Simple Analytical Theory of Saturation and Polarization Spectroscopy of Alkali-metal Atoms by Using Nakayama’s Model

노흥렬 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.57 No.6

This paper presents a simple analytical theory of linshapes in saturated absorption and polarization spectroscopy by using Nakayama’s model [1,2]. Considering the effect of optical pumping, we formulated the analytical spectra of saturated absorption and polarization spectroscopy for general alkali-metal atoms. The spectra could be obtained easily using software programs, such as MATHEMATICA.

Electrostatic Potential of a Charged Ring: Applications to Elliptic Integral Identities

노흥렬 한국물리학회 2017 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.71 No.1

We present a proof of a transformation identity of a complete elliptic integral of the first kind, presented in a recent publication [O. Ciftja et al., Eur. J. Phys. 30, 623 (2009)], where it was derived from an analytical solution of the electrostatic potential due to a uniformly charged ring. In addition, by calculating the electrostatic potential due to a charged ring with a sinusoidal charge distribution, we obtain a new mathematical identity for the complete elliptic integral of the second kind. We show that these two identities can be derived from the existing mathematical identities of elliptic integrals, proving them in a direct manner.

Analytical Study of Optical Pumping for the D1 Line of 85Rb Atoms

노흥렬 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.64 No.11

We present analytical solutions for the populations of the D1 transition line of 85Rb atoms. Thetime evolution of the populations of the magnetic sublevels in the excited state at the weak intensitylimit exhibits several kinds of homogeneous or inhomogeneous second-order differential equations. General solutions of the differential equations result in an analytical form of the population in eachmagnetic sublevel as a function of the elapsed time, laser intensity, and laser frequency detuning.

다준위 원자 자기광학 포획의 포획상수 연구

노흥렬,김기환,제원호 한국물리학회 2006 새물리 Vol.52 No.2

자기광학 포획에서 포획상수를 측정해서 3차원 구조의 다준위 원자에 대한 도플러 냉각 이론을 연구하였다. 포획된 원자에 일정한 자기장을 인가한 다음 자기장이 사라지는 과정에서의 원자의 궤적을 측정해서 감쇠계수와 용수철 상수를 구하였다. 종방향 축과 수직축 방향의 레이저 변수에 의한 포획상수의 변화를 조사해서 비율방정식을 이용한 계산결과와 잘 일치함을 확인하였다. 또한 넓은 레이저 변수 범위에서 평균된 포화세기를 사용하면 근사적으로 포획상수를 기술할 수 있음을 보였다. 특히, 감쇠계수의 결과에서 초도플러 힘이 중요한 역할을 수행함을 확인하였으며 감쇠계수에서 공명 현상을 관측하였다. The Doppler cooling theory for multilevel atoms in a three-dimensional magneto-optical trap was studied by measuring the trap parameters. After the constant magnetic field applied to the trapped atoms had been switched off, the damping coefficients and the spring constants were measured by recording the atomic trajectories. We found that the measured trap parameters depending on the experimental parameters of the longitudinal and the transverse lasers and were in good agreements with the calculated results based on a rate equation model. Also, it was found that the trap parameters of a simple two-level model could be used in terms of the averaged saturation parameter over a broad range of experimental conditions. In particular, we found that the existence of a sub-Doppler trap played an important role in analyzing the damping coefficients and in observing resonance-like phenomena in the damping coefficients.

Analytical Solutions of Birefringence and Dichroism Spectroscopy for the J g =0 → J e =1 Transition

노흥렬 한국광학회 2014 Current Optics and Photonics Vol.18 No.4

We present accurate analytical solutions of the lineshapes of birefringence (rotation) and dichroism (absorption) spectroscopy for a circular anisotropic medium composed of atoms of the transition Jg=0 → Je=1. The susceptibility of a weak probe beam was analytically calculated and was averaged over a Maxwell-Boltzmann velocity distribution. The lineshapes of the two spectroscopies were then presented in analytical forms at arbitrary values of the linewidths of the inhomogeneous (Doppler) broadening and the homogeneous (natural) broadening of the atoms.

Analytical Study of Polarization Spectroscopy for the Jg =0 → Je =1 Transition

노흥렬 한국광학회 2013 Current Optics and Photonics Vol.17 No.3

This work presents a theoretical study on the analytical calculation of the lineshape of polarization spectroscopy (PS) for the transition line 5s2 1S0 → 5s5p 1P1 of 88Sr. From the obtained analytical form of the PS spectrum, we were able to identify how the saturation affected the lineshape of the PS spectrum. The results obtained will be useful for polarization spectroscopy experiments using the alkaline-earth atoms such as Sr or Yb.

포화흡수 분광학의 유사 로렌츠 함수

노흥렬 한국물리학회 2018 새물리 Vol.68 No.5

We present a theoretical study on the Lorentzian-like function $(L(a,b)$ = $1 - \frac{2}{\pi} \int_{-\infty}^\infty \frac{1}{1+4 y^2} \exp \left[-\frac{b}{1+4 (a-y)^2} \right] dy)$ found in analytical solutions of saturated absorption spectra for multilevel atoms. This is analogous to the Lorentzian function and cannot be expressed in an exact analytical form. We find analytical solutions at the two extreme conditions for the parameter $b$, thus determining the linewidth. We also find an exact analytical form for the peak value as $L(0,b)$ = $1-e^{-b/2} I_0 \left( b/2 \right)$, and an approximate expression for the full width at half maximum of the spectral peak as $1+\sqrt{1+b/\ln 2}$. The results obtained in the paper will be used in more accurate calculation of the saturated absorption spectroscopy spectrum for multilevel atoms. 다준위 원자에 대한 포화흡수 분광학 스펙트럼의 해석적 해에 나타나는 유사 로렌츠 함수 $(L(a,b)$ = $1 - \frac{2}{\pi} \int_{-\infty}^\infty \frac{1}{1+4 y^2} \exp \left[-\frac{b}{1+4 (a-y)^2} \right] dy)$에 대한 연구를 수행하였다. 이 함수는 로렌츠 함수와 유사하지만 정확한 해석적인 형태의 해를 구하는 것은 가능하지 않다. 선폭을 결정하는 변수인 $b$가 매우 작은 경우와 큰 경우에 대하여 각각 해석적인 해를 구하였다. 첨두값의 정확한 해석적 해는 $L(0,b)$ = $1-e^{-b/2} I_0 \left( b/2 \right)$로 표현되고, 반치폭은 근사적으로 $1+\sqrt{1+b/\ln 2}$ 로 표현됨을 알 수 있었다. 본 논문에서 구한 결과를 사용하면 다준위 원자에 대한 포화흡수 분광 신호를 더 정확하게 해석적인 형태로 표현할 수 있다.

Analytic Solutions for the Populations of an Opticaly-Pumped Multilevel Atom

노흥렬,문걸,신서로 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.53 No.2

This paper reports an analytical calculation of the populations of the magnetic sublevels of an 87Rb atom. Using a circularly polarized laser beam, we obtained the population of each magnetic sublevel analytically from rate equations as a function of the elapsed time and the laser detuning. Good agreement was observed between the analytic solutions and the numerical results obtained by using the density-matrix approach. The analytical forms of the population obtained can be used to calculate the various spectroscopic signals analytically.

위상차가 수반된 이중 슬릿 회절에 대한 해석적 해

노흥렬 한국물리학회 2023 새물리 Vol.73 No.1

I present analytic solutions for the principal maxima in double-slit diffraction under the Fraunhofer regime in the presence of a constant phase difference between the two slits. By expanding the equation governing the existence of the principal maxima with respect to η=a/d (a: slit width; and d: slit separation), I obtain the phase and irradiance for the principal maxima up to the 12th order in η. The analytic solutions are given as a function of η and ϕ0=2πm+α where m is an integer and α is the initial phase difference in the two slits. 두 슬릿 사이에 일정한 위상차가 존재하는 프라운호퍼 영역의 이중 슬릿 회절에서 주요 최대값의 해석적 해에 관한 연구를 수행하였다. 주요 최대값을 결정하는 방정식을 η=a/d(a: 슬릿 폭; d: 슬릿 간격)에 대하여 전개하여 주요 최대값에 대한 위상과 빛의 세기를 η의 12차 항까지 구하였다. m이 정수이고 α가 두 슬릿에서의 초기 위상차일 때, 해석적 해는 η와 ϕ0=2πm+α의 함수로 표현된다.

Subsidiary and Principal Maxima in Multiple-Slit Interference

노흥렬 한국물리학회 2019 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.74 No.6

We present a theoretical study on the amplitudes and the linewidths of the subsidiary and principal maxima in multiple-slit interference patterns in the Fraunhofer regime. In the limit of a large slit number, we observe that the calculated amplitudes of the subsidiary maxima relative to the principal maximum are slightly different from the values presented in textbooks. We also present the calculation of the widths for the diffracted intensity patterns of the principal and the first several subsidiary maxima.