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An efficient cavity for optically pumped terahertz lasers
Optics Communications 283 (2010) 3171–3175
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
An efficient cavity for optically pumped terahertz lasers Liang Miao, Duluo Zuo, Zhixian Jiu, Zuhai Cheng ⁎ Wuhan National Laboratory for Optoelectronics, College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
a r t i c l e
i n f o
Article history: Received 25 December 2009 Received in revised form 6 April 2010 Accepted 6 April 2010 Keywords: THz laser Cavity Efficient Etalon effect High reflectivity
a b s t r a c t The efficiency of a simply designed cavity for optically pumped pulsed terahertz lasers is studied experimentally. A coated Ge and a crystal quartz act as the input and output windows, respectively. The thickness of the Ge window is designed according to etalon effects to maximize terahertz reflectivity. NH3 is filled in the cavity as the active medium. When NH3 is pumped by the 10P(32) line of a TEA CO2 laser, intense 151.5 μm terahertz radiation is emitted. As high as 19.6 mJ terahertz radiation is extracted from 1.57 J pump energy. The corresponding photon conversion efficiency reaches 35.3%. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Terahertz (THz) waves (30 μm–3 mm) have great applications in imaging, safety inspection, spectroscopy, etc. [1–3]. Since the first optically pumped pulsed THz laser (OPPTL) was invented by Chang et al. in 1970 [4], it has been proven to be a high-power and efficient THz radiation source. Many kinds of cavities have been used in OPPTLs. The input window of pump radiation is the key problem in designing THz cavities. The window should be of high reflectivity for THz radiation and high transmissivity for pump radiation. TEA CO2 lasers were commonly used as pump lasers. Two kinds of widely used input windows were metal meshes and infrared transmission crystals such as BaF2 and NaCl [5–7]. Metal meshes are efficient in theory because of their high reflectivity in the THz range. However, they are difficult to manufacture and align. This disadvantage often made the photon conversion efficiencies of metal mesh cavities less than 30% [5]. The most efficient THz cavity, which utilized complicated transverse intracavity-pumping, had a 47% efficiency to our knowledge [8]. Both BaF2 and NaCl have so low reflectivity for THz radiation that cavities with these crystals as input windows had only about 10% efficiency [6,7]. However, they are still widely used because they are transparent to CO2 laser radiation and easy to process. The main objective of this study was to design an efficient cavity without metal meshes for OPPTLs. The input window was an antireflection-coated Ge, whose etalon effects were applied to increase THz reflectivity. NH3 was the active medium and pumped
⁎ Corresponding author. Tel.: +86 27 87795940; fax: +86 27 87792355. E-mail address: [email protected] (Z. Cheng). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.04.011
by a home-made TEA CO2 laser. From this cavity, 35.3% of photon conversion efficiency was achieved. 2. Experimental setup The experimental apparatus is shown schematically in Fig. 1. It can be divided into four parts: the pump laser, the guiding optics, the THz cavity and the detecting system. The pump laser is a home-made wavelength-tunable TEA CO2 laser. Wavelength tuning of the CO2 laser was realized by replacing the rear reflector by a 150 grooves/mm Littrow-mounted grating, blazed to 10.6 μm. The working gas mixture was fixed to H2: CO2: N2: He = 1: 2: 6: 7 and the total gas pressure was 19 KPa. The 10P(32) line (10.719 μm) was chosen to be the pump line to extract intense 151.5 μm THz radiation from NH3 [6,9]. The pump pulses were focused into the THz cavity by two gold-coated silicon reflectors. A typical pulse shape of the 10P(32) line is shown in Fig. 2. The THz cavity consisted of a quartz glass tube (2 m long, 50 mm i.d.), an antireflection-coated Ge plate (4.810 ± 0.005 mm thick, 25 Ω cm) and an optically polished Z-cut crystal quartz plate (2 mm thick). NH3 was filled in the quartz glass tube as the active medium. The Ge crystal was the input window of the pump radiation. Its thickness was designed according to etalon effects to provide high reflectivity for 151.5 μm wavelength. There was also a coated GaAs plate (4.703 ± 0.005 mm thick, 1 × 108 Ω cm) to act as the input window, alternatively. Antireflection-coated Ge and GaAs are totally transparent to CO2 laser radiation. The crystal quartz was the output window of THz radiation. Detectors behind the output window can only receive THz radiation because crystal quartz is opaque to wavelengths below 40 μm [10]. Close to the output window was a tsurupica lens with 180 mm focal length (Microtech Instruments). An aluminum cone was used to
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L. Miao et al. / Optics Communications 283 (2010) 3171–3175
Fig. 1. Schematic diagram of the optically pumped NH3 THz laser.
collect THz radiation in addition to the lens. THz pulse energy was measured by a high-response pyroelectric detector (Spectrum SPJ-A8-OB) at the focus of the tsurupica lens. The detector has a 7.8 mm diameter aperture and an energy range from 60 nJ to 30 mJ. A highspeed pyroelectric detector (Molectron Instruments P3-01) was used to monitor THz pulse shapes. A pyroelectric camera (Spiricon Pyrocam III) was used for THz laser beam diagnostics. The Pyrocam III has a LiTaO3 pyroelectric crystal with broad wavelength response. The ZnSe window of the camera was changed to a polyethylene one for applications in the THz range.
3. Results and discussion 3.1. Results of the THz radiation Intense 151.5 μm THz radiation saturated the THz energy detector when NH3 was pumped directly by the 10P(32) line. To avoid damage to the detector, the pump radiation was attenuated to 1.57 ± 0.1 J by a 5 mm thick Si plate not shown in Fig. 1. Energy of the THz radiation as a function of NH3 pressure for both cavities with Ge and GaAs input windows are shown in Fig. 3. Every data in this figure is the average of more than three shots. A typical THz pulse shape is shown in Fig. 4.
Fig. 2. Pulse shape of the 10P(32) line. Detected by a HgCdTe detector (Vigo PVM-10.6) and displayed on an oscillograph (Agilent Technology DSO7034A).
L. Miao et al. / Optics Communications 283 (2010) 3171–3175
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Fig. 3. THz pulse energy as a function of NH3 pressure for both cavities with the Ge and GaAs input windows. The error bars indicate the largest deviation to the average energy at the pressure.
As high as 19.6 mJ THz radiation was extracted from the Ge cavity when NH3 was 250 Pa. This value was 45% higher than the maximum energy of the GaAs cavity. For optically pumped THz lasers, the quantum limit of energy conversion efficiency is given by η0 = 12 λλPT [11], where λP is the pump wavelength and λT is the THz wavelength. So the photon conversion efficiency can be expressed as η = η10 EETP , where η0 is the quantum efficiency limit, ET is the THz energy and EP is the pump energy. In this study, the 10P(32) pump line (10.719 μm) had 1.57 J output. The maximum THz energy was 19.6 mJ at 151.5 μm for the Ge cavity. So the corresponding photon conversion efficiency was 35.3%, which was higher than that of most cavities used before and not much lower than the highest record 47% [8].
The Pyrocam III camera was placed at the focus of the tsurupica lens. An image of the 151.5 μm radiation taken by the camera is shown in Fig. 5. The beam width (D-4-Sigma) of the focused THz radiation was 8.5 mm in the X direction and 9.3 mm in the Y direction. The corresponding far-field divergence angles in the X and Y direction were 47 mrad and 51 mrad, respectively. Since the focal spot diameter was larger than the aperture of the THz energy detector, the aluminum cone for THz radiation collection was very helpful. The diffraction-limit divergence is known to be θ = 1:22λ a , where λ is the THz wavelength and a is the radius of the aperture. The THz cavity had an optics aperture of 50 mm diameter and the emitted wavelength was 151.5 μm. So the diffraction-limit divergence angle
Fig. 4. THz pulse shape.
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L. Miao et al. / Optics Communications 283 (2010) 3171–3175
Fig. 5. Beam profile of the 151.5 μm radiation. Taken by the Spiricon Pyrocam III pyroelectric camera.
was 7.4 mrad and the far-field divergence angle in Fig. 5 was about 7 times of the limit. 3.2. Etalon effects of the Ge and GaAs windows It is the reflectivity for THz radiation that determines the efficiencies of input windows. So etalon effects described by way of reflectivity will explain the THz energy results in Section 3.1. It is more convenient to measure the transmissivity of Ge and GaAs directly. The crystal was mounted on a rotating platform and placed in the THz radiation output direction without lens focusing, 30 cm away from the output window. Then the crystal was tuned to be perpendicular to the axis of the THz cavity. Afterwards, the transmissivity were measured as a function of the incidence angle of the 151.5 μm radiation. The measuring results are shown in Fig. 6. The fitting curves were obtained with the thickness of Ge and GaAs as a changeable parameter in the range of the thickness tolerance (±5 μm). The Ge window had obvious etalon effects in contrast to the GaAs window. The fitting curves and the designed thickness of Ge were
both obtained according to the interference theory of plane plates. The theoretical transmissivity is [12]: T=
−αd 2
1−re
ð1−r Þ2 e−αd + 4re−αd sin2
;
where r is about the normally incident reflectivity, given by α d n λ θ
ð1Þ
2πnd λ cosθ
ðn−1Þ2 ðn + 1Þ2
,
is the absorption coefficient, is the thickness of the crystal plate, is the refractive index of the crystal, is the wavelength of the THz radiation, is the refractive angle of the THz radiation.
The average transmissivity were calculated by summing up the data between the maximum and minimum, and then dividing the summation by the number of the data. There were two symmetrical ranges with a maximum and a minimum for both Ge and GaAs. The two symmetrical ranges were both included in the averaging process. So the average transmissivity of the Ge window was given by: n
T¯Ge =
14
∑ yGe; i
i=1
∑ yGe; i
=
n
i=1
14
= 28:6%:
ð2Þ
The average transmissivity of the GaAs window was given by: m
T¯GaAs =
16
∑ yGaAs; i
i=1
m
∑ yGaAs; i
=
i=1
16
= 15:6%:
ð3Þ
The refractive indices of Ge and GaAs at 151.5 μm are 4.004 and 3.608 [13]. According to the average transmissivity and the refractive indices, the absorption coefficients and the reflectivity of the crystals can be calculated conveniently [14]. The reflectivity R is given by: R = 1−Α−T;
Fig. 6. Transmissivity of Ge and GaAs as a function of the incidence angle of the 151.5 μm radiation.
ð4Þ
where A is the total absorption, and T is the transmissivity. The absorption coefficients of the Ge and GaAs windows were calculated to be 0.86 cm−1 and 2.3 cm−1. The results were in good agreement with previous studies [13,15,16]. The reflectivity results are given in Fig. 7. The thickness parameters of the two fitting curves are the same with those in Fig. 6.
L. Miao et al. / Optics Communications 283 (2010) 3171–3175
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Fig. 8. Reflectivity variation as a function of the thickness of Ge. Rmax is the maximum reflectivity when the thickness is the optimal value, about 4.815 mm. Fig. 7. Calculated reflectivity of Ge and GaAs as a function of THz radiation incidence angle.
The reflectivity of Ge and GaAs near zero degree of incidence was the same status when they acted as the input windows. The results of all angles for GaAs were about its single-side reflectivity when the THz radiation was normally incident. The reflectivity of Ge was about 50% higher than that of GaAs near 0°. Moreover, this relation held for more than ±5° so precise aligning of the input window wasn't needed to achieve high reflectivity. The sensitivity of reflectivity to the thickness of Ge can be obtained according to Eqs. (1) and (4) when THz radiation is normally incident on the Ge window. The calculated results are shown in Fig. 8. The reflectivity reaches the maximum when the thickness of Ge is about 4.815 mm. If the thickness has 5 μm offset from the optimal thickness, the reflectivity will decrease by near 20%. If the offset is 3 μm, the reflectivity will decrease by about 5%. So the accuracy of the thickness had better be controlled within ±3 μm to obtain reliable high reflectivity.
at the sacrifice of high transmissivity for pump radiation. Moreover, metal meshes are difficult to be well-manufactured and aligned. These disadvantages often make them even less efficient than the Ge window [5]. Ge crystals with higher resistivity have lower absorption coefficients [13], so higher efficiency can be expected if Ge crystals with higher resistivity are available. 4. Conclusions As high as 35.3% efficiency was achieved from an optically pumped pulsed THz laser in this study. An antireflection-coated Ge plate acted as the input window instead of complicated metal meshes. Etalon effects were applied to design the thickness of the Ge window. Since Ge crystals are easily to process and align, high efficiency can be realized conveniently compared with THz cavities with metal meshes. However, Ge crystals with higher resistivity and higher processing precision are needed to increase the conversion efficiency further.
3.3. Discussion Acknowledgements The absorption of GaAs in the THz range is so severe that there is almost only single-side reflection as shown in Fig. 7. In contrast, Ge has relatively less absorption and larger refractive index, so strong etalon effects have been observed. However, the etalon effects of Ge are still weaker than the theory. It is probably due to the large divergence of the THz radiation and the limited parallelism of the Ge window. The theoretical maximum reflectivity of Ge in the THz range can reach 78% if absorption is ignored for thin Ge plate according to Eqs. (1) and (4). The strong etalon effects of the Ge window make it possible to control its thickness to increase the reflectivity greatly for any needed THz wavelength. In addition, Ge has a larger refractive index and a much lower absorption coefficient than GaAs as mentioned in Section 3.2. So the Ge window has higher reflectivity than the GaAs window. For the 151.5 μm wavelength, near 50% reflectivity of the Ge window provides much feedback. However, most THz radiation illuminating the GaAs window is absorbed by the window or transmits out of the cavity. So the efficiency of the Ge cavity is much higher than that of the GaAs cavity as shown in Fig. 3. ZnSe is another widely used infrared transmission material. It hasn't been chosen to be the input window to compare with Ge and GaAs, because its refractive index is only about 3.0 and the absorption coefficient is around 10 cm−1 in the THz range [14]. Well-designed metal meshes have higher reflectivity in the THz range than Ge in theory. However, its high THz reflectivity is realized
The authors would like to thank Hongmei Huang for technical help in the experiments. This work was supported by Creative Foundation of Wuhan National Laboratory for Optoelectronics (No. Z080007). References [1] B. Ferguson, X.C. Zhang, Nat. Mater. 1 (2002) 26. [2] E. Abraham, A. Younus, A. El Fatimy, J.C. Delagnes, E. Nguéma, P. Mounaix, Opt. Commun. 282 (2009) 3104. [3] A.G. Davies, A.D. Burnett, W.H. Fan, E.H. Linfield, J.E. Cunningham, Mater. Today 11 (2008) 18. [4] T.Y. Chang, T.J. Bridges, Opt. Commun. 1 (1970) 423. [5] P. Woskoboinikow, J.S. Machuzak, W.J. Mulligan, IEEE J. Quantum Electron. 21 (1985) 14. [6] W. Schatz, Infrared Phys. Technol. 36 (1995) 387. [7] C.T. Gross, J. Kiess, A. Mayer, F. Keilmann, IEEE J. Quantum Electron. 23 (1987) 377. [8] H. Hirose, S. Kon, IEEE J. Quantum Electron. 22 (1986) 1600. [9] H.R. Fetterman, H.R. Schlossberg, C.D. Parker, Appl. Phys. Lett. 23 (1973) 684. [10] E.E. Russell, E.E. Bell, J. Opt. Soc. Am. 57 (1967) 341. [11] S. Marchetti, M. Martinelli, R. Simili, R. Fantoni, M. Giorgi, Infrared Phys. Technol. 41 (2000) 197. [12] C.J. Johnson, G.H. Sherman, R. Weil, Appl. Opt. 8 (1969) 1667. [13] D. Grischkowsky, S. Keiding, M.V. Exter, C. Fattinger, J. Opt. Soc. Am. B 7 (1990) 2006. [14] T. Hattori, Y. Homma, A. Mitsuishi, M. Tacke, Opt. Commun. 7 (1973) 229. [15] M.N. Afsar, D.D. Honijk, W.F. Passchier, J. Goulon, IEEE J. Quantum Electron. 25 (1977) 505. [16] R.H. Stolen, Appl. Phys. Lett. 15 (1969) 74.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
An efficient cavity for optically pumped terahertz lasers Liang Miao, Duluo Zuo, Zhixian Jiu, Zuhai Cheng ⁎ Wuhan National Laboratory for Optoelectronics, College of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
a r t i c l e
i n f o
Article history: Received 25 December 2009 Received in revised form 6 April 2010 Accepted 6 April 2010 Keywords: THz laser Cavity Efficient Etalon effect High reflectivity
a b s t r a c t The efficiency of a simply designed cavity for optically pumped pulsed terahertz lasers is studied experimentally. A coated Ge and a crystal quartz act as the input and output windows, respectively. The thickness of the Ge window is designed according to etalon effects to maximize terahertz reflectivity. NH3 is filled in the cavity as the active medium. When NH3 is pumped by the 10P(32) line of a TEA CO2 laser, intense 151.5 μm terahertz radiation is emitted. As high as 19.6 mJ terahertz radiation is extracted from 1.57 J pump energy. The corresponding photon conversion efficiency reaches 35.3%. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Terahertz (THz) waves (30 μm–3 mm) have great applications in imaging, safety inspection, spectroscopy, etc. [1–3]. Since the first optically pumped pulsed THz laser (OPPTL) was invented by Chang et al. in 1970 [4], it has been proven to be a high-power and efficient THz radiation source. Many kinds of cavities have been used in OPPTLs. The input window of pump radiation is the key problem in designing THz cavities. The window should be of high reflectivity for THz radiation and high transmissivity for pump radiation. TEA CO2 lasers were commonly used as pump lasers. Two kinds of widely used input windows were metal meshes and infrared transmission crystals such as BaF2 and NaCl [5–7]. Metal meshes are efficient in theory because of their high reflectivity in the THz range. However, they are difficult to manufacture and align. This disadvantage often made the photon conversion efficiencies of metal mesh cavities less than 30% [5]. The most efficient THz cavity, which utilized complicated transverse intracavity-pumping, had a 47% efficiency to our knowledge [8]. Both BaF2 and NaCl have so low reflectivity for THz radiation that cavities with these crystals as input windows had only about 10% efficiency [6,7]. However, they are still widely used because they are transparent to CO2 laser radiation and easy to process. The main objective of this study was to design an efficient cavity without metal meshes for OPPTLs. The input window was an antireflection-coated Ge, whose etalon effects were applied to increase THz reflectivity. NH3 was the active medium and pumped
⁎ Corresponding author. Tel.: +86 27 87795940; fax: +86 27 87792355. E-mail address: [email protected] (Z. Cheng). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.04.011
by a home-made TEA CO2 laser. From this cavity, 35.3% of photon conversion efficiency was achieved. 2. Experimental setup The experimental apparatus is shown schematically in Fig. 1. It can be divided into four parts: the pump laser, the guiding optics, the THz cavity and the detecting system. The pump laser is a home-made wavelength-tunable TEA CO2 laser. Wavelength tuning of the CO2 laser was realized by replacing the rear reflector by a 150 grooves/mm Littrow-mounted grating, blazed to 10.6 μm. The working gas mixture was fixed to H2: CO2: N2: He = 1: 2: 6: 7 and the total gas pressure was 19 KPa. The 10P(32) line (10.719 μm) was chosen to be the pump line to extract intense 151.5 μm THz radiation from NH3 [6,9]. The pump pulses were focused into the THz cavity by two gold-coated silicon reflectors. A typical pulse shape of the 10P(32) line is shown in Fig. 2. The THz cavity consisted of a quartz glass tube (2 m long, 50 mm i.d.), an antireflection-coated Ge plate (4.810 ± 0.005 mm thick, 25 Ω cm) and an optically polished Z-cut crystal quartz plate (2 mm thick). NH3 was filled in the quartz glass tube as the active medium. The Ge crystal was the input window of the pump radiation. Its thickness was designed according to etalon effects to provide high reflectivity for 151.5 μm wavelength. There was also a coated GaAs plate (4.703 ± 0.005 mm thick, 1 × 108 Ω cm) to act as the input window, alternatively. Antireflection-coated Ge and GaAs are totally transparent to CO2 laser radiation. The crystal quartz was the output window of THz radiation. Detectors behind the output window can only receive THz radiation because crystal quartz is opaque to wavelengths below 40 μm [10]. Close to the output window was a tsurupica lens with 180 mm focal length (Microtech Instruments). An aluminum cone was used to
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L. Miao et al. / Optics Communications 283 (2010) 3171–3175
Fig. 1. Schematic diagram of the optically pumped NH3 THz laser.
collect THz radiation in addition to the lens. THz pulse energy was measured by a high-response pyroelectric detector (Spectrum SPJ-A8-OB) at the focus of the tsurupica lens. The detector has a 7.8 mm diameter aperture and an energy range from 60 nJ to 30 mJ. A highspeed pyroelectric detector (Molectron Instruments P3-01) was used to monitor THz pulse shapes. A pyroelectric camera (Spiricon Pyrocam III) was used for THz laser beam diagnostics. The Pyrocam III has a LiTaO3 pyroelectric crystal with broad wavelength response. The ZnSe window of the camera was changed to a polyethylene one for applications in the THz range.
3. Results and discussion 3.1. Results of the THz radiation Intense 151.5 μm THz radiation saturated the THz energy detector when NH3 was pumped directly by the 10P(32) line. To avoid damage to the detector, the pump radiation was attenuated to 1.57 ± 0.1 J by a 5 mm thick Si plate not shown in Fig. 1. Energy of the THz radiation as a function of NH3 pressure for both cavities with Ge and GaAs input windows are shown in Fig. 3. Every data in this figure is the average of more than three shots. A typical THz pulse shape is shown in Fig. 4.
Fig. 2. Pulse shape of the 10P(32) line. Detected by a HgCdTe detector (Vigo PVM-10.6) and displayed on an oscillograph (Agilent Technology DSO7034A).
L. Miao et al. / Optics Communications 283 (2010) 3171–3175
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Fig. 3. THz pulse energy as a function of NH3 pressure for both cavities with the Ge and GaAs input windows. The error bars indicate the largest deviation to the average energy at the pressure.
As high as 19.6 mJ THz radiation was extracted from the Ge cavity when NH3 was 250 Pa. This value was 45% higher than the maximum energy of the GaAs cavity. For optically pumped THz lasers, the quantum limit of energy conversion efficiency is given by η0 = 12 λλPT [11], where λP is the pump wavelength and λT is the THz wavelength. So the photon conversion efficiency can be expressed as η = η10 EETP , where η0 is the quantum efficiency limit, ET is the THz energy and EP is the pump energy. In this study, the 10P(32) pump line (10.719 μm) had 1.57 J output. The maximum THz energy was 19.6 mJ at 151.5 μm for the Ge cavity. So the corresponding photon conversion efficiency was 35.3%, which was higher than that of most cavities used before and not much lower than the highest record 47% [8].
The Pyrocam III camera was placed at the focus of the tsurupica lens. An image of the 151.5 μm radiation taken by the camera is shown in Fig. 5. The beam width (D-4-Sigma) of the focused THz radiation was 8.5 mm in the X direction and 9.3 mm in the Y direction. The corresponding far-field divergence angles in the X and Y direction were 47 mrad and 51 mrad, respectively. Since the focal spot diameter was larger than the aperture of the THz energy detector, the aluminum cone for THz radiation collection was very helpful. The diffraction-limit divergence is known to be θ = 1:22λ a , where λ is the THz wavelength and a is the radius of the aperture. The THz cavity had an optics aperture of 50 mm diameter and the emitted wavelength was 151.5 μm. So the diffraction-limit divergence angle
Fig. 4. THz pulse shape.
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Fig. 5. Beam profile of the 151.5 μm radiation. Taken by the Spiricon Pyrocam III pyroelectric camera.
was 7.4 mrad and the far-field divergence angle in Fig. 5 was about 7 times of the limit. 3.2. Etalon effects of the Ge and GaAs windows It is the reflectivity for THz radiation that determines the efficiencies of input windows. So etalon effects described by way of reflectivity will explain the THz energy results in Section 3.1. It is more convenient to measure the transmissivity of Ge and GaAs directly. The crystal was mounted on a rotating platform and placed in the THz radiation output direction without lens focusing, 30 cm away from the output window. Then the crystal was tuned to be perpendicular to the axis of the THz cavity. Afterwards, the transmissivity were measured as a function of the incidence angle of the 151.5 μm radiation. The measuring results are shown in Fig. 6. The fitting curves were obtained with the thickness of Ge and GaAs as a changeable parameter in the range of the thickness tolerance (±5 μm). The Ge window had obvious etalon effects in contrast to the GaAs window. The fitting curves and the designed thickness of Ge were
both obtained according to the interference theory of plane plates. The theoretical transmissivity is [12]: T=
−αd 2
1−re
ð1−r Þ2 e−αd + 4re−αd sin2
;
where r is about the normally incident reflectivity, given by α d n λ θ
ð1Þ
2πnd λ cosθ
ðn−1Þ2 ðn + 1Þ2
,
is the absorption coefficient, is the thickness of the crystal plate, is the refractive index of the crystal, is the wavelength of the THz radiation, is the refractive angle of the THz radiation.
The average transmissivity were calculated by summing up the data between the maximum and minimum, and then dividing the summation by the number of the data. There were two symmetrical ranges with a maximum and a minimum for both Ge and GaAs. The two symmetrical ranges were both included in the averaging process. So the average transmissivity of the Ge window was given by: n
T¯Ge =
14
∑ yGe; i
i=1
∑ yGe; i
=
n
i=1
14
= 28:6%:
ð2Þ
The average transmissivity of the GaAs window was given by: m
T¯GaAs =
16
∑ yGaAs; i
i=1
m
∑ yGaAs; i
=
i=1
16
= 15:6%:
ð3Þ
The refractive indices of Ge and GaAs at 151.5 μm are 4.004 and 3.608 [13]. According to the average transmissivity and the refractive indices, the absorption coefficients and the reflectivity of the crystals can be calculated conveniently [14]. The reflectivity R is given by: R = 1−Α−T;
Fig. 6. Transmissivity of Ge and GaAs as a function of the incidence angle of the 151.5 μm radiation.
ð4Þ
where A is the total absorption, and T is the transmissivity. The absorption coefficients of the Ge and GaAs windows were calculated to be 0.86 cm−1 and 2.3 cm−1. The results were in good agreement with previous studies [13,15,16]. The reflectivity results are given in Fig. 7. The thickness parameters of the two fitting curves are the same with those in Fig. 6.
L. Miao et al. / Optics Communications 283 (2010) 3171–3175
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Fig. 8. Reflectivity variation as a function of the thickness of Ge. Rmax is the maximum reflectivity when the thickness is the optimal value, about 4.815 mm. Fig. 7. Calculated reflectivity of Ge and GaAs as a function of THz radiation incidence angle.
The reflectivity of Ge and GaAs near zero degree of incidence was the same status when they acted as the input windows. The results of all angles for GaAs were about its single-side reflectivity when the THz radiation was normally incident. The reflectivity of Ge was about 50% higher than that of GaAs near 0°. Moreover, this relation held for more than ±5° so precise aligning of the input window wasn't needed to achieve high reflectivity. The sensitivity of reflectivity to the thickness of Ge can be obtained according to Eqs. (1) and (4) when THz radiation is normally incident on the Ge window. The calculated results are shown in Fig. 8. The reflectivity reaches the maximum when the thickness of Ge is about 4.815 mm. If the thickness has 5 μm offset from the optimal thickness, the reflectivity will decrease by near 20%. If the offset is 3 μm, the reflectivity will decrease by about 5%. So the accuracy of the thickness had better be controlled within ±3 μm to obtain reliable high reflectivity.
at the sacrifice of high transmissivity for pump radiation. Moreover, metal meshes are difficult to be well-manufactured and aligned. These disadvantages often make them even less efficient than the Ge window [5]. Ge crystals with higher resistivity have lower absorption coefficients [13], so higher efficiency can be expected if Ge crystals with higher resistivity are available. 4. Conclusions As high as 35.3% efficiency was achieved from an optically pumped pulsed THz laser in this study. An antireflection-coated Ge plate acted as the input window instead of complicated metal meshes. Etalon effects were applied to design the thickness of the Ge window. Since Ge crystals are easily to process and align, high efficiency can be realized conveniently compared with THz cavities with metal meshes. However, Ge crystals with higher resistivity and higher processing precision are needed to increase the conversion efficiency further.
3.3. Discussion Acknowledgements The absorption of GaAs in the THz range is so severe that there is almost only single-side reflection as shown in Fig. 7. In contrast, Ge has relatively less absorption and larger refractive index, so strong etalon effects have been observed. However, the etalon effects of Ge are still weaker than the theory. It is probably due to the large divergence of the THz radiation and the limited parallelism of the Ge window. The theoretical maximum reflectivity of Ge in the THz range can reach 78% if absorption is ignored for thin Ge plate according to Eqs. (1) and (4). The strong etalon effects of the Ge window make it possible to control its thickness to increase the reflectivity greatly for any needed THz wavelength. In addition, Ge has a larger refractive index and a much lower absorption coefficient than GaAs as mentioned in Section 3.2. So the Ge window has higher reflectivity than the GaAs window. For the 151.5 μm wavelength, near 50% reflectivity of the Ge window provides much feedback. However, most THz radiation illuminating the GaAs window is absorbed by the window or transmits out of the cavity. So the efficiency of the Ge cavity is much higher than that of the GaAs cavity as shown in Fig. 3. ZnSe is another widely used infrared transmission material. It hasn't been chosen to be the input window to compare with Ge and GaAs, because its refractive index is only about 3.0 and the absorption coefficient is around 10 cm−1 in the THz range [14]. Well-designed metal meshes have higher reflectivity in the THz range than Ge in theory. However, its high THz reflectivity is realized
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