Diffraction Analysis for a Reflecting Volume Bragg grating

A theory which is based on a coupled-wave analysis for plane waves incident on a VBG was first presented by Kogelnik [65]. The PTR VBG consists of a sinusoidally varying refractive index modulation with period Λ according ton n₀ n₁sin(2x/ ) , where the modulation n₁ is up to

10

^3in magnitude. Assume a plane wave incident on the grating with an angle θ and wavelength λ. The reflected wavelength by Bragg condition is expressed as reflecting VBG, there is the maximum wavelength



_B^max, which corresponds to normal incidence at₀ 0,

16

shorter wavelengths incident at larger angles can be reflected by a Bragg mirror. The total power reflectivity at the plane x0 can be expressed as [63]

where m is an integer. m should be altered at the reflectivity zero points to give the phase continuity. The peak diffraction efficiency is at 0,

2 ' 2 1 2 1

The zero-to-zero bandwidth of the reflection is defined as the distance between the two zeros closest to the peak to get a simple expression for the VBG bandwidth. The zero-to-zero bandwidth for the wavelength at constant incidence angle is

2 2

where ₀is the incident angle at Bragg condition. The bandwidth and the reflectivity can be varied independently by varying parameters n₁ and d. At a constant wavelength, the zero-to-zero angular bandwidths for normal incidence are

n 2

The temperature dependence of the central wavelength for normal incidence is

17 dependences of wavelength change are 23.4 pm/℃at 2479 nm [66] and 10 pm/℃ at 1024 nm [67]. As the nonlinear refractive index of PTR [68] the wavelength change with temperature is not directly proportional to the Bragg wavelength. The temperature tuning capability can be used to thermally control laser wavelength. The VBG thermal tuning capability for a solid-state laser was demonstrated in a Ti:sapphire laser system.

[12]

When a thick VBG is used as one of the mirrors of a short Fabry-Perot cavity, the grating’s physical length can be a substantial part of the total cavity length. The effective round trip distance can be calculated from the phase acquired from a reflection of a Bragg grating. The effective cavity length L_cav is deuced to be [13]

1/2 transverse beam profile of a finite incident beam on the grating will be altered in both transmission and reflection, for the different angular components of the incident beam experience different reflectivities. Theory and experiments of finite beams in reflective VBG have been presented in ref. [63] and [69]. In ref. [69], the diffraction efficiency for finite beam incidence was demonstrated and shown in Fig. 2-3. With the finite beam behavior, the VBG can be used as a spatial filter, since higher order transverse modes have a broader angular spectrum. And, adjustingthe beam incident waist can cause the Gaussian mode to be reflected completely, but the higher order

18

ones only partially. Thus the VBG can be used as a mode filter to limit the number of transverse modes in a laser cavity.

The reflection spectrum of our PTR VBG made from OptiGrate is shown in Fig. 2-4 [from 70]. The peak reflectivity is centered at 1069.8 nm with full width at half maximum (FWHM) about 0.356 nm. The peak reflectivity is larger than 0.99 according to OptiGrate.

Fig. 2-3 Comparison of Modeling with experimental diffraction efficiency of finite beam in reflective volume Bragg grating (a) 1.24 mrad beam divergence; (b) 23 mrad beam divergence [from ref. 70]

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Fig. 2-4 Reflection spectrum of the VBG is centered at about 1069.8 nm with FWHM 0.356 nm and peak reflectivity larger than 99%.

[from ref. 70, 71 ]

2.3 Nd:GdVO4 Solid State Laser

A laser is a light source based on light amplification by stimulated emission of radiation.

Every laser system essentially is constructed from three basic components: a gain medium, a pump, and a cavity, shown schematically in Fig. 2-5. A gain medium placed between a pair of optically parallel and highly reflecting mirrors with one of them partially transmitting. An energy source pumps gain medium that has appropriate energy levels, where population inversion is obtained. The cavity provides a resonant amplification via the stimulated emission after the population inversion. The gain media may be solid, liquid, or gas. The basics of the laser theory can be found in photonics textbooks.

In this thesis, the gain medium is lanthanide ions doped in a crystal or glass host

20

and the pump source is a laser diode, the so called diode pump solid-state lasers. The laser cavity feedback was constructed by a dielectric mirrors and a spectrally selective volume Bragg grating.

Fig. 2-5 Schematic diagram of a typical laser, showing the three major components: a gain medium, a pump and a resonant cavity by the mirrors.

2.3.1 Laser Gain Mediun Nd:GdVO₄

The laser crystal is one of the most important components of a solid-state laser, and it can determine the efficiency of the laser. Nd:GdVO4, which is similar to Nd:YVO4

crystal and Nd:GdVO4 crystal, is an excellent laser crystal for diode pumped laser used as a four-level laser pumped at 808 nm. It is common lasing at 1064 nm.

Nd:GdVO₄ have higher optical efficiency than Nd: YAG crystals and better thermal conductivity and higher power output than Nd: YVO₄ crystals, so they are a good choice for high power output diode pumped solid state laser. Also, Nd:GdVO4 can be operated at linear polarization. These properties make Nd:GdVO4 a good laser material for many laser applications. Table 2-1 shows the comparison of Nd-doped solid state materials. Figure 2-6 shows a simplified energy level diagram of the

4F_3/2→⁴I_11/2 manifolds. The close view of ⁴F_3/2→⁴I_11/2 transitions manifold has been shown in Fig. 1-2. It was acquired by an Agilent 70950B optical spectrum analyzer when the crystal is pumped by an optical power of 2.3 W at 808 nm [70]. Nd:GdVO4

21

has an emission line at about 1070 nm, which was used to generate 535 nm laser by second harmonic generation in this thesis work.

Table 2-1 Comparison of Nd-doped solid state material [96, 97]

Nd:GdVO4 Nd:YVO4 Nd:YAG Polarized Laser Emission parallel to optic

axis

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2.3.2 Wavelength Selection

The Nd-doped laser systems are well known for its 1064 nm lasing output wavelength, which belongs to the transition between ⁴F3/2 and one of the Stark levels of ⁴I11/2. The lasing actions between ⁴F3/2 and other Stark levels within ⁴I11/2 manifold are strongly suppressed because of smaller stimulated emission cross sections [72] and close spacing between these Stark levels. Therefore, to achieve 1070.8 nm laser wavelengths of Nd:GdVO4, 1063.2 nm emission has to be suppressed.

Several methods have been commonly used for mode selection and spectral narrowing of a broad band laser toward achieving a single longitudinal mode laser, for example, by introducing an etalon, birefringent plate, surface grating, and (or) prisms in the cavity.The intracavity filters, however, typically induce substantial losses at the desired wavelength to raise the threshold and to lower the slope efficiency. At the same time dispersive elements such as prisms or diffraction gratings necessitates the use of a longer cavity. In most cases multiple selective elements must be used to achieve single frequency laser, and introduce added complexity.

A possible scheme is using a highly spectrally selective cavity mirror. A 1083 nm laser has been achieved and reported using a specially coated dielectric mirror with high reflectivity at 1082.6 nm and lower reflectivity around 1060 nm [10]. However, such a specifically dielectrically coated mirror is impractical for those even closer lines such as 1065 and 1070 nm since these two peaks are too close for coating design and the mirror reflectivity will be too high at 1082.6 nm which makes the 1082.6 nm line dominate in such a system instead of 1070.8 nm.

As a better alternative a highly spectrally selective cavity output coupler can be realized with a new type of robust optical element, a VBG recorded in PTR glass.

23

Owing to its narrow spectral and angular selectivity, VBG offers an advantage of at least 1 order of magnitude in the bandwidth use over a conventional surface diffraction grating. Using a VBG as an end mirror has been demonstrated great reduction of the laser output linewidth from few or few tenth of nm down to few pm or even single mode operation without a decrease in output power [12 , 13 ]. The properties of VBG have been described in Section 2.2.2.

In this thesis, a VBG is used as an output coupler and wavelength selector for obtaining single-frequency-mode generation in an Nd:GdVO4 laser. Changing the temperature of the VBG can move the central peak and then to tune laser emission central wavelength.

2.3.3 Diode-Pumping of Solid State Laser

Diode pumped solid state (DPSS) lasers are solid state lasers made by pumping a solid gain medium with a laser diode. DPSS lasers are efficient because the diode laser provide direct excitation of the pump beam into the absorption band of the gain medium.

And the diode laser itself has an efficient conversion of electric energy to optical energy.

Although the beam quality of a laser diode is not good, it is possible to form a single TEM00 operation through the DPSS laser configuration. There are two types of pumping configuration: side-pumped and end-pumped configurations. In this thesis work, a diode-end-pump solid state laser was developed.

For optimal and efficient pumping, however, requirements have to be considered both spectrally and spatially. The spectral profile of the pump diode should be spectrally overlapped with the absorption line of the gain medium to obtain efficient absorption. And the beam profile of the pump diode should be spatially overlapped with the Gausisian mode of the laser cavity to obtain efficient excitation of only the

24

fundamental transverse cavity mode. A good spatial overlap can be obtained with focusing optics, though the diode laser usually has a divergent beam. The optimal way to do it is that the pump beam is focused to the Gaussian mode size. Besides, twice of Rayleigh length of the focused beam is not longer than the crystal length. Reshaping optics is required for diode lasers which have elliptical beams to obtain a circular spot before the pump beam reach the gain medium.

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Chapter 3

Single Frequency 1070 nm Nd:GdVO

4

Laser Using a Volume Bragg Grating

3.1 Introduction 3.1.1 Motivation

Single frequency lasers are required in the spectroscopy of thallium atom for testing new physics beyond the standard model, which predicts atomic PNC effect arising from exchange of a Z0-Boson between atomic electrons and nucleons. Atomic thallium (Z = 81) plays an important role in PNC experiments, since the PNC effect grows faster than Z³. The PNC effect has been observed in atomic thallium system using 6P1/2  6P3/2

transition in 1995[3,4]. Laser cooling of thallium atoms, in which a 535 nm laser is needed, can improve the atomic PNC measurement. It is reasonable to obtain a 535 nm laser from a frequency doubled 1070 nm solid state laser.

3.1.2 Laser Material

DPSS lasers with advantages of good stability, narrow linewidth, and good beam quality have been found to be outstanding light sources for spectroscopy.

Neodymium-doped gadolinium orthovanadate (Nd:GdVO4) is an ideal laser crystal for the DPSS lasers due to its high pump absorption coefficient and large thermal conductivity [73, 74]. Most researches involving Nd:GdVO4 crystal focused on the high power output at wavelength 1064 nm of the main gain peak [75], however, the fluorescence spectrum of a 0.5 at.% Nd:GdVO4 crystal [71], reveals that there are some weaker emission bands around the main peak. One of the weak emission bands is located at 1070.8 nm which is only 6 nm away from the main peak. As a consequence, a 535 nm light source could be acquired by the second harmonic generation from a

26

1070 nm laser using Nd:GdVO4 crystal. The properties of the Nd:GdVO4 crystal has been described in Chapter 2.3.1

3.1.3 Laser Narrowing by Volume Bragg Grating

To achieve single frequency operation for DPSS, wavelength selection elements are required. From the fluorescence spectrum of a 0.5% at. Nd:GdVO4 crystal (Fig. 1-2), the emission cross section at 1070.8 nm is about 20% of that at 1063.2 nm. Therefore, to obtain a 1070 nm laser operation with Nd:GdVO4 crystal, one must suppress the laser action at 1063.2 nm. A 1083 nm Nd:GdVO4 laser has been demonstrated using a specially coated dielectric mirror with high reflectivity at 1082.6 nm and lower reflectivity around 1060 nm to suppress the lasing at 1064 nm [10]. However, the 1070 nm band is too close to be separated from the 1064 nm band by a dielectric coated mirror. Other methods for wavelength selection were achieved by inserting an intra-cavity dispersive element, e.g. etalon, which introduces additional loss in the laser resonators resulting in raising the lasing threshold.

VBG offer an alternative approach for wavelength selection and line narrowing for solid state lasers [12]. VBG is a periodic phase grating recorded in PTR glass by thermal development after holographic exposure to UV radiation. PTR glass possesses large transparent range with low loss, high damage threshold, and good thermal stability. PTR VBG has extremely narrow spectral width (below 1 nm), good angular selectivity (below 10 mrad), and high relative diffractive efficiency (above 99.9%).

These unique features make VBG ideal for working as intracavity wavelength selectors or resonator couplers in various types of lasers, depending on designed properties.

VBG properties have been described in Section 2.2. CW single-longitudinal-mode Nd:GdVO4 laser operation has been achieved with a short VBG Fabry-Perot cavity [40]

27

or a monolithic VBG cavity [43]. The monolithic VBG cavity provides over 80 GHz single frequency tuning range. However, the power is limited to 30 mW for single frequency operation by the high intracavity loss (~ 10%). In addition, it is not easy to perform fast frequency modulation which is often needed in laser spectroscopy. Figure 3-1 shows the center wavelength and bandwidth of our VBG and the fluorescence spectrum of the Nd:GdVO4 laser crystal.

Fig. 3-1 Center wavelength and band width (blue) of the VBG used in this laser cavity and fluorescence spectrum (red) of the 0.5% at.

Nd:GdVO4 at room temperature

3.2 Experiments and Results

3.2.1 Experimental Setup of the Nd:GdVO4 laser

The schematic diagram of the single frequency Nd:GdVO4 laser is shown in Fig. 3-2.

A short plano-concave cavity was employed in our work. An 808-nm fiber-coupled diode laser with a core-diameter of 800 m and a numerical aperture of 0.12 served as

28

the pump source. The pump beam from the fiber end was focused into the laser crystal with a diameter of about 300 m through the focusing optics formed by a pair of lenses.

The cavity mirror M1 was a concave mirror with radius of curvature of 300 mm. It had anti-reflection (AR) coating at 808 nm (R < 0.5%) and 1064 nm (R < 0.2%) on the flat face, as well as AR coating at 808 nm (R < 5%) and high-reflection (HR) coating at 1064 nm (R > 99.8%) on the curved face. It was mounted on a PZT for fine tuning the laser cavity length. An a-cut 0.5% at. Nd:GdVO4 crystal with a dimension of 3 × 3 × 4 mm³ was used as the laser gain medium. The crystal was AR coated at 808 nm (R < 2%) and 1064 nm (R < 0.2%) on the side near M1 and AR (R < 0.2%) coated at 1064 nm and 532 nm on the other side. It was wrapped with an indium foil and mounted in a copper heat sink plate without temperature control and placed closely to M1. A PTR VBG (Optigrate Inc.) having peak reflectivity > 99% at center wavelength 1069.8 nm with FWHM of 0.356 nm and dimension of 5 × 5 × 4 mm³ worked as the output coupler of the laser cavity. The VBG was AR coated at 1064 nm on both facets. It was wrapped with an indium foil and mounted in a copper heat sink and its temperature could be controlled at 15 to 60 ℃ by a thermoelectric cooler underneath. The distance between M1 and VBG was 10 mm. The output power was measured by a power meter (Scientech 362) at a distance of 100 mm from the VBG output coupler. The output spectrum was monitored by a home-made scanning confocal Fabry-Perot interferometer (FPI) with free spectral range of 1.5 GHz. An InGaAs detector (Thorlabs DET410) connected to an oscilloscope (Tektronix TDS 2024) was used to detect the spectrum signal after FPI. A wavemeter (Burleigh WA1000) and a beam analyzer (DataRay WinCamD) were used to verify the output wavelength and to monitor the output transverse beam profile respectively.

29

3.2.2 Output Properties of the Single Frequency Nd:GdVO4 Laser

The single frequency operation of this plano-concave cavity laser was achieved by the VBG which acted as an output coupler and a wavelength selector. It should be mentioned that there were four weak beams surrounding the laser output beam. These beams were due to the grating plane in VBG was not parallel to the VBG surface and the reflection of VBG surfaces. They can be used to monitor the single frequency operation with the FPI. The output spectrum (shown in Fig. 3-3) monitored by the FPI indicates that the laser was operated at single frequency. The odd FPI trace was due to discrete sampling of digital oscilloscope. The detail output spectral profile (shown in the inset of Fig. 3-3) of the FPI at output power 200 mW showed a linewdith of 23 MHz which was limited by the instrument resolution of the FPI. The wavelength of the laser output could be tuned by the VBG temperature at a tuning coefficient of ~ 10 pm/K (or ~ 2.6 GHz/K). The vacuum wavelength of the laser was 1070.205 nm (280126.5 GHz) when the VBG was kept at 26 ℃. From the Fabry-Perot traces the

M1

piezoelectric transducer; FPI: Fabry-Perot Interferometer; DET:

detector; OSC: oscilloscope.

30

single frequency tuning range by the PZT tuning was about 5.1 GHz at output power 100 mW. The far-field spatial distribution of the beam at output power 200 mW measured by a beam analyzer is shown in Fig. 3-4. A nearly Gaussian intensity profile with good circularity was observed at a distance 45 cm from the output coupler. The

0 670 1340 2010 2680 3350

0 0.2 0.4 0.6 0.8 1

Position (m)

Normalized Intensity (a.u.)

Fig. 3-4 The far-field intensity distribution of the 1070 nm laser at 200 mW output power. The solid curve is the fitted Gaussian distribution.

Fig. 3-3 Fabry-Perot trace of the single frequency Nd:GdVO4 laser.

The inset shows details of the peak. Right inset shows 1070 nm laser spectrum by OSA

31

far field divergence angle of the laser output was around 0.37. To check the beam quality of this laser, we measured the beam radius for the output beam at the 200 mW power level at different distances from a lens with focal length of 100 mm. The measured beam propagation parameter M²was 1.16.

However, the optimal position of focusing optics depends on the pump power as a result of thermal lens effect of the laser crystal under pumping. We need to fine-tune both the focusing optics position and the VBG angle to acquire a single mode laser with a maximum output power at different pump powers. Figure 3-5 shows the experimental results for the optimal output power for single frequency operation as a function of the pump power. Since the current of 808 nm pump laser could be adjusted by an increment of 1 Amp only, the slope efficiency of 14.5% and threshold pump power of 720 mW were obtained by a linear fitting. A single frequency laser output power of 300 mW had been obtained, limited by the reflectivity of the VBG, and it was difficult to obtain single frequency for higher output power. This fine-tuning procedure makes this laser inappropriate for applications where varying laser power is of prime importance.

Fig. 3-5 1070 nm laser single frequency output power as a function of the incident pump power. The red line is the linear fitting result.

0.5 1.0 1.5 2.0 2.5 3.0

32

3.2.3 Frequency Stabilization

To demonstrate the application of this laser to spectroscopy, the resonance peak of the FPI cavity was used as a reference for locking the laser frequency. The experimental arrangement is shown in Fig. 3-6. A sinusoidal signal with a modulation frequency of 20 kHz was sent to the input channel 1 of a piezo amplifier (Physik Instrument E663).

The PZT attached on one of the FPI cavity mirrors was driven by the output 1 of E663

The PZT attached on one of the FPI cavity mirrors was driven by the output 1 of E663

在文檔中 可調單頻 Nd:GdVO4雷射及其光譜應用 (頁 28-0)