A high spectral sensitivity interferometer based on the dispersive property of the semiconductor GaAs

YuanXue Cai; YunDong Zhang; ChaoBo Yang; BoShi Dang; Jinfang Wang; Ping Yuan

doi:10.1364/OE.17.022254

1. Introduction

The interferometer is an important instrument in laser spectroscopy, and the amount of spectral information that can be extracted from a spectrum depends essentially on the attainable spectral resolution and the sensitivity that can be achieved. Especially, the sensitivity of the interferometer depends on the dispersive property of the material used in their system. Several groups are devoted to improving the spectrum performance based on slow light in order to significantly enhance the response ability of the interferometer to slight change of the frequency. And so far some exciting results have been obtained in enhancing the spectral sensitivity by the dispersive property of slow light medium [1–3]. It is important to get large optical path difference of light pulses in the slow light medium in the interferometer [4–7]. This difference brings larger phase variation in small spatial distance and limits the spectrum performance of the interferometer [8, 9]. Moreover, interferometer with high spectral sensitivity may be available for applications such as sensing, metrology, holography, and laser gyros.

Among existing dispersive material systems, semiconductor exhibits strongly interesting dispersive properties in close proximity to their absorption band gap. Moreover, the fact that strongly dispersive region of each semiconductor is different makes it necessary to choose the appropriate material for different applications. Though the spectral sensitivity in the Ref [1]. has been improved through CdS_0.625Se_0.375 near 600nm, the special phenomena that dispersive propriety of the material declines in the near-infrared region makes it difficult to match the spectral sensitivity which has been achieved in the visible region [10]. As far as we know, up to now there are still no relevant experimental reports about the improvement of the spectral sensitivity based on slow light technology in near-infrared region. In this paper, we experimentally demonstrate that the spectral sensitivity of an interferometer can be greatly enhanced by the dispersive property of the semiconductor GaAs in near-infrared region. Furthermore, our results not only lead to enhance the sensitivity of the conventional near-infrared spectroscopy, but also provide a general method that can be extended to the whole infrared spectral region.

2. Theory

Wedge-shape interference as shown in Fig. 1 is used to illustrate how the dispersive property of the material enhances the spectral sensitivity of an interferometer. A beam is normally incident on a wedge plate. Tilt fringes occur at the exit surface after the light waves bounce back and forth between the two surfaces of the wedge plate [11]. When the wedge angle θ is small and satisfies the condition of $L_{0} » y θ$ approximately, the phase of transmission light is a function of the lateral position y and the wavelength λ of the incident wave $ϕ = f (y, λ)$ . The intensity distribution of light transmission is given by:

I_{t} (y, λ) = I_{0} \frac{T^{2} T_{L}}{{(1 - R T_{L})}^{2}} \frac{1}{[1 + F \sin^{2} (Δ ϕ (y, λ))]}

where T and R are the transmissivity and reflectivity at the air-medium interface respectively;

T_{L} \equiv e^{- α L_{0}}

is the transmissivity through the medium;

F \equiv 4 R T_{L} / {(1 - R T_{L})}^{2}

is the finesse coefficient;

Δ ϕ = k_{n} (L_{0} + θ y) + ϕ_{0}

is the phase difference.

Fig. 1 Multiple-beam interference in a wedged plate

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For a spectroscopic interferometer, the intensity of light transmission redistributes by the change of wavelength of the incident wave as Eq. (1) shown. Usually in the practical optical interference experiments, the physical quantity which we detect is the intensity distribution of interference fringes. Therefore, the spectral sensitivity of the interferometer can be expressed by the response ability of the intensity distribution change to the change of wavelength:

S \equiv \frac{d I_{t}}{d λ}

The distribution of the transmitted intensity reflects the intensity distribution of the interference fringes, so we can use the rate of fringe movement to describe the response ability of the interference device for the wavelength of incident wave. The spectral sensitivity can be written as:

S= \frac{d y_{m}}{d λ} = \frac{(m π - ϕ_{0})}{2 π n^{2} θ} n_{g}

where

n_{g} \equiv n - λ \frac{d n}{d λ}

is the group index;

y_{m} = \frac{(m π - ϕ_{0}) λ}{2 π n θ} - \frac{L_{0}}{θ}

is the position of the m-order fringe peak. The position of the fringe peak is a function of the incident wavelength, so slight change of λ will lead to the shift of the position of

y_{m}

. One can also normalize this movement rate by the fringe period

Δ y = \frac{λ}{2 n θ}

and obtain the following normalized expression:

\frac{1}{Δ y} \frac{d y_{m}}{d λ} = \frac{(m π - ϕ_{0})}{π n λ} n_{g} \approx \frac{2 L_{0}}{λ^{2}} n_{g}

As the analysis above, the spectral sensitivity of the wedged-shaped interference can be directly defined as the rate of the fringe movement, which is proportional to the group index $n_{g}$ of the medium, as shown in the Eq. (4). Also, we can define the spectral sensitivity of the non-dispersive medium through replacing $n_{g}$ by the refractive index n in Eq. (4). For common interference system, non-dispersive materials or media with small dispersion are used. Therefore, the spectral sensitivity of an interferometer can be greatly enhanced by dispersive materials than the one with normal element under the same condition. Meanwhile, theoretical analysis shows that a great phase shift will be obtained by large group index of slow light medium in a smaller spatial distance compared with non-dispersive materials. This effect could be conducive to reducing the device size and measuring volume without decreasing the performance of the system-wide.

3. Experiment

3.1 The basis of material selection

Just as the analysis above, the improvement of the spectral sensitivity in the near-infrared region based on slow light technology would provides a basic method to enhance the spectral sensitivity throughout the infrared spectrum region. The semiconductor GaAs, because of which has much larger dispersive property than CdS_0.625Se_0.375 in near-infrared region, will undoubtedly improve the spectral sensitivity in the region. The slow light medium used as the wedge plate in the interferometer is a GaAs n-type single crystal. GaAs is a direct band gap semiconductor and for undoped GaAs, the energy band gap at room temperature is 1.42 eV [12]. The refractive index of GaAs is shown by

n (a) = n (0) - [c_{0} a / n (0)] [π / 2 - c_{1} \tan^{- 1} (y / a)]

where

n (0) = 3.633

is the refractive index near the absorption peak;

a = \sqrt{1 - (h c / λ G)}

;

G = 1.43 e V

is the band gap energy at 890 nm under temperature of 300K;

c_{0} / n (0) = 0.312

; y=0.419 [13]. The calculated refractive index of GaAs is shown in Fig. 2(a) . Theoretical calculation shows that the refractive index of GaAs exhibits fast variation near λ=900 nm, which leads to a large group index corresponding to the refractive index, as shown in Fig. 2(b). According to the Kramers-Kronig relation, the refractive index of this material experiences a rapid change near the absorption edge, which induces a large group index [14]. However, the absorption will reduce the transmittance greatly, brings great difficulty in the detection and raises the demands of the experiment equipment. The total finesse of an interferometer influences the imaging quality of the interference fringes [15]. For the finesse, the main influencing factors of finesse impact from the surface roughness, the medium adsorption and wedge angle et al. The adsorption will decrease the total transmission and broaden the interference fringes, and the inclusion of the small angles will decrease the total fineness. The Fresnel’s formula, furthermore, which says that in the situation of double side reflectivity the theoretical transmittance which we can obtain, though in the ideal material is always less than 56%, we can easily describe the characters of optical wave such as reflectivity and refraction in the isotropic medium [16]. The test result of the transmittance also demonstrates the truth, as shown in Fig. 2(d). Considering the dispersive property of GaAs, imaging quality and the experiment difficulty, 895 nm~910 nm is selected as the spectral window to obtain advantageously high spectral sensitivity, the thickness of the sample tested in the experiment is about 900 μm, and the angle between the two surfaces is about 0.7°.

Fig. 2 (a) The calculation of GaAs refractive index, (b) The calculation of GaAs group index, (c) The refractive index and group index from 895 nm to 910 nm, (d) The transmittance of GaAs as the thickness is 900 μm and the wedge angle is 0.7°.

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Numerically, Fig. 2(c) shows that the value of the group index is about 4.7. Figure 4 (red color line) is the simulation result of spectral sensitivity in the 895 nm~910 nm spectral range. According to the simulation, the rate of the interference fringe is approximate 10 period/nm. The change rate of the normalized fringe movement rate is about 0.05 period/nm² in the detection spectrum region. The movement period of the fringe is about 0.1 period when the wavelength changes 0.01nm. This is much larger than the effect compared with the change rate of the fringe movement rate. Therefore, the reason mentioned above could guarantee the possibility for our experiment to describe the movement law of the fringe and simultaneously make the measurement accuracy satisfied.

Fig. 4 The rate of fringe movement as a function of wavelength: the squares denote the experimental date with standard deviation bars, and the red solid and dotted line are the theoretical simulations.

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3.2 Experimental setup and scheme

The schematic diagram is shown as Fig. 3 which is used to detect the spectral sensitivity of the wedged shear interferometer. The incident beam will be divided into two parts by the beam splitter BS. One beam is normally incident into the slow light medium GaAs through collimator system and the interference fringes occur at the exit surface of the wedge plate. The fringes can be detected by CCD through the imaging lens. Another beam is injected in wavemeter to get the wavelength of the incident light. This experimental arrangement is not only helpful to obtain the stable fringes without particular conditions, but also to detect the interference fringes and measure the corresponding wavelength simultaneously.

Fig. 3 Schematic diagram of wedge shear slow light interferometer

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A solid-state optical parametric oscillator with tuning range from 445nm to 1750nm and at 10 Hz repetition rate is used as the pulsed tunable source in the experiment and a wavemeter is used to measure the wavelength simultaneously. The fringe patterns on the exit surface of the wedge plate are imaged onto a NIR CCD (MTV-1881EX-3, Mintron) imaging module through an imaging lens and recorded digitally. The imaging lens is not essential if the CCD sensor size is much smaller than the fringe width. To determine the spectral sensitivity near each wavelength, the fringe patterns are recorded while the laser is detuned near this wavelength with a detuning step size of 0.01nm by 30 steps. We choose the interference fringe at the same position of each collection and analyze the relation between the intensity distribution and the change of the wavelengths to calculate the moving rate of fringes. The wavelengths at which the spectral sensitivity is measured are chosen from 895 nm to 910nm with an increase of 2.5nm each time. When the laser is detuned, all of fringes move at the same direction with the same distance in ideal condition. To ensure the precision, the measure amount contains three periods, so finally we choose four period ranges to make sure the reliability to calculate average duty of moving distance. Moreover, the resolution limitation of CCD must be considered. In addition, the medium temperature variation acts on the refractive index, so it is necessary to keep medium temperature being constant [17–19].

3.3 Experimental result and discussion

Figure 4 presents the experimental results of the spectral sensitivity of this interferometer at different wavelengths. It is clear that the rate of fringe movement of our interferometer with a slow light medium GaAs decreases from 11.2 period/nm to 10.0 period/nm as the wavelength changes from 895nm to 910nm, which coincides very well with the simulation result of the group index. From Fig. 4 we can find that the spectral sensitivity of the interferometer based on the dispersive property of the slow light medium is approximately twice of the one with non-dispersive medium under the same condition.

The experimental results could be affected by the following aspects: (1) Kramers-Kronig relation shows that the large spectral dispersion dn/dλ is usually accompanied with strong absorption. This will decrease the finesse of the interference fringes and increase the analytical error of the experimental results near the 895 nm. (2) The resolution of the CCD restricts to describe the fringes by more collection points. (3) The technological level of the semiconductor material will also affect the experimental results.

At present, it is a popular way to measure the position of the interference fringes for detecting the spectral sensitivity. However, this method is restricted from the tunable accuracy of the optical source and the resolution of the imaging system. Whereas these limitations could be improved by using narrow linewidth continuously tunable optical source, which is fit for the requirements of a wide experiment and improves the measuring accuracy. Moreover, coating method, with its property of increasing the transmittance and reducing reflectivity loss, could be useful for the experiment and final result.

4. Conclusion

In conclusion, we have developed an interferometer based on the dispersive property of the semiconductor GaAs in near-infrared region and analyzed the factors which influence the results. Comparing with simulation result of non-dispersive material, we experimentally achieved approximately twice of the sensitivity using the wedge plate GaAs in the interferometer. In other words, experimental results demonstrated that the addition of slow light medium with large group index could effectively enhance the spectral sensitivity of interferometer and the sensitivity was proportional to the group index of the material. Also this conclusion could provide an evidence for further application study of the slow light in infrared spectroscopy or more areas.

Acknowledgements

This work was supported by the National High Technology Research and Development Program (863 Program) of China No. 2007AA12Z112 and National Science Foundation of China No. 60878006.

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A high spectral sensitivity interferometer based on the dispersive property of the semiconductor GaAs

Abstract

1. Introduction

2. Theory

3. Experiment

3.1 The basis of material selection

3.2 Experimental setup and scheme

3.3 Experimental result and discussion

4. Conclusion

Acknowledgements

References and links

Cited By

Figures (4)

Equations (5)

Optics Express