No book on problems can claim to exhaust the variety in the limited space. For simplicity, the spectral profile is assumed to be rectangular. Chapter 1 is devoted to the methods of Mathematical physics and covers such topics which are relevant to subsequent chapters. If all the photons emitted by the pump are absorbed by the crystal and used for the lasing process, calculate the maximum power output. %���� Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses. There is a broad range of materials that can be cut with a laser: wood, plastic, cardboard, textile... Laser cutting works by directing the output of a high-power laser through optics. A Q-switched laser emits pulses of 10µJ of duration 1 ns. 2. %PDF-1.5 Calculate the number of longitudinal modes that can oscillate in this cavity. The maximum output power is defined by stream The length of the cavity is equal to 1 m. 1. What is the rate of repetition of the pulses emitted by a mode-locked laser? ^ S��S�r�Ԯ�۶�U=\$��^�������6�i���\�h�3���ǈ���?% /Filter/FlateDecode In a ring lasercavity, the beam passes through the medium only once each turn. Calculate the gap in frequency between two longitudinal modes in a linear cavity whose optic length, L, =300 mm. Question. The solution for non … ���.P��Z1j�������Ծ�܃��Y�4��b��� � �E�>"�e1�[b�M�����#"^�+��3JD��-���u.qUg�{*��^rz��N�~Z�����ٌG�)s�����r� /Filter/FlateDecode The frequency is therefore equal to. laser, concentrated on a very small area, in order to cut or engrave a material. 1. Calculate the energy of each pulse. The linear cavity is 30 cm long. CO2 has a bandwidth equal to x��͎� ��} There are no other energy levels nearby. stream Solution of Problem 4.12 Problem 4.13 A laser emitting at 0=850nm has a gain spectral width of = 32 nm and a peak gain of g(0) 50/cm , Plot g() equation 4.41. An one milliwatt He-Ne laser is highly intense than the sun intensity. fronts in recent years. A mode-locked laser emits an average power P equal to 1 W. The rate of repetition of the pulses from this laser is equal to 100 MHz. Calculate the peak power of the pulses. As the gap in frequency is given by the above formula, the distance that the cavity mirror must be moved is equal to: It is possible to make this fine adjustment by using a piezoelectric actuator. where k is a large integer. endobj TYPES OF LASERS 301 570-640 nm (rhodamine 6G) and many others. . ����rh�c��6��Ĩo�jl�4��n����;�]`��!��bH�g�ȳD�t��zo���KP�c�r2��y��i5�7�ނBV4��Lko)Q����H��җ����ܳ#8Jv�B=�kv�]�q ~�iH�����}P?�م��.M 峩�b�Q,�J��t@0 Suppose when two photons each of amplitude are in phase with other, then young’s principle of superposition, the resultant amplitude of two photons is 2 and the intensity is 4 . Calculate the number of longitudinal modes that can oscillate in this cavity. It is also widely used in industrial production and processing. xڝ�wTT��Ͻwz��0�z�.0��. /N 3 endstream �=��&�[�L�B�F��;���la��]�B�i3֏��9!�hcYD�ٿ�6��Ю�5H��6����h ֢�-6���6{a�S��0QS�8�)���q��*<5I��� �[������5)T��>\�h) ������1�7�M��Q����/��ɹxr΅�6��c���[�����"�@���Q���s� �zhQp�,Lr0u����bC�"Z���ɪMJ���3���bC��AP!�z"�n��OMT-ݭ�%��3 The laser gain medium are organic dyes in solution of ethyl, methyl alcohol, glycerol or water. The energy (E) is therefore found from. endobj << 1. What is the radius of the beam at the waist (considering the waist and the laser are in the same plane)? x��Z͎�6��)��J�~�� /Length 1491 Problems and solutions Session 1. ��� k��p�N����+�.��sKq������qV�CX|�m��Y�8���fɞ��^=�s�E\� These dyes can be excited by optically with Argon lasers for example and emit at 390-435nm (stilbene), 460-515nm (coumarin 102), 7.3. If they are out of phase this must be due to the polarization of the material. A laser is a device that emits light (electromagnetic radiation) through a process called stimulated emission. If the laser is 400 micrometer long and n= 3.6, how many modes will be excited in the this laser? A ring laser cavity is composed of 4 identical mirrors with a reflection coefficient equal to 0.99. Today’s theme is the high-frequency word in laser cutting-carbon steel. 72 0 obj What is the radius of the beam at the waist (considering the waist and the laser are in the same plane)? . /Length 2594 >> �tq�X)I)B>==���� �ȉ��9. t��܊�ͦ���?��DKN����,P#0��I�#EJ���d&M?3��O*�������?��|�>|4Xb�^�S2*���6��~{�ڡ�^��h �l��t�������gj9�YZL��O�,m��/������/?O�*����A��sGw�y�:\$���a Y;�\$�\��"�ǀ�gp�|�M(I���#�O�l�ZyG*\$�SU!�bh�dEX GL�����sVt��qJ*yd�Q�HwT �=[�\4b���OlI� Laser light is highly intense than the convectional light. << Solution of Problem 4.13 The optic length of the cavity, L, is 1 m. The gap between two pulses from a mode-locked laser is defined by 2L/c. Determine the fraction of the population found in this level compared to the ground state population at a temperature of 300 K. Boltzmann's constant is equal to 1.38.10-23JK-1, The conversion from cm-1 to joules is given by: �jN�jWma��]-`ȏl�D?��W@;��&�%�/}vIh�\��ņv�CD�N����湣-�|u_��2��u\d��i��7� �N�� 2. , where Consider a lower energy level situated 200 cm-1 from the ground state. The peak power is the energy of the pulse divided by its duration: 2. ��OU�S1z6��wM�,��7���](�i�yJӲ�i�w6�+�*���&��羸�+-B[��Y�`���1ΗrF��6?�%А᫕�@L��ra�3� |��� La�]��yW�����bX���`���3� If an external electric ﬁeld is applied to a dielectric (not conduct- ing) material the material will be polarized, resulting in a polarization P. The relation is then, E = D "0 P "0) D = "0E +P If P = 0, as in vacuum, E and D are in phase. Consider an optical pump at 940 nm for a Yb:YAG crystal placed in a laser cavity. stream Case study: Diode-pumped Nd: YAG Laser; Lesson questions. g� �����oc�n/�~ X�'a�ؠ���ӗ������S%%r^{) 9=r9�6D�O�.9�O��b_'>o�8��N]ݯ����ܔ�� ��ٞ���9oUW��^� ������,(X0*������`���t7f�7��[ h���m�n\$v���^�>Ǒ��r�~�Kc�}�8~�ε�t�5������� H[��F*�����!��g��i�B�����σKm�|(-�L�Yf�JN��r��tf!����L��F߅h&"��>Ňn�_�I�B� �? I have to say that after reading all kinds of flower problems and solutions, I feel a lot of knowledge. >> \$E}k���yh�y�Rm��333��������:� }�=#�v����ʉe