We demonstrate a compact high-resolution spectrometer scheme using two plane gratings. In this approach, the rays are first diffracted by a fixed grating, then incident on a rotating grating at the Littrow diffraction angle, and are finally diffracted and reflected back to the fixed grating again. Thus, triple dispersion (TD) occurs during measurement, increasing the resolution. The formulae of this compact high-resolution spectrometer are rigorously derived. A design simulation with two gratings of 1050 lines/mm is performed and discussed. In addition, a prototype of this spectrometer has been built and tested. Its spectral resolution reaches a precision of 36 pm.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Optical spectrometers have diverse applications in various fields, and have become a hot topic of research internationally [1,2]. In general, a spectrometer consists of a slit, collimating lens, grating, focusing lens, and detector. The measured light is dispersed by the grating only once, under most circumstances . A typical spectrometer structure is the Czerny–Turner spectrometer . For the limit of the grating groove density currently available, the spectral resolution of this type is usually at the nanometer level. There is also a trade-off between the spectral resolution and size of the device, as high-resolution spectrometer in this type must use large-size grating or lens with long focal length.
In recent years, the development of miniature spectrometers has enabled a host of new applications because of their reduced cost and enhanced portability [5,6]. However, the spectral resolution and wavelength range of miniature spectrometers are barely comparable with those of large bench-top spectrometers and cannot meet the requirements of some accurate measurement situations. In density wavelength-division multiplexing (DWDM) optical communication technology, for example, the systems function in the infrared range has nanometer or sub-nanometer channel spacing. In order to accurately measure the optical signal-to-noise ratio (OSNR) in 400-Gb/s/ch (400G) DWDM optical communication systems, the spectral resolution of spectrometers must be better than 50pm [7,8]. To obtain higher resolutions, researchers often cascade two or three spectrometers together. Clearly, a cascaded spectrometer system is large and complex, which cannot meet the demand of portability for use in outdoor situations. In contrast, to acquire the test spectrum, the gratings in the cascaded spectrometers must be rotated simultaneously, which requires a control system . The demand for compact high-resolution spectrometers is also increasing in various fields [10,11], as they are increasingly used in outdoor situations.
In this study, we develop a concept for a compact thigh-resolution spectrometer design using two plane gratings with triple dispersion (TD). In our proposed structure, after being diffracted by a fixed grating, the diffraction light is diffracted and reflected back to it again by a rotating grating using the Littrow diffraction method; thus, TD occurs during measurement and the resolution is greatly enhanced. In section 2, based on the light path geometry, we rigorously derived the theoretical formulae of the TD spectrometer. In section 3, a design simulation was performed by employing ZEMAX software. In section 4, a prototype of this spectrometer has been built and tested. The optics can fit inside a volume of 15 cm × 9 cm × 5 cm. More details are discussed in the following sections.
2. Optical system and analysis
A schematic of the TD spectrometer system is depicted in Fig. 1. The system has the advantages of simple miniaturized structure and high resolution. We use a doublet as the collimating and focusing lens simultaneously. A two-port fiber array is employed to input and output the signal light. The two gratings have the same grating period. The upper and lower ports of the fiber array are symmetrical about the focus of the doublet in its focal plane. For a grating, the incident light will not be diffracted in the direction parallel to the grooves. Instead, incident light with an angle in this direction will be reflected as if by a mirror. The upper and lower ports of the fiber array are symmetrical about the focus of the doublet in its focal plane in the direction parallel to the grooves. Therefore, the collimated light is incident on the grating with a small angle in this direction. The light will be diffracted in the direction perpendicular to the grooves and be reflected in the direction parallel to the grooves. The entire light path in our design is symmetrical in the direction parallel to the grooves. According to geometrical optical principles, when the light selected by the rotating grating goes back it will be focused to the position symmetrical to where it comes, i.e., it will be focused to the lower port of the fiber array, thus it is coupled into the output fiber.
The signal light to be measured is coupled to the upper fiber and exits from the port of this fiber. The light beam is then collimated by the doublet and propagates onto the fixed grating. Following the diffraction by the fixed grating, the dispersed light then propagates on to the rotating grating, which diffracts and reflects the light back to the fixed grating using Littrow diffraction method. Then, the light is diffracted a second time by the fixed grating and focused by the doublet. A series of monochromatic images of the input fiber port appear in line below the upper fiber port, but only one image with a small spectral band at a time can be collected by the lower fiber. By rotation the rotating grating, the monochromatic images can reach the lower fiber port in turn. Thus, the entire spectrum is obtained and recorded by the detector and the signal processing unit. In the whole process, TD occurs during measurement and high-resolution spectra are acquired.
2.1 Resolution analysis
For a plane grating with the angles of incidence and diffraction of light, and, respectively, with respect to the surface normal of the grating, the diffracted quasi-monochromatic light with wavelength in the mth order can be given by the following grating equation:Figure 2 illustrates the light paths of two beams with different wavelengths in the TD spectrometer. Assuming the rotating grating is at the position shown in Fig. 2, the wavelength of the detected beam is and the wavelength of the other beam is.
When diffracted by the fixed grating for the first time, the two beams satisfy the following grating equations:Eqs. (2) and (3):
In Littrow configuration, the angles of incidence and diffraction of the beam with wavelength have the same value, satisfying the grating equation:Eqs. (4)–(7),and for small values assuming that ,,,, and, we can derive the angular resolution of the TD spectrometer:
Equation (8) indicates that the angular resolution of the TD spectrometer is a function of the angles of incidence, and , and the angle of diffraction in the first grating. These two last parameters are linked by the angle between gratings, say . That is, .The comparison of Eqs. (4) and (8) shows that the angular resolution of the TD spectrometer is more than twice that of the common single-pass spectrometer; actually, it is more than triple, because is the general situation.
2.2 Optical analysis of the proposed spectrometer
For the measurement of a spectrum, the relationship between the detected wavelength and rotated angle of the rotating grating must be known. As shown in Fig. 3, assuming that the starting wavelength is , the wavelength of is detected after the rotating grating has rotated by the angle .
According to the geometry relation of the angles in the light path, the equation for the relationship of the angles can be written as
The simplified calibration equation from Eq. (9) can be easily obtained:
2.3 Problem of the detection of multiple wavelengths
Unlike the reflection situation, the proposed structure may risk having more than one wavelength being detected at the same time, so we consider that here. Assuming that two beams with wavelengths and are detected simultaneously, their light paths will satisfy the relation shown in Fig. 4.
On the condition that in Eq. (10) is zero, we obtain
Making a function:
Clearly, is an increasing function. Therefore, different wavelengths are completely impossible to detect at the same time.
3. Design and simulation
According to the principle mentioned above, a design simulation was performed by employing ZEMAX software . The parameters used in our design are listed in Table 1, and the layout of the designed TD spectrometer is illustrated in Fig. 5.The array space is the distance between the ports of the input fiber and the output fiber .In the design, we employed a fiber array with a space of 0.127 mm, which is common for commercial products. As has been mentioned above, in the direction parallel to the grooves, there is no dispersion. Therefore, this value works for all the wavelengths.
Setting the simulation wavelengths in the ZEMAX software to 1549.95, 1550, and 1550.05nm, the spot diagram is illustrated in Fig. 6.
As shown in Fig. 6, the distances from the spot centers of 1549.95 and 1550.05nm to that of 1550 nm are both approximately 14 μm; hence, the linear dispersion is approximately 280μm/nm. The RMS radius of the spot at 1550 nm is only 0.15μm, which can be ignored compared to the core diameter of the receiving fiber. The core diameter of the receiving fiber is 10μm, while the spectral resolution is equal to the ratio of the core diameter of the receiving fiber to the linear dispersion:Fig. 7, as well as the theoretical calculation results for comparison.
The simulation of a single-pass spectrometer with the same components was also performed to compare with the proposed scheme, and the results are presented in Fig. 8. We can see from Figs. 7 and 8 that the resolution of the TD spectrometer is 10 times better than that of the single-pass scheme. It can be seen in Fig. 7 that the resolution of the TD spectrometer is almost constant at about 36 pm for the entire wavelength range of 1250 to 1650 nm. However, in Fig. 8, in the same wavelength range, the resolution of the single-pass spectrometer varies from 420 pm to 300 pm. Therefore, the TD spectrometer can achieve more constant resolution, which benefits the TD spectrometer for wideband applications. What leads to the difference of their resolution stabilities is that the resolution of TD spectrometer varies less than that of the single-pass spectrometer with the diffraction angle, which relies on the wavelength.
According to the function of the proposed spectrometer mentioned above, the detected wavelength varies with the rotation of the rotating grating. Assuming the starting wavelength is 1450nm, the calibration function at the designed parameters is shown in Fig. 9. The dots in Fig. 9 illustrate the detected wavelength when the rotating grating rotates. The solid line in this graph is the fitting curve of the wavelength versus rotation angle, while the relationship between the rotation angle and wavelength has been derived and is shown as a fourth-order polynomial equation.
Over the entire wavelength range of 1250 to 1650 nm, the range of the rotation angle of the rotating grating is 48.77°. To achieve 36-pm resolution, the required rotation accuracy must be higher than 0.0022° (when only the point of maximum is sampled within the full width at half maximum (FWHM), in which situation a peak can be roughed out with only three points). Such accuracy is not very hard to achieve. The wavelength accuracy is the difference between the real wavelengths and the calculated wavelengths. The real wavelengths are selected by step in the design, and their relevant rotation angles can be accurately calculated by Eq. (10). We can then fit a polynomial equation as shown in Fig. 9. In practical, the rotation angles can be obtained by the rotating system, and the wavelengths are calculated by the polynomial equation. Therefore, the root-mean-squared error can define the wavelength accuracy, which is as high as 6.3 × 10−5nm in our design.
Based on the simulation, a prototype of the TD spectrometer was fabricated, as shown in Fig. 10, and its optical parameters are the same as the simulation. The optics can fit inside a volume of 15 cm × 9 cm × 5 cm. Figure 11 is the absolute efficiency curve of the plane grating. In high-speed fiber communication systems, the signal light has two mutually perpendicular states of polarization (SOPs). However, the diffraction efficiency of gratings to the different SOPs varies tremendously. To achieve high diffraction efficiency and maintain the dispersed light intensity at peak level, we use a polarization beam splitter (PBS) to divide the input signal light into two beams. The output ports of the PBS are coupled to the monochromator section by two polarization-maintaining fibers (PMFs), which are input fibers of two doublets with the same parameters. The birefringence axis of one of the PMFs is twisted 90° relative to that of the other. When leaving the output ports of the PBS, the two beams have parallel polarization directions and are perpendicular to the groove lines of the grating. Thus, the diffraction efficiency can be maximized. The grating we used in our design has efficiency higher than 90% in the whole wavelength range, so the total efficiency only reduces to no less than 81% compared with that of the single-pass spectrometer, accordingly the optical signal-to-noise ratio will reduce only 0.9 dB. Figure 12 presents the spectrum of a tunable laser obtained with our spectrometer. From Fig. 12, the center spectral wavelength of the measured laser is about 1551.645nm. The FWHM of the spectrum indicates the wavelength resolution of the spectrometer, which equals to 3dBm width in Fig. 12 according to the relationship between mW and dBmW. Judging from Fig. 12, the FWHM is about 36 pm, which indicates that the wavelength resolution of the prototype is in excellent agreement with the simulation.
In this paper, a compact high-resolution spectrometer is presented, in which two plane gratings are employed to enhance the resolution with a simple structure. The rotating grating uses the Littrow diffraction method such that it diffracts and reflects the light back to the first grating again; thus, TD occurs during measurement and the resolution increases. Formulae for this spectrometer are derived and design simulations with two gratings of 1050 lines/mm are performed and discussed. The simulation results indicate that the spectral resolution of our design is 10 times better than that of the single-pass spectrometer when the focal length, the grooves density, and the angle of incidence are 20 mm, 1050 l/mm, and 75°, respectively. Moreover, the spectral resolution is almost constant over a wide wavelength range from 1250 to 1650 nm. Its wavelength accuracy reaches a value as precise as 6.3 × 10−5nm calculated by a simple fourth-order polynomial equation. Accordingly, a prototype of the TD spectrometer was built and tested. Its spectral resolution reaches a precision of 36 pm, which shows excellent agreement with the simulation. The optics can fit inside a volume of 15 cm × 9 cm × 5 cm. This spectrometer will be suitable for the OSNR measurement for 400G DWDM fiber communication systems with a higher efficiency, as well as in optoelectronic device testing. It is anticipated that this design will greatly expand the availability of the grating spectrometer concept in a wide range of applications.
National Key Scientific Instrument and Equipment Development Project of China (2014YQ510403); National Natural Science Foundation of China (NSFC) (61505143); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB09040100).
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