Recent Progress of 40 GHz high-speed
LiNbO3 optical modulator

Makoto Minakata
Research Institute of Electronics, Shizuoka University / Hamamatsu, Japan


ABSTRACT

　This paper describes the recent progress and status of 40 GHz high-speed LiNbO3 optical modulators, and newly designed two types - a backslot type and a ridge type- LiNbO3 optical modulators with high-speed and low-switching voltage. The backslot is formed on the backside of LiNbO3 substrate by using micro-machining laser etching. The backslot type modulator is designed, fabricated and characterized. The ridge type modulator with an overhanged upper electrode is also calculated. The properties of the designed two types modulators, effective refractive index for the modulation wave nm, modulation bandwidth fm, overlap integral Γ and switching voltage Vπ are calculated. The optimum properties of the backslot type modulator, fm=73GHz and the switching voltage Vπ=2.8V is calculated , and fm=130GHz and Vπ =1.9V is achieved for the ridge type modulator at a wavelength 1.5μm. The fabricated backslot type modulator achieved the optical 3dB bandwidth fm≧28GHz and the driving voltage Vπ =2.8V.

Keywords: Optical modulator, ridge waveguide, traveling-wave electrode, LiNbO3, Mach-Zehnder, velocity-matching

1. INTRODUCTION

　Advancements in the Internet, cellular-phones, and multimedia communications have increased the needs for large-capacity optical transmission systems. Up to now, TDM single channel 640Gbit/s transmission experiments over 60 km have been accomplished [1], and 3 Tbit/s (160 Gbit/s x 19 channel) optical TDM and WDM transmission experiment has been reported [2]. In the near future, Single-carrier 40 Gbit/s optical transmission systems will soon be available to support " Information Technology". The LiNbO3 (hereafter LN) optical modulator with traveling-wave electrode and Mach-Zehnder optical waveguide is a promising device for such high-speed systems, because the low-frequency chirp, wide bandwidth and low-switching voltage are practicable. In this paper, I would like to introduce the recent progress and status of these devices. Recently, general information and status of modulators in detail have been reported , please refer to them [3-4].
　Up to now, broad-band LN optical waveguide modulators by using a traveling-wave type electrode or a coded phase reversal type electrode have been developed [5-9]. To realize more efficient and extremely broad-band modulators, studies on traveling-wave devices have been made successfully in the world. In this paper, two types novel LN traveling-wave modulators with 3-dimensional structures - a backslot type and a ridge type- are proposed, and basic experimental results are reported. This modulator can satisfy the perfect velocity matching condition between an optical wave and a modulating wave. Therefore an extremely wide-band optical modulator can be realized theoretically, which is restricted by the electrode loss or dispersion [8]. The ridge type modulator is also high efficient, because it has a large overlap internal factor between the optical wave and applied electric field [3]. To confirm the basic performance, the backslot type modulator was fabricated and characterized. The important microwave index was determined by the measurement of Time Domain Refractometry. These results show that the modulating wave gains in speed and closes to the optical wave. The modulation frequency was confirmed more than 28 GHz and the driving voltage of 2.8V at a wavelength 1.5μm.

2. LIMITATION FACTORS OF MAXIMUM MODULATION BANDWIDTH

　For a traveling-wave optical waveguide modulator, the maximum modulation band-width is generally limited by �@ the threshold frequency of the electrooptical effect, �A velocity mismatching (the propagation speed difference) between an optical wave and a modulating wave (for example, applied electrical field in microwave), �B the electrode loss in the high-frequency field, and �C structural dispersion and material dispersion [3]. Since electrooptic effect functions in a wide frequency range from DC to infrared (THz), factor �@ is no problem. Factor �A to �C depend on the electrode and its structure. Among them, the achievable bandwidth is mainly restricted by velocity mismatching. A modulation bandwidth fm of the modulator is reversely proportional to the difference between an optical wave velocity Vo= c/no and a modulating wave velocity Vm= c/nm, where c is a velocity of light, and no, nm is refractive index for an optical wave and a modulating wave, respectively. The bandwidth also increases as an electrode length l is decreased at the expense of a large drive power. Thus, 3dB-down modulation band-width fm is proportional to 1/(Vo-Vm) l, as shown in Fig.1. For a modulator with a coplanar traveling-wave electrode (see Fig.1), Vo is 1.95 times faster than Vm (no=2.15, nm=4.2). Therefore, the product of fml is limited to 9.2GHzcm[5].


Figure 1: A modulator with a co-planar traveling-wave electrode(a), and the definition of the modulation bandwidth fm (b).

　For example, in the directional coupler type device with l=2.5mm, fm=40GHz and a switching voltage Vπ=26V( at a wavelength λo=1.5μm) was reported as shown in Fig.2 [10]. If the perfect velocity matching condition of Vo=Vm is satisfied, the bandwidth fm is theoretically infinite. However, the bandwidth is limited by the electrode loss even under the perfect velocity matching condition. For example , when copper electrodes are used at 100 GHz, the microwave skin depth δ is 0.2μm because of the high conductivity of copper[11]. In this case, slight roughness in the electrode surface causes scattering and radiation loss. Therefore, mirror finish of electrode is required. Although the electrode is mirror-finished, the dimensions of the electrode cross section are finite and the microwave attenuates in proportion to exp(−αl). Therefore, the attenuation increases with an increase of l.
　The material dispersion of LN mentioned in factor �C is almost constant at frequencies up to 300GHz. In the electrode construction where the TEM wave approximation holds, it is believed to be constant at frequencies up to at least 200GHz.
　On the other hand, the upper limit of optical modulation frequency and the modulation voltage are inversely proportional to the electrode length. Therefore, it is difficult to fabricate a high-speed and wideband optical modulator using low driving voltage.
　To overcome this problem -velocity mismatching limitation and trade off-, many efforts have been made [5-9] as shown in Fig.1. For a modulator with a coplanar traveling-wave electrode (see Fig.1), Vo is 1.95 times faster than Vm (no=2.15, nm=4.2). Therefore, the product of fml is limited to 9.2GHzcm[5].


Figure 2: Recently developed wideband optical modulators.

　Fig.2. In methods (a) to (f) [7,10,11,12,6,13], the modulation wave velocity should be close to the velocity of light to achieve wide bandwidth. In case (g), the electrode structure is coded to diffuse the spectrum, resulting in the achievement of wideband[9]. In case (e), a ridge waveguide is used, where the 3 dB-down bandwidth is 70GHz and Vπ=5V [13]. An optical modulator with YBaCuO-based superconducting electrodes was reported. The electrode loss at 77K is 10^-3 of those of Cu and Al. In this device, the center frequency is 18GHz and Vpp=2.3V[14]. Optical modulation at 94 GHz was achieved by coupling a dielectric tapered guide and electrode antenna[15].

3. A PROPOSED TRAVELING-WAVE OPTICAL MODULATOR -Backslot Type-

3.1 Velocity matching
　The proposed modulator -backslot type-, shown in Fig.3, is composed of a planar waveguide, a traveling-wave electrode and a backside slot. By changing the thickness of the substrate, the microwave index nm is considerably decreased, and the applied electric fields is increased. The reasons are as follows; 1) the electric field leaks out effectively into the backside (air) so that nm decreases to be satisfied the perfect velocity matching conditions, 2) an overlap integral Γ is about 2 times larger than that of the existing planar electrode modulator with a thick buffer layer (see Fig.3(b)). The Configuration of actual designed device is shown in Fig.4 with a CPW electrode.


Figure 3: (a) The proposed LiNbO3 modulator structure with a backside slot, and (b) the conventional planar type modulator structure with SiO2 buffer layer.




Figure 4: Schematic diagram of the proposed modulator. The element is the Mach-Zehnder intensity optical modulator with the CPW traveling-wave electrode. Backside of the substrate is etched to achieve the velocity matching.

3.2 Electrode loss and dispersion
　In the range from microwave to millimeter wave, the electrode loss increase with an increase in frequency cased by the skin-effect [3]. The electrooptically induced "optical phase shift" which is integrated along the electrode length is reduced with an increase in electrode loss. Thus, the bandwidth is reduced by the electrode loss. Under the perfect velocity matching condition [3], achievable modulation bandwidth fm is given by

fm^loss=(6.84/α₀l)² (1)

where α₀ is an attenuation constant of the modulation microwave. Furthermore in the designed modulator, the actual bandwidth is less than a limited bandwidth based on the structural dispersion and the material dispersion [3].

4. DESIGN OF THE MODULATOR (1) - Backslot Type -

4.1 nm and fm
　A wavelength of microwave is fair longer than the electrode gap. For example, when the electrode gap is 10 μm and the wavelength is about 2mm at frequency 100 GHz. Therefore we assume that modulating wave is a transverse electric and magnetic wave. That is Ex=Hx=0. By this assumption, nm is given by eq.(2),



　　(2)



where εr is relative dielectric constant and S0 is the cross section including the one-side electrode per unit length. n is a unit vector perpendicular to ds. Et is the transverse electric field induced by applied modulation voltage. C is a capacitance per unit length of the modulator, and C0 is a capacitance when only the electrode is existing in air. Here, Et is




Figure 5: The applied electric field of z-component distribution calculated by the SOR method for (a) substrate thickness d=30 μm, (b) d=5μm for y-cut (or x-cut) LiNbO3 substrate, respectively
given by the potential distributionΦ. Φ is calculated by Laplace's equation:

　　　(3)


and solved by a successive over relaxation (SOR) method [3]. �\Et�\and its distribution are calculated based on Φ as shown in Fig.5. When the propagation microwave is lossless [3], fm is given by

　　(4).


4.2 Vπ and Γ
　Switching voltage (halfwave voltage) Vπ is given by

　 (5)

where wavelength λ is the wavelength of light, S is the electrode gap, r₃₃ is the electrooptic coefficient. Γ is the overlap integral factor between the applied electric field E (y, z) and the optical electric field ε(y,z), and given by


　 (6)


where E is an applied average electric field. ε(y,z) is calculated by combining an effective index method[3]. The using relative index difference is 6.5x10^-3 and the depth of waveguide is 2μm. E(y,z) is the transverse electric field calculated by the SOR method (shown in Fig.5).

4.3 Calculated Results
　Figure 6 shows the relationship between the bandwidth and the substrate thickness normalized by electrode gap S. Where αo is an attenuation constant of the modulation microwave, and depends on the electrode conductivity and geometry.
　When the d/S=0.19 for y-cut, and 0.12 for z-cut, no=nm=2.15. That is, the perfect velocity matching conditions is satisfied, the maximum value of fm is obtained 292 GHz with l=10mm, on both cut of the substrate. Figure 7 shows the relationship between Vπ and the substrate thickness d. The concentration of the z component electric field is strongly depend on the substrate direction. The y-cut substrate has much better concentration as compared with the z-cut, with a decrease in d. Table 1 shows the calculated relationship between a substrate thickness and characteristics. Where we assume the Mach-Zehnder type switch as shown in Fig.4, and Au electrode is used at a 1.5 μm wavelength. The designed modulator for y-cut (x-cut) substrate has a broad bandwidth and high efficiency compared with existing modulators. The optimum properties fm =73 GHz and Vπ=2.8V at a wavelength 1.5μm, is achieved for the y-cut (x-cut) LiNbO3 substrate, with l=20 mm, d=3.8μm, under the perfect velocity matching condition.


Figure 6: The relationship between modulation bandwidth fm and d/S (substrate thickness / electrode gap) for y-cut and z-cut LiNbO3 substrate, for αo= 0.4 dB/cm GHz^1/2 and l = 1 cm.



Figure 7: The relationship between switching voltage Vπ and substrate thickness d for y-cut and z-cut LiNbO3.

Table 1: The values of the modulation bandwidth fm, switching voltage Vp and substrate thickness d for y-cut and zcut LiNbO3 substrate (S=20nm, l=2cm,αo=0.4dB/cm GHz^1/2).


4.4 Experimental
　To confirm the basic performance, a x-cut LN substrate backside-etched modulator was fabricated and characterized. The optical waveguide was fabricated using x-cut LN substrate by the Ti diffusion method. The CPW electrode was directly electroplated to the substrate. The gap S=40μm, the width of the center electrode w=30μm, and the interaction length l=40 mm, respectively. The backside slot was fabricated by KrF excimer laser ablation. The cross-section of the modulator is shown in Fig.8. Less than 10μm thickness of LN substrate just under the traveling wave electrode have been fabricated. The end faces of the modulator were polished and pigtail fibers were successfully connected by using ultraviolet-cured adhesive. From measured TDR (Time Domain Refractometry) characteristics date, it is clear that the microwave in the modulator with backside slot has less shorter traveling-time compare to the modulator which has the same dimension and no backside slot. That is, the microwave propagation speed Vm along the optical waveguide is higher than that without backside slot. The modulator with backside slot has also high impedance compare to that one.



Figure 8: The cross-section SEM photograph of the fabricated modulator with a backside slot.

　Then, to confirm the modulator performance, the S-parameters, S11 and S21, of the modulator are measured up to 25GHz by a vector network analyzer. S11 is below -10 dB over the entire frequency range, since the impedance matching is sufficient. S21 is shown to be smooth and the conductor loss is very low. Fig.9 shows the frequency response of the fabricated modulator. Based on these results, the parameters nm, Zo, and αo are calculated to be 2.25, 45.6 ohm, and 0.2 dB/cmGHz^1/2, respectively. The optical 3 dB bandwidth is higher than 28GHz by calculated from S-parameter, and the half-wave voltage Vπ is 2.8V at a wavelength l =1.5μm. Measured extinction ratio is 25 dB, and the total insertion loss is 6.1dB.


Figure 9: Frequency response of the fabricated modulator.

　This section describes another proposed design of the ridge type optical modulator with an overhanged upper electrode to achieve the high-speed and low-switching voltage as shown in Figure10. The conventional ridge structure is effective to lower the switching voltage[3,13]．The proposed structure makes use of the ridge type for low-switching voltage, and is simultaneously aiming at the perfect velocity matching and low-electrode loss to achieve the high-speed modulation．
　We calculated the distribution of the applied electric field by using the successive over relaxation(SOR) method (see Figure 11)．The properties of the designed modulator, effective refractive index for the modulation wave nm , modulation bandwidth fm , overlap integralΓ, switching voltage Vπ and the characteristic impedance Z0 , are calculated based on the electric field and the optical intensity distribution as shown in Figure 12-15．The optimum design parameters to give the



Figure 10: The proposed modulator structures on the z-cut LiNbO3 substrate with the overhanged upper electrode. The structure is formed on only one of the waveguide of the Mach-Zehnder intensity optical modulator with the traveling-wave type electrode.


Figure 11: The z-direction component of the applied electric field calculated by the succesive-over relaxation method for the ridge type modulator ,where d_r/w=0.5 and L/w=4.0 .

Figure 12: The plot of V_pl (product of switching voltage and electrode length) and overlap integral Γ versus d_r/w for the ridge type .


Figure 13: The relationship between effective refractive index for the modulation wave n_m, L/w and d_r/w for the ridge type (1). The velocity matching (n_m=n_o) is achieved for L/w=3.9 and d_r/w=0.5 , shown as the dotted line.


Figure 14: The relationship between modulation bandwidth f_m and d_r/w (L/w=3.9) for the ridge type . The velocity mismatching and the electrode loss terms are included in the calculation.


Figure 15: The relationship between characteristic impedance Z₀, L/w and d_r/w for the ridge type (1). Z₀ becomes 18.4Ω for the optimum design (L/w=3.9 and d_r/w=0.5) .

Table 2: The values of the bandwidth, switching-voltage and performance index for planar-type, back slot-type, ridge-type structure (l =2cm).

highest-speed modulation and the lowest-switching voltage are d_r/w=0.5 and L/w=3.9 for the ridge type, where d_r : the ridge height，w : the ridge width and L : the upper electrode width. For the electrode length (l =2cm) and the electrode loss constant (a₀=0.3dB/cmGHz^1/2)，obtained properties of the designed modulator are f_m=130GHz，V_π=1.9V and performance index f_m/ V_π= 68 GHz/V．These properties are superior to the conventional LN modulators with the planar type electrodes, where the typical value of f_m/V_π is 4 GHz/V. In summary, Table 2 shows the calculated properties of the backside slot type and the ridge type modulator.

　The recent progress and status of 40 GHz high-speed LiNbO3 optical modulators have been described . Limitation factors of the high-speed / broad-band LN modulators have been discussed. The efficient and broad-band LiNbO3 optical modulator with 3-dimensional novel structures have been proposed. These constructions can be obtained perfect velocity matching between the optical wave and the modulating wave. Therefore an extremely wide-band optical modulator can be realized theoretically. The calculated values of the well designed backside slot type modulator was fm=73 GHz and Vπ=2.8V for the y-cut (x-cut) LiNbO3 substrate, and the well designed ridge type modulator was f_m=130GHz, V_π=1.9V at a wavelength 1.5μm,with l=20 mm.

　The author would like to thank Dr.A.K.Dutta and Prof. Y. Hatanaka for valuable recommendation, and to Dr. M.Goto and H.Awano for many calculations and valuable support, and also to Dr. M. Imaeda, J.Kondo, A.Kondo, K.Aoli, O. Mitomi and Y.Kozuka for calculation and fabrication of the backslot modulator. Part of this work is supported by Monbukagakusho Grant-in-Aid for Scientific Research (11450139).

REFERENCES