1. Introduction

Optical spectrometers are widely used in fields such as chemical and biological sensing, material analysis, and light source characterization [1–3]. Many efforts have been made to realize a spectrometer working in a wide wavelength range with a high spectral resolution [4–8]. Usually, spectrometers use a grating or a prism to disperse light, and the spectral resolution scales with the focal length of the imaging lens or mirror before the detector. There is a trade-off between the spectral resolution and the size [3]. In recent years, the development of miniature spectrometers has enabled a host of new applications due to their reduced cost and enhanced portability [9,10]. However, the spectral resolution and the wavelength range of miniature spectrometers are hardly comparable with those of the large bench-top ones, and cannot meet the requirements of some accurate measurement situations. In density wavelength-division multiplexing (DWDM) optical communication technology, for example, systems work in the infrared range with nanometer or sub-nanometer channel spacing. To measure the optical signal-to-noise ratio (OSNR) in 100Gb/s/ch (100G) DWDM optical communication system, the spectral resolution of spectrometers must be higher than 0.1 nm [11,12]. Moreover, the instrument size is also very important, as they are usually used in outdoor situations. To solve these problems, more studies are required into compact broadband high-resolution spectrometers.

In this study, we develop a concept for a compact broadband high-resolution spectrometer. A dihedral reflector is used to reflect the dispersed light back to the grating for a second diffraction, which greatly enhances the spectrometer’s performance. In this manner, we built a prototype of a miniature spectrometer that works in the infrared fiber communication wavelength range (1250–1650 nm) with a spectral resolution of 57 pm. The optics can fit inside a volume of 12 cm × 14 cm × 5 cm. The system was designed to have a multiplexed grating with a dihedral reflector and a single-point infrared detector. This structure has some merits: by diffracting the light twice, the resolution is increased; moreover, the dihedral reflector behaves as a wavelength-selecting device through the rotation in wide angular range, which broadens the wavelength range of the spectrometer. Furthermore, it reduces both the volume and the weight of the spectrometer by folding the light path. Those merits lead to the possibility of efficient in situ spectral analysis. The principle and the performance of the system are described in details in the following sections.

2. Principle and analysis

2.1 System construction

A schematic of the multiplexed grating spectrometer system for high-speed fiber communication system testing is shown in Fig. 1(a). The main components are a polarization beam splitter (PBS), two off-axis parabolic mirrors, two fiber arrays, a plane grating, a dihedral reflector, and a single-point infrared detector.

 

Fig. 1 The multiplexed grating spectrometer system. (a) Schematic of the spectrometer: M1, the collimating off-axis parabolic mirror; M2, the focusing off-axis parabolic mirror; R, the dihedral reflector; G, the plane grating; D, the single-point detector; and PBS, the polarization beam splitter. The beam colors of red and blue represent the two beams with different original states of polarization (SOPs). (b) Side view of the dihedral reflector.

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In high-speed fiber communication systems, the signal light has two mutually perpendicular states of polarization (SOPs) [12]. However, the diffraction efficiency of gratings to the different SOPs varies tremendously [13]. To balance the diffraction efficiency and maintain the dispersed light intensity at peak level, we use a 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 (PM) fibers. The birefringence axis of one of the PM fibers is twisted ${\text{90}}^{°}$ 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 incident slit and the exit slit are both single mode two-point fiber arrays with 10-μm-diameter fiber cores. In each of the fiber arrays, the inter-fiber separation is greater than the “spot size” in the non-dispersive dimension of a signal in the focal plane. When the optical system is optimized, there is nearly no aberration, and the “spot size” will almost equal to the core diameter of the input fiber. In our setup, the fiber array dimensions are 10 mm × 2.5 mm × 2.5 mm, and the separation between the two fiber centers is 0.25 mm. By such an amount that cross-talk is substantially avoided. On the other hand, the two internal fibers are sufficiently close to ensure the two ports are as near as possible to the focus of the off-axis parabolic mirrors. Thus, the two beams follow nearly parallel light paths and aberrations are minimized.

In the monochromator section, the two polarized light beams from the input fibers are collimated by the off-axis parabolic mirror M1, then diffracted and reflected by the grating G. After that, the light beams are directed to the right-angled dihedral reflector R. The arrangement is such that the light beams impinge upon one of the reflective facets of the dihedral reflector R at a first angle of the order of ${\text{45}}^{°}$, and are reflected to the other facet, which reflect them again at the ${\text{90}}^{°}$ complement of the first angle; this is so that they leave the dihedral reflector R in the opposite direction to that of arrival. This process is described in Fig. 1(b). The dispersed light returns to the grating G and is diffracted once again, but at a position displaced perpendicularly with respect to the plane of diffraction in which it was first incident. The re-diffracted light is focused by the off-axis parabolic mirror M2 and imaged onto the output fibers. The light transmitted through the fibers will reach the detector D, which supplies their corresponding electrical signals to a microprocessor for processing.

Only a tiny range of wavelengths can be imaged on the detector at a time. For the entire wavelength range, the dispersed light is scanned by rotating the dihedral reflector R. When the angle between R and G varies, the wavelength of light for re-diffraction is correspondingly changed. Thus, the entire spectrum is obtained by the detector and microprocessor.

2.2 Optical function

To obtain a complete spectrum, wavelength calibration is necessary. For a plane grating with the angles of incidence and diffraction, $i$ and $\theta$, respectively, with respect to the surface normal of the grating, the diffracted quasi-monochromatic light with the wavelength $\lambda$ will be given by:

Assuming that ${\theta }_0$ is the diffraction angle when the rotation angle of the dihedral reflector $\delta$ is ${\text{0}}^{°}$, ${\lambda }_0$ is the corresponding wavelength. The relation between wavelength $\lambda$ and the dihedral reflector rotation angle $\delta$ can be written as:

The dihedral reflector is mounted upon the rotary shaft of a stepping motor, whose rotation angle is determined by the number of the pulses of its driver. Once the number of pulses is known, the rotation angle of the dihedral reflector $\delta$ and the corresponding wavelength $\lambda$ are then known.

2.3 Angular resolution

In the proposed spectrometer system, the incident light is diffracted by the grating twice, and the spectral resolution is enhanced accordingly. Figure 2 shows the light paths of two different wavelengths.

 

Fig. 2 Diffraction light paths.

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When the dihedral reflector is at the position shown in Fig. 2, the wavelength of the detected light is assumed to be ${\lambda }_0$, and the wavelength of the other light is ${\lambda }_0+\Delta \lambda$. Angles $i_{\text{0}}$, ${\theta }_{\text{0}}$, and ${\theta }_0+\Delta {\theta }_{\text{1}}$ refer to the incident angle of the measured light, the first diffraction angle of ${\lambda }_{\text{0}}$, and the first diffraction angle of ${\lambda }_0+\Delta \lambda$, respectively. The beams of ${\lambda }_0$ and ${\lambda }_0+\Delta \lambda$ satisfy the grating equations:

The beams then will be reflected by the dihedral reflector, and we assume the beam of ${\lambda }_{\text{0}}$ will be perpendicularly incident on the dihedral reflector. After that, they will impinge the grating for the second diffraction. The light paths follow the laws of diffraction and refraction, so they satisfy the grating equations:

Equation (9) indicates that when $i_0={\theta }_{\text{0}}$, the angular resolution of the multiplexed grating approach is twice of that of the one-time diffraction scheme; when $i_0>{\theta }_{\text{0}}$, the angular resolution of multiplexed grating approach is more than twice of that of the one-time diffraction scheme ; and when $i_0<{\theta }_{\text{0}}$, the angular resolution of multiplexed grating approach is less than twice of that of the one-time diffraction scheme. Therefore, we can design a high-resolution approach through selecting a suitable incident angle. Equation (9) also indicates that in the multiplexed grating approach, when m and d are constant, the angular resolution is determined only by the incident angle $i_{\text{0}}$, while in the one-time diffraction scheme the angular resolution is determined by the diffraction angle, which relies on the wavelength. This advantage benefits the design of a high-resolution approach over a wide wavelength range. When the incident angle is selected, the resolution will be constant over the entire wavelength range.

We compared the angular resolution between our multiplexed grating approach and the one-time diffraction scheme. A grating of 1050 lines/mm was used. The angular resolution of the multiplexed grating approach and the one-time diffraction scheme over the entire wavelength range of 1250 nm to 1650 nm is shown in Fig. 3, for $m=\text{1}$ and $i_0=\text{7}{5}^{\circ }$. The angular resolution of our approach is 5 times higher than that of the one-time diffraction scheme.

 

Fig. 3 Comparison of angular resolution between multiplexed grating and one-time diffraction spectrometers.

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3. Simulation and design

A simulation was implemented using software ZEMAX to compare the performances of a common one-time diffraction scheme and the multiplexed grating approach [14]. The design parameters and the optimized layout of the multiplexed grating approach are shown in Table 1 and Fig. 4. Figure 5(a) shows the spot diagram of the multiplexed grating approach in ZEMAX, and Fig. 4(b) shows the spot diagram of the one-time diffraction scheme, whose optical components are the same as the former. The results show that the linear resolution of the multiplexed grating approach at 1550 nm is 175 μm/nm, while that of the one-time diffraction scheme is only 30 μm/nm.

Table 1. Basic parameters of the spectrometer scheme

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Fig. 4 Optimized layout of the multiplexed grating approach.

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Fig. 5 Spot diagrams in ZEMAX. (a) Spot diagram of the multiplexed grating approach. (b) Spot diagram of the one-time diffraction scheme.

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The instrument resolution equals the ratio of the core diameter of the output fiber, which is 10 μm, and the linear resolution. We obtained the instrument resolutions of the two spectrometer designs over the entire spectral range, as summarized in Fig. 6. The multiplexed grating approach is shown to improve the instrument resolution to 60 pm across the entire spectral range, while that of the one-time diffraction scheme is 300 pm or more. Meanwhile, the instrument resolution of the multiplexed grating approach is more consistent.

 

Fig. 6 Comparison of instrument resolution between multiplexed grating (MG) and one-time diffraction (OTD) spectrometer schemes.

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Based on the simulation, a prototype of the multiplexed grating spectrometer was fabricated, as shown in Fig. 7. Figure 8 presents the spectrum of a distributed feedback laser with a 12.5 MHz linewidth, obtained with our spectrometer. Judging from Fig. 8, the center spectral wavelength of the measured laser is 1553.41 nm, and its full width at half maximum (FWHM) is 57 pm, which indicates that the wavelength resolution of the prototype is in good agreement with the simulation. Moreover, the dynamic range of the designed spectrometer is 45dB at 0.2 nm, which meets the requirement for DWDM measurements.

 

Fig. 7 The prototype of the multiplexed grating spectrometer.

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Fig. 8 The DFB laser spectrum as measured using the proposed multiplexed grating spectrometer.

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Figure 9 presents the spectrum of a broadband source as measured using the proposed multiplexed grating spectrometer. It indicates that the wavelength range of the proposed spectrometer completely covers the fiber communication band of 1250–1650 nm.

 

Fig. 9 The broadband source spectrum as measured using the proposed multiplexed grating spectrometer.

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4. Conclusions

This paper presents the theoretical analysis, simulation, and design of a compact, broadband, and high-resolution spectrometer, in which a dihedral reflector is used to reflect the dispersed light back for a re-diffraction. The dihedral reflector folds the optical path, and scans the dispersed light to ensure all the wavelengths can be detected with high resolution. The optics can fit inside a volume of 12 cm × 14 cm × 5 cm, while its wavelength resolution is as high as 57 pm. This spectrometer will be suitable for the OSNR measurement for 100G 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 grating spectrometer concept in a wide range of applications.