrated piezoelectric translator (PZT) to act as the guiding layer of the optical waveguide. As shown in Fig.15, the sample for minute displacement measurement is composed of two parts: one is a glass prism on its base precoated with a thin gold film; the other is a 500 μm thick LiNbO3 slab sandwiched between two 400 nm thick gold films and serves as a PZT. The two components, separated by an air gap with a thickness of 100 mm, are rigidly mounted on a heavy platform. The gold films deposited on the prism and the upper surface of LiNbO3 slab, together with the air gap form an SMCW.
As soon as applying a dc voltage on the pair electrodes of the PZT, the air gap changes its thickness due to the piezoelectric effect of the LiNbO3 slab. As a result, the reflection dip shifts its peak position and result in a change of the reflectivity. According to the resolution of the reflectivity variation, displacement can be evaluated from the applied voltage and the piezoelectric coefficient of the LiNbO3 slab. In the intensity interrogation, SI can be cast in the form of
We can also use UHM as the sensing probe to achieve higher sensitivity. Test experiment has been performed with the waveguide parameters as follows:
In the GH shift interrogation, the sensor structure is the same as Fig. 15. The experiment was performed with the following parameters: ε2=−28+1.8i, ε1=1, ε3=2.25,
3.2.4. Wavelength sensing
In the intensity interrogation, the wavelength sensitivity SI can be written as
It is found that the effective index is extremely sensitive to
For the GH shift measurement, the waveguide parameters are given as follows:
3.3. Optical modulators
The configuration of electro-optic (EO) modulator is a SMCW on a glass (K9) flat. The cover and the substrate are both gold film, and the waveguide is EO polymer film. An applied electric field modulates refractive index of the EO polymer, resulting in the change of the effective refractive index for the guided modes, shifting the resonance dips along the angular direction in ATR spectrum. If we define γ33 as the EO coefficient of the polymer and E is the applied electric field across the EO polymer film. The refractive index change of guiding layer Δn1 is written as :
At the midst of the fall-offs of resonance dip, where a considerably good linearity is observed, the change of the light reflectivity R is:
Therefore the reflected light is modulated by the applied electric field. Higher sensitivity is obtained at the midst of the fall-off of the resonance dip excited at smaller resonance angle with thicker guiding layer, so that enhanced modulation is realized by enabling the device to operate with stronger modulation depth and lower driving voltage.
In the experiment, the gold film about 300nm was sputtered onto the surface of the K9 glass flat to serve as substrate and one electrode. A PMMA-based second-order nonlinear optical (NLO) side-chain material containing the disperse red chromophore was synthesized through copolymerization for electro-optic device. The polymer was dissolved in toluene, 25% polymer to 75% toluene by weight. A 12-thick polymer film was spin coated onto the gold film substrate, and then was tempered at 40o in a vacuum for 12 hours to remove the residual solvent. The refractive index of polymer is 1.52 at wavelength 832nm. In order to remove the centrosymmetric structure of the chromophores, the film was corona-poled in the air by an applied electric voltage of 4000V at 110o for 25 min with inter-electrode distance being 20mm, and cooled down to room temperature with the field still applied. Finally, the upper gold film about 30nm thick was deposited on the polymer film by sputtering technique to serve as the coupling layer and another electrode. The complex dielectric constant of the gold film is
3.4. Slow light devices
The scheme diagram of the SMCW for verifying slow light effect is illustrated in Fig. 21. The advantages of this geometry are that the slow light properties can be tailored to the desired wavelength and the delay is tunable by varying the incident angle and the parameters of the guiding layer. This is important because the applications of slow light require a degree of tunability. These make the proposed slow light scheme useful and practical.
Test experiment has been performed with the waveguide parameters as follows:
In the experimental arrangement, the source is a collimated light beam at a wavelength of 650 nm, which is modulated by an EO modulator to produce a signal of 1.0 GHz sinusoidal pulse train. Two photodiodes are setup to detect the light intensity. The first photodiode (PD1) takes in the reflected light beam, which serves as the reference beam. The second photodiode (PD2) is used to measure the time delay of the slowed light beam. The tunable delay is measured by an oscilloscope with the bandwidth of 2 GHz. We measure the delay times
The properties of UHM in a SMCW and its applications on optical devices have been demonstrated in this chapter. It is found that the effective refractive index of UHM is sensitive to the refractive index, the thickness of the waveguide layer and the incident wavelength. UHM has also shown strong dispersion and polarization independent effects. Then, a polarization independent and tunable comb filter based on SMCW has been introduced, which has greater than 12 dB channel isolation, less than 0.2 dB insertion loss, and accurate 0.8 nm channel spacing in optical communication range. Taking the reflectivity and GH shift as the sensing probe, a new oscillating wave sensor is investigated to measure minute changes in various parameters such as the refractive index of the guiding layer, the thickness of the waveguide layer and the incident wavelength. It is demonstrated both theoretically and experimentally that its sensitivity is enhanced by one order of magnitude than that of evanescent wave sensor. Furthermore, an EO polymer modulator employing an SMCW is presented. The fabricated modulator achieves an 8.2% modulation depth with 10Vp-p driving voltage at 1 MHz. Finally, a new mechanism for slow light assisted by UHMs excited in the SMCW is introduced. A delay bandwidth product greater than 2 is demonstrated in the experiment with a signal of 1.0 GHz sinusoidal pulse train. Without use of any coherent or material resonance, this scheme is not subject to limitations of the delay bandwidth product and can generate arbitrarily small group velocities over an unusually large frequency bandwidth. We think such SMCWs possess unique and advantageous properties over the state-of-the-art and may have great potential for next generation optical devices.
The author thanks Ning Yang and YinQi Bao, students from the University of Shanghai for Science and Technology, for editing the manuscript of this chapter. This work is partly supported by the Leading Academic Discipline Project of Shanghai Municipal Government (S30502), “Chen Guang” Research Fund from Shanghai Municipal Education Commission and Shanghai Education Development Foundation (09CG49), and the Basic Research Program of Shanghai from Shanghai Committee of Science and Technology (11ZR1425000).