Dense wavelength division multiplexing (WDM) is becoming a leading technology in fiber-optic networks.^{1, 2, 3} Dynamic WDM technologies with reconfigurable channels, bandwidth, and network topologies are expected to support aggregate bandwidth and low latency requirements of both civilian and military applications such as Internet access, high-quality videoconferencing, and information acquiring and sharing in aerospace. Tunable optical filters are among the key devices in realizing the dynamic WDM networks due to their capability of providing various dynamic functions such as wavelength tunable receivers, optical channel/wavelength selections, and reconfigurations.^{3, 4} To achieve these functionalities, general requirements for tunable optical filters include a large wavelength tuning range covering all WDM channels, low insertion loss, narrow passband, low polarization-dependent loss (PDL), and low channel cross talk. Existing electro-optic (EO) tunable optical filter technologies include fiber Fabry-Perot (F-P) interferometers, arrayed waveguide gratings (AWG), liquid crystal F-P interferometers, Mach-Zehnder interferometers, acousto-optic filters, and fiber Bragg gratings (FBG).^{4, 5, 6, 7, 8, 9} While these optical filters have been employed in various optical networks, however, the major limitation is the small wavelength tuning range of a few nm, mainly due to the small EO coefficients
$(<90\phantom{\rule{0.3em}{0ex}}\mathrm{pm}\u2215\mathrm{V})$
of existing materials, such as
${\mathrm{LiNbO}}_{3}$
and EO polymers.^{3, 10, 11} The small wavelength tuning range makes these devices unsuitable for broadband channel selections and reconfigurations across the whole WDM wavelength range (for example, C-band,
$1530\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
to
$1565\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
). In this paper, we present a new EO filter structure based on a long-period-grating-assisted asymmetric waveguide coupling mechanism. An ultra-large wavelength tuning range exceeding
$30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
in the C-band (
$1530\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
to
$1565\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
) and a narrow passband of
$<0.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
can be achieved at a low driving voltage
$\sim 16\phantom{\rule{0.3em}{0ex}}\mathrm{V}$
with a low channel cross talk of
$\sim -25\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
.

The cross section and top views of the EO tunable filter are shown in Figs. 1a and 1b, respectively. The EO tunable filter consists of an input waveguide, an output waveguide, and a pair of coplanar EO tuning electrodes on top of the input waveguide. The input waveguide and the electrodes are separated by an
${\mathrm{SiO}}_{2}$
cladding layer. The waveguides are Ti-diffused
${\mathrm{LiNbO}}_{3}$
waveguides on an X-cut
${\mathrm{LiNbO}}_{3}$
substrate. The input and output waveguides are asymmetric so that the coupling of optical signals between the two waveguides are phase-mismatched. The input waveguide has a long-period grating to generate an addition
$k$
vector to provide phase-matched coupling for a certain wavelength. The phase-matching condition for optical coupling can be written as^{12, 13}:

## 1

$$\frac{2\pi}{{\lambda}_{0}}{n}_{eff,in}-\frac{2\pi}{\Lambda}=\frac{2\pi}{{\lambda}_{0}}{n}_{eff,out},$$The tuning of phase-matched wavelength ${\lambda}_{0}$ can thus be achieved by electro-optically changing the effective index of the input waveguide ${n}_{eff,in}$ . As shown in Fig. 1a, the bias voltage would generate an electric field along the $z$ direction. The EO-induced refractive index tuning can therefore be written as:

where ${\gamma}_{33}\approx 31\phantom{\rule{0.3em}{0ex}}\mathrm{pm}\u2215\mathrm{V}$ is the EO coefficient of ${\mathrm{LiNbO}}_{3}$ along the $z$ direction (as shown in Fig. 1). The wavelength tuning can thus be written as:## 4

$$\mathrm{\Delta}{\lambda}_{0}=\mathrm{\Delta}{n}_{eff,in}\Lambda =(-\frac{1}{2}{n}_{e,eff,in}^{3}{\gamma}_{33}\frac{V}{d})\Lambda ,$$The phase mismatch
$\mathrm{\Delta}\beta $
for the wavelength away from the central wavelength can be written as^{12, 13}:

## 5

$$\mathrm{\Delta}\beta =\frac{2\pi}{{\lambda}^{\prime}}{n}_{eff,in}-\frac{2\pi}{{\lambda}^{\prime}}{n}_{eff,out}-\frac{2\pi}{\Lambda}=2\pi \bullet \left(\frac{\mathrm{\Delta}\lambda}{{\lambda}^{\prime}\Lambda}\right),$$## 6.

^{14}The total device insertion loss is therefore less than $8\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ .

In conclusion, we present an EO tunable filter structure based on long-period-grating-assisted asymmetric waveguide coupling. This type of EO tunable filter overcomes the low EO coefficient limitation of convention materials and offers a large wavelength tuning range exceeding $30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ at a low driving voltage $\sim 16\phantom{\rule{0.3em}{0ex}}\mathrm{V}$ . It is expected to enable fast wavelength selection, communication channel reconfiguration, and packet- or cell-level switching for highly dynamic WDM optical networks.