![Cut off wavelength of a planar waveguide](https://kumkoniak.com/111.png)
![cut off wavelength of a planar waveguide cut off wavelength of a planar waveguide](http://web.mit.edu/6.013_book/www/chapter13/ch13-1353.gif)
The previous studies used this mechanism to build a Fabry-Perot cavity by placing two narrow waveguides to both the left and the right of a broader square channel-waveguide cavity.
![cut off wavelength of a planar waveguide cut off wavelength of a planar waveguide](https://ofiber.readthedocs.io/en/latest/_images/3-Planar-Waveguide-Modes_4_0.png)
Cutoff frequency increases by decreasing the width, thus the narrower waveguide acts as a mirror. The dispersion curve of the square channel-waveguide has a cutoff frequency, and adjacent two channel-waveguides with different widths make a mode gap since the cutoff frequency shifts depending on the waveguide width. Plasmonic channel-waveguide, which can be designed as a sub-micrometer cavity to apply to a nanolaser or a refractive index sensor, has been studied in recent years. Many studies of the spectrometer with micrometer scale have come out recently, while the sub-micrometer region is still a challenge to design and operate. However, the primitive grating-based-spectrometers should have large enough size to support diffraction and imaging of light, thus they have an intrinsic limit to miniaturizing their operating size. Recently, it has become very important to reduce size and integrate devices in order to construct a lab-on-a-chip device. Their key characteristic of spectral-to-spatial mapping is widely applicable in chemical and biological fields. Optical spectrometers have a long history from early human civilization to today.
![Cut off wavelength of a planar waveguide](https://kumkoniak.com/111.png)